The sons of Reuben are listed four times (Genesis 46:9; Exodus 6:14; Numbers 26:5-6; 1 Chronicles 5:3), with no differences between the list. In order, they are:
Additionally, in Numbers 26:8-9, the son of Pallu is given as Eliab, and the three sons of Eliab as Nemuel, Dathan, and Abiram. Deuteronomy 11:6 also gives Dathan and Abiram as sons of Eliab, son of Reuben.
Both of these passages refer back to the events of Numbers 16, in which Dathan and Abiram die, however, the actual story itself seems somewhat confused. Numbers 16:1 indeed gives Dathan and Abiram as sons of Eliab, but do not specify Eliab's own father. Instead mention is made of an additional On, son of Peleth, son of Reuben, who is otherwise absent from the story. Something has clearly dropped out or been corrupted here, whether at the time the rebellion of the Reubenite's was merged with Korah's, or simply during transmission. One possibility is that Peleth is an alternative name or corruption of Pallu, and the figure of 'On' having been accidentally invented by a scribal error, in which case a genealogy equivalent to that of the other two passages is restored.
Prior to the wilderness wandering, the leader of Reuben is given in Numbers 1:5 as Elizur, son of Shedeur, and the Reubenite spy sent to Canaan is given in Numbers 13:4 as Shammua, son of Zaccur. Nothing is said of where these people fit into the genealogy.
Nothing else is said about these Reubenite clans, and the lack of any differences between the lists means that no chronological information can be gleaned from them. Is this the list of extant clans at the time they were conquered by Assyria? Or some earlier date? Are Dathan and Abiram clans that were lost/wiped out prior to the rest of Reuben, or are they a purely literary invention?
Fortunately, we are not left completely in the dark on the matter: clans with the same names also appear in lists related to the surrounding tribes and nations, and it can be assumed that these are in some regard related to those of Reuben. These are:
The most interesting of these associations is that of Hezron with Judah. Certainly it is the most commonly referenced, presumably because the Hezronites remained prominent for a significant time. It is not hard to see why: Ruth 4 and 1 Chronicles 2:9-15 give Hezron, son of Perez as being the paternal ancestor of King David himself (via his son Ram), and thus of the whole Judean line of kings! And not only David, but also of the Calebites, according to 1 Chronicles 2:18 (but note that their ancestry differs from passage to passage), who are given the important Judean city of Hebron, which served as David's first capital, in Joshua 14 and Judges 1.
1 Chronicles 2 further lists four more sons of this Judean Hezron: Jerahmeel, Chelubai, Segub, and Ashhur. While Ram, the ancestor of David, is given as a son of Hezron directly in v.9, in v.25 he is instead the firstborn of Jerahmeel. A substantial amount more is said about Jerahmeel's descendants in the chapter, but little of note can be gleaned, other than that the clan was clearly important. Segub, however, is of greater significance for our current discussion: he is said to be son of Hezron via a daughter of Machir, the father of Gilead. That suggests a connection between Segub and the Trans-Jordan, which is curious, considering that territory there is allocated to Reuben, not Judah. And indeed, this Segub is there said to have been the father of Jair, who had 23 towns in the Gilead. This Jair notably also appears in Joshua 32, where he is instead a son of Manasseh, and in Judges 10, where he is a Gileadite.
What conclusion should we draw from all this? That a son of the Judean Hezron was associated with the Trans-Jordan confirms that this Hezron is one and the same with the Reubenite Hezron. The clear importance of the Judean Hezron through to the comparatively late time at which Chronicles was written makes it clear that Hezron was not an archaic Judean clan that was only later absorbed into Judah, but that any migration must have happened in the opposite direction. Most plausibly, we could imagine the clan having fled from Reuben to Judah at the time of the Assyrian conquest, ultimately assimilating into the established clan of Perez.
But what then of the Hezronite ancestry of David and the Calebites? One option is to say that these are simply a late invention: nothing is said of the ancestry of David's father Jesse in the books of Samuel, and there is no shortage of other potential ancestries for the Calebites. It should be cautioned, however, that the relation is maybe not that trivial: if we look at 1 Chronicles 4, we get the genealogy Judah -> Hezron -> Carmi -> Shobal.
The Judean Carmi is puzzling. His main appearance is in Joshua 7, in which he is the father of Achan, who is executed in the Valley of Achor. The exact location of this valley is unknown, but it is presumably not far from Jericho, assigned in Joshua 18 to the tribe of Benjamin, and in Joshua 16 is said to also be on the edge of Ephraim's border: in other words it does not seem to be in the territory of Judah (or of Reuben either, although the territory directly across the Jordan from Jericho was indeed Reubenite), as one might expect. Yet there is a strange connection between Jericho and Reuben: according to 1 Kings 16:34, Hiel of Bethel rebuilt Jericho in the time of King Ahab at the cost of his sons Abiram and Segub. Abiram, of course, sharing a name with Reuben's great-grandson who perished in the wilderness rebellion, and Segub with the trans-Jordania1n son of Hezron discussed above. Neither of these nanes appears in any other place in the Bible.
This Carmi is said in Joshua to be descended from Judah via Zerah. It should be noted here that Zerah is also said in Numbers 26:13 to be a son of Simeon, and in Genesis 36:13 to be a grandson of Esau via Reuel. Both of these identifications seem to place the Zerahites on the southeast fringe of Judea, and suggest that they shifted affiliations on multiple occasions.
Let us return, however, to Chronicles. In 1 Chronicles 2:7, we get a mention of the transgression of Achar, son of Carmi, in the middle of a section of Judean genealogies. Note that here his name is Achar, whereas in Joshua 7 it is instead Achan: perhaps there was a confusion with the name of the Valley of Achor. Also to be noted, is that no further genealogy here is given for Carmi, with this verse seeming to just be a loose fragment.
The final mention of Carmi is that in 1 Chronicles 4, introduced above. Here, he is given as the father of Hur, father of Shobal. This should be contrasted with 1 Chronicles 2:19, in which Hur is instead a son of Caleb by Ephrath, and of both 1 Chronicles 2:50 and 4:4, where he is instead the first-born of Ephrathah (a Judean of unstated origin). In the latter passage, Ephrathah is stated to also be father of Bethleham (but cf. 2:51, where Bethleham is instead said to be the son of Salma, the great-grandfather of Jesse). At any rate, the relation between Hur and David, who according to 1 Samuel 17 was an Ephrathite of Bethlehem, should be very clear. As for Shobal, 1 Chronicles 2:50 identifies him as father to Kiriath-jearim, the city at which the ark of the covenant was located in 1 Samuel 6. According to Joshua 9, Kiriath-jearim was originally a Gibeonite city, before being allocated to Benjamin in Joshua 9. It's association with Judah is perhaps comparatively late, although is included in it's territory in Joshua 15.
Intriguingly, Shobal is also identified in Genesis 36 and 1 Chronicles 1 as being a son of Seir the Horite. There, one of the Horite Shobal's sons is said to be Onam, who in 1 Chronicles 2:26 is instead the son of Jerahmeel, firstborn of Hezron. Likewise, another of his sons is Manahath, while in 1 Chronicles 2:54, it is said that Salma father of Bethleham also birthed the Zorites, half of the Manahathites. These Zorites are likely to be the same as the Zorathites, whose ancestry is traced in 1 Chronicles 4:2 from Shobal.
Following the deaths of Dathan and Abiram, Nemuel is the only remaining descendant of Pallu who is known. According to Numbers 26:12, Nemuel was also the name of a son of Simeon, who is likely the same as Jemuel, a son of Simeon listed in Genesis 46:10 and Exodus 6:15. Note that Numbers 26 is also, as mentioned above, the only place in which Zerah, associated with Carmi, is identified as a son of Simeon. There is also Reuel, son of Esau according to Genesis 36, who I mentioned above for his association with Shobal, but whether he is also connected with Nemuel/Jemuel is unclear. Another Reuel, a Midianite who in Exodus 2 and Numbers 10 is said to be the father-in-law of Moses, perhaps also bears mentions.
Unfortunately, the history of Simeon is even more obscure than that of Reuben, such that little more can be said of Nemuel.
The case of Hanoch offers even further clues. He is said in Genesis 25 to be a son of Midian, but this helps little, considering almost nothing is said of Midian chronologically in the Bible after the era of the Judges.
In the above, I associate the Reubenite clans with those of Judah, of Simeon, of Edom, and even of Midean. Why those specific peoples? Well, because those are the peoples for whom we have clan lists. Reuben's territory bordered on Moab and Ammon as well... but without any knowledge of the clans of these nations, we have no way of knowing of any potential overlap. Additionally, the genealogy for the Reubenites is awfully short: perhaps we can glean some more information by comparing with those of, for instance, the Judean Hezron, but otherwise the surviving information on the clan structure of Reuben is quite lacking, probably derived in its entirety from a single short northern list that came south to Judah after the Assyrian conquest.