Coalition to Restore the Republic
The CRR is the most powerful faction in the United Corsair Confederation, responsible for its formation and the closest thing it has to a leader. Originally, the CRR consisted of naval remnants from the Third Battle of Elysion, but it later grew in size as other surviving republican loyalist forces were brought on-board, both military and civilian. Properly understood, the CRR was in its early years not a piratical army, as they are frequently painted, but an actual remnant of the ICR itself. As the only power within the UCC with true warships, the CRR is far and away the most powerful faction even to this day, though its numbers dwindle constantly. The CRR has attempted to maintain some semblance of military professionalism, and its crews are in general considered to be superior to other members of the Confederation. The steady loss of warships to combat or rot and the decompsition of the officer corps have reduced the CRR to a shadow of its former self, no longer a significant military threat but a nuisance.
New Haven Cooperative
When the Humanist Union siezed New Haven and the other planets local to the sector, they immediately engaged in a campaign to stamp out the local pirates. This was the New Haven Cooperative, a mixed band of criminals and naval deserters, largely from New Haven, who preyed on that planet's commerce and that of other, less built-up local worlds. Though not large, the New Haven Cooperative was healthy for a pirate organization, with the only credible local fleet being capable of little force projection. The threat of the Humanist Union and its vicious anti-piracy measures have lead the NHC to join as a member of the United Corsair Confederation, who benefit from their relative health.
Republican Privateers' Association
In the early days of the republic, when it lacked an effective space navy, the nascent government instead paid off civilians and existing criminal elements to act as privateers, harassing the republic's enemies and protecting it from less cooperative pirate forces. With the growth of the republic into an actual state, the need for privateers decreased rapidly: indeed, they ultimately would pose a diplomatic risk for their predations on foreign planets. Attempts to peacefully bring the RPA into civilian (or even military) life with bribes and offices were largely ineffective, and the RPA turned on their former benefactors, becoming the longest-lived pirate association in that area of space. The civil war saw their power grow significantly as they were courted by both sides to serve in a mercenary role. They were the first pirate group the CRR courted when forming the United Corsair Confederation, having been given promises of restored legitimacy.
Rim Independence Army
The republic's steady collapse and the vicious nature of the civil war led many systems on the borderlands to agitate for independence from the corrupt, dying federal goverment. When peaceful measures failed and more robust ones were met with violence, many systems took up open resistance. During the civil war, many of these groups would incorporate themselves in the Progressive military as "proletarian patriots," but less trusting elements continued to push for independence throughout the Progressive Civil War and into the formative years of the CCP and Humanist Union. Neither infant state was willing to tolerate this, and resisting "navies" were largely destroyed in systematic military campaigns. What remained turned to piracy. The Rim Independence Army is still broadly interested in the freedom of the far reaches from far-off Elysion, but common support has largely evaporated.
The UCC calls many lesser pirate bands brothers, though none have any political influence worth anything within the structure of the confederacy, and sometimes find themselves as the prey of their ostensible comrades-in-criminality. As the main factions of the United Corsair Confederation rot away under the military might of the Humanist Union and their own unstable nature, a larger and larger portion of the pirate vessels that prowl in Union space are reduced to "minor" status. Ultimately, this is expected to be the fate of the entire Confederation - an amorphous mass of single ships and small groups incapable of real cooperation.