The Allegiant is the titular rebel organization "allied with the original purpose of our city" (4.13). They "claim that we're meant to be in factions because we've been in them since the beginning" (4.15). Isn't that like claiming we're not meant to use cars because we started out life as cavemen without a wheel?
Although the number of people in the Allegiant is unclear, we are sure that they are led by Cara and Johanna and include Zeke and Tori (who ends up dying shortly after leaving the city).
Honestly, the Allegiant don't play a large part in the novel at all once everyone is out of the city. We see them start to mount an assault against Evelyn and her factionless ways, and we see Johanna carrying a gun and allying with Marcus, but in the end, everyone—both the Allegiant and Evelyn—decides to just give up and start over. Maybe that actually is the original purpose of civilization: to let everyone live the life he or she wants to lead.