The posthuman hegemony was composed of all of the human-descended cultures which existed after the destruction of Earth.
The posthuman era was traditionally defined by the destruction of Earth, ten million years after humanity's ghost point. Without Earth, the vast panoply of human-descended cultures no longer had any common reference point. Where previously a militantly assimilationist cybernetic human group had been reviled for its otherness in comparison to Earth, post-Earth it became another not-particularly-interesting variety of posthumanity.
In spite of the implications of the term "hegemony," posthuman cultures did not have any consistent biological differences from their ancestors — though individual posthuman groups had enormous biological and cultural differences, so that they would often not even be recognisable to pre-posthuman humanity. Neither was there any hegemonic element to posthumanity's political makeup: there were myriad fractal factions, often existing on worlds where contact with (or even memory of) Earth or greater human civilisation was long lost.
However, early posthumanity could still be roughly divided into two political inclinations. The first was the Arcadians, who considered themselves "guardians" of Earth's culture (some members had actually lived on it) and immediately set up a replacement Earth on the closest similar planet. They created the isolationist Arcadian Union, but eventually all either died of boredom or transcended their mortal existence. The second, more successful ideology was that of the "decadent" tendency: those groups who realised that they were unbound from their history in a way they had never been before, and that they essentially had the power to do anything they wanted. The decadent ideology was exemplified by the Blood Coteries of Siloportem. (PROSE: The Book of the War)