I've been listening to a listening to a few podcasts and reading a few books about the early church and the Eastern Roman Empire, and I came across the Christian sect of Monophysites. They featured prominently in the historical record and in several councils, but then seemed to have disappeared for the most part after the Arabs arrived. Were they suppressed, absorbed, or did they continue to exist but were no longer the focus?
This is a problem of naming and categories. "Monophysitism," or as modern people prefer, "miaphysitism," isn't a branch of Christianity. It's one expression of Christology, that is, how believers understand the paradox that Christ is both entirely human and entirely divine. At the Council of Chalcedon, as you know, one group of Christians decided their grammar was better and dubbed the other group heretics.
The Christians rejected by the Byzantine/Roman Church of course didn't see themselves as heretics. Because different areas of "miaphysite" belief enjoyed more internal autonomy, the regional churches developed their own names--the Coptic Church, Ethiopian Tewahedo Orthodox Church, and so forth. Although many many Greek and Oriental Orthodox (as these churches are collectively known) Christians did eventually convert to Islam, (a) the process took centuries (b) there is still a thriving Coptic Church in Egypt, to sya nothing of Ethiopia (which of course stayed independent). And so forth!