mid-15c., "having an inferior rank," from Medieval Latin subordinatus "placed in a lower order, made subject," past participle of subordinare "place in a lower order," from Latin sub "under" (see sub-) + ordinare "arrange, set in order," from ordo (genitive ordinis) "row, rank, series, arrangement" (see order (n.)). Related: Subordinance; subordinant; subordinately. For "of or pertaining to the classificatory rank of a suborder," subordinal (1842) is used.
word-forming element meaning "above, over, beyond," from Latin super (adverb and preposition) "above, over, on the top (of), beyond, besides, in addition to," from *(s)uper-, variant form of PIE root *uper "over." In English words from Old French, it appears as sur-. The primary sense seems to have shifted over time from usually meaning "beyond" to usually meaning "very much," which can be contradictory. E.g. supersexual, which is attested from 1895 as "transcending sexuality," from 1968 as "very sexual."