sub- Look up sub- at Dictionary.com
word-forming element meaning "under, beneath; behind; from under; resulting from further division," from Latin preposition sub "under, below, beneath, at the foot of," also "close to, up to, towards;" of time, "within, during;" figuratively "subject to, in the power of;" also "a little, somewhat" (as in sub-horridus "somewhat rough").

This is said to be from PIE *(s)up- (perhaps representing *ex-upo-), a variant form of the root *upo- "from below," hence "turning upward, upward, up, up from under, over, beyond" (cognates: Sanskrit upa "near, under, up to, on," Greek hypo "under," Gothic iup, Old Norse, Old English upp "up, upward," Hittite up-zi "rises"). The Latin word also was used as a prefix and in various combinations.

In Latin assimilated to following -c-, -f-, -g-, -p-, and often -r- and -m-. In Old French the prefix appears in the full Latin form only "in learned adoptions of old Latin compounds" [OED], and in popular use it was represented by sous-, sou-; as in French souvenir from Latin subvenire, souscrire (Old French souzescrire) from subscribere, etc.

The original meaning is now obscured in many words from Latin (suggest, suspect, subject, etc.). The prefix is active in Modern English, sometimes meaning "subordinate" (as in subcontractor); "inferior" (17c., as in subhuman); "smaller" (18c.); "a part or division of" (c.1800, as in subcontinent).