Longman Dictionary of Contemporary English
The Collaborative International Dictionary
Sub- \Sub-\ [L. sub under, below; akin to Gr. ?, Skr. upa to, on, under, over. Cf. Hypo-, Super-.]
A prefix signifying under, below, beneath, and hence often, in an inferior position or degree, in an imperfect or partial state, as in subscribe, substruct, subserve, subject, subordinate, subacid, subastringent, subgranular, suborn. Sub- in Latin compounds often becomes sum- before m, sur before r, and regularly becomes suc-, suf-, sug-, and sup- before c, f, g, and p respectively. Before c, p, and t it sometimes takes form sus- (by the dropping of b from a collateral form, subs-).
(Chem.) A prefix denoting that the ingredient (of a compound) signified by the term to which it is prefixed,is present in only a small proportion, or less than the normal amount; as, subsulphide, suboxide, etc. Prefixed to the name of a salt it is equivalent to basic; as, subacetate or basic acetate. [Obsoles.]
Douglas Harper's Etymology Dictionary
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").\n
\nThis 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.\n
\nIn 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.\n
\nThe 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).
Wiktionary
pre. 1 under, beneath 2 subsidiary, secondary 3 almost, nearly