Etymology
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infra- 
word-forming element meaning "below, beneath," from Latin infra (adverb and preposition) "below, underneath, on the under side, beneath," also "later than; smaller than; inferior to," related to infernus "low, below," from PIE *ndher "under" (source also of Sanskrit adnah "below," Old English under "under, among;" see under). Modern popular use of it dates from the 1920s, as an opposite to super-, often in science fiction. "This use of infra- is scarcely a Latin one" [OED].
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sub- 
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"), from PIE *(s)up- (perhaps representing *ex-upo-), a variant form of the root *upo "under," also "up from under." 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).
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