propagate has 10 distinct synonyms spread across 2 of its 8 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
transmit from one generation to the next
“propagate these characteristics”
travel through the air
“sound and light propagate in this medium”
transmit
“propagate sound or light through air”
transmit or cause to broaden or spread
“This great civilization was propagated throughout the land”
cause to become widely known
“spread information”
Synonyms, antonyms and the broader and narrower relations for propagate come from Princeton University’s WordNet. Full sources and licences.