supported has no recorded synonym. 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. Its one recorded opposite is unsupported.
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.
sustained or maintained by aid (as distinct from physical support)
“a club entirely supported by membership dues”
held up or having the weight borne especially from below
“supported joints in a railroad track have ties directly under the rail ends”
Synonyms, antonyms and the broader and narrower relations for supported come from Princeton University’s WordNet. Full sources and licences.