Bad hand and bad play - looking for a -

I folded and he showed. Any idea what he had?

Party Poker (8 handed)

Preflop: Hero is BB with , .
5 folds, Hero checks.

Flop: , , (3 players)
Hero checks, Button bets $1, Hero calls.

Turn: (2 players)
Hero checks. Button bets $1.

River: (2 players)

Hero bets $4, button all in for $30.

He can not have a bigger flush? That leaves a Full House?

Quads.

Why can't he have the bigger flush? [Jh] or [Jh] or [Jh]

K3 - he could have a bigger flush, I guess but I thougt it more likely since I had 2 s so less likely.

He had J6. I mucked and he showed.

Thanks