QQ earlyish in the PS $500k

[stevepa]

UTG is pretty bad, makes abnormally large bets a lot but has folded to raises in the past. MP1/MP3 have both been fairly straightforward. SB is a 2+2er I'm pretty sure (MazeOrBowie) and has been fairly aggressive to this point.

UTG ~2500
UTG+2 (Me) ~3600
MP1 ~2500
MP3 ~2500
SB ~2800

Blinds (25/50)

I'm dealt QQ

UTG raises to 150, I call, MP1 calls, MP3 calls (I yell at myself for not reraising), SB makes it 900 after some thought. UTG folds. I...?

It's either push or fold right? Basically is this ever a squeeze play vs. this many people? If not, then his range is probably AA-QQ, AK. So even then I guess pushing isn't so bad (1.5-1 underdog getting ~1.3-1). So is this an easy push then?

Any thoughts on the first call preflop? At the time I was thinking he'll probably commit way too many chips postflop with a worse hand, but maybe I don't want to be letting a bunch of people in behind me...?

Steve