Greeks here tend to run the SGA and senate. It's not so much "the machine" but more because chapter will vote for a sister or brother who is running. Also, since the greeks on our campus all know each other, we vote for one another in elections.
I was walking to class yesterday when I overheard a girl (obviously an independent) start whining to her friend, "The SGA is all greeks because the people in fraternities and sororities have all the people on Greek Park vote for them although they probably won't do any good in their position."
I happen to think that UCF's SGA has done a spectacular job for all the years I've been here.