How do I get to parties?

Hello,

I'm 17 years old and have a large, but not particularly small, circle of friends. I know that many of my friends enjoy going to parties. But I've never been invited to one before. I know, of course, that you shouldn't invite yourself, but how can I show my friends that I'd like to come along? Given that I have three different groups of friends, I can imagine that each of them might think I go to parties with the others.