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I've been asked to find all proper lie subgroups of $SU(2)$.

I seem to recall thinking that $U(1)$ is the only nontrivial connected lie subgroup, but I can't quite remember how I came up with this (don't you hate that feeling when you did something, you move on to something else to keep momentum, and then forget what you did originally?)

But as for the notsoconnected subgroups, I'm very stuck. I can only think to look at the lie algebra... How should I proceed?

Thanks for your help -

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Do you require Lie subgroups to be closed? –  Eric O. Korman May 13 '12 at 15:50
    
@Eric: Yes, I do –  BigThumb May 13 '12 at 17:18

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