The finite subgroups of $SU(2)$ consist of the symmetry groups of the Platonic solids plus the finite subgroups of $O(2)$. I would like to know if there are any results concerning $SU(3)$. In general, are there classification results as to the finite subgroups of compact simple Lie groups over $\mathbb{C}$?

Update: Thanks everyone for the references.



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