How much the discrete subgroups of $\mathrm{O}(n)$ can be complicated?

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I have no intuition about the difficulty of classification of discrete subgroups of $\mathrm{O}(n)$ and I wanna to know about it.

How much the discrete subgroups of $\mathrm{O}(n)$ can be complicated?

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Any finite group can be embedded in some $O(n)$. If you believe finite groups are complicated, then that should give you some answer