Is there a complete list of infinite subgroups of SU(2)?

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Is there any reference that classifies all infinite subgroups of $SU(2)$?

I found this https://math.stackexchange.com/a/4398724/1079528 which claims that the only infinite maximal (closed) subgroup is $\langle U(1), \begin{pmatrix} 0 && -1\\ 1 && 0\end{pmatrix}\Big\rangle$. First, I can't find the reference for this claim. Second, I can't find anything about "non-closed" subgroups of $SU(2)$.