Does there exist any results regarding the structure of non-abelian subgroups of group of unitary matrices? I would like to use the probable results to see if a proper non-abelian subgroup containing diagonal matrices exists or not. The final motivations is to answer this [question][1].


  [1]: https://mathoverflow.net/questions/361477/smallest-subgroup-of-unitary-group-containing-diagonal-matrices-and-a-fixed-uni/361483?noredirect=1#comment911218_361483