Geodesic
Subgroups of the unitary group that contain the group of diagonal matrices
Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 19-29

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In the group $U(n,\mathbf C)$ of all complex unitary matrices we obtain a description of the lattice of those subgroups $H$ that contain the group of diagonal unitarymatrices. This lattice is finite, and the connected intermediate subgroups $H$ are in bijective correspondence with the equivalence relations on a set of $n$ elements. 
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     author = {Z. I. Borevich and S. L. Krupetskii},
     title = {Subgroups of the unitary group that contain the group of diagonal matrices},
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     volume = {86},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a2/}
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Z. I. Borevich; S. L. Krupetskii. Subgroups of the unitary group that contain the group of diagonal matrices. Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 19-29. http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a2/