Subgroups of the unitary group that contain the group of diagonal matrices

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.