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What is known about normal subgroups of $UT_n(q)$, the group of upper triangular matrices with entries in the finite field $\mathbb{F}_q$ and ones on the diagonal? Is there an interpretation of the lattice of its normal subgroups or of some sublattices of the lattice of normal subgroups?

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    $\begingroup$ your groups is typically denoted by $UT_n(q)$. $U_n(q)$ is used for unitary groups. $\endgroup$ Sep 3, 2015 at 19:48
  • $\begingroup$ It has a huge number of normal subgroups. I think you need to make your question more focused. $\endgroup$
    – Derek Holt
    Sep 4, 2015 at 7:47
  • $\begingroup$ Is there an interpretation of the lattice of normal subgroups or of some sublattices of the lattice of normal subgroups? $\endgroup$ Sep 5, 2015 at 0:20

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