Is the Suzuki group \(\mathrm{Sz}(8)\) a subgroup of the Monster? (Q2801730)

The Monster \(\mathbb M\) is the largest of the 26 finite sporadic simple groups, and the only one whose maximal subgroups are not yet completely classified. As a contribution to eventual solution of the problem of the determination of the maximal subgroups of \(\mathbb M\) the author shows that there is no subgroup isomorphic to the Suzuki group \(Sz(8)\) in \(\mathbb M\). This also completes the determination of exactly which simple groups are subgroups of which sporadic simple groups. The proof is largely, though not entirely, computer-free.