The uniqueness of PSU 3(8) in the Monster

As a contribution to an eventual solution of the problem of the determination of the maximal subgroups of the Monster we show that there is a unique conjugacy class of subgroups isomorphic to PSU 3(8) . It follows that there is no maximal subgroup with socle PSU 3(8) . The argument depends on some computations in various subgroups, but not on computations in the Monster itself.