In his paper Todd (1966), J. A. Todd produced a list of eight maximal subgroups of M24, but he did not claim that the list was complete. Some years later McKay and Wales found a subgroup isomorphic to the linear group L2(7) that they were able to show lay in no copy of a group in Todd’s list. In this chapter we give a short combinatorial proof that the resulting list of nine subgroups is complete; we describe each of the nine in some detail, giving a canonical version of each of them as it appears in the MOG. We also describe two further non-maximal subgroups that are of interest in their own right.