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The subgroup structure of the Lyons group

The main purpose of this paper is to classify the maximal p-local subgroups of the Lyons group Ly, of order 51,765,179,004,000,000 = 28.37.56.7.11.31.37.67, for each primes dividing the order of the group. We also determine which of these are maximal subgroups of Ly, and in Sections 5 and 6 we give some information on the non-local subgroups.