Abstract

What ingredients are necessary to describe all maximal subgroups of the general analysis. finite group G? This paper is concerned with providing such an A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal subgroup N of G correspond, under the natural projection, to the maximal subgroups of the quotient group G/N. Let PZ = PQ denote the collection of maximal subgroups of G, and let e * be the subset of those ME?)z with Ker,(M) = 1, where Ker,(M) denotes the largest normal subgroup of G contained in M. Then the first isomorphism theorem allows us to identify +Z with the disjoint union UN,, ms,N. Actually, what we really want to parameterize are the conjugacy classes of maximal subgroups, but this too works well: If

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