many aspects of the structure of the group. Local control Much of the structure of a finite group is carried in the structure of its so-called local subgroups, the normalizers of non-identity p-subgroups. The large elementary abelian subgroups of a finite group exert control over the group that was used in the proof of the Feit–Thompson theorem. Certain central extensions of elementary abelian groups called extraspecial groups help describe the structure of groups as acting on symplectic vector spaces. Richard Brauer classified all groups whose Sylow 2-subgroups are the direct product of two cyclic groups of order 4, and John Walter, Daniel Gorenstein, Helmut Bender, Michio Suzuki, George Glauberman, and others classified those simple groups whose Sylow 2-subgroups were abelian, dihedral, semidihedral, or quaternion. See also Elementary group Prüfer rank Regular p-group Footnotes Notes Citations References — An exhaustive catalog of the 340 non-abelian groups of order dividing 64 with detailed tables of defining relations, constants, and lattice presentations of each group in the notation the text defines. "Of enduring value to those interested in finite groups" (from the preface). Further reading External links