Subgroups — #37525708

Order 22939.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₁₁₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁₃⋊C₇	—	29	1	no	maximal, Hall
3	C₂₉⋊C₇	—	113	1	no	maximal, Hall
4	C₁₁₃	C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
5	C₂₉	C₁₁₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
6	C₇	—	3277	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉×C₁₁₃	C₇
LCS	G ▷ C₂₉×C₁₁₃
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.