Subgroups — C₁₁×C₄₂₁⋊C₇ #44569742

Order 32417.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₄₂₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₂₁⋊C₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₂₁	C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
4	C₇×C₁₁	—	421	1	no	maximal, Hall
5	C₁₁	C₄₂₁⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
6	C₇	—	421	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₄₂₁⋊C₇
commutator, cosocle, hypocenter	C₄₂₁	C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₄₂₁	C₇
LCS	G ▷ C₄₂₁
UCS	C₁ ◁ C₁₁

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.