Finite Group Databasebeta

← C₁₁⋊(D₂₁₁⋊C₇) #44570656

Subgroups — C₁₁⋊(D₂₁₁⋊C₇) #44570656

Order 32494.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₁₁⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₃₂₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	D₂₁₁⋊C₇	—	11	1	no	maximal, Hall
4	C₁₁×C₂₁₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
5	C₂₁₁⋊C₇	D₁₁	1	1	yes	characteristic, complemented, Hall
6	D₂₁₁	—	11	1	no	Hall
7	C₂₁₁	C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
8	C₇×D₁₁	—	211	1	no	maximal, Hall
9	C₇×C₁₁	—	211	1	no	Hall
10	D₁₁	—	211	1	no	Hall
11	C₂×C₇	—	2321	1	no	Hall
12	C₁₁	D₂₁₁⋊C₇	1	1	yes	characteristic, complemented, Sylow
13	C₇	—	211	1	no	Sylow
14	C₂	—	2321	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₂₁₁	C₂×C₇
LCS	G ▷ C₁₁×C₂₁₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₂₁₁⋊C₇	C₂	semidirect
2. D₂₃₂₁	C₇	semidirect
4. C₁₁×C₂₁₁	C₂×C₇	semidirect
5. C₂₁₁⋊C₇	D₁₁	semidirect
7. C₂₁₁	C₇×D₁₁	semidirect
12. C₁₁	D₂₁₁⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₂₁₁⋊C₇	2
D₂₃₂₁	7
D₂₁₁⋊C₇	11
C₇×D₁₁	211