Subgroups — C₁₁⋊D₁₁ #6852

Order 242.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₁₁	—	11	12	no	maximal
3	C₁₁	D₁₁	1	12	yes	complemented
4	C₂	—	121	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²	C₂
LCS	G ▷ C₁₁²
UCS	C₁

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

N	H ≅ G/N	type
1. C₁₁²	C₂	semidirect
3. C₁₁	D₁₁	semidirect

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

subgroup	index
C₁₁²	2
D₁₁	11