Subgroups — C₁₁⋊Dic₁₁ #92148

Order 484.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁²	C₂	1	1	yes	maximal, characteristic
2	C₁₁²	C₄	1	1	yes	characteristic, complemented, Sylow
3	Dic₁₁	—	11	12	no	maximal
4	C₂×C₁₁	D₁₁	1	12	yes	—
5	C₁₁	Dic₁₁	1	12	yes	complemented
6	C₄	—	121	1	no	Sylow
7	C₂	C₁₁⋊D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊D₁₁
commutator, hypocenter	C₁₁²	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁²	C₂
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
2. C₁₁²	C₄	semidirect
5. C₁₁	Dic₁₁	semidirect

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

subgroup	index
C₂×C₁₁²	2
Dic₁₁	11