Subgroups — Dic₁₂₁ #92143

Order 484.

9 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₁	C₂	1	1	yes	maximal, characteristic
2	C₁₂₁	C₄	1	1	yes	characteristic, complemented, Sylow
3	Dic₁₁	—	11	1	no	maximal
4	C₂×C₁₁	D₁₁	1	1	yes	characteristic
5	C₁₁	Dic₁₁	1	1	yes	characteristic
6	C₄	—	121	1	no	Sylow
7	C₂	D₁₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₁₂₁
commutator, hypocenter	C₁₂₁	C₄
Frattini, socle, prime radical	C₂×C₁₁	D₁₁
Fitting, cosocle	C₂×C₁₂₁	C₂
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
2. C₁₂₁	C₄	semidirect

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

subgroup	index
C₂×C₁₂₁	2
Dic₁₁	11