Subgroups — Dic₁₃₅₄₁ #72289639

Order 54164.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₂₃₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₂₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₂₃₁	—	11	1	no	maximal, Hall
4	C₂×C₁₂₃₁	D₁₁	1	1	yes	characteristic
5	C₁₂₃₁	Dic₁₁	1	1	yes	characteristic, complemented, Sylow
6	Dic₁₁	—	1231	1	no	maximal, Hall
7	C₂×C₁₁	D₁₂₃₁	1	1	yes	characteristic
8	C₁₁	Dic₁₂₃₁	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	13541	1	no	Sylow
10	C₂	D₁₃₅₄₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₃₅₄₁
commutator, hypocenter	C₁₁×C₁₂₃₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₂₃₁	C₂
LCS	G ▷ C₁₁×C₁₂₃₁
UCS	C₁ ◁ C₂

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.