Subgroups — Dic₂₉₅₁ #26044648

Order 11804.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₂₂₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₂₂₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₂₂₇	—	13	1	no	maximal, Hall
4	C₂×C₂₂₇	D₁₃	1	1	yes	characteristic
5	C₂₂₇	Dic₁₃	1	1	yes	characteristic, complemented, Sylow
6	Dic₁₃	—	227	1	no	maximal, Hall
7	C₂×C₁₃	D₂₂₇	1	1	yes	characteristic
8	C₁₃	Dic₂₂₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	2951	1	no	Sylow
10	C₂	D₂₉₅₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₉₅₁
commutator, hypocenter	C₁₃×C₂₂₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₃×C₂₂₇	C₂
LCS	G ▷ C₁₃×C₂₂₇
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.