Subgroups — Dic₆₇₃₁ #41002189

Order 26924.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₅₃×C₁₂₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₂₇	—	53	1	no	maximal, Hall
4	C₂×C₁₂₇	D₅₃	1	1	yes	characteristic
5	Dic₅₃	—	127	1	no	maximal, Hall
6	C₁₂₇	Dic₅₃	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₅₃	D₁₂₇	1	1	yes	characteristic
8	C₅₃	Dic₁₂₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	6731	1	no	Sylow
10	C₂	D₆₇₃₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₇₃₁
commutator, hypocenter	C₅₃×C₁₂₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅₃×C₁₂₇	C₂
LCS	G ▷ C₅₃×C₁₂₇
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.