Subgroups — Dic₆₄₅₇ #38788890

Order 25828.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₅₈₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₅₈₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₅₈₇	—	11	1	no	maximal, Hall
4	C₂×C₅₈₇	D₁₁	1	1	yes	characteristic
5	C₅₈₇	Dic₁₁	1	1	yes	characteristic, complemented, Sylow
6	Dic₁₁	—	587	1	no	maximal, Hall
7	C₂×C₁₁	D₅₈₇	1	1	yes	characteristic
8	C₁₁	Dic₅₈₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	6457	1	no	Sylow
10	C₂	D₆₄₅₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₄₅₇
commutator, hypocenter	C₁₁×C₅₈₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₅₈₇	C₂
LCS	G ▷ C₁₁×C₅₈₇
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.