Subgroups — Dic₇₈₀₇ #44530273

Order 31228.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃₇×C₂₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₂₁₁	—	37	1	no	maximal, Hall
4	C₂×C₂₁₁	D₃₇	1	1	yes	characteristic
5	C₂₁₁	Dic₃₇	1	1	yes	characteristic, complemented, Sylow
6	Dic₃₇	—	211	1	no	maximal, Hall
7	C₂×C₃₇	D₂₁₁	1	1	yes	characteristic
8	C₃₇	Dic₂₁₁	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	7807	1	no	Sylow
10	C₂	D₇₈₀₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₈₀₇
commutator, hypocenter	C₃₇×C₂₁₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃₇×C₂₁₁	C₂
LCS	G ▷ C₃₇×C₂₁₁
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.