Subgroups — Dic₈₃₀₉ #45685015

Order 33236.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁₈₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁₈₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁₈₇	—	7	1	no	maximal, Hall
4	C₂×C₁₁₈₇	D₇	1	1	yes	characteristic
5	C₁₁₈₇	Dic₇	1	1	yes	characteristic, complemented, Sylow
6	Dic₇	—	1187	1	no	maximal, Hall
7	C₂×C₇	D₁₁₈₇	1	1	yes	characteristic
8	C₇	Dic₁₁₈₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	8309	1	no	Sylow
10	C₂	D₈₃₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₃₀₉
commutator, hypocenter	C₇×C₁₁₈₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₁₁₈₇	C₂
LCS	G ▷ C₇×C₁₁₈₇
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.