Subgroups — Dic₁₄₅₀₁ #72291237

Order 58004.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₈₅₃	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₈₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₈₅₃	—	17	1	no	maximal, Hall
4	C₂×C₈₅₃	D₁₇	1	1	yes	characteristic
5	C₈₅₃	Dic₁₇	1	1	yes	characteristic, complemented, Sylow
6	Dic₁₇	—	853	1	no	maximal, Hall
7	C₂×C₁₇	D₈₅₃	1	1	yes	characteristic
8	C₁₇	Dic₈₅₃	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	14501	1	no	Sylow
10	C₂	D₁₄₅₀₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₄₅₀₁
commutator, hypocenter	C₁₇×C₈₅₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₇×C₈₅₃	C₂
LCS	G ▷ C₁₇×C₈₅₃
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.