Subgroups — #34062001

Order 19108.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇×C₂₈₁	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₂₈₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₂₈₁	—	17	1	no	maximal, Hall
4	C₂×C₂₈₁	—	17	1	no	—
5	C₂₈₁	#595	1	1	yes	characteristic, complemented, Sylow
6	#595	—	281	1	no	maximal, Hall
7	D₁₇	D₂₈₁	1	1	yes	characteristic
8	C₁₇	Dic₂₈₁	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	4777	1	no	Sylow
10	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₇×C₂₈₁	C₄
prime radical, cosocle	D₁₇×C₂₈₁	C₂
LCS	G ▷ C₁₇×C₂₈₁
UCS	C₁

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.