Subgroups — #34062002

Order 19108.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₂₈₁	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₂₈₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#11765499	—	17	1	no	maximal, Hall
4	D₂₈₁	D₁₇	1	1	yes	characteristic
5	C₂₈₁	Dic₁₇	1	1	yes	characteristic, complemented, Sylow
6	Dic₁₇	—	281	1	no	maximal, Hall
7	C₂×C₁₇	—	281	1	no	—
8	C₁₇	#11765499	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	4777	1	no	Sylow
10	C₂	—	281	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₇×C₂₈₁	C₄
prime radical, cosocle	C₁₇×D₂₈₁	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.