Subgroups — #37523909

Order 22916.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₇₂₉	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₃₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#13062438	—	17	1	no	maximal, Hall
4	D₃₃₇	—	17	1	no	—
5	C₃₃₇	#595	1	1	yes	characteristic, complemented, Sylow
6	#595	—	337	1	no	maximal, Hall
7	D₁₇	—	337	1	no	—
8	C₁₇	#13062438	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	5729	1	no	Sylow
10	C₂	—	5729	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₇×C₃₃₇	C₄
prime radical, cosocle	D₅₇₂₉	C₂
LCS	G ▷ C₁₇×C₃₃₇
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.