Subgroups — C₃₁⋊(C₁₇²⋊C₃) #41001852

Order 26877.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇²⋊C₃	—	31	1	no	maximal, Hall
3	C₁₇×C₃₁	—	3	6	no	—
4	C₁₇²	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
5	C₃₁⋊C₃	—	289	1	no	maximal, Hall
6	C₃₁	C₁₇²⋊C₃	1	1	yes	characteristic, complemented, Sylow
7	C₁₇	—	3	6	no	—
8	C₃	—	8959	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇²×C₃₁	C₃
LCS	G ▷ C₁₇²×C₃₁
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.