Subgroups — C₃₁×C₃₃₇⋊C₃ #44531366

Order 31341.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₃₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₃₇⋊C₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₃₇	C₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₃₁	—	337	1	no	maximal, Hall
5	C₃₁	C₃₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃	—	337	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	C₃₃₇⋊C₃
commutator, cosocle, hypocenter	C₃₃₇	C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃₁×C₃₃₇	C₃
LCS	G ▷ C₃₃₇
UCS	C₁ ◁ C₃₁

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.