Subgroups — (C₃₁⋊C₃)⋊C₄ #67308

Order 372.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Sylow
6	C₃×C₄	—	31	1	no	maximal, Hall
7	C₂×C₃	—	31	1	no	—
8	C₄	—	31	1	no	Sylow
9	C₃	—	31	1	no	Sylow
10	C₂	D₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₁⋊C₃
commutator, hypocenter	C₃₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₃₁	C₂×C₃
prime radical	C₂×C₃₁⋊C₃	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂

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.