Subgroups — C₂×C₂₂₃⋊C₃₇ #30658178

Order 16502.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₂₃⋊C₃₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₂₃	C₃₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₂₃	C₂×C₃₇	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₃₇	—	223	1	no	maximal, Hall
5	C₃₇	—	223	1	no	Sylow
6	C₂	C₂₂₃⋊C₃₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₂₂₃⋊C₃₇
commutator, cosocle, hypocenter	C₂₂₃	C₂×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₂₂₃	C₃₇
LCS	G ▷ C₂₂₃
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.