Subgroups — C₃₇⋊C₃×C₂₆₃ #44415940

Order 29193.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₂₆₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₂₆₃	—	37	1	no	maximal, Hall
3	C₂₆₃	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
4	C₃₇⋊C₃	C₂₆₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃₇	C₃×C₂₆₃	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₆₃	C₃₇⋊C₃
commutator, cosocle, hypocenter	C₃₇	C₃×C₂₆₃
Frattini	C₁	G
Fitting, socle	C₃₇×C₂₆₃	C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂₆₃

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.