Subgroups — C₇×C₇₅₇⋊C₇ #49150615

Order 37093.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₇₅₇	C₇	1	1	yes	maximal, characteristic, complemented
2	C₇₅₇⋊C₇	C₇	1	7	yes	maximal, direct product factor
3	C₇₅₇	C₇²	1	1	yes	characteristic, complemented, Sylow
4	C₇²	—	757	1	no	maximal, Sylow
5	C₇	—	757	7	no	—
6	C₇	C₇₅₇⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₇	C₇₅₇⋊C₇
commutator, cosocle, hypocenter	C₇₅₇	C₇²
Frattini	C₁	G
Fitting, socle	C₇×C₇₅₇	C₇
LCS	G ▷ C₇₅₇
UCS	C₁ ◁ C₇

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.