Subgroups — C₇×C₇₄₃⋊C₇ #49138658

Order 36407.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₇₄₃	C₇	1	1	yes	maximal, characteristic, complemented
2	C₇₄₃⋊C₇	C₇	1	7	yes	maximal, direct product factor
3	C₇₄₃	C₇²	1	1	yes	characteristic, complemented, Sylow
4	C₇²	—	743	1	no	maximal, Sylow
5	C₇	—	743	7	no	—
6	C₇	C₇₄₃⋊C₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₇	C₇₄₃⋊C₇
commutator, cosocle, hypocenter	C₇₄₃	C₇²
Frattini	C₁	G
Fitting, socle	C₇×C₇₄₃	C₇
LCS	G ▷ C₇₄₃
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.