Subgroups — C₇²×C₇₁⋊C₇ #37567015

Order 24353.

232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₇₁	C₇	1	1	yes	maximal, characteristic, complemented
2	C₇×C₇₁⋊C₇	C₇	1	56	yes	maximal, direct product factor
3	C₇×C₇₁	C₇²	1	8	yes	complemented
4	C₇₁⋊C₇	C₇²	1	49	yes	direct product factor
5	C₇³	—	71	1	no	maximal, Sylow
6	C₇₁	C₇³	1	1	yes	characteristic, complemented, Sylow
7	C₇²	—	71	56	no	—
8	C₇²	C₇₁⋊C₇	1	1	yes	characteristic, direct product factor
9	C₇	—	71	49	no	—
10	C₇	C₇×C₇₁⋊C₇	1	8	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₇²	C₇₁⋊C₇
commutator, cosocle, hypocenter	C₇₁	C₇³
Frattini	C₁	G
Fitting, socle	C₇²×C₇₁	C₇
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₇²

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.