Subgroups — C₇⋊S₄ #4276

Order 168.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₇	—	3	1	no	maximal, Hall
3	D₂₁	—	4	1	no	maximal
4	C₂²×C₇	D₃	1	1	yes	characteristic, complemented
5	C₂×D₇	—	3	1	no	—
6	Dic₇	—	3	1	no	—
7	S₄	—	7	1	no	maximal, Hall
8	C₃×C₇	—	4	1	no	Hall
9	C₂×C₇	—	3	1	no	—
10	D₇	—	6	1	no	—
11	A₄	D₇	1	1	yes	characteristic, complemented
12	D₄	—	21	1	no	Sylow
13	C₇	S₄	1	1	yes	characteristic, complemented, Sylow
14	D₃	—	28	1	no	—
15	C₂²	—	21	1	no	—
16	C₂²	D₂₁	1	1	yes	characteristic, complemented
17	C₄	—	21	1	no	—
18	C₃	—	4	1	no	Sylow
19	C₂	—	3	1	no	—
20	C₂	—	42	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₇×A₄	C₂
Fitting, socle	C₂²×C₇	D₃
LCS	G ▷ C₇×A₄
UCS	C₁

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.