Subgroups — C₂×C₇⋊S₄ #66746

Order 336.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇⋊S₄	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₂²⋊D₇	—	3	1	no	maximal, Hall
4	C₂×D₂₁	—	4	1	no	maximal
5	C₇×A₄	C₂²	1	1	yes	characteristic, complemented
6	C₂³×C₇	D₃	1	1	yes	characteristic, complemented
7	C₂²×D₇	—	3	1	no	—
8	C₂²⋊D₇	—	3	2	no	—
9	C₂²⋊D₇	—	3	2	no	—
10	C₂×Dic₇	—	3	1	no	—
11	C₂×S₄	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	—	4	1	no	—
13	D₂₁	—	4	2	no	—
14	C₂²×C₇	—	3	1	no	—
15	C₂²×C₇	—	3	1	no	—
16	C₂²×C₇	C₂×D₃	1	1	yes	characteristic, complemented
17	C₂×D₇	—	3	2	no	—
18	C₂×D₇	—	6	1	no	—
19	C₂×D₇	—	6	1	no	—
20	Dic₇	—	3	2	no	—
21	C₂×A₄	D₇	1	1	yes	characteristic, complemented
22	S₄	—	7	2	no	—
23	C₃×C₇	—	4	1	no	Hall
24	C₂×D₄	—	21	1	no	Sylow
25	C₂×C₇	—	3	1	no	—
26	C₂×C₇	—	3	1	no	—
27	C₂×C₇	S₄	1	1	yes	characteristic, complemented
28	D₇	—	6	2	no	—
29	C₂×D₃	—	28	1	no	—
30	A₄	C₂×D₇	1	1	yes	characteristic, complemented
31	C₂³	—	21	1	no	—
32	C₂³	D₂₁	1	1	yes	characteristic, complemented
33	D₄	—	21	2	no	—
34	D₄	—	21	2	no	—
35	C₂×C₄	—	21	1	no	—
36	C₇	C₂×S₄	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃	—	4	1	no	—
38	D₃	—	28	2	no	—
39	C₂²	—	3	1	no	—
40	C₂²	—	3	1	no	—
41	C₂²	—	21	2	no	—
42	C₂²	—	42	1	no	—
43	C₂²	—	42	1	no	—
44	C₂²	C₂×D₂₁	1	1	yes	characteristic, complemented
45	C₄	—	21	2	no	—
46	C₃	—	4	1	no	Sylow
47	C₂	—	3	1	no	—
48	C₂	—	3	1	no	—
49	C₂	—	42	2	no	—
50	C₂	C₇⋊S₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₇⋊S₄
commutator, cosocle, hypocenter	C₇×A₄	C₂²
Frattini	C₁	G
Fitting, socle	C₂³×C₇	D₃
LCS	G ▷ C₇×A₄
UCS	C₁ ◁ C₂

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.