Subgroups — C₇×A₄⋊C₈ #10620697

Order 672.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×A₄	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂²⋊C₈	—	3	1	no	maximal, Hall
3	C₂×C₇×A₄	C₄	1	1	yes	characteristic
4	C₇×C₃⋊C₈	—	4	1	no	maximal
5	C₂²×C₄×C₇	D₃	1	1	yes	characteristic
6	C₂×C₇×C₈	—	3	1	no	—
7	C₂×C₇×C₈	—	3	1	no	—
8	A₄⋊C₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×A₄	C₈	1	1	yes	characteristic, complemented
10	C₃×C₄×C₇	—	4	1	no	—
11	C₂³×C₇	Dic₃	1	1	yes	characteristic
12	C₂×C₄×C₇	—	3	1	no	—
13	C₂×C₄×C₇	—	3	1	no	—
14	C₇×C₈	—	6	1	no	—
15	C₇×C₈	—	6	1	no	—
16	C₄×A₄	C₂×C₇	1	1	yes	characteristic
17	C₂×C₃×C₇	—	4	1	no	—
18	C₂²⋊C₈	—	3	1	no	Sylow
19	C₂²×C₇	—	3	1	no	—
20	C₂²×C₇	—	3	1	no	—
21	C₂²×C₇	C₃⋊C₈	1	1	yes	characteristic, complemented
22	C₄×C₇	—	3	1	no	—
23	C₄×C₇	S₄	1	1	yes	characteristic
24	C₂×A₄	C₄×C₇	1	1	yes	characteristic
25	C₃⋊C₈	—	4	1	no	—
26	C₃×C₇	—	4	1	no	Hall
27	C₂²×C₄	D₃×C₇	1	1	yes	characteristic
28	C₂×C₈	—	3	1	no	—
29	C₂×C₈	—	3	1	no	—
30	C₂×C₇	—	3	1	no	—
31	C₂×C₇	—	3	1	no	—
32	C₂×C₇	SL(2,ℤ/4)	1	1	yes	characteristic
33	A₄	C₇×C₈	1	1	yes	characteristic, complemented
34	C₃×C₄	—	4	1	no	—
35	C₂³	C₇×Dic₃	1	1	yes	characteristic
36	C₂×C₄	—	3	1	no	—
37	C₂×C₄	—	3	1	no	—
38	C₈	—	6	1	no	—
39	C₈	—	6	1	no	—
40	C₇	A₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	4	1	no	—
42	C₂²	—	3	1	no	—
43	C₂²	—	3	1	no	—
44	C₂²	C₇×C₃⋊C₈	1	1	yes	characteristic, complemented
45	C₄	—	3	1	no	—
46	C₄	C₇×S₄	1	1	yes	characteristic
47	C₃	—	4	1	no	Sylow
48	C₂	—	3	1	no	—
49	C₂	—	3	1	no	—
50	C₂	C₇×SL(2,ℤ/4)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₇	S₄
commutator, hypocenter	A₄	C₇×C₈
Frattini	C₄	C₇×S₄
Fitting	C₂²×C₄×C₇	D₃
socle	C₂³×C₇	Dic₃
prime radical	C₂×C₇×A₄	C₄
cosocle	C₄×A₄	C₂×C₇
LCS	G ▷ A₄
UCS	C₁ ◁ C₄×C₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
8. A₄⋊C₈	C₇	direct (N × H)
9. C₇×A₄	C₈	semidirect
21. C₂²×C₇	C₃⋊C₈	semidirect
33. A₄	C₇×C₈	semidirect
40. C₇	A₄⋊C₈	direct (N × H)
44. C₂²	C₇×C₃⋊C₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₇×A₄	2
C₇×C₂²⋊C₈	3
C₇×C₃⋊C₈	4
A₄⋊C₈	7

Subgroups — C7×A4⋊C8 #10620697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×A₄⋊C₈ #10620697