Subgroups — C₇×#4094 #11765192

Order 1120.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×#41	C₂	1	1	yes	maximal, characteristic
2	C₇×#681	C₂	1	3	yes	maximal, complemented
3	C₂×C₇×#168	C₂	1	3	yes	maximal, complemented
4	C₅×C₇×Q₈	C₄	1	1	yes	characteristic
5	C₅×C₇×D₄	C₄	1	3	yes	—
6	C₂×C₄×C₅×C₇	C₂²	1	3	yes	—
7	C₇×#168	C₂²	1	1	yes	characteristic
8	C₇×#168	C₂²	1	3	yes	—
9	C₇×#131	—	5	1	no	maximal, Hall
10	#4094	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₅×C₇	C₂×C₄	1	3	yes	—
12	C₄×C₅×C₇	C₂×C₄	1	3	yes	—
13	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
14	C₇×#41	D₅	1	1	yes	characteristic
15	C₇×M₁₆	—	5	3	no	—
16	C₂×C₇×C₈	—	5	3	no	—
17	C₅×#41	C₂×C₇	1	1	yes	characteristic
18	#681	C₂×C₇	1	3	yes	complemented
19	C₂×#168	C₂×C₇	1	3	yes	complemented
20	C₂×C₅×C₇	—	2	3	no	—
21	C₂×C₅×C₇	C₂²×C₄	1	1	yes	characteristic
22	C₇×Q₈	Dic₅	1	1	yes	characteristic
23	C₇×D₄	Dic₅	1	3	yes	—
24	C₂×C₄×C₇	C₂×D₅	1	3	yes	—
25	C₇×C₈	—	5	1	no	—
26	C₇×C₈	—	5	3	no	—
27	C₅×Q₈	C₄×C₇	1	1	yes	characteristic
28	C₅×D₄	C₄×C₇	1	3	yes	—
29	C₂×C₄×C₅	C₂²×C₇	1	3	yes	—
30	#168	C₂²×C₇	1	1	yes	characteristic
31	#168	C₂²×C₇	1	3	yes	—
32	C₅×C₇	#131	1	1	yes	characteristic, complemented, Hall
33	#131	—	5	1	no	Sylow
34	C₂²×C₇	C₂×Dic₅	1	3	yes	—
35	C₄×C₇	C₂×Dic₅	1	3	yes	—
36	C₄×C₇	C₂²×D₅	1	1	yes	characteristic
37	C₂²×C₅	C₂×C₄×C₇	1	3	yes	—
38	C₄×C₅	C₂×C₄×C₇	1	3	yes	—
39	C₄×C₅	C₂³×C₇	1	1	yes	characteristic
40	#41	C₇×D₅	1	1	yes	characteristic
41	M₁₆	—	5	3	no	—
42	C₂×C₈	—	5	3	no	—
43	C₂×C₇	—	2	3	no	—
44	C₂×C₇	C₂²×Dic₅	1	1	yes	characteristic
45	C₂×C₅	—	2	3	no	—
46	C₂×C₅	C₂²×C₄×C₇	1	1	yes	characteristic
47	Q₈	C₇×Dic₅	1	1	yes	characteristic
48	D₄	C₇×Dic₅	1	3	yes	—
49	C₂×C₄	C₂×C₇×D₅	1	3	yes	—
50	C₈	—	5	1	no	—
51	C₈	—	5	3	no	—
52	C₇	#4094	1	1	yes	characteristic, direct product factor, Sylow
53	C₅	C₇×#131	1	1	yes	characteristic, complemented, Sylow
54	C₂²	C₂×C₇×Dic₅	1	3	yes	—
55	C₄	C₂×C₇×Dic₅	1	3	yes	—
56	C₄	C₂²×C₇×D₅	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂²×C₇×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇	C₂²×D₅
commutator	C₂×C₅	C₂²×C₄×C₇
Frattini	C₄	C₂²×C₇×D₅
Fitting, prime radical	C₅×C₇×#41	C₂
socle	C₂×C₅×C₇	C₂²×C₄
cosocle	C₄×C₅	C₂³×C₇
hypercenter	C₇×#41	D₅
hypocenter	C₅	C₇×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₇ ◁ C₇×#41

Complements

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

N	H ≅ G/N	type
2. C₇×#681	C₂	semidirect
3. C₂×C₇×#168	C₂	semidirect
10. #4094	C₇	direct (N × H)
18. #681	C₂×C₇	semidirect
19. C₂×#168	C₂×C₇	semidirect
32. C₅×C₇	#131	semidirect
52. C₇	#4094	direct (N × H)
53. C₅	C₇×#131	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×#41	2
C₇×#681	2
C₂×C₇×#168	2
C₇×#131	5
#4094	7

Subgroups — C7×#4094 #11765192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#4094 #11765192