Subgroups — C₇×#63254 #14274160

Order 1904.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₂²⋊D₁₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×Dic₁₇	C₂	1	2	yes	maximal, complemented
4	C₄×C₇×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×Dic₃₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×C₁₇	C₂²	1	2	yes	—
7	C₂×C₇×D₁₇	C₂²	1	1	yes	characteristic
8	C₄×C₇×C₁₇	C₂²	1	1	yes	characteristic
9	C₇×Dic₁₇	C₂²	1	2	yes	—
10	C₇×Dic₁₇	C₂²	1	1	yes	characteristic
11	#63254	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₇×C₁₇	—	2	2	no	—
13	C₂×C₇×C₁₇	C₂³	1	1	yes	characteristic
14	C₇×D₁₇	—	2	1	no	—
15	D₄×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
16	C₂²⋊D₁₇	C₂×C₇	1	2	yes	complemented
17	C₂×Dic₁₇	C₂×C₇	1	2	yes	complemented
18	C₄×D₁₇	C₂×C₇	1	1	yes	characteristic, complemented
19	Dic₃₄	C₂×C₇	1	1	yes	characteristic, complemented
20	C₇×C₁₇	#41	1	1	yes	characteristic, complemented, Hall
21	C₇×#41	—	17	1	no	maximal, Hall
22	C₂²×C₁₇	C₂²×C₇	1	2	yes	—
23	C₂×D₁₇	C₂²×C₇	1	1	yes	characteristic
24	C₄×C₁₇	C₂²×C₇	1	1	yes	characteristic
25	Dic₁₇	C₂²×C₇	1	2	yes	—
26	Dic₁₇	C₂²×C₇	1	1	yes	characteristic
27	C₇×Q₈	—	17	1	no	—
28	C₇×D₄	—	17	2	no	—
29	C₇×D₄	D₁₇	1	1	yes	characteristic, complemented
30	C₂×C₄×C₇	—	17	2	no	—
31	C₂×C₄×C₇	—	17	1	no	—
32	C₂×C₁₇	—	2	2	no	—
33	C₂×C₁₇	C₂³×C₇	1	1	yes	characteristic
34	D₁₇	—	2	1	no	—
35	C₂²×C₇	—	17	1	no	—
36	C₂²×C₇	C₂×D₁₇	1	2	yes	—
37	C₄×C₇	—	17	1	no	—
38	C₄×C₇	—	17	2	no	—
39	C₄×C₇	C₂×D₁₇	1	1	yes	characteristic
40	C₁₇	C₇×#41	1	1	yes	characteristic, complemented, Sylow
41	#41	—	17	1	no	Sylow
42	C₂×C₇	—	2	2	no	—
43	C₂×C₇	—	34	1	no	—
44	C₂×C₇	C₂²×D₁₇	1	1	yes	characteristic
45	Q₈	—	17	1	no	—
46	D₄	—	17	2	no	—
47	D₄	C₇×D₁₇	1	1	yes	characteristic, complemented
48	C₂×C₄	—	17	2	no	—
49	C₂×C₄	—	17	1	no	—
50	C₇	#63254	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²	—	17	1	no	—
52	C₂²	C₂×C₇×D₁₇	1	2	yes	—
53	C₄	—	17	1	no	—
54	C₄	—	17	2	no	—
55	C₄	C₂×C₇×D₁₇	1	1	yes	characteristic
56	C₂	—	2	2	no	—
57	C₂	—	34	1	no	—
58	C₂	C₂²×C₇×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	C₂²×D₁₇
commutator, cosocle	C₂×C₁₇	C₂³×C₇
Frattini	C₂	C₂²×C₇×D₁₇
Fitting	C₇×D₄×C₁₇	C₂
socle	C₂×C₇×C₁₇	C₂³
hypercenter	C₇×D₄	D₁₇
hypocenter	C₁₇	C₇×#41
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₇ ◁ C₇×D₄

Complements

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

N	H ≅ G/N	type
1. C₇×D₄×C₁₇	C₂	semidirect
2. C₇×C₂²⋊D₁₇	C₂	semidirect
3. C₂×C₇×Dic₁₇	C₂	semidirect
4. C₄×C₇×D₁₇	C₂	semidirect
5. C₇×Dic₃₄	C₂	semidirect
11. #63254	C₇	direct (N × H)
15. D₄×C₁₇	C₂×C₇	semidirect
16. C₂²⋊D₁₇	C₂×C₇	semidirect
17. C₂×Dic₁₇	C₂×C₇	semidirect
18. C₄×D₁₇	C₂×C₇	semidirect
19. Dic₃₄	C₂×C₇	semidirect
20. C₇×C₁₇	#41	semidirect
29. C₇×D₄	D₁₇	semidirect
40. C₁₇	C₇×#41	semidirect
47. D₄	C₇×D₁₇	semidirect
50. C₇	#63254	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₄×C₁₇	2
C₇×C₂²⋊D₁₇	2
C₂×C₇×Dic₁₇	2
C₄×C₇×D₁₇	2
C₇×Dic₃₄	2
#63254	7
C₇×#41	17

Subgroups — C7×#63254 #14274160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#63254 #14274160