Subgroups — C₇×D₄×D₁₇ #14274159

Order 1904.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₁₇	C₂	1	2	yes	maximal, complemented
2	C₇×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂²⋊D₁₇	C₂	1	2	yes	maximal, complemented
4	C₇×D₆₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₇×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×C₁₇	C₂²	1	2	yes	complemented
7	C₂×C₇×D₁₇	—	2	4	no	—
8	C₂×C₇×D₁₇	C₂²	1	1	yes	characteristic
9	C₂×C₇×D₁₇	C₂²	1	2	yes	complemented
10	C₄×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented
11	C₇×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
12	D₄×D₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₇×C₁₇	—	2	2	no	—
14	C₂×C₇×C₁₇	C₂³	1	1	yes	characteristic
15	C₇×D₁₇	—	2	2	no	—
16	C₇×D₁₇	D₄	1	2	yes	direct product factor
17	C₂²×D₁₇	C₂×C₇	1	2	yes	complemented
18	D₄×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
19	C₂²⋊D₁₇	C₂×C₇	1	2	yes	complemented
20	D₆₈	C₂×C₇	1	1	yes	characteristic, complemented
21	C₄×D₁₇	C₂×C₇	1	1	yes	characteristic, complemented
22	C₇×C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×D₄	—	17	1	no	maximal, Hall
24	C₂²×C₁₇	C₂²×C₇	1	2	yes	complemented
25	C₂×D₁₇	—	2	4	no	—
26	C₂×D₁₇	C₂²×C₇	1	1	yes	characteristic
27	C₂×D₁₇	C₂²×C₇	1	2	yes	complemented
28	C₄×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented
29	Dic₁₇	C₂²×C₇	1	1	yes	characteristic, complemented
30	C₂³×C₇	—	17	2	no	—
31	C₇×D₄	—	17	2	no	—
32	C₇×D₄	—	17	1	no	—
33	C₇×D₄	D₁₇	1	1	yes	characteristic, direct product factor
34	C₂×C₄×C₇	—	17	1	no	—
35	C₂×C₁₇	—	2	2	no	—
36	C₂×C₁₇	C₂³×C₇	1	1	yes	characteristic
37	D₁₇	—	2	2	no	—
38	D₁₇	C₇×D₄	1	2	yes	direct product factor
39	C₂²×C₇	—	17	1	no	—
40	C₂²×C₇	—	17	2	no	—
41	C₂²×C₇	—	34	4	no	—
42	C₂²×C₇	C₂×D₁₇	1	2	yes	complemented
43	C₄×C₇	—	17	1	no	—
44	C₄×C₇	C₂×D₁₇	1	1	yes	characteristic, complemented
45	C₁₇	C₂×C₇×D₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₄	—	17	1	no	Sylow
47	C₂×C₇	—	2	2	no	—
48	C₂×C₇	—	17	2	no	—
49	C₂×C₇	—	34	2	no	—
50	C₂×C₇	C₂²×D₁₇	1	1	yes	characteristic
51	C₂³	—	17	2	no	—
52	D₄	—	17	2	no	—
53	D₄	—	17	1	no	—
54	D₄	C₇×D₁₇	1	1	yes	characteristic, direct product factor
55	C₂×C₄	—	17	1	no	—
56	C₇	D₄×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²	—	17	1	no	—
58	C₂²	—	17	2	no	—
59	C₂²	—	34	4	no	—
60	C₂²	C₂×C₇×D₁₇	1	2	yes	complemented
61	C₄	—	17	1	no	—
62	C₄	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented
63	C₂	—	2	2	no	—
64	C₂	—	17	2	no	—
65	C₂	—	34	2	no	—
66	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	C₂×C₇×D₄
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. C₂²×C₇×D₁₇	C₂	semidirect
2. C₇×D₄×C₁₇	C₂	semidirect
3. C₇×C₂²⋊D₁₇	C₂	semidirect
4. C₇×D₆₈	C₂	semidirect
5. C₄×C₇×D₁₇	C₂	semidirect
6. C₂²×C₇×C₁₇	C₂²	semidirect
9. C₂×C₇×D₁₇	C₂²	semidirect
10. C₄×C₇×C₁₇	C₂²	semidirect
11. C₇×Dic₁₇	C₂²	semidirect
12. D₄×D₁₇	C₇	direct (N × H)
16. C₇×D₁₇	D₄	direct (N × H)
17. C₂²×D₁₇	C₂×C₇	semidirect
18. D₄×C₁₇	C₂×C₇	semidirect
19. C₂²⋊D₁₇	C₂×C₇	semidirect
20. D₆₈	C₂×C₇	semidirect
21. C₄×D₁₇	C₂×C₇	semidirect
22. C₇×C₁₇	C₂×D₄	semidirect
24. C₂²×C₁₇	C₂²×C₇	semidirect
27. C₂×D₁₇	C₂²×C₇	semidirect
28. C₄×C₁₇	C₂²×C₇	semidirect
29. Dic₁₇	C₂²×C₇	semidirect
33. C₇×D₄	D₁₇	direct (N × H)
38. D₁₇	C₇×D₄	direct (N × H)
42. C₂²×C₇	C₂×D₁₇	semidirect
44. C₄×C₇	C₂×D₁₇	semidirect
45. C₁₇	C₂×C₇×D₄	semidirect
54. D₄	C₇×D₁₇	direct (N × H)
56. C₇	D₄×D₁₇	direct (N × H)
60. C₂²	C₂×C₇×D₁₇	semidirect
62. C₄	C₂×C₇×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇×D₁₇	2
C₇×D₄×C₁₇	2
C₇×C₂²⋊D₁₇	2
C₇×D₆₈	2
C₄×C₇×D₁₇	2
D₄×D₁₇	7
C₂×C₇×D₄	17

Subgroups — C7×D4×D17 #14274159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₄×D₁₇ #14274159