Subgroups — C₃×C₇×D₇×D₁₇ #23756232

Order 9996.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₁₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇²×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₇×D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₁₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₇×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇²×D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₃×C₇×D₁₇	—	7	1	no	maximal
10	C₃×D₇×D₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor
11	C₇²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₇×C₁₇	—	7	1	no	—
13	C₃×D₁₁₉	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×D₇×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
15	C₃×C₇×D₁₇	—	2	3	no	—
16	C₃×C₇×D₁₇	—	7	1	no	—
17	C₃×C₇×D₁₇	D₇	1	1	yes	characteristic, direct product factor
18	C₃×C₇×D₁₇	C₂×C₇	1	1	yes	characteristic, complemented
19	C₂×C₃×C₇×D₇	—	17	1	no	maximal, Hall
20	C₂×C₇×D₁₇	—	7	1	no	—
21	D₇×D₁₇	C₃×C₇	1	1	yes	characteristic, direct product factor
22	C₃×C₇×C₁₇	—	2	3	no	—
23	C₃×C₇×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented
24	C₃×C₇×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented
25	C₂×C₃×C₇²	—	17	1	no	—
26	C₃×C₇×D₇	—	17	1	no	—
27	C₃×C₇×D₇	D₁₇	1	1	yes	characteristic, direct product factor
28	C₂×C₇×C₁₇	—	7	1	no	—
29	D₁₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
30	C₇×D₁₇	—	2	3	no	—
31	C₇×D₁₇	—	7	1	no	—
32	C₇×D₁₇	C₃×D₇	1	1	yes	characteristic, direct product factor
33	C₇×D₁₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
34	D₇×C₁₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
35	C₂×C₃×D₁₇	—	7	1	no	Hall
36	C₂×C₇×D₇	—	17	1	no	Hall
37	C₃×C₇²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
38	C₇×C₁₇	—	2	3	no	—
39	C₇×C₁₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented
40	C₇×C₁₇	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
41	C₂×C₃×C₁₇	—	7	1	no	—
42	C₃×D₁₇	—	7	1	no	—
43	C₃×D₁₇	C₇×D₇	1	1	yes	characteristic, direct product factor
44	C₂×C₇²	—	17	1	no	—
45	C₇×D₇	—	17	1	no	—
46	C₇×D₇	C₃×D₁₇	1	1	yes	characteristic, direct product factor
47	C₂²×C₃×C₇	—	119	1	no	—
48	C₂×C₃×D₇	—	17	1	no	—
49	C₂×D₁₇	—	7	1	no	Hall
50	C₃×C₁₇	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
51	C₇²	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃×C₇	—	7	1	no	—
53	C₂×C₃×C₇	—	17	1	no	—
54	C₂×C₃×C₇	—	17	1	no	—
55	C₂×C₃×C₇	—	34	3	no	—
56	C₂×C₃×C₇	—	119	1	no	—
57	C₃×D₇	—	17	1	no	—
58	C₃×D₇	C₇×D₁₇	1	1	yes	characteristic, direct product factor
59	C₂×C₁₇	—	7	1	no	—
60	D₁₇	—	7	1	no	—
61	D₁₇	C₃×C₇×D₇	1	1	yes	characteristic, direct product factor
62	C₂²×C₇	—	119	1	no	—
63	C₂×D₇	—	17	1	no	—
64	C₃×C₇	—	2	3	no	—
65	C₃×C₇	D₇×D₁₇	1	1	yes	characteristic, direct product factor
66	C₃×C₇	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented
67	C₁₇	C₂×C₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₇	—	7	1	no	—
69	C₂×C₇	—	17	1	no	—
70	C₂×C₇	—	17	1	no	—
71	C₂×C₇	—	34	3	no	—
72	C₂×C₇	—	119	1	no	—
73	D₇	—	17	1	no	—
74	D₇	C₃×C₇×D₁₇	1	1	yes	characteristic, direct product factor
75	C₂²×C₃	—	119	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	C₃×D₇×D₁₇	1	1	yes	characteristic, direct product factor
78	C₇	C₂×C₃×C₇×D₁₇	1	1	yes	characteristic, complemented
79	C₂×C₃	—	7	1	no	—
80	C₂×C₃	—	17	1	no	—
81	C₂×C₃	—	119	1	no	—
82	C₂²	—	119	1	no	Sylow
83	C₃	C₇×D₇×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	7	1	no	—
85	C₂	—	17	1	no	—
86	C₂	—	119	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₇	D₇×D₁₇
commutator, cosocle, hypocenter	C₇×C₁₇	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₇	C₂²
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₁₁₉	C₂	semidirect
2. C₃×C₇×D₇×C₁₇	C₂	semidirect
3. C₃×C₇²×D₁₇	C₂	semidirect
4. C₇×D₇×D₁₇	C₃	direct (N × H)
5. C₃×C₇²×C₁₇	C₂²	semidirect
6. C₇×D₁₁₉	C₂×C₃	semidirect
7. C₇×D₇×C₁₇	C₂×C₃	semidirect
8. C₇²×D₁₇	C₂×C₃	semidirect
10. C₃×D₇×D₁₇	C₇	direct (N × H)
11. C₇²×C₁₇	C₂²×C₃	semidirect
13. C₃×D₁₁₉	C₂×C₇	semidirect
14. C₃×D₇×C₁₇	C₂×C₇	semidirect
17. C₃×C₇×D₁₇	D₇	direct (N × H)
18. C₃×C₇×D₁₇	C₂×C₇	semidirect
21. D₇×D₁₇	C₃×C₇	direct (N × H)
23. C₃×C₇×C₁₇	C₂×D₇	semidirect
24. C₃×C₇×C₁₇	C₂²×C₇	semidirect
27. C₃×C₇×D₇	D₁₇	direct (N × H)
29. D₁₁₉	C₂×C₃×C₇	semidirect
32. C₇×D₁₇	C₃×D₇	direct (N × H)
33. C₇×D₁₇	C₂×C₃×C₇	semidirect
34. D₇×C₁₇	C₂×C₃×C₇	semidirect
37. C₃×C₇²	C₂×D₁₇	semidirect
39. C₇×C₁₇	C₂×C₃×D₇	semidirect
40. C₇×C₁₇	C₂²×C₃×C₇	semidirect
43. C₃×D₁₇	C₇×D₇	direct (N × H)
46. C₇×D₇	C₃×D₁₇	direct (N × H)
50. C₃×C₁₇	C₂×C₇×D₇	semidirect
51. C₇²	C₂×C₃×D₁₇	semidirect
58. C₃×D₇	C₇×D₁₇	direct (N × H)
61. D₁₇	C₃×C₇×D₇	direct (N × H)
65. C₃×C₇	D₇×D₁₇	direct (N × H)
66. C₃×C₇	C₂×C₇×D₁₇	semidirect
67. C₁₇	C₂×C₃×C₇×D₇	semidirect
74. D₇	C₃×C₇×D₁₇	direct (N × H)
77. C₇	C₃×D₇×D₁₇	direct (N × H)
78. C₇	C₂×C₃×C₇×D₁₇	semidirect
83. C₃	C₇×D₇×D₁₇	direct (N × H)

Subgroups — C3×C7×D7×D17 #23756232

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×D₇×D₁₇ #23756232