Subgroups — C₇×D₁₇×D₂₁ #23756244

Order 9996.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₃₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₇×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇²×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₇×D₁₇	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₁₁₉	—	3	1	no	—
7	C₇×D₇×C₁₇	—	3	1	no	—
8	C₇²×D₁₇	D₃	1	1	yes	characteristic, complemented
9	D₁₇×D₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor
10	D₃×C₇×D₁₇	—	7	1	no	maximal
11	C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₃₅₇	C₂×C₇	1	1	yes	characteristic, complemented
13	C₁₇×D₂₁	C₂×C₇	1	1	yes	characteristic, complemented
14	C₇×D₅₁	—	7	1	no	—
15	D₃×C₇×C₁₇	—	7	1	no	—
16	C₃×C₇×D₁₇	—	2	3	no	—
17	C₃×C₇×D₁₇	D₇	1	1	yes	characteristic, complemented
18	C₃×C₇×D₁₇	C₂×C₇	1	1	yes	characteristic, complemented
19	C₂×C₇×D₂₁	—	17	1	no	maximal, Hall
20	C₂×C₇×D₁₇	—	21	1	no	—
21	D₇×D₁₇	—	3	1	no	—
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	C₇×D₂₁	—	17	1	no	—
27	C₇×D₂₁	D₁₇	1	1	yes	characteristic, direct product factor
28	C₂×C₇×C₁₇	—	21	1	no	—
29	D₁₁₉	—	3	1	no	—
30	C₇×D₁₇	—	2	3	no	—
31	C₇×D₁₇	—	21	1	no	—
32	C₇×D₁₇	D₃×C₇	1	1	yes	characteristic, complemented
33	C₇×D₁₇	D₂₁	1	1	yes	characteristic, direct product factor
34	D₇×C₁₇	—	3	1	no	—
35	D₃×D₁₇	—	7	1	no	Hall
36	C₂×C₇×D₇	—	51	1	no	Hall
37	C₃×C₇²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
38	C₇×C₁₇	—	2	3	no	—
39	C₇×C₁₇	C₂×D₃×C₇	1	1	yes	characteristic, complemented
40	C₇×C₁₇	C₂×D₂₁	1	1	yes	characteristic, complemented
41	D₅₁	—	7	1	no	—
42	C₃×D₁₇	C₇×D₇	1	1	yes	characteristic, complemented
43	D₃×C₁₇	—	7	1	no	—
44	C₂×C₇²	—	17	1	no	—
45	C₇×D₇	—	3	1	no	—
46	C₇×D₇	—	51	1	no	—
47	C₂×D₂₁	—	17	1	no	—
48	C₂×D₃×C₇	—	119	1	no	—
49	C₂×D₁₇	—	21	1	no	Hall
50	C₃×C₁₇	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
51	C₇²	D₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃×C₇	—	17	1	no	—
53	C₂×C₃×C₇	—	17	1	no	—
54	C₂×C₃×C₇	—	34	3	no	—
55	D₂₁	—	17	1	no	—
56	D₂₁	C₇×D₁₇	1	1	yes	characteristic, direct product factor
57	D₃×C₇	—	7	1	no	—
58	D₃×C₇	—	119	1	no	—
59	C₂×C₁₇	—	21	1	no	—
60	D₁₇	—	21	1	no	—
61	D₁₇	C₇×D₂₁	1	1	yes	characteristic, direct product factor
62	C₂²×C₇	—	357	1	no	—
63	C₂×D₇	—	51	1	no	—
64	C₃×C₇	—	2	3	no	—
65	C₃×C₇	D₇×D₁₇	1	1	yes	characteristic, complemented
66	C₃×C₇	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented
67	C₁₇	C₂×C₇×D₂₁	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₇	—	17	1	no	—
69	C₂×C₇	—	17	1	no	—
70	C₂×C₇	—	21	1	no	—
71	C₂×C₇	—	34	3	no	—
72	C₂×C₇	—	357	1	no	—
73	D₇	—	3	1	no	—
74	D₇	—	51	1	no	—
75	C₂×D₃	—	119	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₃×C₇×D₁₇	1	1	yes	characteristic, complemented
78	C₇	D₁₇×D₂₁	1	1	yes	characteristic, direct product factor
79	C₂×C₃	—	17	1	no	—
80	D₃	—	7	1	no	—
81	D₃	—	119	1	no	—
82	C₂²	—	357	1	no	Sylow
83	C₃	C₇×D₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	17	1	no	—
85	C₂	—	21	1	no	—
86	C₂	—	357	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₁₇×D₂₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₇	C₂²
LCS	G ▷ C₃×C₇×C₁₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₃₅₇	C₂	semidirect
2. C₇×C₁₇×D₂₁	C₂	semidirect
3. C₃×C₇²×D₁₇	C₂	semidirect
5. C₃×C₇²×C₁₇	C₂²	semidirect
8. C₇²×D₁₇	D₃	semidirect
9. D₁₇×D₂₁	C₇	direct (N × H)
11. C₇²×C₁₇	C₂×D₃	semidirect
12. D₃₅₇	C₂×C₇	semidirect
13. C₁₇×D₂₁	C₂×C₇	semidirect
17. C₃×C₇×D₁₇	D₇	semidirect
18. C₃×C₇×D₁₇	C₂×C₇	semidirect
23. C₃×C₇×C₁₇	C₂×D₇	semidirect
24. C₃×C₇×C₁₇	C₂²×C₇	semidirect
27. C₇×D₂₁	D₁₇	direct (N × H)
32. C₇×D₁₇	D₃×C₇	semidirect
33. C₇×D₁₇	D₂₁	direct (N × H)
37. C₃×C₇²	C₂×D₁₇	semidirect
39. C₇×C₁₇	C₂×D₃×C₇	semidirect
40. C₇×C₁₇	C₂×D₂₁	semidirect
42. C₃×D₁₇	C₇×D₇	semidirect
50. C₃×C₁₇	C₂×C₇×D₇	semidirect
51. C₇²	D₃×D₁₇	semidirect
56. D₂₁	C₇×D₁₇	direct (N × H)
61. D₁₇	C₇×D₂₁	direct (N × H)
65. C₃×C₇	D₇×D₁₇	semidirect
66. C₃×C₇	C₂×C₇×D₁₇	semidirect
67. C₁₇	C₂×C₇×D₂₁	semidirect
77. C₇	D₃×C₇×D₁₇	semidirect
78. C₇	D₁₇×D₂₁	direct (N × H)
83. C₃	C₇×D₇×D₁₇	semidirect

Subgroups — C7×D17×D21 #23756244

Conjugacy classes of subgroups

Complements

Subgroups — C₇×D₁₇×D₂₁ #23756244