Subgroups — D₇×C₁₇×D₂₁ #23756255

Order 9996.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₇×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇²×C₁₇	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₇×C₇⋊D₇	—	3	1	no	—
7	C₇×D₇×C₁₇	—	3	1	no	—
8	C₇×D₇×C₁₇	D₃	1	1	yes	characteristic, complemented
9	C₂×C₁₇×D₂₁	—	7	1	no	maximal
10	D₃×D₇×C₁₇	—	7	1	no	maximal
11	C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₇×C₁₇	—	7	1	no	—
13	C₁₇×D₂₁	—	7	1	no	—
14	C₁₇×D₂₁	—	7	1	no	—
15	C₁₇×D₂₁	—	14	3	no	—
16	C₁₇×D₂₁	D₇	1	1	yes	characteristic, direct product factor
17	D₃×C₇×C₁₇	—	7	1	no	—
18	C₃×D₇×C₁₇	D₇	1	1	yes	characteristic, complemented
19	D₇×D₂₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×D₇×C₁₇	—	21	1	no	—
21	C₂×D₇×C₁₇	—	21	1	no	—
22	C₃×C₇×C₁₇	—	2	3	no	—
23	C₃×C₇×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented
24	C₃×C₇×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented
25	C₃⋊(C₇⋊D₇)	C₂×C₁₇	1	1	yes	characteristic, complemented
26	C₇×D₂₁	C₂×C₁₇	1	1	yes	characteristic, complemented
27	C₃×C₇×D₇	C₂×C₁₇	1	1	yes	characteristic, complemented
28	C₂×C₇×C₁₇	—	7	1	no	—
29	C₂×C₇×C₁₇	—	21	1	no	—
30	D₇×C₁₇	—	3	1	no	—
31	D₇×C₁₇	—	21	1	no	—
32	D₇×C₁₇	—	21	1	no	—
33	D₇×C₁₇	—	42	3	no	—
34	D₇×C₁₇	D₂₁	1	1	yes	characteristic, direct product factor
35	C₂×D₃×C₁₇	—	49	1	no	Hall
36	D₇²	—	3	1	no	Hall
37	C₃×C₇²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
38	C₇×C₁₇	—	2	3	no	—
39	C₇×C₁₇	D₃×D₇	1	1	yes	characteristic, complemented
40	C₇×C₁₇	C₂×D₂₁	1	1	yes	characteristic, complemented
41	C₂×C₃×C₁₇	—	7	1	no	—
42	D₃×C₁₇	—	7	1	no	—
43	D₃×C₁₇	—	49	1	no	—
44	C₇⋊D₇	—	3	1	no	—
45	C₇×D₇	—	3	1	no	—
46	C₇×D₇	D₃×C₁₇	1	1	yes	characteristic, complemented
47	C₂×D₂₁	—	7	1	no	—
48	D₃×D₇	—	7	1	no	—
49	C₂²×C₁₇	—	147	1	no	Hall
50	C₃×C₁₇	D₇²	1	1	yes	characteristic, complemented, Hall
51	C₇²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃×C₇	—	7	1	no	—
53	D₂₁	—	7	1	no	—
54	D₂₁	—	7	1	no	—
55	D₂₁	—	14	3	no	—
56	D₂₁	D₇×C₁₇	1	1	yes	characteristic, direct product factor
57	C₃×D₇	D₇×C₁₇	1	1	yes	characteristic, complemented
58	D₃×C₇	—	7	1	no	—
59	C₂×C₁₇	—	7	1	no	—
60	C₂×C₁₇	—	21	1	no	—
61	C₂×C₁₇	—	147	1	no	—
62	C₂×D₇	—	21	1	no	—
63	C₂×D₇	—	21	1	no	—
64	C₃×C₇	—	2	3	no	—
65	C₃×C₇	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented
66	C₃×C₇	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented
67	C₁₇	D₇×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
68	C₂×C₇	—	7	1	no	—
69	C₂×C₇	—	21	1	no	—
70	D₇	—	3	1	no	—
71	D₇	—	21	1	no	—
72	D₇	—	21	1	no	—
73	D₇	—	42	3	no	—
74	D₇	C₁₇×D₂₁	1	1	yes	characteristic, direct product factor
75	C₂×D₃	—	49	1	no	Hall
76	C₇	—	2	3	no	—
77	C₇	D₃×D₇×C₁₇	1	1	yes	characteristic, complemented
78	C₇	C₂×C₁₇×D₂₁	1	1	yes	characteristic, complemented
79	C₂×C₃	—	7	1	no	—
80	D₃	—	7	1	no	—
81	D₃	—	49	1	no	—
82	C₂²	—	147	1	no	Sylow
83	C₃	D₇²×C₁₇	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	7	1	no	—
85	C₂	—	21	1	no	—
86	C₂	—	147	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	D₇×D₂₁
commutator, cosocle, hypocenter	C₃×C₇²	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₇	C₂²
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊(C₇⋊D₇)	C₂	semidirect
2. C₇×C₁₇×D₂₁	C₂	semidirect
3. C₃×C₇×D₇×C₁₇	C₂	semidirect
5. C₃×C₇²×C₁₇	C₂²	semidirect
8. C₇×D₇×C₁₇	D₃	semidirect
11. C₇²×C₁₇	C₂×D₃	semidirect
16. C₁₇×D₂₁	D₇	direct (N × H)
18. C₃×D₇×C₁₇	D₇	semidirect
19. D₇×D₂₁	C₁₇	direct (N × H)
23. C₃×C₇×C₁₇	C₂×D₇	semidirect
24. C₃×C₇×C₁₇	C₂×D₇	semidirect
25. C₃⋊(C₇⋊D₇)	C₂×C₁₇	semidirect
26. C₇×D₂₁	C₂×C₁₇	semidirect
27. C₃×C₇×D₇	C₂×C₁₇	semidirect
34. D₇×C₁₇	D₂₁	direct (N × H)
37. C₃×C₇²	C₂²×C₁₇	semidirect
39. C₇×C₁₇	D₃×D₇	semidirect
40. C₇×C₁₇	C₂×D₂₁	semidirect
46. C₇×D₇	D₃×C₁₇	semidirect
50. C₃×C₁₇	D₇²	semidirect
51. C₇²	C₂×D₃×C₁₇	semidirect
56. D₂₁	D₇×C₁₇	direct (N × H)
57. C₃×D₇	D₇×C₁₇	semidirect
65. C₃×C₇	C₂×D₇×C₁₇	semidirect
66. C₃×C₇	C₂×D₇×C₁₇	semidirect
67. C₁₇	D₇×D₂₁	direct (N × H)
74. D₇	C₁₇×D₂₁	direct (N × H)
77. C₇	D₃×D₇×C₁₇	semidirect
78. C₇	C₂×C₁₇×D₂₁	semidirect
83. C₃	D₇²×C₁₇	semidirect

Subgroups — D7×C17×D21 #23756255

Conjugacy classes of subgroups

Complements

Subgroups — D₇×C₁₇×D₂₁ #23756255