Subgroups — C₂×C₁₇×C₇⋊D₆₃ #44472624

Order 29988.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₇⋊D₆₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₉×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×C₃⋊(C₇⋊D₇)	—	3	1	no	maximal
4	C₇²×C₉×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₇×C₃⋊(C₇⋊D₇)	—	3	2	no	—
6	C₂×C₃×C₇²×C₁₇	D₃	1	1	yes	characteristic
7	C₂×C₁₇×D₆₃	—	7	8	no	maximal
8	C₂×C₁₇×C₇⋊D₇	—	9	1	no	Hall
9	C₃×C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic
10	C₁₇×D₆₃	—	7	16	no	—
11	C₂×C₇×C₉×C₁₇	D₇	1	8	yes	complemented
12	C₂×C₇⋊D₆₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₇²×C₁₇	D₉	1	1	yes	characteristic, complemented
14	C₁₇×C₇⋊D₇	—	9	2	no	—
15	C₂×C₁₇×D₂₁	—	21	8	no	—
16	C₇×C₉×C₁₇	C₂×D₇	1	8	yes	complemented
17	C₂×C₇²×C₉	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₇⋊D₆₃	C₂×C₁₇	1	2	yes	direct product factor
19	C₇²×C₁₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₇×C₁₇	D₂₁	1	8	yes	—
21	C₁₇×D₂₁	—	21	16	no	—
22	C₂×C₁₇×D₉	—	49	1	no	Hall
23	C₂×C₃⋊(C₇⋊D₇)	—	3	1	no	—
24	C₂×D₇×C₁₇	—	63	8	no	—
25	C₇²×C₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇×C₁₇	C₂×D₂₁	1	8	yes	—
27	C₂×C₉×C₁₇	C₇⋊D₇	1	1	yes	characteristic, complemented
28	C₁₇×D₉	—	49	2	no	—
29	C₂×C₃×C₇²	D₃×C₁₇	1	1	yes	characteristic
30	C₃⋊(C₇⋊D₇)	—	3	2	no	—
31	C₂×D₆₃	—	7	8	no	—
32	C₂×C₇×C₁₇	D₆₃	1	8	yes	complemented
33	D₇×C₁₇	—	63	16	no	—
34	C₂×D₃×C₁₇	—	147	1	no	—
35	C₂×C₇⋊D₇	—	9	1	no	Hall
36	C₉×C₁₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇²	C₂×D₃×C₁₇	1	1	yes	characteristic
38	C₂×C₇×C₉	D₇×C₁₇	1	8	yes	complemented
39	D₆₃	—	7	16	no	—
40	C₇×C₁₇	C₂×D₆₃	1	8	yes	complemented
41	C₂×C₃×C₁₇	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
42	D₃×C₁₇	—	147	2	no	—
43	C₂×C₇²	C₁₇×D₉	1	1	yes	characteristic, complemented
44	C₇⋊D₇	—	9	2	no	—
45	C₂×D₂₁	—	21	8	no	—
46	C₂²×C₁₇	—	441	1	no	Hall
47	C₇×C₉	C₂×D₇×C₁₇	1	8	yes	complemented
48	C₃×C₁₇	C₂×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
49	C₇²	C₂×C₁₇×D₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃×C₇	C₁₇×D₂₁	1	8	yes	—
51	D₂₁	—	21	16	no	—
52	C₂×D₉	—	49	1	no	Hall
53	C₂×C₁₇	—	441	2	no	—
54	C₂×C₁₇	C₇⋊D₆₃	1	1	yes	characteristic, direct product factor
55	C₂×D₇	—	63	8	no	—
56	C₃×C₇	C₂×C₁₇×D₂₁	1	8	yes	—
57	C₂×C₉	C₁₇×C₇⋊D₇	1	1	yes	characteristic, complemented
58	D₉	—	49	2	no	—
59	C₁₇	C₂×C₇⋊D₆₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₇	C₁₇×D₆₃	1	8	yes	complemented
61	D₇	—	63	16	no	—
62	C₂×D₃	—	147	1	no	—
63	C₉	C₂×C₁₇×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₂×C₁₇×D₆₃	1	8	yes	complemented
65	C₂×C₃	C₁₇×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
66	D₃	—	147	2	no	—
67	C₂²	—	441	1	no	Sylow
68	C₃	C₂×C₁₇×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
69	C₂	—	441	2	no	—
70	C₂	C₁₇×C₇⋊D₆₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₇⋊D₆₃
commutator, cosocle, hypocenter	C₇²×C₉	C₂²×C₁₇
Frattini	C₃	C₂×C₁₇×C₃⋊(C₇⋊D₇)
Fitting	C₂×C₇²×C₉×C₁₇	C₂
socle	C₂×C₃×C₇²×C₁₇	D₃
LCS	G ▷ C₇²×C₉
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₇⋊D₆₃	C₂	direct (N × H)
2. C₂×C₇²×C₉×C₁₇	C₂	semidirect
4. C₇²×C₉×C₁₇	C₂²	semidirect
11. C₂×C₇×C₉×C₁₇	D₇	semidirect
12. C₂×C₇⋊D₆₃	C₁₇	direct (N × H)
13. C₂×C₇²×C₁₇	D₉	semidirect
16. C₇×C₉×C₁₇	C₂×D₇	semidirect
17. C₂×C₇²×C₉	C₂×C₁₇	semidirect
18. C₇⋊D₆₃	C₂×C₁₇	direct (N × H)
19. C₇²×C₁₇	C₂×D₉	semidirect
25. C₇²×C₉	C₂²×C₁₇	semidirect
27. C₂×C₉×C₁₇	C₇⋊D₇	semidirect
32. C₂×C₇×C₁₇	D₆₃	semidirect
36. C₉×C₁₇	C₂×C₇⋊D₇	semidirect
38. C₂×C₇×C₉	D₇×C₁₇	semidirect
40. C₇×C₁₇	C₂×D₆₃	semidirect
43. C₂×C₇²	C₁₇×D₉	semidirect
47. C₇×C₉	C₂×D₇×C₁₇	semidirect
49. C₇²	C₂×C₁₇×D₉	semidirect
54. C₂×C₁₇	C₇⋊D₆₃	direct (N × H)
57. C₂×C₉	C₁₇×C₇⋊D₇	semidirect
59. C₁₇	C₂×C₇⋊D₆₃	direct (N × H)
60. C₂×C₇	C₁₇×D₆₃	semidirect
63. C₉	C₂×C₁₇×C₇⋊D₇	semidirect
64. C₇	C₂×C₁₇×D₆₃	semidirect
70. C₂	C₁₇×C₇⋊D₆₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₇⋊D₆₃	2
C₂×C₇²×C₉×C₁₇	2
C₂×C₁₇×C₃⋊(C₇⋊D₇)	3
C₂×C₁₇×D₆₃	7
C₂×C₇⋊D₆₃	17

Subgroups — C2×C17×C7⋊D63 #44472624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₇⋊D₆₃ #44472624