Subgroups — C₃×C₇×D₄₂₉ #31825089

Order 18018.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₄₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇×D₁₄₃	—	3	1	no	maximal
4	C₃×C₇×C₁₁×C₁₃	—	2	1	no	—
5	C₃×C₇×C₁₁×C₁₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₄₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×D₁₄₃	—	3	1	no	Hall
9	C₃×C₇×D₃₉	—	11	1	no	maximal, Hall
10	C₃×C₇×D₃₃	—	13	1	no	maximal, Hall
11	C₃²×C₁₁×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₁×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	D₄₂₉	C₃×C₇	1	1	yes	characteristic, direct product factor
14	C₃×D₁₄₃	—	3	1	no	—
15	C₃²×C₇×C₁₃	D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇×C₁₁	D₁₃	1	1	yes	characteristic, complemented, Hall
17	C₇×D₃₉	—	11	1	no	—
18	C₃×C₇×D₁₃	—	33	1	no	—
19	C₇×D₃₃	—	13	1	no	—
20	C₃×C₇×D₁₁	—	39	1	no	—
21	C₃×C₁₁×C₁₃	—	2	1	no	—
22	C₃×C₁₁×C₁₃	D₃×C₇	1	1	yes	characteristic, complemented
23	C₃×C₁₁×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
24	D₁₄₃	—	3	1	no	Hall
25	C₃×C₇×C₁₃	—	2	1	no	—
26	C₃×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented
27	C₃×C₇×C₁₃	D₃₃	1	1	yes	characteristic, complemented
28	C₃×D₃₉	—	11	1	no	Hall
29	C₃×C₇×C₁₁	—	2	1	no	—
30	C₃×C₇×C₁₁	C₃×D₁₃	1	1	yes	characteristic, complemented
31	C₃×C₇×C₁₁	D₃₉	1	1	yes	characteristic, complemented
32	C₃×D₃₃	—	13	1	no	Hall
33	C₇×D₁₃	—	33	1	no	Hall
34	C₇×D₁₁	—	39	1	no	Hall
35	C₁₁×C₁₃	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Hall
36	C₃×D₃×C₇	—	143	1	no	Hall
37	C₃²×C₁₃	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
38	C₃²×C₁₁	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
39	C₇×C₁₃	C₃×D₃₃	1	1	yes	characteristic, complemented, Hall
40	D₃₉	—	11	1	no	—
41	C₃×D₁₃	—	33	1	no	—
42	C₇×C₁₁	C₃×D₃₉	1	1	yes	characteristic, complemented, Hall
43	D₃₃	—	13	1	no	—
44	C₃×D₁₁	—	39	1	no	—
45	C₃²×C₇	D₁₄₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₇	—	429	1	no	—
47	D₃×C₇	—	143	1	no	—
48	C₃×C₁₃	—	2	1	no	—
49	C₃×C₁₃	C₃×C₇×D₁₁	1	1	yes	characteristic, complemented
50	C₃×C₁₃	C₇×D₃₃	1	1	yes	characteristic, complemented
51	C₃×C₁₁	—	2	1	no	—
52	C₃×C₁₁	C₃×C₇×D₁₃	1	1	yes	characteristic, complemented
53	C₃×C₁₁	C₇×D₃₉	1	1	yes	characteristic, complemented
54	D₁₃	—	33	1	no	Hall
55	D₁₁	—	39	1	no	Hall
56	C₃×C₇	—	2	1	no	—
57	C₃×C₇	C₃×D₁₄₃	1	1	yes	characteristic, complemented
58	C₃×C₇	D₄₂₉	1	1	yes	characteristic, direct product factor
59	C₃×D₃	—	143	1	no	Hall
60	C₂×C₇	—	429	1	no	Hall
61	C₁₃	C₃×C₇×D₃₃	1	1	yes	characteristic, complemented, Sylow
62	C₁₁	C₃×C₇×D₃₉	1	1	yes	characteristic, complemented, Sylow
63	C₃²	C₇×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₃×D₄₂₉	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₃	—	429	1	no	—
66	D₃	—	143	1	no	—
67	C₃	—	2	1	no	—
68	C₃	C₃×C₇×D₁₄₃	1	1	yes	characteristic, complemented
69	C₃	C₇×D₄₂₉	1	1	yes	characteristic, direct product factor
70	C₂	—	429	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₄₂₉
commutator, cosocle, hypocenter	C₃×C₁₁×C₁₃	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₃×C₁₁×C₁₃
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₃	C₂	semidirect
2. C₇×D₄₂₉	C₃	direct (N × H)
5. C₃×C₇×C₁₁×C₁₃	D₃	semidirect
6. C₃×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
7. C₃×D₄₂₉	C₇	direct (N × H)
11. C₃²×C₁₁×C₁₃	C₂×C₇	semidirect
12. C₇×C₁₁×C₁₃	C₃×D₃	semidirect
13. D₄₂₉	C₃×C₇	direct (N × H)
15. C₃²×C₇×C₁₃	D₁₁	semidirect
16. C₃²×C₇×C₁₁	D₁₃	semidirect
22. C₃×C₁₁×C₁₃	D₃×C₇	semidirect
23. C₃×C₁₁×C₁₃	C₂×C₃×C₇	semidirect
26. C₃×C₇×C₁₃	C₃×D₁₁	semidirect
27. C₃×C₇×C₁₃	D₃₃	semidirect
30. C₃×C₇×C₁₁	C₃×D₁₃	semidirect
31. C₃×C₇×C₁₁	D₃₉	semidirect
35. C₁₁×C₁₃	C₃×D₃×C₇	semidirect
37. C₃²×C₁₃	C₇×D₁₁	semidirect
38. C₃²×C₁₁	C₇×D₁₃	semidirect
39. C₇×C₁₃	C₃×D₃₃	semidirect
42. C₇×C₁₁	C₃×D₃₉	semidirect
45. C₃²×C₇	D₁₄₃	semidirect
49. C₃×C₁₃	C₃×C₇×D₁₁	semidirect
50. C₃×C₁₃	C₇×D₃₃	semidirect
52. C₃×C₁₁	C₃×C₇×D₁₃	semidirect
53. C₃×C₁₁	C₇×D₃₉	semidirect
57. C₃×C₇	C₃×D₁₄₃	semidirect
58. C₃×C₇	D₄₂₉	direct (N × H)
61. C₁₃	C₃×C₇×D₃₃	semidirect
62. C₁₁	C₃×C₇×D₃₉	semidirect
63. C₃²	C₇×D₁₄₃	semidirect
64. C₇	C₃×D₄₂₉	direct (N × H)
68. C₃	C₃×C₇×D₁₄₃	semidirect
69. C₃	C₇×D₄₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₁×C₁₃	2
C₇×D₄₂₉	3
C₃×C₇×D₁₄₃	3
C₃×D₄₂₉	7
C₃×C₇×D₃₉	11
C₃×C₇×D₃₃	13

Subgroups — C3×C7×D429 #31825089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₄₂₉ #31825089