Subgroups — C₂×C₃×D₃₁₂₉ #49176406

Order 37548.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃₁₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₀₄₃	—	3	1	no	maximal
4	C₂×D₃₁₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₇×C₁₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₁₂₉	C₂×C₃	1	2	yes	direct product factor
7	C₃×D₁₀₄₃	—	3	2	no	—
8	C₂×C₃×C₇×C₁₄₉	—	2	1	no	—
9	C₂×C₃×C₇×C₁₄₉	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₇×C₁₄₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×D₄₄₇	—	7	1	no	maximal, Hall
12	C₂×D₁₀₄₃	—	3	1	no	Hall
13	C₃×C₇×C₁₄₉	—	2	1	no	—
14	C₃×C₇×C₁₄₉	C₂×D₃	1	1	yes	characteristic, complemented
15	C₃×C₇×C₁₄₉	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₃×D₄₄₇	—	7	2	no	—
17	C₂×C₃²×C₁₄₉	D₇	1	1	yes	characteristic, complemented
18	C₂×C₇×C₁₄₉	C₃×D₃	1	1	yes	characteristic, complemented
19	D₁₀₄₃	—	3	2	no	—
20	C₂×D₄₄₇	—	7	1	no	—
21	C₂×C₃×D₁₄₉	—	21	1	no	—
22	C₃²×C₁₄₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
23	C₇×C₁₄₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₁₄₉	—	2	1	no	—
25	C₂×C₃×C₁₄₉	C₃×D₇	1	1	yes	characteristic, complemented
26	C₂×C₃×C₁₄₉	D₂₁	1	1	yes	characteristic, complemented
27	D₄₄₇	—	7	2	no	—
28	C₃×D₁₄₉	—	21	2	no	—
29	C₂×D₁₄₉	—	21	1	no	Hall
30	C₃×C₁₄₉	—	2	1	no	—
31	C₃×C₁₄₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented
32	C₃×C₁₄₉	C₂×D₂₁	1	1	yes	characteristic, complemented
33	C₂×C₁₄₉	C₃×D₂₁	1	1	yes	characteristic, complemented
34	D₁₄₉	—	21	2	no	—
35	C₂×C₃×D₂₁	—	149	1	no	maximal, Hall
36	C₁₄₉	C₂×C₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²×C₇	D₁₄₉	1	1	yes	characteristic, complemented
38	C₃×D₂₁	—	149	2	no	—
39	C₂×D₂₁	—	149	1	no	—
40	C₂×C₃×D₇	—	447	1	no	—
41	C₃²×C₇	C₂×D₁₄₉	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₇	—	2	1	no	—
43	C₂×C₃×C₇	C₃×D₁₄₉	1	1	yes	characteristic, complemented
44	C₂×C₃×C₇	D₄₄₇	1	1	yes	characteristic, complemented
45	D₂₁	—	149	2	no	—
46	C₃×D₇	—	447	2	no	—
47	C₂×C₃×D₃	—	1043	1	no	Hall
48	C₂×D₇	—	447	1	no	Hall
49	C₃×C₇	—	2	1	no	—
50	C₃×C₇	C₂×C₃×D₁₄₉	1	1	yes	characteristic, complemented
51	C₃×C₇	C₂×D₄₄₇	1	1	yes	characteristic, complemented
52	C₂×C₃²	D₁₀₄₃	1	1	yes	characteristic, complemented
53	C₃×D₃	—	1043	2	no	—
54	C₂×C₇	C₃×D₄₄₇	1	1	yes	characteristic, complemented
55	D₇	—	447	2	no	—
56	C₂²×C₃	—	3129	1	no	—
57	C₂×D₃	—	1043	1	no	—
58	C₃²	C₂×D₁₀₄₃	1	1	yes	characteristic, complemented, Sylow
59	C₇	C₂×C₃×D₄₄₇	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	3129	2	no	—
62	C₂×C₃	C₃×D₁₀₄₃	1	1	yes	characteristic, complemented
63	C₂×C₃	D₃₁₂₉	1	1	yes	characteristic, direct product factor
64	D₃	—	1043	2	no	—
65	C₂²	—	3129	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×D₃₁₂₉	1	1	yes	characteristic, direct product factor
68	C₃	C₂×C₃×D₁₀₄₃	1	1	yes	characteristic, complemented
69	C₂	—	3129	2	no	—
70	C₂	C₃×D₃₁₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃₁₂₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₄₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₄₉	C₂
LCS	G ▷ C₃×C₇×C₁₄₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₃₁₂₉	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₁₄₉	C₂	semidirect
4. C₂×D₃₁₂₉	C₃	direct (N × H)
5. C₃²×C₇×C₁₄₉	C₂²	semidirect
6. D₃₁₂₉	C₂×C₃	direct (N × H)
9. C₂×C₃×C₇×C₁₄₉	D₃	semidirect
10. C₂×C₃×C₇×C₁₄₉	C₂×C₃	semidirect
14. C₃×C₇×C₁₄₉	C₂×D₃	semidirect
15. C₃×C₇×C₁₄₉	C₂²×C₃	semidirect
17. C₂×C₃²×C₁₄₉	D₇	semidirect
18. C₂×C₇×C₁₄₉	C₃×D₃	semidirect
22. C₃²×C₁₄₉	C₂×D₇	semidirect
23. C₇×C₁₄₉	C₂×C₃×D₃	semidirect
25. C₂×C₃×C₁₄₉	C₃×D₇	semidirect
26. C₂×C₃×C₁₄₉	D₂₁	semidirect
31. C₃×C₁₄₉	C₂×C₃×D₇	semidirect
32. C₃×C₁₄₉	C₂×D₂₁	semidirect
33. C₂×C₁₄₉	C₃×D₂₁	semidirect
36. C₁₄₉	C₂×C₃×D₂₁	semidirect
37. C₂×C₃²×C₇	D₁₄₉	semidirect
41. C₃²×C₇	C₂×D₁₄₉	semidirect
43. C₂×C₃×C₇	C₃×D₁₄₉	semidirect
44. C₂×C₃×C₇	D₄₄₇	semidirect
50. C₃×C₇	C₂×C₃×D₁₄₉	semidirect
51. C₃×C₇	C₂×D₄₄₇	semidirect
52. C₂×C₃²	D₁₀₄₃	semidirect
54. C₂×C₇	C₃×D₄₄₇	semidirect
58. C₃²	C₂×D₁₀₄₃	semidirect
59. C₇	C₂×C₃×D₄₄₇	semidirect
62. C₂×C₃	C₃×D₁₀₄₃	semidirect
63. C₂×C₃	D₃₁₂₉	direct (N × H)
67. C₃	C₂×D₃₁₂₉	direct (N × H)
68. C₃	C₂×C₃×D₁₀₄₃	semidirect
70. C₂	C₃×D₃₁₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₃₁₂₉	2
C₂×C₃²×C₇×C₁₄₉	2
C₂×C₃×D₁₀₄₃	3
C₂×D₃₁₂₉	3
C₂×C₃×D₄₄₇	7
C₂×C₃×D₂₁	149

Subgroups — C2×C3×D3129 #49176406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃₁₂₉ #49176406