Subgroups — C₂×C₃×D₃×C₇×C₁₂₇ #44544921

Order 32004.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₇×C₁₂₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₇×C₁₂₇	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂²×C₃×C₇×C₁₂₇	—	3	1	no	maximal
5	C₃²×C₇×C₁₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₇×C₁₂₇	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₃×C₇×C₁₂₇	—	2	1	no	—
8	C₂×C₃×C₇×C₁₂₇	—	3	2	no	—
9	C₂×C₃×C₇×C₁₂₇	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×D₃×C₁₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₇×C₁₂₇	—	3	1	no	Hall
13	C₃×C₇×C₁₂₇	—	2	1	no	—
14	C₃×C₇×C₁₂₇	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₃×C₇×C₁₂₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₃×D₃×C₁₂₇	C₂×C₇	1	2	yes	direct product factor
17	C₂×C₃²×C₁₂₇	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×C₇×C₁₂₇	—	3	2	no	—
19	C₂×C₇×C₁₂₇	C₃×D₃	1	1	yes	characteristic, direct product factor
20	C₂²×C₃×C₁₂₇	—	3	1	no	—
21	C₂×D₃×C₁₂₇	C₃×C₇	1	1	yes	characteristic, direct product factor
22	C₃²×C₁₂₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
23	C₇×C₁₂₇	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×C₁₂₇	—	2	1	no	—
25	C₂×C₃×C₁₂₇	—	3	2	no	—
26	C₂×C₃×C₁₂₇	D₃×C₇	1	1	yes	characteristic, direct product factor
27	C₂×C₃×C₁₂₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
28	D₃×C₁₂₇	C₂×C₃×C₇	1	2	yes	direct product factor
29	C₂²×C₁₂₇	—	3	1	no	Hall
30	C₃×C₁₂₇	—	2	1	no	—
31	C₃×C₁₂₇	C₂×D₃×C₇	1	1	yes	characteristic, direct product factor
32	C₃×C₁₂₇	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
33	C₂×C₁₂₇	—	3	2	no	—
34	C₂×C₁₂₇	C₃×D₃×C₇	1	1	yes	characteristic, direct product factor
35	C₂×C₃×D₃×C₇	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₁₂₇	C₂×C₃×D₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃²×C₇	C₂×C₁₂₇	1	1	yes	characteristic, complemented
38	C₃×D₃×C₇	C₂×C₁₂₇	1	2	yes	direct product factor
39	C₂²×C₃×C₇	—	3	1	no	—
40	C₂×D₃×C₇	C₃×C₁₂₇	1	1	yes	characteristic, direct product factor
41	C₃²×C₇	C₂²×C₁₂₇	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₇	—	2	1	no	—
43	C₂×C₃×C₇	—	3	2	no	—
44	C₂×C₃×C₇	D₃×C₁₂₇	1	1	yes	characteristic, direct product factor
45	C₂×C₃×C₇	C₂×C₃×C₁₂₇	1	1	yes	characteristic, complemented
46	D₃×C₇	C₂×C₃×C₁₂₇	1	2	yes	direct product factor
47	C₂×C₃×D₃	C₇×C₁₂₇	1	1	yes	characteristic, direct product factor, Hall
48	C₂²×C₇	—	3	1	no	Hall
49	C₃×C₇	—	2	1	no	—
50	C₃×C₇	C₂×D₃×C₁₂₇	1	1	yes	characteristic, direct product factor
51	C₃×C₇	C₂²×C₃×C₁₂₇	1	1	yes	characteristic, complemented
52	C₂×C₃²	C₂×C₇×C₁₂₇	1	1	yes	characteristic, complemented
53	C₃×D₃	C₂×C₇×C₁₂₇	1	2	yes	direct product factor
54	C₂×C₇	—	3	2	no	—
55	C₂×C₇	C₃×D₃×C₁₂₇	1	1	yes	characteristic, direct product factor
56	C₂²×C₃	—	3	1	no	—
57	C₂×D₃	C₃×C₇×C₁₂₇	1	1	yes	characteristic, direct product factor
58	C₃²	C₂²×C₇×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
59	C₇	C₂×C₃×D₃×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	3	2	no	—
62	C₂×C₃	C₂×C₃×C₇×C₁₂₇	1	1	yes	characteristic, complemented
63	C₂×C₃	D₃×C₇×C₁₂₇	1	1	yes	characteristic, direct product factor
64	D₃	C₂×C₃×C₇×C₁₂₇	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂²×C₃×C₇×C₁₂₇	1	1	yes	characteristic, complemented
68	C₃	C₂×D₃×C₇×C₁₂₇	1	1	yes	characteristic, direct product factor
69	C₂	—	3	2	no	—
70	C₂	C₃×D₃×C₇×C₁₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₂₇	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₇×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₂₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₇×C₁₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₇×C₁₂₇	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₁₂₇	C₂	semidirect
3. C₂×D₃×C₇×C₁₂₇	C₃	direct (N × H)
5. C₃²×C₇×C₁₂₇	C₂²	semidirect
6. D₃×C₇×C₁₂₇	C₂×C₃	direct (N × H)
9. C₂×C₃×C₇×C₁₂₇	D₃	direct (N × H)
10. C₂×C₃×C₇×C₁₂₇	C₂×C₃	semidirect
11. C₂×C₃×D₃×C₁₂₇	C₇	direct (N × H)
14. C₃×C₇×C₁₂₇	C₂×D₃	direct (N × H)
15. C₃×C₇×C₁₂₇	C₂²×C₃	semidirect
16. C₃×D₃×C₁₂₇	C₂×C₇	direct (N × H)
17. C₂×C₃²×C₁₂₇	C₂×C₇	semidirect
19. C₂×C₇×C₁₂₇	C₃×D₃	direct (N × H)
21. C₂×D₃×C₁₂₇	C₃×C₇	direct (N × H)
22. C₃²×C₁₂₇	C₂²×C₇	semidirect
23. C₇×C₁₂₇	C₂×C₃×D₃	direct (N × H)
26. C₂×C₃×C₁₂₇	D₃×C₇	direct (N × H)
27. C₂×C₃×C₁₂₇	C₂×C₃×C₇	semidirect
28. D₃×C₁₂₇	C₂×C₃×C₇	direct (N × H)
31. C₃×C₁₂₇	C₂×D₃×C₇	direct (N × H)
32. C₃×C₁₂₇	C₂²×C₃×C₇	semidirect
34. C₂×C₁₂₇	C₃×D₃×C₇	direct (N × H)
35. C₂×C₃×D₃×C₇	C₁₂₇	direct (N × H)
36. C₁₂₇	C₂×C₃×D₃×C₇	direct (N × H)
37. C₂×C₃²×C₇	C₂×C₁₂₇	semidirect
38. C₃×D₃×C₇	C₂×C₁₂₇	direct (N × H)
40. C₂×D₃×C₇	C₃×C₁₂₇	direct (N × H)
41. C₃²×C₇	C₂²×C₁₂₇	semidirect
44. C₂×C₃×C₇	D₃×C₁₂₇	direct (N × H)
45. C₂×C₃×C₇	C₂×C₃×C₁₂₇	semidirect
46. D₃×C₇	C₂×C₃×C₁₂₇	direct (N × H)
47. C₂×C₃×D₃	C₇×C₁₂₇	direct (N × H)
50. C₃×C₇	C₂×D₃×C₁₂₇	direct (N × H)
51. C₃×C₇	C₂²×C₃×C₁₂₇	semidirect
52. C₂×C₃²	C₂×C₇×C₁₂₇	semidirect
53. C₃×D₃	C₂×C₇×C₁₂₇	direct (N × H)
55. C₂×C₇	C₃×D₃×C₁₂₇	direct (N × H)
57. C₂×D₃	C₃×C₇×C₁₂₇	direct (N × H)
58. C₃²	C₂²×C₇×C₁₂₇	semidirect
59. C₇	C₂×C₃×D₃×C₁₂₇	direct (N × H)
62. C₂×C₃	C₂×C₃×C₇×C₁₂₇	semidirect
63. C₂×C₃	D₃×C₇×C₁₂₇	direct (N × H)
64. D₃	C₂×C₃×C₇×C₁₂₇	direct (N × H)
67. C₃	C₂²×C₃×C₇×C₁₂₇	semidirect
68. C₃	C₂×D₃×C₇×C₁₂₇	direct (N × H)
70. C₂	C₃×D₃×C₇×C₁₂₇	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×D₃×C₇×C₁₂₇	2
C₂×C₃²×C₇×C₁₂₇	2
C₂×D₃×C₇×C₁₂₇	3
C₂²×C₃×C₇×C₁₂₇	3
C₂×C₃×D₃×C₁₂₇	7
C₂×C₃×D₃×C₇	127

Subgroups — C2×C3×D3×C7×C127 #44544921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃×C₇×C₁₂₇ #44544921