Subgroups — C₂×D₃×C₇×C₁₂₇⋊C₃ #44544867

Order 32004.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₁₂₇⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₇×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₇×C₁₂₇⋊C₃	—	3	1	no	maximal
5	C₃×C₇×C₁₂₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₇×C₁₂₇	C₂×C₃	1	2	yes	complemented
7	C₂×C₇×C₁₂₇⋊C₃	—	2	1	no	—
8	C₂×C₇×C₁₂₇⋊C₃	—	3	2	no	—
9	C₂×C₇×C₁₂₇⋊C₃	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×D₃×C₁₂₇⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₇×C₁₂₇	—	3	1	no	Hall
13	C₃×C₇×C₁₂₇	C₂²×C₃	1	1	yes	characteristic, complemented
14	C₇×C₁₂₇⋊C₃	—	2	1	no	—
15	C₇×C₁₂₇⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₁₂₇⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
17	D₃×C₁₂₇⋊C₃	C₂×C₇	1	2	yes	direct product factor
18	C₂×C₇×C₁₂₇	—	3	2	no	—
19	C₂×C₇×C₁₂₇	C₃×D₃	1	1	yes	characteristic, complemented
20	C₂×D₃×C₁₂₇	C₃×C₇	1	1	yes	characteristic, complemented
21	C₂²×C₁₂₇⋊C₃	—	3	1	no	—
22	C₃×C₁₂₇⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
23	C₇×C₁₂₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₁₂₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
25	D₃×C₁₂₇	C₂×C₃×C₇	1	2	yes	complemented
26	C₂×C₁₂₇⋊C₃	—	2	1	no	—
27	C₂×C₁₂₇⋊C₃	—	3	2	no	—
28	C₂×C₁₂₇⋊C₃	D₃×C₇	1	1	yes	characteristic, direct product factor
29	C₂²×C₁₂₇	—	3	1	no	Hall
30	C₃×C₁₂₇	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
31	C₁₂₇⋊C₃	—	2	1	no	—
32	C₁₂₇⋊C₃	C₂×D₃×C₇	1	1	yes	characteristic, direct product factor
33	C₂×C₁₂₇	—	3	2	no	—
34	C₂×C₁₂₇	C₃×D₃×C₇	1	1	yes	characteristic, complemented
35	C₂×C₃×D₃×C₇	—	127	1	no	maximal, Hall
36	C₁₂₇	C₂×C₃×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²×C₇	—	127	1	no	—
38	C₃×D₃×C₇	—	127	2	no	—
39	C₂²×C₃×C₇	—	381	1	no	—
40	C₂×D₃×C₇	C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
41	C₃²×C₇	—	127	1	no	Hall
42	C₂×C₃×C₇	—	381	2	no	—
43	C₂×C₃×C₇	—	127	1	no	—
44	C₂×C₃×C₇	—	254	1	no	—
45	C₂×C₃×C₇	C₂×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
46	D₃×C₇	C₂×C₁₂₇⋊C₃	1	2	yes	direct product factor
47	C₂×C₃×D₃	—	127	1	no	Hall
48	C₂²×C₇	—	3	1	no	Hall
49	C₃×C₇	—	127	1	no	—
50	C₃×C₇	—	254	1	no	—
51	C₃×C₇	C₂²×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
52	C₂×C₃²	—	127	1	no	—
53	C₃×D₃	—	127	2	no	—
54	C₂×C₇	—	3	2	no	—
55	C₂×C₇	D₃×C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
56	C₂²×C₃	—	381	1	no	—
57	C₂×D₃	C₇×C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
58	C₃²	—	127	1	no	Sylow
59	C₇	C₂×D₃×C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₃	—	381	2	no	—
61	C₂×C₃	—	127	1	no	—
62	C₂×C₃	—	254	1	no	—
63	C₂×C₃	C₂×C₇×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
64	D₃	C₂×C₇×C₁₂₇⋊C₃	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	127	1	no	—
67	C₃	—	254	1	no	—
68	C₃	C₂²×C₇×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	D₃×C₇×C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₇×C₁₂₇⋊C₃	C₂	semidirect
2. D₃×C₇×C₁₂₇⋊C₃	C₂	direct (N × H)
3. C₂×D₃×C₇×C₁₂₇	C₃	semidirect
5. C₃×C₇×C₁₂₇⋊C₃	C₂²	semidirect
6. D₃×C₇×C₁₂₇	C₂×C₃	semidirect
9. C₂×C₇×C₁₂₇⋊C₃	D₃	direct (N × H)
10. C₂×C₃×C₇×C₁₂₇	C₂×C₃	semidirect
11. C₂×D₃×C₁₂₇⋊C₃	C₇	direct (N × H)
13. C₃×C₇×C₁₂₇	C₂²×C₃	semidirect
15. C₇×C₁₂₇⋊C₃	C₂×D₃	direct (N × H)
16. C₂×C₃×C₁₂₇⋊C₃	C₂×C₇	semidirect
17. D₃×C₁₂₇⋊C₃	C₂×C₇	direct (N × H)
19. C₂×C₇×C₁₂₇	C₃×D₃	semidirect
20. C₂×D₃×C₁₂₇	C₃×C₇	semidirect
22. C₃×C₁₂₇⋊C₃	C₂²×C₇	semidirect
23. C₇×C₁₂₇	C₂×C₃×D₃	semidirect
24. C₂×C₃×C₁₂₇	C₂×C₃×C₇	semidirect
25. D₃×C₁₂₇	C₂×C₃×C₇	semidirect
28. C₂×C₁₂₇⋊C₃	D₃×C₇	direct (N × H)
30. C₃×C₁₂₇	C₂²×C₃×C₇	semidirect
32. C₁₂₇⋊C₃	C₂×D₃×C₇	direct (N × H)
34. C₂×C₁₂₇	C₃×D₃×C₇	semidirect
36. C₁₂₇	C₂×C₃×D₃×C₇	semidirect
40. C₂×D₃×C₇	C₁₂₇⋊C₃	direct (N × H)
45. C₂×C₃×C₇	C₂×C₁₂₇⋊C₃	semidirect
46. D₃×C₇	C₂×C₁₂₇⋊C₃	direct (N × H)
51. C₃×C₇	C₂²×C₁₂₇⋊C₃	semidirect
55. C₂×C₇	D₃×C₁₂₇⋊C₃	direct (N × H)
57. C₂×D₃	C₇×C₁₂₇⋊C₃	direct (N × H)
59. C₇	C₂×D₃×C₁₂₇⋊C₃	direct (N × H)
63. C₂×C₃	C₂×C₇×C₁₂₇⋊C₃	semidirect
64. D₃	C₂×C₇×C₁₂₇⋊C₃	direct (N × H)
68. C₃	C₂²×C₇×C₁₂₇⋊C₃	semidirect
70. C₂	D₃×C₇×C₁₂₇⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₂₇⋊C₃	2
D₃×C₇×C₁₂₇⋊C₃	2
C₂×D₃×C₇×C₁₂₇	3
C₂²×C₇×C₁₂₇⋊C₃	3
C₂×D₃×C₁₂₇⋊C₃	7
C₂×C₃×D₃×C₇	127

Subgroups — C2×D3×C7×C127⋊C3 #44544867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₇×C₁₂₇⋊C₃ #44544867