Subgroups — C₃×D₇×D₁₂₇⋊C₃ #44544813

Order 32004.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₇×C₁₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×(C₁₂₇⋊C₃)⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₁₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×D₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
5	D₇×D₁₂₇⋊C₃	C₃	1	3	yes	maximal, direct product factor
6	C₃×C₇×C₁₂₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	(C₁₂₇⋊C₃)⋊D₇	C₂×C₃	1	3	yes	complemented
8	D₇×C₁₂₇⋊C₃	C₂×C₃	1	3	yes	complemented
9	C₇×D₁₂₇⋊C₃	C₂×C₃	1	3	yes	complemented
10	C₃×D₈₈₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×D₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₇×D₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₃×D₁₂₇⋊C₃	—	7	1	no	maximal, Hall
14	D₇×D₁₂₇	C₃²	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇×C₁₂₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₇×C₁₂₇⋊C₃	C₂²×C₃	1	3	yes	complemented
17	C₂×C₃×C₁₂₇⋊C₃	—	7	1	no	—
18	C₃×D₁₂₇⋊C₃	—	7	1	no	—
19	C₃×D₁₂₇⋊C₃	D₇	1	1	yes	characteristic, direct product factor
20	D₈₈₉	C₂×C₃²	1	1	yes	characteristic, complemented
21	C₇×D₁₂₇	C₂×C₃²	1	1	yes	characteristic, complemented
22	D₇×C₁₂₇	C₂×C₃²	1	1	yes	characteristic, complemented
23	C₂×C₃×D₁₂₇	—	7	1	no	—
24	C₂×D₁₂₇⋊C₃	—	7	3	no	—
25	C₃×C₁₂₇⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
26	C₇×C₁₂₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₁₂₇	—	7	1	no	—
28	C₃×D₁₂₇	—	7	1	no	—
29	C₃×D₁₂₇	C₃×D₇	1	1	yes	characteristic, complemented
30	C₂×C₁₂₇⋊C₃	—	7	3	no	—
31	D₁₂₇⋊C₃	—	7	3	no	—
32	D₁₂₇⋊C₃	C₃×D₇	1	3	yes	direct product factor
33	C₂×D₁₂₇	—	7	1	no	Hall
34	C₃×C₁₂₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented
35	C₁₂₇⋊C₃	C₂×C₃×D₇	1	3	yes	complemented
36	C₂×C₁₂₇	—	7	1	no	—
37	D₁₂₇	—	7	1	no	—
38	D₁₂₇	C₃²×D₇	1	1	yes	characteristic, complemented
39	C₂×C₃²×D₇	—	127	1	no	maximal, Hall
40	C₁₂₇	C₂×C₃²×D₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃²×C₇	—	127	1	no	—
42	C₃²×D₇	—	127	1	no	—
43	C₃²×D₇	—	127	1	no	—
44	C₂×C₃×D₇	—	127	3	no	—
45	C₂×C₃×D₇	—	127	1	no	—
46	C₃²×C₇	—	127	1	no	Hall
47	C₂×C₃×C₇	—	127	3	no	—
48	C₂×C₃×C₇	—	127	1	no	—
49	C₃×D₇	—	127	3	no	—
50	C₃×D₇	—	127	1	no	—
51	C₃×D₇	—	127	3	no	—
52	C₃×D₇	D₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
53	C₂²×C₃²	—	889	1	no	Hall
54	C₂×D₇	—	127	1	no	Hall
55	C₃×C₇	—	127	3	no	—
56	C₃×C₇	C₂×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented
57	C₂×C₃²	—	889	1	no	—
58	C₂×C₃²	—	889	1	no	—
59	C₂×C₃²	—	127	1	no	—
60	C₂×C₇	—	127	1	no	—
61	D₇	—	127	1	no	—
62	D₇	C₃×D₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
63	C₂²×C₃	—	889	1	no	—
64	C₂²×C₃	—	889	3	no	—
65	C₃²	—	127	1	no	Sylow
66	C₇	C₂×C₃×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃	—	7	1	no	—
68	C₂×C₃	—	889	3	no	—
69	C₂×C₃	—	889	3	no	—
70	C₂×C₃	—	889	1	no	—
71	C₂×C₃	—	127	3	no	—
72	C₂×C₃	—	127	1	no	—
73	C₂²	—	889	1	no	Sylow
74	C₃	—	127	3	no	—
75	C₃	D₇×D₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
76	C₂	—	7	1	no	—
77	C₂	—	889	1	no	—
78	C₂	—	127	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₇×D₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₂₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₂₇	C₂²×C₃
LCS	G ▷ C₇×C₁₂₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₇×C₁₂₇⋊C₃	C₂	semidirect
2. C₃×(C₁₂₇⋊C₃)⋊D₇	C₂	semidirect
3. C₃×C₇×D₁₂₇⋊C₃	C₂	semidirect
4. C₃×D₇×D₁₂₇	C₃	semidirect
5. D₇×D₁₂₇⋊C₃	C₃	direct (N × H)
6. C₃×C₇×C₁₂₇⋊C₃	C₂²	semidirect
7. (C₁₂₇⋊C₃)⋊D₇	C₂×C₃	semidirect
8. D₇×C₁₂₇⋊C₃	C₂×C₃	semidirect
9. C₇×D₁₂₇⋊C₃	C₂×C₃	semidirect
10. C₃×D₈₈₉	C₂×C₃	semidirect
11. C₃×D₇×C₁₂₇	C₂×C₃	semidirect
12. C₃×C₇×D₁₂₇	C₂×C₃	semidirect
14. D₇×D₁₂₇	C₃²	semidirect
15. C₃×C₇×C₁₂₇	C₂²×C₃	semidirect
16. C₇×C₁₂₇⋊C₃	C₂²×C₃	semidirect
19. C₃×D₁₂₇⋊C₃	D₇	direct (N × H)
20. D₈₈₉	C₂×C₃²	semidirect
21. C₇×D₁₂₇	C₂×C₃²	semidirect
22. D₇×C₁₂₇	C₂×C₃²	semidirect
25. C₃×C₁₂₇⋊C₃	C₂×D₇	semidirect
26. C₇×C₁₂₇	C₂²×C₃²	semidirect
29. C₃×D₁₂₇	C₃×D₇	semidirect
32. D₁₂₇⋊C₃	C₃×D₇	direct (N × H)
34. C₃×C₁₂₇	C₂×C₃×D₇	semidirect
35. C₁₂₇⋊C₃	C₂×C₃×D₇	semidirect
38. D₁₂₇	C₃²×D₇	semidirect
40. C₁₂₇	C₂×C₃²×D₇	semidirect
52. C₃×D₇	D₁₂₇⋊C₃	direct (N × H)
56. C₃×C₇	C₂×D₁₂₇⋊C₃	semidirect
62. D₇	C₃×D₁₂₇⋊C₃	direct (N × H)
66. C₇	C₂×C₃×D₁₂₇⋊C₃	semidirect
75. C₃	D₇×D₁₂₇⋊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
C₃×D₇×C₁₂₇⋊C₃	2
C₃×(C₁₂₇⋊C₃)⋊D₇	2
C₃×C₇×D₁₂₇⋊C₃	2
C₃×D₇×D₁₂₇	3
D₇×D₁₂₇⋊C₃	3
C₂×C₃×D₁₂₇⋊C₃	7
C₂×C₃²×D₇	127

Subgroups — C3×D7×D127⋊C3 #44544813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×D₁₂₇⋊C₃ #44544813