Subgroups — D₃×C₁₁×C₁₃×D₇ #26046559

Order 12012.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×C₁₃×D₇	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×C₁₃×D₇	—	3	1	no	—
7	C₁₁×C₁₃×D₇	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₇×C₁₁×C₁₃	—	3	1	no	—
9	C₂×D₃×C₁₁×C₁₃	—	7	1	no	maximal, Hall
10	D₃×C₁₃×D₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₃×C₁₁×D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₁₁×C₁₃	—	7	1	no	—
14	D₃×C₁₁×C₁₃	—	7	1	no	—
15	D₃×C₁₁×C₁₃	D₇	1	1	yes	characteristic, direct product factor
16	C₂²×C₁₁×C₁₃	—	21	1	no	Hall
17	C₁₃×D₂₁	C₂×C₁₁	1	1	yes	characteristic, complemented
18	D₃×C₇×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₃×C₁₃×D₇	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₁₁×D₂₁	C₂×C₁₃	1	1	yes	characteristic, complemented
21	D₃×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₃×C₁₁×D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₃×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₃×D₇	—	3	1	no	Hall
25	C₂×C₁₁×D₇	—	3	1	no	Hall
26	C₂×C₁₁×C₁₃	—	3	1	no	—
27	C₂×C₁₁×C₁₃	—	7	1	no	—
28	C₂×C₁₁×C₁₃	—	21	1	no	—
29	C₃×C₇×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
30	C₃×C₇×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇×C₁₃	—	3	1	no	—
32	C₁₃×D₇	—	3	1	no	—
33	C₁₃×D₇	D₃×C₁₁	1	1	yes	characteristic, direct product factor
34	C₂×D₃×C₁₃	—	7	1	no	Hall
35	C₂×C₇×C₁₁	—	3	1	no	—
36	C₁₁×D₇	—	3	1	no	—
37	C₁₁×D₇	D₃×C₁₃	1	1	yes	characteristic, direct product factor
38	C₁₁×C₁₃	D₃×D₇	1	1	yes	characteristic, direct product factor, Hall
39	C₂×D₃×C₁₁	—	7	1	no	Hall
40	C₇×C₁₃	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
41	D₃×D₇	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₃×C₁₃	—	7	1	no	—
43	D₃×C₁₃	—	7	1	no	—
44	D₃×C₁₃	C₁₁×D₇	1	1	yes	characteristic, direct product factor
45	C₇×C₁₁	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₁₁	—	7	1	no	—
47	D₃×C₁₁	—	7	1	no	—
48	D₃×C₁₁	C₁₃×D₇	1	1	yes	characteristic, direct product factor
49	C₂²×C₁₃	—	21	1	no	Hall
50	C₂²×C₁₁	—	21	1	no	Hall
51	D₂₁	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
52	C₃×D₇	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
53	D₃×C₇	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
54	C₃×C₁₃	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
55	C₃×C₁₁	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
56	C₂×D₇	—	3	1	no	Hall
57	C₂×C₁₃	—	3	1	no	—
58	C₂×C₁₃	—	7	1	no	—
59	C₂×C₁₃	—	21	1	no	—
60	C₂×C₁₁	—	3	1	no	—
61	C₂×C₁₁	—	7	1	no	—
62	C₂×C₁₁	—	21	1	no	—
63	C₃×C₇	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
64	C₂×C₇	—	3	1	no	—
65	D₇	—	3	1	no	—
66	D₇	D₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
67	C₁₃	D₃×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Sylow
68	C₂×D₃	—	7	1	no	Hall
69	C₁₁	D₃×C₁₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
70	C₇	C₂×D₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	7	1	no	—
72	D₃	—	7	1	no	—
73	D₃	C₁₁×C₁₃×D₇	1	1	yes	characteristic, direct product factor
74	C₂²	—	21	1	no	Sylow
75	C₃	C₂×C₁₁×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	7	1	no	—
78	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₃	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×D₂₁	C₂	semidirect
2. D₃×C₇×C₁₁×C₁₃	C₂	semidirect
3. C₃×C₁₁×C₁₃×D₇	C₂	semidirect
5. C₃×C₇×C₁₁×C₁₃	C₂²	semidirect
7. C₁₁×C₁₃×D₇	D₃	direct (N × H)
10. D₃×C₁₃×D₇	C₁₁	direct (N × H)
11. C₇×C₁₁×C₁₃	C₂×D₃	semidirect
12. D₃×C₁₁×D₇	C₁₃	direct (N × H)
15. D₃×C₁₁×C₁₃	D₇	direct (N × H)
17. C₁₃×D₂₁	C₂×C₁₁	semidirect
18. D₃×C₇×C₁₃	C₂×C₁₁	semidirect
19. C₃×C₁₃×D₇	C₂×C₁₁	semidirect
20. C₁₁×D₂₁	C₂×C₁₃	semidirect
21. D₃×C₇×C₁₁	C₂×C₁₃	semidirect
22. C₃×C₁₁×D₇	C₂×C₁₃	semidirect
23. C₃×C₁₁×C₁₃	C₂×D₇	semidirect
29. C₃×C₇×C₁₃	C₂²×C₁₁	semidirect
30. C₃×C₇×C₁₁	C₂²×C₁₃	semidirect
33. C₁₃×D₇	D₃×C₁₁	direct (N × H)
37. C₁₁×D₇	D₃×C₁₃	direct (N × H)
38. C₁₁×C₁₃	D₃×D₇	direct (N × H)
40. C₇×C₁₃	C₂×D₃×C₁₁	semidirect
41. D₃×D₇	C₁₁×C₁₃	direct (N × H)
44. D₃×C₁₃	C₁₁×D₇	direct (N × H)
45. C₇×C₁₁	C₂×D₃×C₁₃	semidirect
48. D₃×C₁₁	C₁₃×D₇	direct (N × H)
51. D₂₁	C₂×C₁₁×C₁₃	semidirect
52. C₃×D₇	C₂×C₁₁×C₁₃	semidirect
53. D₃×C₇	C₂×C₁₁×C₁₃	semidirect
54. C₃×C₁₃	C₂×C₁₁×D₇	semidirect
55. C₃×C₁₁	C₂×C₁₃×D₇	semidirect
63. C₃×C₇	C₂²×C₁₁×C₁₃	semidirect
66. D₇	D₃×C₁₁×C₁₃	direct (N × H)
67. C₁₃	D₃×C₁₁×D₇	direct (N × H)
69. C₁₁	D₃×C₁₃×D₇	direct (N × H)
70. C₇	C₂×D₃×C₁₁×C₁₃	semidirect
73. D₃	C₁₁×C₁₃×D₇	direct (N × H)
75. C₃	C₂×C₁₁×C₁₃×D₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×D₂₁	2
D₃×C₇×C₁₁×C₁₃	2
C₃×C₁₁×C₁₃×D₇	2
C₂×C₁₁×C₁₃×D₇	3
C₂×D₃×C₁₁×C₁₃	7
D₃×C₁₃×D₇	11
D₃×C₁₁×D₇	13

Subgroups — D3×C11×C13×D7 #26046559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₁×C₁₃×D₇ #26046559