Subgroups — C₁₁×D₁₃×D₂₁ #26046552

Order 12012.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₂₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₁₃×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₁×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×D₇×D₁₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₉₁	—	3	1	no	—
7	C₁₁×C₁₃×D₇	—	3	1	no	—
8	C₇×C₁₁×D₁₃	D₃	1	1	yes	characteristic, complemented
9	D₃×C₁₁×D₁₃	—	7	1	no	maximal, Hall
10	D₁₃×D₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×D₂₁	—	13	1	no	maximal, Hall
13	C₁₁×D₃₉	—	7	1	no	—
14	D₃×C₁₁×C₁₃	—	7	1	no	—
15	C₃×C₁₁×D₁₃	D₇	1	1	yes	characteristic, complemented
16	C₂×C₁₁×D₁₃	—	21	1	no	Hall
17	D₂₇₃	C₂×C₁₁	1	1	yes	characteristic, complemented
18	C₁₃×D₂₁	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₃×C₇×D₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₂×C₃×C₇×C₁₁	—	13	1	no	—
21	C₁₁×D₂₁	—	13	1	no	—
22	C₁₁×D₂₁	D₁₃	1	1	yes	characteristic, direct product factor
23	C₃×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	D₇×D₁₃	—	3	1	no	Hall
25	C₂×C₁₁×D₇	—	39	1	no	Hall
26	C₂×C₁₁×C₁₃	—	21	1	no	—
27	C₁₁×D₁₃	—	21	1	no	—
28	C₁₁×D₁₃	D₂₁	1	1	yes	characteristic, direct product factor
29	C₃×C₇×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
30	C₃×C₇×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	D₉₁	—	3	1	no	—
32	C₇×D₁₃	D₃×C₁₁	1	1	yes	characteristic, complemented
33	C₁₃×D₇	—	3	1	no	—
34	D₃×D₁₃	—	7	1	no	Hall
35	C₂×C₇×C₁₁	—	13	1	no	—
36	C₁₁×D₇	—	3	1	no	—
37	C₁₁×D₇	—	39	1	no	—
38	C₁₁×C₁₃	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
39	C₂×D₃×C₁₁	—	91	1	no	Hall
40	C₇×C₁₃	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
41	C₂×D₂₁	—	13	1	no	Hall
42	D₃₉	—	7	1	no	—
43	C₃×D₁₃	C₁₁×D₇	1	1	yes	characteristic, complemented
44	D₃×C₁₃	—	7	1	no	—
45	C₇×C₁₁	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₁₁	—	13	1	no	—
47	D₃×C₁₁	—	7	1	no	—
48	D₃×C₁₁	—	91	1	no	—
49	C₂×D₁₃	—	21	1	no	Hall
50	C₂²×C₁₁	—	273	1	no	Hall
51	C₂×C₃×C₇	—	13	1	no	—
52	D₂₁	—	13	1	no	—
53	D₂₁	C₁₁×D₁₃	1	1	yes	characteristic, direct product factor
54	C₃×C₁₃	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
55	C₃×C₁₁	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
56	C₂×D₇	—	39	1	no	Hall
57	C₂×C₁₃	—	21	1	no	—
58	D₁₃	—	21	1	no	—
59	D₁₃	C₁₁×D₂₁	1	1	yes	characteristic, direct product factor
60	C₂×C₁₁	—	13	1	no	—
61	C₂×C₁₁	—	273	1	no	—
62	C₂×C₁₁	—	21	1	no	—
63	C₃×C₇	C₂×C₁₁×D₁₃	1	1	yes	characteristic, complemented, Hall
64	C₂×C₇	—	13	1	no	—
65	D₇	—	3	1	no	—
66	D₇	—	39	1	no	—
67	C₁₃	C₂×C₁₁×D₂₁	1	1	yes	characteristic, complemented, Sylow
68	C₂×D₃	—	91	1	no	Hall
69	C₁₁	D₁₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
70	C₇	D₃×C₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	13	1	no	—
72	D₃	—	7	1	no	—
73	D₃	—	91	1	no	—
74	C₂²	—	273	1	no	Sylow
75	C₃	C₁₁×D₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	13	1	no	—
77	C₂	—	273	1	no	—
78	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₁₃×D₂₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₃	C₂²
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₂₇₃	C₂	semidirect
2. C₁₁×C₁₃×D₂₁	C₂	semidirect
3. C₃×C₇×C₁₁×D₁₃	C₂	semidirect
5. C₃×C₇×C₁₁×C₁₃	C₂²	semidirect
8. C₇×C₁₁×D₁₃	D₃	semidirect
10. D₁₃×D₂₁	C₁₁	direct (N × H)
11. C₇×C₁₁×C₁₃	C₂×D₃	semidirect
15. C₃×C₁₁×D₁₃	D₇	semidirect
17. D₂₇₃	C₂×C₁₁	semidirect
18. C₁₃×D₂₁	C₂×C₁₁	semidirect
19. C₃×C₇×D₁₃	C₂×C₁₁	semidirect
22. C₁₁×D₂₁	D₁₃	direct (N × H)
23. C₃×C₁₁×C₁₃	C₂×D₇	semidirect
28. C₁₁×D₁₃	D₂₁	direct (N × H)
29. C₃×C₇×C₁₃	C₂²×C₁₁	semidirect
30. C₃×C₇×C₁₁	C₂×D₁₃	semidirect
32. C₇×D₁₃	D₃×C₁₁	semidirect
38. C₁₁×C₁₃	C₂×D₂₁	semidirect
40. C₇×C₁₃	C₂×D₃×C₁₁	semidirect
43. C₃×D₁₃	C₁₁×D₇	semidirect
45. C₇×C₁₁	D₃×D₁₃	semidirect
53. D₂₁	C₁₁×D₁₃	direct (N × H)
54. C₃×C₁₃	C₂×C₁₁×D₇	semidirect
55. C₃×C₁₁	D₇×D₁₃	semidirect
59. D₁₃	C₁₁×D₂₁	direct (N × H)
63. C₃×C₇	C₂×C₁₁×D₁₃	semidirect
67. C₁₃	C₂×C₁₁×D₂₁	semidirect
69. C₁₁	D₁₃×D₂₁	direct (N × H)
70. C₇	D₃×C₁₁×D₁₃	semidirect
75. C₃	C₁₁×D₇×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×D₂₇₃	2
C₁₁×C₁₃×D₂₁	2
C₃×C₇×C₁₁×D₁₃	2
C₁₁×D₇×D₁₃	3
D₃×C₁₁×D₁₃	7
D₁₃×D₂₁	11
C₂×C₁₁×D₂₁	13

Subgroups — C11×D13×D21 #26046552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₃×D₂₁ #26046552