Subgroups — C₂×C₁₁×C₁₃×D₂₁ #26046587

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	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×C₁₃×D₇	—	3	1	no	maximal, Hall
4	C₃×C₇×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₁₃×D₇	—	3	2	no	—
6	C₂×C₇×C₁₁×C₁₃	D₃	1	1	yes	characteristic, complemented
7	C₂×D₃×C₁₁×C₁₃	—	7	1	no	maximal, Hall
8	C₂×C₁₃×D₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×D₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₁₁×C₁₃	D₇	1	1	yes	characteristic, complemented
12	D₃×C₁₁×C₁₃	—	7	2	no	—
13	C₂²×C₁₁×C₁₃	—	21	1	no	Hall
14	C₂×C₃×C₇×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
15	C₁₃×D₂₁	C₂×C₁₁	1	2	yes	direct product factor
16	C₂×C₃×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₁₁×D₂₁	C₂×C₁₃	1	2	yes	direct product factor
18	C₃×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₃×D₇	—	3	1	no	Hall
20	C₂×C₁₁×D₇	—	3	1	no	Hall
21	C₂×C₁₁×C₁₃	—	21	2	no	—
22	C₂×C₁₁×C₁₃	D₂₁	1	1	yes	characteristic, direct product factor
23	C₃×C₇×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₁₃	D₃×C₁₁	1	1	yes	characteristic, complemented
26	C₁₃×D₇	—	3	2	no	—
27	C₂×D₃×C₁₃	—	7	1	no	Hall
28	C₂×C₇×C₁₁	D₃×C₁₃	1	1	yes	characteristic, complemented
29	C₁₁×D₇	—	3	2	no	—
30	C₁₁×C₁₃	C₂×D₂₁	1	1	yes	characteristic, direct product factor, Hall
31	C₂×D₃×C₁₁	—	7	1	no	Hall
32	C₇×C₁₃	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
33	C₂×D₂₁	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₁₃	C₁₁×D₇	1	1	yes	characteristic, complemented
35	D₃×C₁₃	—	7	2	no	—
36	C₇×C₁₁	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₁₁	C₁₃×D₇	1	1	yes	characteristic, complemented
38	D₃×C₁₁	—	7	2	no	—
39	C₂²×C₁₃	—	21	1	no	Hall
40	C₂²×C₁₁	—	21	1	no	Hall
41	C₂×C₃×C₇	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
42	D₂₁	C₂×C₁₁×C₁₃	1	2	yes	direct product factor
43	C₃×C₁₃	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
44	C₃×C₁₁	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
45	C₂×D₇	—	3	1	no	Hall
46	C₂×C₁₃	—	21	2	no	—
47	C₂×C₁₃	C₁₁×D₂₁	1	1	yes	characteristic, direct product factor
48	C₂×C₁₁	—	21	2	no	—
49	C₂×C₁₁	C₁₃×D₂₁	1	1	yes	characteristic, direct product factor
50	C₃×C₇	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×C₇	D₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented
52	D₇	—	3	2	no	—
53	C₁₃	C₂×C₁₁×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×D₃	—	7	1	no	Hall
55	C₁₁	C₂×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
56	C₇	C₂×D₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	C₁₁×C₁₃×D₇	1	1	yes	characteristic, complemented
58	D₃	—	7	2	no	—
59	C₂²	—	21	1	no	Sylow
60	C₃	C₂×C₁₁×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	21	2	no	—
62	C₂	C₁₁×C₁₃×D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₃	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×D₂₁	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₁×C₁₃	C₂	semidirect
4. C₃×C₇×C₁₁×C₁₃	C₂²	semidirect
6. C₂×C₇×C₁₁×C₁₃	D₃	semidirect
8. C₂×C₁₃×D₂₁	C₁₁	direct (N × H)
9. C₇×C₁₁×C₁₃	C₂×D₃	semidirect
10. C₂×C₁₁×D₂₁	C₁₃	direct (N × H)
11. C₂×C₃×C₁₁×C₁₃	D₇	semidirect
14. C₂×C₃×C₇×C₁₃	C₂×C₁₁	semidirect
15. C₁₃×D₂₁	C₂×C₁₁	direct (N × H)
16. C₂×C₃×C₇×C₁₁	C₂×C₁₃	semidirect
17. C₁₁×D₂₁	C₂×C₁₃	direct (N × H)
18. C₃×C₁₁×C₁₃	C₂×D₇	semidirect
22. C₂×C₁₁×C₁₃	D₂₁	direct (N × H)
23. C₃×C₇×C₁₃	C₂²×C₁₁	semidirect
24. C₃×C₇×C₁₁	C₂²×C₁₃	semidirect
25. C₂×C₇×C₁₃	D₃×C₁₁	semidirect
28. C₂×C₇×C₁₁	D₃×C₁₃	semidirect
30. C₁₁×C₁₃	C₂×D₂₁	direct (N × H)
32. C₇×C₁₃	C₂×D₃×C₁₁	semidirect
33. C₂×D₂₁	C₁₁×C₁₃	direct (N × H)
34. C₂×C₃×C₁₃	C₁₁×D₇	semidirect
36. C₇×C₁₁	C₂×D₃×C₁₃	semidirect
37. C₂×C₃×C₁₁	C₁₃×D₇	semidirect
41. C₂×C₃×C₇	C₂×C₁₁×C₁₃	semidirect
42. D₂₁	C₂×C₁₁×C₁₃	direct (N × H)
43. C₃×C₁₃	C₂×C₁₁×D₇	semidirect
44. C₃×C₁₁	C₂×C₁₃×D₇	semidirect
47. C₂×C₁₃	C₁₁×D₂₁	direct (N × H)
49. C₂×C₁₁	C₁₃×D₂₁	direct (N × H)
50. C₃×C₇	C₂²×C₁₁×C₁₃	semidirect
51. C₂×C₇	D₃×C₁₁×C₁₃	semidirect
53. C₁₃	C₂×C₁₁×D₂₁	direct (N × H)
55. C₁₁	C₂×C₁₃×D₂₁	direct (N × H)
56. C₇	C₂×D₃×C₁₁×C₁₃	semidirect
57. C₂×C₃	C₁₁×C₁₃×D₇	semidirect
60. C₃	C₂×C₁₁×C₁₃×D₇	semidirect
62. C₂	C₁₁×C₁₃×D₂₁	direct (N × H)

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

Subgroups — C2×C11×C13×D21 #26046587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₁₃×D₂₁ #26046587