Subgroups — C₂×C₃²×C₅×C₁₁⋊D₁₁ #36345375

Order 21780.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₁⋊D₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₁₁⋊D₁₁	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×C₁₁⋊D₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₁₁⋊D₁₁	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅×C₁₁²	C₂×C₃	1	4	yes	complemented
8	C₂×C₅×C₁₁⋊D₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃²×C₁₁⋊D₁₁	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃²×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₃²×C₅×D₁₁	—	11	12	no	maximal
12	C₃×C₅×C₁₁²	C₂²×C₃	1	4	yes	complemented
13	C₂×C₃×C₁₁⋊D₁₁	C₃×C₅	1	4	yes	direct product factor
14	C₂×C₅×C₁₁²	C₂×C₃²	1	1	yes	characteristic, complemented
15	C₅×C₁₁⋊D₁₁	C₂×C₃²	1	2	yes	direct product factor
16	C₃²×C₁₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃²×C₅×C₁₁	D₁₁	1	12	yes	complemented
18	C₃²×C₅×D₁₁	—	11	24	no	—
19	C₂×C₃×C₁₁²	C₂×C₃×C₅	1	4	yes	complemented
20	C₃×C₁₁⋊D₁₁	C₂×C₃×C₅	1	8	yes	direct product factor
21	C₂×C₃×C₅×D₁₁	—	11	48	no	—
22	C₅×C₁₁²	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₃²×C₅×C₁₁	C₂×D₁₁	1	12	yes	complemented
24	C₂×C₁₁⋊D₁₁	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃²×D₁₁	—	11	12	no	—
26	C₃×C₁₁²	C₂²×C₃×C₅	1	4	yes	complemented
27	C₂×C₃×C₅×C₁₁	C₃×D₁₁	1	48	yes	complemented
28	C₃×C₅×D₁₁	—	11	96	no	—
29	C₂×C₁₁²	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
30	C₁₁⋊D₁₁	C₂×C₃²×C₅	1	2	yes	direct product factor
31	C₂×C₅×D₁₁	—	11	12	no	—
32	C₂×C₃²×C₁₁	C₅×D₁₁	1	12	yes	complemented
33	C₃²×D₁₁	—	11	24	no	—
34	C₂²×C₃²×C₅	—	121	1	no	Hall
35	C₃×C₅×C₁₁	C₂×C₃×D₁₁	1	48	yes	complemented
36	C₂×C₃×D₁₁	—	11	48	no	—
37	C₁₁²	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₅×C₁₁	C₃²×D₁₁	1	12	yes	complemented
39	C₅×D₁₁	—	11	24	no	—
40	C₃²×C₁₁	C₂×C₅×D₁₁	1	12	yes	complemented
41	C₂×C₃²×C₅	—	121	2	no	—
42	C₂×C₃²×C₅	C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
43	C₂×C₃×C₁₁	C₃×C₅×D₁₁	1	48	yes	complemented
44	C₃×D₁₁	—	11	96	no	—
45	C₂²×C₃×C₅	—	121	4	no	—
46	C₅×C₁₁	C₂×C₃²×D₁₁	1	12	yes	complemented
47	C₃²×C₅	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Hall
48	C₂×D₁₁	—	11	12	no	—
49	C₂²×C₃²	—	121	1	no	Hall
50	C₃×C₁₁	C₂×C₃×C₅×D₁₁	1	48	yes	complemented
51	C₂×C₃×C₅	—	121	8	no	—
52	C₂×C₃×C₅	C₃×C₁₁⋊D₁₁	1	4	yes	direct product factor
53	C₂×C₁₁	C₃²×C₅×D₁₁	1	12	yes	complemented
54	D₁₁	—	11	24	no	—
55	C₂²×C₅	—	121	1	no	Hall
56	C₂×C₃²	—	121	2	no	—
57	C₂×C₃²	C₅×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
58	C₃×C₅	C₂×C₃×C₁₁⋊D₁₁	1	4	yes	direct product factor
59	C₂²×C₃	—	121	4	no	—
60	C₁₁	C₂×C₃²×C₅×D₁₁	1	12	yes	complemented
61	C₂×C₅	—	121	2	no	—
62	C₂×C₅	C₃²×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor
63	C₃²	C₂×C₅×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	121	8	no	—
65	C₂×C₃	C₃×C₅×C₁₁⋊D₁₁	1	4	yes	direct product factor
66	C₅	C₂×C₃²×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	—	121	1	no	Sylow
68	C₃	C₂×C₃×C₅×C₁₁⋊D₁₁	1	4	yes	direct product factor
69	C₂	—	121	2	no	—
70	C₂	C₃²×C₅×C₁₁⋊D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅	C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₁₁²	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁²	C₂
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₁⋊D₁₁	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₁²	C₂	semidirect
3. C₂×C₃×C₅×C₁₁⋊D₁₁	C₃	direct (N × H)
4. C₃²×C₅×C₁₁²	C₂²	semidirect
5. C₂×C₃²×C₁₁⋊D₁₁	C₅	direct (N × H)
6. C₃×C₅×C₁₁⋊D₁₁	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₁₁²	C₂×C₃	semidirect
8. C₂×C₅×C₁₁⋊D₁₁	C₃²	direct (N × H)
9. C₃²×C₁₁⋊D₁₁	C₂×C₅	direct (N × H)
10. C₂×C₃²×C₁₁²	C₂×C₅	semidirect
12. C₃×C₅×C₁₁²	C₂²×C₃	semidirect
13. C₂×C₃×C₁₁⋊D₁₁	C₃×C₅	direct (N × H)
14. C₂×C₅×C₁₁²	C₂×C₃²	semidirect
15. C₅×C₁₁⋊D₁₁	C₂×C₃²	direct (N × H)
16. C₃²×C₁₁²	C₂²×C₅	semidirect
17. C₂×C₃²×C₅×C₁₁	D₁₁	semidirect
19. C₂×C₃×C₁₁²	C₂×C₃×C₅	semidirect
20. C₃×C₁₁⋊D₁₁	C₂×C₃×C₅	direct (N × H)
22. C₅×C₁₁²	C₂²×C₃²	semidirect
23. C₃²×C₅×C₁₁	C₂×D₁₁	semidirect
24. C₂×C₁₁⋊D₁₁	C₃²×C₅	direct (N × H)
26. C₃×C₁₁²	C₂²×C₃×C₅	semidirect
27. C₂×C₃×C₅×C₁₁	C₃×D₁₁	semidirect
29. C₂×C₁₁²	C₂×C₃²×C₅	semidirect
30. C₁₁⋊D₁₁	C₂×C₃²×C₅	direct (N × H)
32. C₂×C₃²×C₁₁	C₅×D₁₁	semidirect
35. C₃×C₅×C₁₁	C₂×C₃×D₁₁	semidirect
37. C₁₁²	C₂²×C₃²×C₅	semidirect
38. C₂×C₅×C₁₁	C₃²×D₁₁	semidirect
40. C₃²×C₁₁	C₂×C₅×D₁₁	semidirect
42. C₂×C₃²×C₅	C₁₁⋊D₁₁	direct (N × H)
43. C₂×C₃×C₁₁	C₃×C₅×D₁₁	semidirect
46. C₅×C₁₁	C₂×C₃²×D₁₁	semidirect
47. C₃²×C₅	C₂×C₁₁⋊D₁₁	direct (N × H)
50. C₃×C₁₁	C₂×C₃×C₅×D₁₁	semidirect
52. C₂×C₃×C₅	C₃×C₁₁⋊D₁₁	direct (N × H)
53. C₂×C₁₁	C₃²×C₅×D₁₁	semidirect
57. C₂×C₃²	C₅×C₁₁⋊D₁₁	direct (N × H)
58. C₃×C₅	C₂×C₃×C₁₁⋊D₁₁	direct (N × H)
60. C₁₁	C₂×C₃²×C₅×D₁₁	semidirect
62. C₂×C₅	C₃²×C₁₁⋊D₁₁	direct (N × H)
63. C₃²	C₂×C₅×C₁₁⋊D₁₁	direct (N × H)
65. C₂×C₃	C₃×C₅×C₁₁⋊D₁₁	direct (N × H)
66. C₅	C₂×C₃²×C₁₁⋊D₁₁	direct (N × H)
68. C₃	C₂×C₃×C₅×C₁₁⋊D₁₁	direct (N × H)
70. C₂	C₃²×C₅×C₁₁⋊D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₁⋊D₁₁	2
C₂×C₃²×C₅×C₁₁²	2
C₂×C₃×C₅×C₁₁⋊D₁₁	3
C₂×C₃²×C₁₁⋊D₁₁	5
C₂×C₃²×C₅×D₁₁	11

Subgroups — C2×C32×C5×C11⋊D11 #36345375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×C₁₁⋊D₁₁ #36345375