Subgroups — C₃×C₁₁×D₁₁×D₁₃ #34038435

Order 18876.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×D₁₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₁×C₁₃×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×D₁₁×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₁₄₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁×C₁₃×D₁₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₁²×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₃×C₁₁×D₁₃	—	11	1	no	maximal
10	C₃×D₁₁×D₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor
11	C₁₁²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₁×D₁₁	—	13	1	no	maximal, Hall
13	C₂×C₃×C₁₁×C₁₃	—	11	1	no	—
14	C₃×D₁₄₃	C₂×C₁₁	1	1	yes	characteristic, complemented
15	C₃×C₁₃×D₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₃×C₁₁×D₁₃	—	2	5	no	—
17	C₃×C₁₁×D₁₃	—	11	1	no	—
18	C₃×C₁₁×D₁₃	D₁₁	1	1	yes	characteristic, direct product factor
19	C₃×C₁₁×D₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₂×C₃×C₁₁²	—	13	1	no	—
21	C₃×C₁₁×D₁₁	—	13	1	no	—
22	C₃×C₁₁×D₁₁	D₁₃	1	1	yes	characteristic, direct product factor
23	C₂×C₁₁×D₁₃	—	11	1	no	—
24	D₁₁×D₁₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor
25	C₂×C₁₁×D₁₁	—	13	1	no	Hall
26	C₃×C₁₁×C₁₃	—	2	5	no	—
27	C₃×C₁₁×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented
28	C₃×C₁₁×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented
29	C₃×C₁₁²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₁×C₁₃	—	11	1	no	—
31	D₁₄₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
32	C₁₁×D₁₃	—	2	5	no	—
33	C₁₁×D₁₃	—	11	1	no	—
34	C₁₁×D₁₃	C₃×D₁₁	1	1	yes	characteristic, direct product factor
35	C₁₁×D₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
36	C₁₃×D₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
37	C₂×C₁₁²	—	13	1	no	—
38	C₁₁×D₁₁	—	13	1	no	—
39	C₁₁×D₁₁	C₃×D₁₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃×D₁₃	—	11	1	no	Hall
41	C₁₁×C₁₃	—	2	5	no	—
42	C₁₁×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented
43	C₁₁×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented
44	C₂²×C₃×C₁₁	—	143	1	no	—
45	C₂×C₃×D₁₁	—	13	1	no	—
46	C₁₁²	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃×C₁₃	—	11	1	no	—
48	C₃×D₁₃	—	11	1	no	—
49	C₃×D₁₃	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
50	C₂×C₃×C₁₁	—	11	1	no	—
51	C₂×C₃×C₁₁	—	13	1	no	—
52	C₂×C₃×C₁₁	—	13	1	no	—
53	C₂×C₃×C₁₁	—	26	5	no	—
54	C₂×C₃×C₁₁	—	143	1	no	—
55	C₃×D₁₁	—	13	1	no	—
56	C₃×D₁₁	C₁₁×D₁₃	1	1	yes	characteristic, direct product factor
57	C₂×D₁₃	—	11	1	no	Hall
58	C₂²×C₁₁	—	143	1	no	—
59	C₂×D₁₁	—	13	1	no	—
60	C₃×C₁₃	C₂×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
61	C₃×C₁₁	—	2	5	no	—
62	C₃×C₁₁	D₁₁×D₁₃	1	1	yes	characteristic, direct product factor
63	C₃×C₁₁	C₂×C₁₁×D₁₃	1	1	yes	characteristic, complemented
64	C₂×C₁₃	—	11	1	no	—
65	D₁₃	—	11	1	no	—
66	D₁₃	C₃×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
67	C₂×C₁₁	—	11	1	no	—
68	C₂×C₁₁	—	13	1	no	—
69	C₂×C₁₁	—	13	1	no	—
70	C₂×C₁₁	—	26	5	no	—
71	C₂×C₁₁	—	143	1	no	—
72	D₁₁	—	13	1	no	—
73	D₁₁	C₃×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor
74	C₁₃	C₂×C₃×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₃	—	143	1	no	Hall
76	C₁₁	—	2	5	no	—
77	C₁₁	C₃×D₁₁×D₁₃	1	1	yes	characteristic, direct product factor
78	C₁₁	C₂×C₃×C₁₁×D₁₃	1	1	yes	characteristic, complemented
79	C₂×C₃	—	11	1	no	—
80	C₂×C₃	—	13	1	no	—
81	C₂×C₃	—	143	1	no	—
82	C₂²	—	143	1	no	Sylow
83	C₃	C₁₁×D₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	11	1	no	—
85	C₂	—	13	1	no	—
86	C₂	—	143	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₁	D₁₁×D₁₃
commutator, cosocle, hypocenter	C₁₁×C₁₃	C₂²×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₁₃	C₂²
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×D₁₄₃	C₂	semidirect
2. C₃×C₁₁×C₁₃×D₁₁	C₂	semidirect
3. C₃×C₁₁²×D₁₃	C₂	semidirect
4. C₁₁×D₁₁×D₁₃	C₃	direct (N × H)
5. C₃×C₁₁²×C₁₃	C₂²	semidirect
6. C₁₁×D₁₄₃	C₂×C₃	semidirect
7. C₁₁×C₁₃×D₁₁	C₂×C₃	semidirect
8. C₁₁²×D₁₃	C₂×C₃	semidirect
10. C₃×D₁₁×D₁₃	C₁₁	direct (N × H)
11. C₁₁²×C₁₃	C₂²×C₃	semidirect
14. C₃×D₁₄₃	C₂×C₁₁	semidirect
15. C₃×C₁₃×D₁₁	C₂×C₁₁	semidirect
18. C₃×C₁₁×D₁₃	D₁₁	direct (N × H)
19. C₃×C₁₁×D₁₃	C₂×C₁₁	semidirect
22. C₃×C₁₁×D₁₁	D₁₃	direct (N × H)
24. D₁₁×D₁₃	C₃×C₁₁	direct (N × H)
27. C₃×C₁₁×C₁₃	C₂×D₁₁	semidirect
28. C₃×C₁₁×C₁₃	C₂²×C₁₁	semidirect
29. C₃×C₁₁²	C₂×D₁₃	semidirect
31. D₁₄₃	C₂×C₃×C₁₁	semidirect
34. C₁₁×D₁₃	C₃×D₁₁	direct (N × H)
35. C₁₁×D₁₃	C₂×C₃×C₁₁	semidirect
36. C₁₃×D₁₁	C₂×C₃×C₁₁	semidirect
39. C₁₁×D₁₁	C₃×D₁₃	direct (N × H)
42. C₁₁×C₁₃	C₂×C₃×D₁₁	semidirect
43. C₁₁×C₁₃	C₂²×C₃×C₁₁	semidirect
46. C₁₁²	C₂×C₃×D₁₃	semidirect
49. C₃×D₁₃	C₁₁×D₁₁	direct (N × H)
56. C₃×D₁₁	C₁₁×D₁₃	direct (N × H)
60. C₃×C₁₃	C₂×C₁₁×D₁₁	semidirect
62. C₃×C₁₁	D₁₁×D₁₃	direct (N × H)
63. C₃×C₁₁	C₂×C₁₁×D₁₃	semidirect
66. D₁₃	C₃×C₁₁×D₁₁	direct (N × H)
73. D₁₁	C₃×C₁₁×D₁₃	direct (N × H)
74. C₁₃	C₂×C₃×C₁₁×D₁₁	semidirect
77. C₁₁	C₃×D₁₁×D₁₃	direct (N × H)
78. C₁₁	C₂×C₃×C₁₁×D₁₃	semidirect
83. C₃	C₁₁×D₁₁×D₁₃	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×C₁₁×D₁₄₃	2
C₃×C₁₁×C₁₃×D₁₁	2
C₃×C₁₁²×D₁₃	2
C₁₁×D₁₁×D₁₃	3
C₂×C₃×C₁₁×D₁₃	11
C₃×D₁₁×D₁₃	11
C₂×C₃×C₁₁×D₁₁	13

Subgroups — C3×C11×D11×D13 #34038435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×D₁₁×D₁₃ #34038435