Subgroups — C₃×C₇×C₁₁×D₃₃ #29503909

Order 15246.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₁×D₃₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇×C₁₁×D₁₁	—	3	1	no	maximal
4	C₃×C₇×C₁₁²	—	2	1	no	—
5	C₃×C₇×C₁₁²	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×C₁₁×D₃₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₁×D₁₁	—	3	1	no	Hall
9	C₃×C₇×D₃₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor
10	C₃×D₃×C₇×C₁₁	—	11	1	no	maximal
11	C₃²×C₁₁²	C₂×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₁²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₁₁×D₃₃	C₃×C₇	1	1	yes	characteristic, direct product factor
14	C₃×C₁₁×D₁₁	—	3	1	no	—
15	C₃²×C₇×C₁₁	—	2	5	no	—
16	C₃²×C₇×C₁₁	D₁₁	1	1	yes	characteristic, complemented
17	C₃²×C₇×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
18	C₂×C₃×C₇×C₁₁	—	33	1	no	—
19	C₇×D₃₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor
20	D₃×C₇×C₁₁	—	11	1	no	—
21	C₃×C₇×D₁₁	—	3	1	no	—
22	C₃×C₁₁²	—	2	1	no	—
23	C₃×C₁₁²	D₃×C₇	1	1	yes	characteristic, complemented
24	C₃×C₁₁²	C₂×C₃×C₇	1	1	yes	characteristic, complemented
25	C₁₁×D₁₁	—	3	1	no	Hall
26	C₃×C₇×C₁₁	—	2	10	no	—
27	C₃×C₇×C₁₁	—	2	1	no	—
28	C₃×C₇×C₁₁	—	2	1	no	—
29	C₃×C₇×C₁₁	—	2	5	no	—
30	C₃×C₇×C₁₁	—	2	5	no	—
31	C₃×C₇×C₁₁	D₃×C₁₁	1	1	yes	characteristic, complemented
32	C₃×C₇×C₁₁	C₃×D₁₁	1	1	yes	characteristic, complemented
33	C₃×C₇×C₁₁	D₃₃	1	1	yes	characteristic, direct product factor
34	C₃×C₇×C₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
35	C₃×D₃₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor
36	C₃×D₃×C₁₁	—	11	1	no	—
37	C₂×C₇×C₁₁	—	33	1	no	—
38	C₇×D₁₁	—	3	1	no	—
39	C₃×D₃×C₇	—	11	1	no	Hall
40	C₁₁²	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
41	C₃²×C₁₁	—	2	5	no	—
42	C₃²×C₁₁	C₇×D₁₁	1	1	yes	characteristic, complemented
43	C₃²×C₁₁	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
44	C₇×C₁₁	—	2	5	no	—
45	C₇×C₁₁	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented
46	C₇×C₁₁	C₃×D₃₃	1	1	yes	characteristic, direct product factor
47	C₂×C₃×C₁₁	—	33	1	no	—
48	D₃₃	C₃×C₇×C₁₁	1	1	yes	characteristic, direct product factor
49	C₃×D₁₁	—	3	1	no	—
50	D₃×C₁₁	—	11	1	no	—
51	C₃²×C₇	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
52	C₂×C₃×C₇	—	33	1	no	—
53	D₃×C₇	—	11	1	no	—
54	C₃×C₁₁	—	2	10	no	—
55	C₃×C₁₁	—	2	1	no	—
56	C₃×C₁₁	—	2	1	no	—
57	C₃×C₁₁	—	2	5	no	—
58	C₃×C₁₁	—	2	5	no	—
59	C₃×C₁₁	C₃×C₇×D₁₁	1	1	yes	characteristic, complemented
60	C₃×C₁₁	D₃×C₇×C₁₁	1	1	yes	characteristic, complemented
61	C₃×C₁₁	C₇×D₃₃	1	1	yes	characteristic, direct product factor
62	C₃×C₁₁	C₂×C₃×C₇×C₁₁	1	1	yes	characteristic, complemented
63	C₂×C₁₁	—	33	1	no	—
64	D₁₁	—	3	1	no	—
65	C₃×C₇	—	2	1	no	—
66	C₃×C₇	C₃×C₁₁×D₁₁	1	1	yes	characteristic, complemented
67	C₃×C₇	C₁₁×D₃₃	1	1	yes	characteristic, direct product factor
68	C₃×D₃	—	11	1	no	Hall
69	C₂×C₇	—	33	1	no	Hall
70	C₁₁	—	2	5	no	—
71	C₁₁	C₃×D₃×C₇×C₁₁	1	1	yes	characteristic, complemented
72	C₁₁	C₃×C₇×D₃₃	1	1	yes	characteristic, direct product factor
73	C₃²	C₇×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
74	C₇	C₃×C₁₁×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×C₃	—	33	1	no	—
76	D₃	—	11	1	no	—
77	C₃	—	2	1	no	—
78	C₃	C₃×C₇×C₁₁×D₁₁	1	1	yes	characteristic, complemented
79	C₃	C₇×C₁₁×D₃₃	1	1	yes	characteristic, direct product factor
80	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₁	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₃×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₃×C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁²	C₂	semidirect
2. C₇×C₁₁×D₃₃	C₃	direct (N × H)
5. C₃×C₇×C₁₁²	D₃	semidirect
6. C₃×C₇×C₁₁²	C₂×C₃	semidirect
7. C₃×C₁₁×D₃₃	C₇	direct (N × H)
9. C₃×C₇×D₃₃	C₁₁	direct (N × H)
11. C₃²×C₁₁²	C₂×C₇	semidirect
12. C₇×C₁₁²	C₃×D₃	semidirect
13. C₁₁×D₃₃	C₃×C₇	direct (N × H)
16. C₃²×C₇×C₁₁	D₁₁	semidirect
17. C₃²×C₇×C₁₁	C₂×C₁₁	semidirect
19. C₇×D₃₃	C₃×C₁₁	direct (N × H)
23. C₃×C₁₁²	D₃×C₇	semidirect
24. C₃×C₁₁²	C₂×C₃×C₇	semidirect
31. C₃×C₇×C₁₁	D₃×C₁₁	semidirect
32. C₃×C₇×C₁₁	C₃×D₁₁	semidirect
33. C₃×C₇×C₁₁	D₃₃	direct (N × H)
34. C₃×C₇×C₁₁	C₂×C₃×C₁₁	semidirect
35. C₃×D₃₃	C₇×C₁₁	direct (N × H)
40. C₁₁²	C₃×D₃×C₇	semidirect
42. C₃²×C₁₁	C₇×D₁₁	semidirect
43. C₃²×C₁₁	C₂×C₇×C₁₁	semidirect
45. C₇×C₁₁	C₃×D₃×C₁₁	semidirect
46. C₇×C₁₁	C₃×D₃₃	direct (N × H)
48. D₃₃	C₃×C₇×C₁₁	direct (N × H)
51. C₃²×C₇	C₁₁×D₁₁	semidirect
59. C₃×C₁₁	C₃×C₇×D₁₁	semidirect
60. C₃×C₁₁	D₃×C₇×C₁₁	semidirect
61. C₃×C₁₁	C₇×D₃₃	direct (N × H)
62. C₃×C₁₁	C₂×C₃×C₇×C₁₁	semidirect
66. C₃×C₇	C₃×C₁₁×D₁₁	semidirect
67. C₃×C₇	C₁₁×D₃₃	direct (N × H)
71. C₁₁	C₃×D₃×C₇×C₁₁	semidirect
72. C₁₁	C₃×C₇×D₃₃	direct (N × H)
73. C₃²	C₇×C₁₁×D₁₁	semidirect
74. C₇	C₃×C₁₁×D₃₃	direct (N × H)
78. C₃	C₃×C₇×C₁₁×D₁₁	semidirect
79. C₃	C₇×C₁₁×D₃₃	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×C₇×C₁₁²	2
C₇×C₁₁×D₃₃	3
C₃×C₇×C₁₁×D₁₁	3
C₃×C₁₁×D₃₃	7
C₃×C₇×D₃₃	11
C₃×D₃×C₇×C₁₁	11

Subgroups — C3×C7×C11×D33 #29503909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₁×D₃₃ #29503909