Subgroups — C₃²×C₇×D₁₁² #44479180

Order 30492.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×D₁₁	C₂	1	2	yes	maximal, complemented
2	C₃²×C₇×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₁₁²	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₁₁⋊D₁₁	C₂×C₃	1	4	yes	complemented
6	C₃×C₇×C₁₁×D₁₁	C₂×C₃	1	8	yes	complemented
7	C₃²×D₁₁²	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×D₁₁²	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₇×D₁₁	—	11	2	no	maximal
10	C₃×C₇×C₁₁²	C₂²×C₃	1	4	yes	complemented
11	C₃²×C₁₁⋊D₁₁	C₂×C₇	1	1	yes	characteristic, complemented
12	C₃²×C₁₁×D₁₁	C₂×C₇	1	2	yes	complemented
13	C₇×C₁₁⋊D₁₁	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₇×C₁₁×D₁₁	C₂×C₃²	1	2	yes	complemented
15	C₃×D₁₁²	C₃×C₇	1	4	yes	direct product factor
16	C₂×C₃²×C₇×C₁₁	—	11	2	no	—
17	C₃²×C₇×D₁₁	—	11	2	no	—
18	C₃²×C₇×D₁₁	—	22	5	no	—
19	C₃²×C₇×D₁₁	D₁₁	1	2	yes	direct product factor
20	C₃²×C₁₁²	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇×D₁₁	—	11	8	no	—
22	C₇×C₁₁²	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₁⋊D₁₁	C₂×C₃×C₇	1	4	yes	complemented
24	C₃×C₁₁×D₁₁	C₂×C₃×C₇	1	8	yes	complemented
25	C₃²×C₇×C₁₁	—	2	5	no	—
26	C₃²×C₇×C₁₁	C₂×D₁₁	1	2	yes	complemented
27	D₁₁²	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₇×C₁₁	—	11	8	no	—
29	C₃×C₇×D₁₁	—	11	8	no	—
30	C₃×C₇×D₁₁	—	22	20	no	—
31	C₃×C₇×D₁₁	C₃×D₁₁	1	8	yes	direct product factor
32	C₂×C₃²×D₁₁	—	11	2	no	—
33	C₃×C₁₁²	C₂²×C₃×C₇	1	4	yes	complemented
34	C₂×C₇×D₁₁	—	11	2	no	—
35	C₂²×C₃²×C₇	—	121	1	no	Hall
36	C₁₁⋊D₁₁	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
37	C₁₁×D₁₁	C₂×C₃²×C₇	1	2	yes	complemented
38	C₃×C₇×C₁₁	—	2	20	no	—
39	C₃×C₇×C₁₁	C₂×C₃×D₁₁	1	8	yes	complemented
40	C₂×C₃²×C₁₁	—	11	2	no	—
41	C₃²×D₁₁	—	11	2	no	—
42	C₃²×D₁₁	—	22	5	no	—
43	C₃²×D₁₁	C₇×D₁₁	1	2	yes	direct product factor
44	C₂×C₇×C₁₁	—	11	2	no	—
45	C₇×D₁₁	—	11	2	no	—
46	C₇×D₁₁	—	22	5	no	—
47	C₇×D₁₁	C₃²×D₁₁	1	2	yes	direct product factor
48	C₂×C₃×D₁₁	—	11	8	no	—
49	C₂×C₃²×C₇	—	11	2	no	—
50	C₂×C₃²×C₇	—	121	1	no	—
51	C₁₁²	C₂²×C₃²×C₇	1	1	yes	characteristic, complemented, Sylow
52	C₃²×C₁₁	—	2	5	no	—
53	C₃²×C₁₁	C₂×C₇×D₁₁	1	2	yes	complemented
54	C₂²×C₃×C₇	—	121	4	no	—
55	C₇×C₁₁	—	2	5	no	—
56	C₇×C₁₁	C₂×C₃²×D₁₁	1	2	yes	complemented
57	C₂×C₃×C₁₁	—	11	8	no	—
58	C₃×D₁₁	—	11	8	no	—
59	C₃×D₁₁	—	22	20	no	—
60	C₃×D₁₁	C₃×C₇×D₁₁	1	8	yes	direct product factor
61	C₃²×C₇	D₁₁²	1	1	yes	characteristic, direct product factor, Hall
62	C₂×D₁₁	—	11	2	no	—
63	C₂×C₃×C₇	—	11	8	no	—
64	C₂×C₃×C₇	—	121	4	no	—
65	C₂²×C₃²	—	121	1	no	Hall
66	C₃×C₁₁	—	2	20	no	—
67	C₃×C₁₁	C₂×C₃×C₇×D₁₁	1	8	yes	complemented
68	C₂²×C₇	—	121	1	no	Hall
69	C₂×C₁₁	—	11	2	no	—
70	D₁₁	—	11	2	no	—
71	D₁₁	—	22	5	no	—
72	D₁₁	C₃²×C₇×D₁₁	1	2	yes	direct product factor
73	C₃×C₇	C₃×D₁₁²	1	4	yes	direct product factor
74	C₂×C₃²	—	11	2	no	—
75	C₂×C₃²	—	121	1	no	—
76	C₂×C₇	—	11	2	no	—
77	C₂×C₇	—	121	1	no	—
78	C₂²×C₃	—	121	4	no	—
79	C₁₁	—	2	5	no	—
80	C₁₁	C₂×C₃²×C₇×D₁₁	1	2	yes	complemented
81	C₃²	C₇×D₁₁²	1	1	yes	characteristic, direct product factor, Sylow
82	C₇	C₃²×D₁₁²	1	1	yes	characteristic, direct product factor, Sylow
83	C₂×C₃	—	11	8	no	—
84	C₂×C₃	—	121	4	no	—
85	C₂²	—	121	1	no	Sylow
86	C₃	C₃×C₇×D₁₁²	1	4	yes	direct product factor
87	C₂	—	11	2	no	—
88	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₁₁²
commutator, cosocle, hypocenter	C₁₁²	C₂²×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₂²
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×D₁₁	C₂	semidirect
2. C₃²×C₇×C₁₁⋊D₁₁	C₂	semidirect
3. C₃×C₇×D₁₁²	C₃	direct (N × H)
4. C₃²×C₇×C₁₁²	C₂²	semidirect
5. C₃×C₇×C₁₁⋊D₁₁	C₂×C₃	semidirect
6. C₃×C₇×C₁₁×D₁₁	C₂×C₃	semidirect
7. C₃²×D₁₁²	C₇	direct (N × H)
8. C₇×D₁₁²	C₃²	direct (N × H)
10. C₃×C₇×C₁₁²	C₂²×C₃	semidirect
11. C₃²×C₁₁⋊D₁₁	C₂×C₇	semidirect
12. C₃²×C₁₁×D₁₁	C₂×C₇	semidirect
13. C₇×C₁₁⋊D₁₁	C₂×C₃²	semidirect
14. C₇×C₁₁×D₁₁	C₂×C₃²	semidirect
15. C₃×D₁₁²	C₃×C₇	direct (N × H)
19. C₃²×C₇×D₁₁	D₁₁	direct (N × H)
20. C₃²×C₁₁²	C₂²×C₇	semidirect
22. C₇×C₁₁²	C₂²×C₃²	semidirect
23. C₃×C₁₁⋊D₁₁	C₂×C₃×C₇	semidirect
24. C₃×C₁₁×D₁₁	C₂×C₃×C₇	semidirect
26. C₃²×C₇×C₁₁	C₂×D₁₁	semidirect
27. D₁₁²	C₃²×C₇	direct (N × H)
31. C₃×C₇×D₁₁	C₃×D₁₁	direct (N × H)
33. C₃×C₁₁²	C₂²×C₃×C₇	semidirect
36. C₁₁⋊D₁₁	C₂×C₃²×C₇	semidirect
37. C₁₁×D₁₁	C₂×C₃²×C₇	semidirect
39. C₃×C₇×C₁₁	C₂×C₃×D₁₁	semidirect
43. C₃²×D₁₁	C₇×D₁₁	direct (N × H)
47. C₇×D₁₁	C₃²×D₁₁	direct (N × H)
51. C₁₁²	C₂²×C₃²×C₇	semidirect
53. C₃²×C₁₁	C₂×C₇×D₁₁	semidirect
56. C₇×C₁₁	C₂×C₃²×D₁₁	semidirect
60. C₃×D₁₁	C₃×C₇×D₁₁	direct (N × H)
61. C₃²×C₇	D₁₁²	direct (N × H)
67. C₃×C₁₁	C₂×C₃×C₇×D₁₁	semidirect
72. D₁₁	C₃²×C₇×D₁₁	direct (N × H)
73. C₃×C₇	C₃×D₁₁²	direct (N × H)
80. C₁₁	C₂×C₃²×C₇×D₁₁	semidirect
81. C₃²	C₇×D₁₁²	direct (N × H)
82. C₇	C₃²×D₁₁²	direct (N × H)
86. C₃	C₃×C₇×D₁₁²	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×C₁₁×D₁₁	2
C₃²×C₇×C₁₁⋊D₁₁	2
C₃×C₇×D₁₁²	3
C₃²×D₁₁²	7
C₂×C₃²×C₇×D₁₁	11

Subgroups — C32×C7×D112 #44479180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×D₁₁² #44479180