Subgroups — C₁₁²×D₇×C₃⋊D₃ #44479240

Order 30492.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁²×D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₁²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁²×C₃⋊D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₁²×D₇	—	3	4	no	maximal
5	C₃²×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁²×D₂₁	—	3	4	no	—
7	D₃×C₇×C₁₁²	—	3	4	no	—
8	C₃×C₁₁²×D₇	D₃	1	4	yes	complemented
9	C₂×C₁₁²×C₃⋊D₃	—	7	1	no	maximal, Hall
10	C₂×C₁₁²×D₇	—	9	1	no	Hall
11	C₁₁×D₇×C₃⋊D₃	C₁₁	1	12	yes	maximal, direct product factor
12	C₃×C₇×C₁₁²	C₂×D₃	1	4	yes	complemented
13	C₁₁²×C₃⋊D₃	—	7	1	no	—
14	C₁₁²×C₃⋊D₃	D₇	1	1	yes	characteristic, direct product factor
15	C₂×C₃²×C₁₁²	—	7	1	no	—
16	C₂×C₇×C₁₁²	—	9	1	no	—
17	C₁₁²×D₇	—	9	1	no	—
18	C₁₁²×D₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	C₂×D₃×C₁₁²	—	21	4	no	—
20	C₁₁×C₃⋊D₂₁	C₂×C₁₁	1	12	yes	complemented
21	C₇×C₁₁×C₃⋊D₃	C₂×C₁₁	1	12	yes	complemented
22	C₃²×C₁₁×D₇	C₂×C₁₁	1	12	yes	complemented
23	C₃²×C₁₁²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	D₃×C₁₁×D₇	—	3	48	no	—
25	C₇×C₁₁²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₁²	—	7	4	no	—
27	D₃×C₁₁²	—	3	4	no	—
28	D₃×C₁₁²	—	21	4	no	—
29	C₃²×C₇×C₁₁	C₂²×C₁₁	1	12	yes	complemented
30	C₂²×C₁₁²	—	63	1	no	Hall
31	C₁₁×D₂₁	—	3	48	no	—
32	D₃×C₇×C₁₁	—	3	48	no	—
33	C₃×C₁₁×D₇	D₃×C₁₁	1	48	yes	complemented
34	C₂×C₁₁×C₃⋊D₃	—	7	12	no	—
35	C₃×C₁₁²	D₃×D₇	1	4	yes	complemented
36	C₂×C₁₁×D₇	—	9	12	no	—
37	D₇×C₃⋊D₃	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₁₁²	—	7	1	no	—
39	C₂×C₁₁²	—	9	1	no	—
40	C₂×C₁₁²	—	63	1	no	—
41	C₃×C₇×C₁₁	C₂×D₃×C₁₁	1	48	yes	complemented
42	C₂×C₃²×C₁₁	—	7	12	no	—
43	C₁₁×C₃⋊D₃	—	7	12	no	—
44	C₁₁×C₃⋊D₃	C₁₁×D₇	1	12	yes	direct product factor
45	C₂×C₇×C₁₁	—	9	12	no	—
46	C₁₁×D₇	—	9	12	no	—
47	C₁₁×D₇	C₁₁×C₃⋊D₃	1	12	yes	direct product factor
48	C₂×D₃×C₁₁	—	21	48	no	—
49	C₃⋊D₂₁	C₂×C₁₁²	1	1	yes	characteristic, complemented
50	C₇×C₃⋊D₃	C₂×C₁₁²	1	1	yes	characteristic, complemented
51	C₃²×D₇	C₂×C₁₁²	1	1	yes	characteristic, complemented
52	C₁₁²	D₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
53	C₃²×C₁₁	C₂×C₁₁×D₇	1	12	yes	complemented
54	D₃×D₇	—	3	4	no	—
55	C₇×C₁₁	C₂×C₁₁×C₃⋊D₃	1	12	yes	complemented
56	C₂×C₃×C₁₁	—	7	48	no	—
57	D₃×C₁₁	—	3	48	no	—
58	D₃×C₁₁	—	21	48	no	—
59	C₃²×C₇	C₂²×C₁₁²	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₁₁	—	63	12	no	—
61	D₂₁	—	3	4	no	—
62	C₃×D₇	D₃×C₁₁²	1	4	yes	complemented
63	D₃×C₇	—	3	4	no	—
64	C₂×C₃⋊D₃	—	7	1	no	Hall
65	C₃×C₁₁	D₃×C₁₁×D₇	1	48	yes	complemented
66	C₂×D₇	—	9	1	no	Hall
67	C₂×C₁₁	—	7	12	no	—
68	C₂×C₁₁	—	9	12	no	—
69	C₂×C₁₁	—	63	12	no	—
70	C₃×C₇	C₂×D₃×C₁₁²	1	4	yes	complemented
71	C₂×C₃²	—	7	1	no	—
72	C₃⋊D₃	—	7	1	no	—
73	C₃⋊D₃	C₁₁²×D₇	1	1	yes	characteristic, direct product factor
74	C₂×C₇	—	9	1	no	—
75	D₇	—	9	1	no	—
76	D₇	C₁₁²×C₃⋊D₃	1	1	yes	characteristic, direct product factor
77	C₂×D₃	—	21	4	no	—
78	C₁₁	C₁₁×D₇×C₃⋊D₃	1	12	yes	direct product factor
79	C₃²	C₂×C₁₁²×D₇	1	1	yes	characteristic, complemented, Sylow
80	C₇	C₂×C₁₁²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	7	4	no	—
82	D₃	—	3	4	no	—
83	D₃	—	21	4	no	—
84	C₂²	—	63	1	no	Sylow
85	C₃	D₃×C₁₁²×D₇	1	4	yes	complemented
86	C₂	—	7	1	no	—
87	C₂	—	9	1	no	—
88	C₂	—	63	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁²	D₇×C₃⋊D₃
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₁₁²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₁²×D₇	C₂	semidirect
2. C₇×C₁₁²×C₃⋊D₃	C₂	semidirect
3. C₁₁²×C₃⋊D₂₁	C₂	semidirect
5. C₃²×C₇×C₁₁²	C₂²	semidirect
8. C₃×C₁₁²×D₇	D₃	semidirect
11. C₁₁×D₇×C₃⋊D₃	C₁₁	direct (N × H)
12. C₃×C₇×C₁₁²	C₂×D₃	semidirect
14. C₁₁²×C₃⋊D₃	D₇	direct (N × H)
18. C₁₁²×D₇	C₃⋊D₃	direct (N × H)
20. C₁₁×C₃⋊D₂₁	C₂×C₁₁	semidirect
21. C₇×C₁₁×C₃⋊D₃	C₂×C₁₁	semidirect
22. C₃²×C₁₁×D₇	C₂×C₁₁	semidirect
23. C₃²×C₁₁²	C₂×D₇	semidirect
25. C₇×C₁₁²	C₂×C₃⋊D₃	semidirect
29. C₃²×C₇×C₁₁	C₂²×C₁₁	semidirect
33. C₃×C₁₁×D₇	D₃×C₁₁	semidirect
35. C₃×C₁₁²	D₃×D₇	semidirect
37. D₇×C₃⋊D₃	C₁₁²	direct (N × H)
41. C₃×C₇×C₁₁	C₂×D₃×C₁₁	semidirect
44. C₁₁×C₃⋊D₃	C₁₁×D₇	direct (N × H)
47. C₁₁×D₇	C₁₁×C₃⋊D₃	direct (N × H)
49. C₃⋊D₂₁	C₂×C₁₁²	semidirect
50. C₇×C₃⋊D₃	C₂×C₁₁²	semidirect
51. C₃²×D₇	C₂×C₁₁²	semidirect
52. C₁₁²	D₇×C₃⋊D₃	direct (N × H)
53. C₃²×C₁₁	C₂×C₁₁×D₇	semidirect
55. C₇×C₁₁	C₂×C₁₁×C₃⋊D₃	semidirect
59. C₃²×C₇	C₂²×C₁₁²	semidirect
62. C₃×D₇	D₃×C₁₁²	semidirect
65. C₃×C₁₁	D₃×C₁₁×D₇	semidirect
70. C₃×C₇	C₂×D₃×C₁₁²	semidirect
73. C₃⋊D₃	C₁₁²×D₇	direct (N × H)
76. D₇	C₁₁²×C₃⋊D₃	direct (N × H)
78. C₁₁	C₁₁×D₇×C₃⋊D₃	direct (N × H)
79. C₃²	C₂×C₁₁²×D₇	semidirect
80. C₇	C₂×C₁₁²×C₃⋊D₃	semidirect
85. C₃	D₃×C₁₁²×D₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₁²×D₇	2
C₇×C₁₁²×C₃⋊D₃	2
C₁₁²×C₃⋊D₂₁	2
D₃×C₁₁²×D₇	3
C₂×C₁₁²×C₃⋊D₃	7
C₁₁×D₇×C₃⋊D₃	11

Subgroups — C112×D7×C3⋊D3 #44479240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁²×D₇×C₃⋊D₃ #44479240