Subgroups — C₉²×D₁₂ #14517279

Order 1944.

488 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₉²	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₉²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×D₁₂	C₃	1	4	yes	maximal
4	D₄×C₉²	—	3	1	no	maximal
5	C₂×C₃×C₉²	C₂²	1	1	yes	characteristic
6	D₃×C₉²	—	2	2	no	—
7	C₂×C₃×D₃×C₉	C₂×C₃	1	8	yes	—
8	C₃²×C₄×C₉	C₂×C₃	1	4	yes	—
9	C₂²×C₉²	—	3	2	no	—
10	C₄×C₉²	—	2	4	no	—
11	C₄×C₉²	D₃	1	1	yes	characteristic, complemented
12	C₃×C₉²	D₄	1	1	yes	characteristic, complemented, Sylow
13	C₃²×D₁₂	C₃²	1	1	yes	characteristic
14	C₃×D₄×C₉	—	3	4	no	—
15	C₉×D₁₂	C₉	1	12	yes	direct product factor
16	C₂×C₃²×C₉	C₂²×C₃	1	4	yes	—
17	C₃×D₃×C₉	—	2	8	no	—
18	C₂×C₉²	—	2	4	no	—
19	C₂×C₉²	—	6	2	no	—
20	C₂×C₉²	C₂×D₃	1	1	yes	characteristic
21	C₂×C₃²×D₃	C₂×C₃²	1	2	yes	—
22	C₃³×C₄	C₂×C₃²	1	1	yes	characteristic
23	C₂²×C₃×C₉	—	3	8	no	—
24	C₂×D₃×C₉	C₂×C₉	1	24	yes	complemented
25	C₃×C₄×C₉	—	2	4	no	—
26	C₃×C₄×C₉	—	2	12	no	—
27	C₃×C₄×C₉	C₂×C₉	1	12	yes	complemented
28	C₃×C₄×C₉	C₃×D₃	1	4	yes	—
29	C₃²×C₉	C₃×D₄	1	4	yes	—
30	C₉²	—	2	4	no	—
31	C₉²	D₁₂	1	1	yes	characteristic, direct product factor
32	C₃²×D₄	—	3	1	no	—
33	C₃×D₁₂	C₃×C₉	1	4	yes	—
34	D₄×C₉	—	3	12	no	—
35	C₂×C₃³	C₂²×C₃²	1	1	yes	characteristic
36	C₃²×D₃	—	2	2	no	—
37	C₂×C₃×C₉	—	2	4	no	—
38	C₂×C₃×C₉	—	2	12	no	—
39	C₂×C₃×C₉	—	6	8	no	—
40	C₂×C₃×C₉	C₂²×C₉	1	12	yes	—
41	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
42	D₃×C₉	—	2	24	no	—
43	C₂²×C₃²	—	3	2	no	—
44	C₂×C₃×D₃	C₂×C₃×C₉	1	8	yes	—
45	C₃²×C₄	—	2	4	no	—
46	C₃²×C₄	C₂×C₃×C₉	1	4	yes	—
47	C₃²×C₄	C₃²×D₃	1	1	yes	characteristic
48	C₂²×C₉	—	3	24	no	—
49	C₄×C₉	—	2	12	no	—
50	C₄×C₉	D₃×C₉	1	12	yes	complemented
51	C₃³	C₃²×D₄	1	1	yes	characteristic
52	C₃×C₉	—	2	4	no	—
53	C₃×C₉	—	2	12	no	—
54	C₃×C₉	D₄×C₉	1	12	yes	complemented
55	C₃×C₉	C₃×D₁₂	1	4	yes	—
56	C₃×D₄	—	3	4	no	—
57	D₁₂	C₉²	1	1	yes	characteristic, direct product factor
58	C₂×C₃²	—	2	4	no	—
59	C₂×C₃²	—	6	2	no	—
60	C₂×C₃²	C₂²×C₃×C₉	1	4	yes	—
61	C₂×C₃²	C₂×C₃²×D₃	1	1	yes	characteristic
62	C₃×D₃	—	2	8	no	—
63	C₂×C₉	—	2	12	no	—
64	C₂×C₉	—	6	24	no	—
65	C₂×C₉	C₂×D₃×C₉	1	12	yes	—
66	C₂²×C₃	—	3	8	no	—
67	C₂×D₃	C₂×C₉²	1	2	yes	complemented
68	C₃×C₄	—	2	4	no	—
69	C₃×C₄	C₂×C₉²	1	1	yes	characteristic, complemented
70	C₃×C₄	C₃×D₃×C₉	1	4	yes	—
71	C₃²	—	2	4	no	—
72	C₃²	C₃×D₄×C₉	1	4	yes	—
73	C₃²	C₃²×D₁₂	1	1	yes	characteristic
74	C₉	—	2	12	no	—
75	C₉	C₉×D₁₂	1	12	yes	direct product factor
76	D₄	—	3	1	no	Sylow
77	C₂×C₃	—	2	4	no	—
78	C₂×C₃	—	6	8	no	—
79	C₂×C₃	C₂²×C₉²	1	1	yes	characteristic
80	C₂×C₃	C₂×C₃×D₃×C₉	1	4	yes	—
81	D₃	—	2	2	no	—
82	C₂²	—	3	2	no	—
83	C₄	D₃×C₉²	1	1	yes	characteristic, complemented
84	C₃	—	2	4	no	—
85	C₃	D₄×C₉²	1	1	yes	characteristic, complemented
86	C₃	C₃×C₉×D₁₂	1	4	yes	—
87	C₂	—	6	2	no	—
88	C₂	C₂×D₃×C₉²	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉²	C₂×D₃
commutator	C₂×C₃	C₂²×C₉²
Frattini	C₂×C₃²	C₂×C₃²×D₃
Fitting	C₃×C₄×C₉²	C₂
socle, cosocle	C₂×C₃³	C₂²×C₃²
prime radical	C₃²×D₁₂	C₃²
hypercenter	C₄×C₉²	D₃
hypocenter	C₃	D₄×C₉²
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉² ◁ C₄×C₉²

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×C₉²	C₂	semidirect
2. C₃×C₄×C₉²	C₂	semidirect
11. C₄×C₉²	D₃	semidirect
12. C₃×C₉²	D₄	semidirect
15. C₉×D₁₂	C₉	direct (N × H)
24. C₂×D₃×C₉	C₂×C₉	semidirect
27. C₃×C₄×C₉	C₂×C₉	semidirect
31. C₉²	D₁₂	direct (N × H)
50. C₄×C₉	D₃×C₉	semidirect
54. C₃×C₉	D₄×C₉	semidirect
57. D₁₂	C₉²	direct (N × H)
67. C₂×D₃	C₂×C₉²	semidirect
69. C₃×C₄	C₂×C₉²	semidirect
75. C₉	C₉×D₁₂	direct (N × H)
83. C₄	D₃×C₉²	semidirect
85. C₃	D₄×C₉²	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₉²	2
C₃×C₄×C₉²	2
C₃×C₉×D₁₂	3
D₄×C₉²	3

Subgroups — C92×D12 #14517279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉²×D₁₂ #14517279