Subgroups — C₄⋊(C₃⋊(C₉⋊D₉)) #14517721

Order 1944.

1008 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₉⋊D₉)	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₉²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊(C₃⋊D₉))	—	3	4	no	maximal
4	C₄⋊(C₉⋊D₉)	—	3	9	no	maximal
5	C₂×C₃×C₉²	C₂²	1	1	yes	characteristic
6	C₃⋊(C₉⋊D₉)	—	2	2	no	—
7	C₂×C₃⋊(C₃⋊D₉)	—	3	8	no	—
8	C₃²×C₄×C₉	D₃	1	4	yes	—
9	C₂×C₉⋊D₉	—	3	18	no	—
10	C₄×C₉²	D₃	1	9	yes	complemented
11	C₃×C₉²	D₄	1	1	yes	characteristic, complemented, Sylow
12	C₄⋊(C₃⋊(C₃⋊D₃))	—	9	1	no	—
13	C₄⋊(C₃⋊D₉)	—	9	36	no	—
14	C₄⋊(C₃⋊D₉)	—	9	12	no	—
15	C₂×C₃²×C₉	C₂×D₃	1	4	yes	—
16	C₃⋊(C₃⋊D₉)	—	6	8	no	—
17	C₂×C₉²	C₂×D₃	1	9	yes	—
18	C₉⋊D₉	—	6	18	no	—
19	C₂×C₃⋊(C₃⋊D₃)	—	9	2	no	—
20	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
21	C₂×C₃⋊D₉	—	9	72	no	—
22	C₂×C₃⋊D₉	—	9	24	no	—
23	C₃×C₄×C₉	D₉	1	36	yes	complemented
24	C₃×C₄×C₉	C₃⋊D₃	1	12	yes	—
25	C₃²×C₉	D₁₂	1	4	yes	—
26	C₉²	D₁₂	1	9	yes	complemented
27	C₄⋊(C₃⋊D₃)	—	27	12	no	—
28	C₄⋊(C₃⋊D₃)	—	27	1	no	—
29	D₃₆	—	27	36	no	—
30	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
31	C₃⋊(C₃⋊D₃)	—	18	2	no	—
32	C₂×C₃×C₉	C₂×D₉	1	36	yes	—
33	C₂×C₃×C₉	C₂×C₃⋊D₃	1	12	yes	—
34	C₃⋊D₉	—	18	72	no	—
35	C₃⋊D₉	—	18	24	no	—
36	C₂×C₃⋊D₃	—	27	24	no	—
37	C₂×C₃⋊D₃	—	27	2	no	—
38	C₃²×C₄	C₃⋊D₉	1	12	yes	—
39	C₃²×C₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
40	C₂×D₉	—	27	72	no	—
41	C₄×C₉	C₃⋊D₉	1	36	yes	complemented
42	C₃³	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
43	C₃×C₉	D₃₆	1	36	yes	complemented
44	C₃×C₉	C₄⋊(C₃⋊D₃)	1	12	yes	—
45	D₁₂	—	81	9	no	—
46	D₁₂	—	81	4	no	—
47	C₂×C₃²	C₂×C₃⋊D₉	1	12	yes	—
48	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
49	C₃⋊D₃	—	54	24	no	—
50	C₃⋊D₃	—	54	2	no	—
51	C₂×C₉	C₂×C₃⋊D₉	1	36	yes	—
52	D₉	—	54	72	no	—
53	C₂×D₃	—	81	18	no	—
54	C₂×D₃	—	81	8	no	—
55	C₃×C₄	C₉⋊D₉	1	9	yes	complemented
56	C₃×C₄	C₃⋊(C₃⋊D₉)	1	4	yes	—
57	C₃²	C₄⋊(C₃⋊D₉)	1	12	yes	—
58	C₃²	C₄⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
59	C₉	C₄⋊(C₃⋊D₉)	1	36	yes	complemented
60	D₄	—	243	1	no	Sylow
61	C₂×C₃	C₂×C₉⋊D₉	1	9	yes	—
62	C₂×C₃	C₂×C₃⋊(C₃⋊D₉)	1	4	yes	—
63	D₃	—	162	18	no	—
64	D₃	—	162	8	no	—
65	C₂²	—	243	2	no	—
66	C₄	C₃⋊(C₉⋊D₉)	1	1	yes	characteristic, complemented
67	C₃	C₄⋊(C₉⋊D₉)	1	9	yes	complemented
68	C₃	C₄⋊(C₃⋊(C₃⋊D₉))	1	4	yes	—
69	C₂	—	486	2	no	—
70	C₂	C₂×C₃⋊(C₉⋊D₉)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₃⋊(C₉⋊D₉)
commutator, cosocle	C₂×C₃×C₉²	C₂²
Frattini	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)
Fitting	C₃×C₄×C₉²	C₂
socle	C₂×C₃³	C₂×C₃⋊D₃
hypercenter	C₄	C₃⋊(C₉⋊D₉)
hypocenter	C₃×C₉²	D₄
LCS	G ▷ C₂×C₃×C₉² ▷ C₃×C₉²
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊(C₉⋊D₉)	C₂	semidirect
2. C₃×C₄×C₉²	C₂	semidirect
10. C₄×C₉²	D₃	semidirect
11. C₃×C₉²	D₄	semidirect
23. C₃×C₄×C₉	D₉	semidirect
26. C₉²	D₁₂	semidirect
41. C₄×C₉	C₃⋊D₉	semidirect
43. C₃×C₉	D₃₆	semidirect
55. C₃×C₄	C₉⋊D₉	semidirect
59. C₉	C₄⋊(C₃⋊D₉)	semidirect
66. C₄	C₃⋊(C₉⋊D₉)	semidirect
67. C₃	C₄⋊(C₉⋊D₉)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊(C₉⋊D₉)	2
C₃×C₄×C₉²	2
C₄⋊(C₃⋊(C₃⋊D₉))	3
C₄⋊(C₉⋊D₉)	3

Subgroups — C4⋊(C3⋊(C9⋊D9)) #14517721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₃⋊(C₉⋊D₉)) #14517721