Subgroups — C₃×C₄⋊(C₉⋊D₉) #14517489

Order 1944.

488 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	C₃×C₄⋊(C₃⋊D₉)	—	3	4	no	maximal
4	C₄⋊(C₉⋊D₉)	C₃	1	1	yes	maximal, characteristic, direct product factor
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	C₂×C₃	1	2	yes	complemented
10	C₄×C₉²	—	2	4	no	—
11	C₄×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₉²	D₄	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₄⋊(C₃⋊D₃)	—	9	1	no	—
14	C₄⋊(C₃⋊D₉)	—	3	4	no	—
15	C₃×D₃₆	—	9	12	no	—
16	C₂×C₃²×C₉	C₂×D₃	1	4	yes	—
17	C₃×C₃⋊D₉	—	6	8	no	—
18	C₂×C₉²	—	2	4	no	—
19	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
20	C₉⋊D₉	—	2	2	no	—
21	C₂×C₃×C₃⋊D₃	—	9	2	no	—
22	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
23	C₂×C₃⋊D₉	—	3	8	no	—
24	C₂×C₃×D₉	—	9	24	no	—
25	C₃×C₄×C₉	—	2	4	no	—
26	C₃×C₄×C₉	—	2	12	no	—
27	C₃×C₄×C₉	D₉	1	12	yes	complemented
28	C₃×C₄×C₉	C₃×D₃	1	4	yes	—
29	C₃²×C₉	D₁₂	1	4	yes	—
30	C₉²	—	2	4	no	—
31	C₉²	C₃×D₄	1	1	yes	characteristic, complemented
32	C₄⋊(C₃⋊D₃)	—	9	1	no	—
33	C₃×D₁₂	—	27	4	no	—
34	D₃₆	—	9	12	no	—
35	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
36	C₃×C₃⋊D₃	—	18	2	no	—
37	C₂×C₃×C₉	—	2	4	no	—
38	C₂×C₃×C₉	—	2	12	no	—
39	C₂×C₃×C₉	C₂×D₉	1	12	yes	—
40	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
41	C₃⋊D₉	—	6	8	no	—
42	C₃×D₉	—	18	24	no	—
43	C₂×C₃⋊D₃	—	9	2	no	—
44	C₂×C₃×D₃	—	27	8	no	—
45	C₃²×C₄	—	2	4	no	—
46	C₃²×C₄	C₃⋊D₉	1	4	yes	—
47	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
48	C₂×D₉	—	9	24	no	—
49	C₄×C₉	—	2	12	no	—
50	C₄×C₉	C₃×D₉	1	12	yes	complemented
51	C₃³	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
52	C₃×C₉	—	2	4	no	—
53	C₃×C₉	—	2	12	no	—
54	C₃×C₉	D₃₆	1	12	yes	complemented
55	C₃×C₉	C₃×D₁₂	1	4	yes	—
56	C₃×D₄	—	81	1	no	—
57	D₁₂	—	27	4	no	—
58	C₂×C₃²	—	2	4	no	—
59	C₂×C₃²	C₂×C₃⋊D₉	1	4	yes	—
60	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
61	C₃⋊D₃	—	18	2	no	—
62	C₃×D₃	—	54	8	no	—
63	C₂×C₉	—	2	12	no	—
64	C₂×C₉	C₂×C₃×D₉	1	12	yes	—
65	D₉	—	18	24	no	—
66	C₂²×C₃	—	81	2	no	—
67	C₂×D₃	—	27	8	no	—
68	C₃×C₄	—	2	4	no	—
69	C₃×C₄	C₉⋊D₉	1	1	yes	characteristic, complemented
70	C₃×C₄	C₃×C₃⋊D₉	1	4	yes	—
71	C₃²	—	2	4	no	—
72	C₃²	C₄⋊(C₃⋊D₉)	1	4	yes	—
73	C₃²	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
74	C₉	—	2	12	no	—
75	C₉	C₃×D₃₆	1	12	yes	complemented
76	D₄	—	81	1	no	Sylow
77	C₂×C₃	—	2	4	no	—
78	C₂×C₃	—	162	2	no	—
79	C₂×C₃	C₂×C₉⋊D₉	1	1	yes	characteristic
80	C₂×C₃	C₂×C₃×C₃⋊D₉	1	4	yes	—
81	D₃	—	54	8	no	—
82	C₂²	—	81	2	no	—
83	C₄	C₃×C₉⋊D₉	1	1	yes	characteristic, complemented
84	C₃	—	2	4	no	—
85	C₃	C₄⋊(C₉⋊D₉)	1	1	yes	characteristic, direct product factor
86	C₃	C₃×C₄⋊(C₃⋊D₉)	1	4	yes	—
87	C₂	—	162	2	no	—
88	C₂	C₂×C₃×C₉⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×C₉⋊D₉
commutator, cosocle	C₂×C₉²	C₂²×C₃
Frattini	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₃×C₄×C₉²	C₂
socle	C₂×C₃³	C₂×C₃⋊D₃
hypercenter	C₃×C₄	C₉⋊D₉
hypocenter	C₉²	C₃×D₄
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×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
4. C₄⋊(C₉⋊D₉)	C₃	direct (N × H)
9. C₂×C₉⋊D₉	C₂×C₃	semidirect
11. C₄×C₉²	C₂×C₃	semidirect
12. C₃×C₉²	D₄	semidirect
27. C₃×C₄×C₉	D₉	semidirect
31. C₉²	C₃×D₄	semidirect
50. C₄×C₉	C₃×D₉	semidirect
54. C₃×C₉	D₃₆	semidirect
69. C₃×C₄	C₉⋊D₉	semidirect
75. C₉	C₃×D₃₆	semidirect
83. C₄	C₃×C₉⋊D₉	semidirect
85. C₃	C₄⋊(C₉⋊D₉)	direct (N × H)

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
C₃×C₄⋊(C₃⋊D₉)	3
C₄⋊(C₉⋊D₉)	3

Subgroups — C3×C4⋊(C9⋊D9) #14517489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄⋊(C₉⋊D₉) #14517489