Subgroups — C₂×C₃⋊(C₉⋊Dic₉) #14517749

Order 1944.

1008 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉²	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₉⋊Dic₉)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊(C₃⋊Dic₉)	—	3	4	no	maximal
4	C₂×C₉⋊Dic₉	—	3	9	no	maximal
5	C₂×C₃×C₉²	C₄	1	2	yes	complemented
6	C₂×C₃×C₉²	C₂²	1	1	yes	characteristic
7	C₂²×C₃²×C₉	D₃	1	4	yes	—
8	C₃⋊(C₃⋊Dic₉)	—	3	8	no	—
9	C₂²×C₉²	D₃	1	9	yes	—
10	C₉⋊Dic₉	—	3	18	no	—
11	C₃×C₉²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃⋊(C₃⋊Dic₃)	—	9	1	no	—
13	C₂×C₃⋊Dic₉	—	9	36	no	—
14	C₂×C₃⋊Dic₉	—	9	12	no	—
15	C₂×C₃²×C₉	Dic₃	1	8	yes	—
16	C₂×C₃²×C₉	C₂×D₃	1	4	yes	—
17	C₂×C₉²	Dic₃	1	18	yes	complemented
18	C₂×C₉²	C₂×D₃	1	9	yes	—
19	C₂²×C₃³	C₃⋊D₃	1	1	yes	characteristic
20	C₃⋊(C₃⋊Dic₃)	—	9	2	no	—
21	C₂²×C₃×C₉	D₉	1	36	yes	—
22	C₂²×C₃×C₉	C₃⋊D₃	1	12	yes	—
23	C₃⋊Dic₉	—	9	72	no	—
24	C₃⋊Dic₉	—	9	24	no	—
25	C₃²×C₉	C₂×Dic₃	1	4	yes	—
26	C₉²	C₂×Dic₃	1	9	yes	complemented
27	C₂×C₃⋊Dic₃	—	27	12	no	—
28	C₂×C₃⋊Dic₃	—	27	1	no	—
29	C₂×Dic₉	—	27	36	no	—
30	C₂×C₃³	C₃⋊Dic₃	1	2	yes	—
31	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
32	C₂×C₃×C₉	Dic₉	1	72	yes	complemented
33	C₂×C₃×C₉	C₂×D₉	1	36	yes	—
34	C₂×C₃×C₉	C₃⋊Dic₃	1	24	yes	—
35	C₂×C₃×C₉	C₂×C₃⋊D₃	1	12	yes	—
36	C₂²×C₃²	C₃⋊D₉	1	12	yes	—
37	C₂²×C₃²	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
38	C₃⋊Dic₃	—	27	24	no	—
39	C₃⋊Dic₃	—	27	2	no	—
40	C₂²×C₉	C₃⋊D₉	1	36	yes	—
41	Dic₉	—	27	72	no	—
42	C₃³	C₂×C₃⋊Dic₃	1	1	yes	characteristic
43	C₃×C₉	C₂×Dic₉	1	36	yes	complemented
44	C₃×C₉	C₂×C₃⋊Dic₃	1	12	yes	—
45	C₂×Dic₃	—	81	9	no	—
46	C₂×Dic₃	—	81	4	no	—
47	C₂×C₃²	C₃⋊Dic₉	1	24	yes	—
48	C₂×C₃²	C₂×C₃⋊D₉	1	12	yes	—
49	C₂×C₃²	C₃⋊(C₃⋊Dic₃)	1	2	yes	—
50	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
51	C₂×C₉	C₃⋊Dic₉	1	72	yes	complemented
52	C₂×C₉	C₂×C₃⋊D₉	1	36	yes	—
53	C₂²×C₃	C₉⋊D₉	1	9	yes	—
54	C₂²×C₃	C₃⋊(C₃⋊D₉)	1	4	yes	—
55	Dic₃	—	81	18	no	—
56	Dic₃	—	81	8	no	—
57	C₃²	C₂×C₃⋊Dic₉	1	12	yes	—
58	C₃²	C₂×C₃⋊(C₃⋊Dic₃)	1	1	yes	characteristic
59	C₉	C₂×C₃⋊Dic₉	1	36	yes	complemented
60	C₂×C₄	—	243	1	no	Sylow
61	C₂×C₃	C₉⋊Dic₉	1	18	yes	complemented
62	C₂×C₃	C₂×C₉⋊D₉	1	9	yes	—
63	C₂×C₃	C₃⋊(C₃⋊Dic₉)	1	8	yes	—
64	C₂×C₃	C₂×C₃⋊(C₃⋊D₉)	1	4	yes	—
65	C₂²	C₃⋊(C₉⋊D₉)	1	1	yes	characteristic
66	C₄	—	243	2	no	—
67	C₃	C₂×C₉⋊Dic₉	1	9	yes	complemented
68	C₃	C₂×C₃⋊(C₃⋊Dic₉)	1	4	yes	—
69	C₂	C₃⋊(C₉⋊Dic₉)	1	2	yes	direct product factor
70	C₂	C₂×C₃⋊(C₉⋊D₉)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₉⋊Dic₉)	C₂	direct (N × H)
5. C₂×C₃×C₉²	C₄	semidirect
11. C₃×C₉²	C₂×C₄	semidirect
17. C₂×C₉²	Dic₃	semidirect
26. C₉²	C₂×Dic₃	semidirect
32. C₂×C₃×C₉	Dic₉	semidirect
43. C₃×C₉	C₂×Dic₉	semidirect
51. C₂×C₉	C₃⋊Dic₉	semidirect
59. C₉	C₂×C₃⋊Dic₉	semidirect
61. C₂×C₃	C₉⋊Dic₉	semidirect
67. C₃	C₂×C₉⋊Dic₉	semidirect
69. C₂	C₃⋊(C₉⋊Dic₉)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₉²	2
C₃⋊(C₉⋊Dic₉)	2
C₂×C₃⋊(C₃⋊Dic₉)	3
C₂×C₉⋊Dic₉	3

Subgroups — C2×C3⋊(C9⋊Dic9) #14517749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(C₉⋊Dic₉) #14517749