Subgroups — #92264⋊C₂ #11757706

Order 972.

123 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#92309	C₂	1	1	yes	maximal, characteristic, complemented
2	#92264	C₂	1	2	yes	maximal, complemented
3	D₃×AGL(1,ℤ/9)	—	3	2	no	maximal
4	D₉²	C₃	1	1	yes	maximal, characteristic, complemented
5	#6896	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₃⋊AGL(1,ℤ/9)	—	3	2	no	—
7	D₃×3₋¹⁺²	—	3	2	no	—
8	C₃×AGL(1,ℤ/9)	D₃	1	2	yes	—
9	C₉⋊D₉	C₂×C₃	1	1	yes	characteristic, complemented
10	D₉⋊C₉	—	2	2	no	—
11	#4169	—	6	1	no	—
12	C₉×D₉	C₂×C₃	1	2	yes	complemented
13	C₃×D₃²	—	9	1	no	—
14	C₂×AGL(1,ℤ/9)	—	9	2	no	—
15	D₃×D₉	—	3	2	no	—
16	C₃×3₋¹⁺²	C₂×D₃	1	2	yes	—
17	C₉⋊C₉	—	2	2	no	—
18	C₉⋊C₉	—	4	1	no	—
19	C₃²⋊C₉	—	2	1	no	—
20	C₉²	C₂²×C₃	1	1	yes	characteristic, complemented
21	C₃×C₃⋊D₃	—	9	1	no	—
22	C₃²×D₃	—	3	2	no	—
23	C₂×3₋¹⁺²	—	9	2	no	—
24	C₃⋊D₉	—	3	2	no	—
25	C₃⋊D₉	—	6	1	no	—
26	AGL(1,ℤ/9)	—	3	2	no	—
27	AGL(1,ℤ/9)	—	9	2	no	—
28	AGL(1,ℤ/9)	—	18	2	no	—
29	D₃×C₉	—	3	2	no	—
30	D₃×C₉	—	6	2	no	—
31	C₃×D₉	C₃×D₃	1	2	yes	—
32	C₂×C₃×D₃	—	27	2	no	—
33	D₃²	—	9	1	no	—
34	C₂×D₉	—	9	2	no	—
35	C₃³	D₃²	1	1	yes	characteristic
36	3₋¹⁺²	—	3	2	no	—
37	3₋¹⁺²	—	6	2	no	—
38	C₃×C₉	—	2	2	no	—
39	C₃×C₉	—	2	1	no	—
40	C₃×C₉	—	4	1	no	—
41	C₃×C₉	C₂×C₃×D₃	1	2	yes	—
42	C₂×C₃²	—	9	2	no	—
43	C₃⋊D₃	—	9	1	no	—
44	C₃×D₃	—	3	2	no	—
45	C₃×D₃	—	9	2	no	—
46	C₃×D₃	—	27	2	no	—
47	C₃×D₃	—	54	1	no	—
48	C₂×C₉	—	9	2	no	—
49	C₂×C₉	—	18	2	no	—
50	D₉	—	9	2	no	—
51	D₉	—	18	2	no	—
52	D₉	—	54	1	no	—
53	D₉	AGL(1,ℤ/9)	1	2	yes	complemented
54	C₂²×C₃	—	81	1	no	—
55	C₂×D₃	—	27	2	no	—
56	C₃²	—	3	2	no	—
57	C₃²	—	6	1	no	—
58	C₃²	C₃×D₃²	1	1	yes	characteristic
59	C₉	—	2	2	no	—
60	C₉	—	6	1	no	—
61	C₉	—	6	2	no	—
62	C₉	—	12	1	no	—
63	C₉	C₂×AGL(1,ℤ/9)	1	2	yes	complemented
64	C₂×C₃	—	9	2	no	—
65	C₂×C₃	—	27	2	no	—
66	C₂×C₃	—	81	1	no	—
67	D₃	—	3	2	no	—
68	D₃	—	27	2	no	—
69	D₃	—	54	1	no	—
70	C₂²	—	81	1	no	Sylow
71	C₃	—	2	1	no	—
72	C₃	—	9	1	no	—
73	C₃	D₃×AGL(1,ℤ/9)	1	2	yes	—
74	C₂	—	9	2	no	—
75	C₂	—	81	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉²	C₂²×C₃
Frattini, socle	C₃²	C₃×D₃²
Fitting	#6896	C₂²
LCS	G ▷ C₉²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #92309	C₂	semidirect
2. #92264	C₂	semidirect
4. D₉²	C₃	semidirect
5. #6896	C₂²	semidirect
9. C₉⋊D₉	C₂×C₃	semidirect
12. C₉×D₉	C₂×C₃	semidirect
20. C₉²	C₂²×C₃	semidirect
53. D₉	AGL(1,ℤ/9)	semidirect
63. C₉	C₂×AGL(1,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
#92309	2
#92264	2
D₃×AGL(1,ℤ/9)	3
D₉²	3

Subgroups — #92264⋊C2 #11757706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #92264⋊C₂ #11757706