Subgroups — C₂³×D₉⋊C₉ #13048186

Order 1296.

667 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₉⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₉⋊C₉	C₂	1	14	yes	maximal, direct product factor
3	C₂³×D₃×C₉	—	3	1	no	maximal
4	C₂³×C₃×D₉	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₉⋊C₉	C₂²	1	7	yes	complemented
6	C₂×D₉⋊C₉	C₂²	1	28	yes	direct product factor
7	C₂³×C₃×C₉	—	2	1	no	—
8	C₂³×C₃×C₉	D₃	1	1	yes	characteristic
9	C₂³×C₃×C₉	C₂×C₃	1	1	yes	characteristic
10	C₂²×D₃×C₉	—	3	14	no	—
11	C₂²×C₃×D₉	C₂×C₃	1	14	yes	—
12	C₂×C₉⋊C₉	C₂³	1	7	yes	complemented
13	D₉⋊C₉	C₂³	1	8	yes	direct product factor
14	C₂³×C₃×D₃	—	3	1	no	—
15	C₂⁴×C₉	—	9	1	no	—
16	C₂³×D₉	C₉	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₉	—	2	7	no	—
18	C₂²×C₃×C₉	C₂×D₃	1	7	yes	—
19	C₂²×C₃×C₉	C₂²×C₃	1	7	yes	—
20	C₂×D₃×C₉	—	3	28	no	—
21	C₂×C₃×D₉	C₂²×C₃	1	28	yes	—
22	C₉⋊C₉	C₂⁴	1	1	yes	characteristic, complemented, Sylow
23	C₂³×C₃²	C₃×D₃	1	1	yes	characteristic
24	C₂²×C₃×D₃	—	3	14	no	—
25	C₂³×C₉	—	2	1	no	—
26	C₂³×C₉	—	3	1	no	—
27	C₂³×C₉	—	6	1	no	—
28	C₂³×C₉	—	9	14	no	—
29	C₂³×C₉	C₂×C₉	1	1	yes	characteristic, complemented
30	C₂²×D₉	C₂×C₉	1	14	yes	complemented
31	C₂×C₃×C₉	—	2	7	no	—
32	C₂×C₃×C₉	C₂²×D₃	1	7	yes	—
33	C₂×C₃×C₉	C₂³×C₃	1	7	yes	—
34	D₃×C₉	—	3	8	no	—
35	C₃×D₉	C₂³×C₃	1	8	yes	—
36	C₂⁴×C₃	—	9	1	no	—
37	C₂³×D₃	—	3	1	no	—
38	C₂²×C₃²	C₂×C₃×D₃	1	7	yes	—
39	C₂×C₃×D₃	—	3	28	no	—
40	C₂²×C₉	—	2	7	no	—
41	C₂²×C₉	—	3	7	no	—
42	C₂²×C₉	—	6	7	no	—
43	C₂²×C₉	—	9	28	no	—
44	C₂²×C₉	C₂²×C₉	1	7	yes	complemented
45	C₂×D₉	C₂²×C₉	1	28	yes	complemented
46	C₃×C₉	—	2	1	no	—
47	C₃×C₉	C₂³×D₃	1	1	yes	characteristic
48	C₃×C₉	C₂⁴×C₃	1	1	yes	characteristic
49	C₂³×C₃	—	2	1	no	—
50	C₂³×C₃	—	9	14	no	—
51	C₂³×C₃	D₃×C₉	1	1	yes	characteristic
52	C₂³×C₃	AGL(1,ℤ/9)	1	1	yes	characteristic
53	C₂²×D₃	—	3	14	no	—
54	C₂×C₃²	C₂²×C₃×D₃	1	7	yes	—
55	C₃×D₃	—	3	8	no	—
56	C₂×C₉	—	2	7	no	—
57	C₂×C₉	—	3	7	no	—
58	C₂×C₉	—	6	7	no	—
59	C₂×C₉	—	9	8	no	—
60	C₂×C₉	C₂³×C₉	1	7	yes	complemented
61	D₉	C₂³×C₉	1	8	yes	complemented
62	C₂⁴	—	9	1	no	Sylow
63	C₂²×C₃	—	2	7	no	—
64	C₂²×C₃	—	9	28	no	—
65	C₂²×C₃	C₂×D₃×C₉	1	7	yes	—
66	C₂²×C₃	C₂×AGL(1,ℤ/9)	1	7	yes	—
67	C₂×D₃	—	3	28	no	—
68	C₃²	C₂³×C₃×D₃	1	1	yes	characteristic
69	C₉	—	2	1	no	—
70	C₉	—	3	1	no	—
71	C₉	—	6	1	no	—
72	C₉	C₂⁴×C₉	1	1	yes	characteristic, complemented
73	C₂³	—	9	14	no	—
74	C₂³	D₉⋊C₉	1	1	yes	characteristic, direct product factor
75	C₂×C₃	—	2	7	no	—
76	C₂×C₃	—	9	8	no	—
77	C₂×C₃	C₂²×D₃×C₉	1	7	yes	—
78	C₂×C₃	C₂²×AGL(1,ℤ/9)	1	7	yes	—
79	D₃	—	3	8	no	—
80	C₂²	—	9	28	no	—
81	C₂²	C₂×D₉⋊C₉	1	7	yes	direct product factor
82	C₃	—	2	1	no	—
83	C₃	C₂³×D₃×C₉	1	1	yes	characteristic
84	C₃	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
85	C₂	—	9	8	no	—
86	C₂	C₂²×D₉⋊C₉	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³×C₃	AGL(1,ℤ/9)
commutator, hypocenter	C₉	C₂⁴×C₉
Frattini	C₃²	C₂³×C₃×D₃
Fitting	C₂³×C₉⋊C₉	C₂
socle	C₂³×C₃²	C₃×D₃
prime radical	C₂³×C₃×D₉	C₃
cosocle	C₃×C₉	C₂⁴×C₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂³×C₃

Complements

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

N	H ≅ G/N	type
1. C₂³×C₉⋊C₉	C₂	semidirect
2. C₂²×D₉⋊C₉	C₂	direct (N × H)
5. C₂²×C₉⋊C₉	C₂²	semidirect
6. C₂×D₉⋊C₉	C₂²	direct (N × H)
12. C₂×C₉⋊C₉	C₂³	semidirect
13. D₉⋊C₉	C₂³	direct (N × H)
16. C₂³×D₉	C₉	semidirect
22. C₉⋊C₉	C₂⁴	semidirect
29. C₂³×C₉	C₂×C₉	semidirect
30. C₂²×D₉	C₂×C₉	semidirect
44. C₂²×C₉	C₂²×C₉	semidirect
45. C₂×D₉	C₂²×C₉	semidirect
60. C₂×C₉	C₂³×C₉	semidirect
61. D₉	C₂³×C₉	semidirect
72. C₉	C₂⁴×C₉	semidirect
74. C₂³	D₉⋊C₉	direct (N × H)
81. C₂²	C₂×D₉⋊C₉	direct (N × H)
86. C₂	C₂²×D₉⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₉⋊C₉	2
C₂²×D₉⋊C₉	2
C₂³×D₃×C₉	3
C₂³×C₃×D₉	3

Subgroups — C23×D9⋊C9 #13048186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₉⋊C₉ #13048186