Subgroups — C₂³×C₃×C₉⋊C₉ #14518554

Order 1944.

1440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉⋊C₉	C₂	1	7	yes	maximal, direct product factor
2	C₂³×C₃²×C₉	C₃	1	3	yes	maximal
3	C₂³×C₃²×C₉	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₉⋊C₉	C₃	1	9	yes	maximal, direct product factor
5	C₂×C₃×C₉⋊C₉	C₂²	1	7	yes	direct product factor
6	C₂²×C₃²×C₉	C₂×C₃	1	21	yes	—
7	C₂²×C₃²×C₉	C₂×C₃	1	7	yes	—
8	C₂²×C₉⋊C₉	C₂×C₃	1	63	yes	direct product factor
9	C₃×C₉⋊C₉	C₂³	1	1	yes	characteristic, direct product factor, Sylow
10	C₂³×C₃³	C₃²	1	1	yes	characteristic
11	C₂³×C₃×C₉	—	3	9	no	—
12	C₂³×C₃×C₉	C₉	1	9	yes	complemented
13	C₂³×C₃×C₉	C₃²	1	9	yes	—
14	C₂³×C₃×C₉	C₃²	1	3	yes	—
15	C₂×C₃²×C₉	C₂²×C₃	1	21	yes	—
16	C₂×C₃²×C₉	C₂²×C₃	1	7	yes	—
17	C₂×C₉⋊C₉	C₂²×C₃	1	63	yes	direct product factor
18	C₂²×C₃³	C₂×C₃²	1	7	yes	—
19	C₂²×C₃×C₉	—	3	63	no	—
20	C₂²×C₃×C₉	C₂×C₉	1	63	yes	complemented
21	C₂²×C₃×C₉	C₂×C₃²	1	63	yes	—
22	C₂²×C₃×C₉	C₂×C₃²	1	21	yes	—
23	C₃²×C₉	C₂³×C₃	1	3	yes	—
24	C₃²×C₉	C₂³×C₃	1	1	yes	characteristic
25	C₉⋊C₉	C₂³×C₃	1	9	yes	direct product factor
26	C₂³×C₃²	C₃×C₉	1	3	yes	—
27	C₂³×C₃²	3₋¹⁺²	1	9	yes	—
28	C₂³×C₃²	C₃³	1	1	yes	characteristic
29	C₂³×C₉	—	3	9	no	—
30	C₂³×C₉	C₃×C₉	1	9	yes	complemented
31	C₂×C₃³	C₂²×C₃²	1	7	yes	—
32	C₂×C₃×C₉	—	3	63	no	—
33	C₂×C₃×C₉	C₂²×C₉	1	63	yes	complemented
34	C₂×C₃×C₉	C₂²×C₃²	1	63	yes	—
35	C₂×C₃×C₉	C₂²×C₃²	1	21	yes	—
36	C₂²×C₃²	C₂×C₃×C₉	1	21	yes	—
37	C₂²×C₃²	C₂×3₋¹⁺²	1	63	yes	—
38	C₂²×C₃²	C₂×C₃³	1	7	yes	—
39	C₂²×C₉	—	3	63	no	—
40	C₂²×C₉	C₂×C₃×C₉	1	63	yes	complemented
41	C₃³	C₂³×C₃²	1	1	yes	characteristic
42	C₃×C₉	—	3	9	no	—
43	C₃×C₉	C₂³×C₉	1	9	yes	complemented
44	C₃×C₉	C₂³×C₃²	1	9	yes	—
45	C₃×C₉	C₂³×C₃²	1	3	yes	—
46	C₂³×C₃	C₉⋊C₉	1	9	yes	direct product factor
47	C₂³×C₃	C₃²×C₉	1	1	yes	characteristic
48	C₂³×C₃	C₃×3₋¹⁺²	1	3	yes	—
49	C₂×C₃²	C₂²×C₃×C₉	1	21	yes	—
50	C₂×C₃²	C₂²×3₋¹⁺²	1	63	yes	—
51	C₂×C₃²	C₂²×C₃³	1	7	yes	—
52	C₂×C₉	—	3	63	no	—
53	C₂×C₉	C₂²×C₃×C₉	1	63	yes	complemented
54	C₂²×C₃	C₂×C₉⋊C₉	1	63	yes	direct product factor
55	C₂²×C₃	C₂×C₃²×C₉	1	7	yes	—
56	C₂²×C₃	C₂×C₃×3₋¹⁺²	1	21	yes	—
57	C₃²	C₂³×C₃×C₉	1	3	yes	—
58	C₃²	C₂³×3₋¹⁺²	1	9	yes	—
59	C₃²	C₂³×C₃³	1	1	yes	characteristic
60	C₉	—	3	9	no	—
61	C₉	C₂³×C₃×C₉	1	9	yes	complemented
62	C₂³	C₃×C₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₃	C₂²×C₉⋊C₉	1	63	yes	direct product factor
64	C₂×C₃	C₂²×C₃²×C₉	1	7	yes	—
65	C₂×C₃	C₂²×C₃×3₋¹⁺²	1	21	yes	—
66	C₂²	C₂×C₃×C₉⋊C₉	1	7	yes	direct product factor
67	C₃	C₂³×C₉⋊C₉	1	9	yes	direct product factor
68	C₃	C₂³×C₃²×C₉	1	1	yes	characteristic
69	C₃	C₂³×C₃×3₋¹⁺²	1	3	yes	—
70	C₂	C₂²×C₃×C₉⋊C₉	1	7	yes	direct product factor

	subgroup	G/H
center, socle, prime radical	C₂³×C₃³	C₃²
commutator	C₃	C₂³×C₃²×C₉
Frattini, cosocle	C₃²	C₂³×C₃³
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂³×C₃³ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₉⋊C₉	C₂	direct (N × H)
4. C₂³×C₉⋊C₉	C₃	direct (N × H)
5. C₂×C₃×C₉⋊C₉	C₂²	direct (N × H)
8. C₂²×C₉⋊C₉	C₂×C₃	direct (N × H)
9. C₃×C₉⋊C₉	C₂³	direct (N × H)
12. C₂³×C₃×C₉	C₉	semidirect
17. C₂×C₉⋊C₉	C₂²×C₃	direct (N × H)
20. C₂²×C₃×C₉	C₂×C₉	semidirect
25. C₉⋊C₉	C₂³×C₃	direct (N × H)
30. C₂³×C₉	C₃×C₉	semidirect
33. C₂×C₃×C₉	C₂²×C₉	semidirect
40. C₂²×C₉	C₂×C₃×C₉	semidirect
43. C₃×C₉	C₂³×C₉	semidirect
46. C₂³×C₃	C₉⋊C₉	direct (N × H)
53. C₂×C₉	C₂²×C₃×C₉	semidirect
54. C₂²×C₃	C₂×C₉⋊C₉	direct (N × H)
61. C₉	C₂³×C₃×C₉	semidirect
62. C₂³	C₃×C₉⋊C₉	direct (N × H)
63. C₂×C₃	C₂²×C₉⋊C₉	direct (N × H)
66. C₂²	C₂×C₃×C₉⋊C₉	direct (N × H)
67. C₃	C₂³×C₉⋊C₉	direct (N × H)
70. C₂	C₂²×C₃×C₉⋊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
C₂²×C₃×C₉⋊C₉	2
C₂³×C₃²×C₉	3
C₂³×C₉⋊C₉	3

Subgroups — C23×C3×C9⋊C9 #14518554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₉⋊C₉ #14518554