Finite Group Databasebeta

← C23×C3⋊(C3⋊D9) #13049357

Subgroups — C23×C3⋊(C3⋊D9) #13049357

Order 1296.

3350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×C9C211yesmaximal, characteristic, complemented
2C22×C3⋊(C3⋊D9)C2114yesmaximal, direct product factor
3C23×C3⋊(C3⋊D3)—31nomaximal
4C23×C3⋊D9—312nomaximal
5C22×C32×C9C2217yescomplemented
6C2×C3⋊(C3⋊D9)C22128yesdirect product factor
7C23×C33D311yescharacteristic
8C22×C3⋊(C3⋊D3)—314no—
9C23×C3×C9D3112yescomplemented
10C22×C3⋊D9—3168no—
11C2×C32×C9C2317yescomplemented
12C3⋊(C3⋊D9)C2318yesdirect product factor
13C23×C3⋊D3—99no—
14C23×C3⋊D3—94no—
15C23×D9—99no—
16C22×C33C2×D317yes—
17C2×C3⋊(C3⋊D3)—328no—
18C22×C3×C9C2×D3184yescomplemented
19C2×C3⋊D9—3336no—
20C32×C9C2411yescharacteristic, complemented, Sylow
21C23×C32D919yescomplemented
22C23×C32C3⋊D314yes—
23C22×C3⋊D3—9126no—
24C22×C3⋊D3—956no—
25C23×C9C3⋊D319yescomplemented
26C22×D9—9126no—
27C2×C33C22×D317yes—
28C3⋊(C3⋊D3)—38no—
29C2×C3×C9C22×D3184yescomplemented
30C3⋊D9—396no—
31C23×D3—2712no—
32C23×D3—271no—
33C22×C32C2×D9163yescomplemented
34C22×C32C2×C3⋊D3128yes—
35C2×C3⋊D3—9252no—
36C2×C3⋊D3—9112no—
37C22×C9C2×C3⋊D3163yescomplemented
38C2×D9—9252no—
39C33C23×D311yescharacteristic
40C3×C9C23×D3112yescomplemented
41C23×C3C3⋊D9112yescomplemented
42C23×C3C3⋊(C3⋊D3)11yescharacteristic
43C22×D3—27168no—
44C22×D3—2714no—
45C2×C32C22×D9163yescomplemented
46C2×C32C22×C3⋊D3128yes—
47C3⋊D3—932no—
48C3⋊D3—972no—
49C2×C9C22×C3⋊D3163yescomplemented
50D9—972no—
51C24—811noSylow
52C22×C3C2×C3⋊D9184yescomplemented
53C22×C3C2×C3⋊(C3⋊D3)17yes—
54C2×D3—27336no—
55C2×D3—2728no—
56C32C23×D919yescomplemented
57C32C23×C3⋊D314yes—
58C9C23×C3⋊D319yescomplemented
59C23—8114no—
60C23C3⋊(C3⋊D9)11yescharacteristic, direct product factor
61C2×C3C22×C3⋊D9184yescomplemented
62C2×C3C22×C3⋊(C3⋊D3)17yes—
63D3—278no—
64D3—2796no—
65C22—8128no—
66C22C2×C3⋊(C3⋊D9)17yesdirect product factor
67C3C23×C3⋊D9112yescomplemented
68C3C23×C3⋊(C3⋊D3)11yescharacteristic
69C2—818no—
70C2C22×C3⋊(C3⋊D9)17yesdirect product factor
subgroupG/H
center, hypercenterC23C3⋊(C3⋊D9)
commutator, cosocle, hypocenterC32×C9C24
FrattiniC3C23×C3⋊(C3⋊D3)
FittingC23×C32×C9C2
socleC23×C33D3
LCSG ▷ C32×C9
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×C32×C9C2semidirect
2. C22×C3⋊(C3⋊D9)C2direct (N × H)
5. C22×C32×C9C22semidirect
6. C2×C3⋊(C3⋊D9)C22direct (N × H)
9. C23×C3×C9D3semidirect
11. C2×C32×C9C23semidirect
12. C3⋊(C3⋊D9)C23direct (N × H)
18. C22×C3×C9C2×D3semidirect
20. C32×C9C24semidirect
21. C23×C32D9semidirect
25. C23×C9C3⋊D3semidirect
29. C2×C3×C9C22×D3semidirect
33. C22×C32C2×D9semidirect
37. C22×C9C2×C3⋊D3semidirect
40. C3×C9C23×D3semidirect
41. C23×C3C3⋊D9semidirect
45. C2×C32C22×D9semidirect
49. C2×C9C22×C3⋊D3semidirect
52. C22×C3C2×C3⋊D9semidirect
56. C32C23×D9semidirect
58. C9C23×C3⋊D3semidirect
60. C23C3⋊(C3⋊D9)direct (N × H)
61. C2×C3C22×C3⋊D9semidirect
66. C22C2×C3⋊(C3⋊D9)direct (N × H)
67. C3C23×C3⋊D9semidirect
70. C2C22×C3⋊(C3⋊D9)direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×C92
C22×C3⋊(C3⋊D9)2
C23×C3⋊(C3⋊D3)3
C23×C3⋊D93