Finite Group Databasebeta

← D9×D299 #24924493

Subgroups — D9×D299 #24924493

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D2691C211yesmaximal, characteristic, complemented
2C13×D9×C23C211yesmaximal, characteristic, complemented
3C9×D299C211yesmaximal, characteristic, complemented
4D3×D299—31nomaximal
5C9×C13×C23C2211yescharacteristic, complemented, Hall
6D897—31no—
7D3×C13×C23—31no—
8C3×D299D311yescharacteristic
9C2×D299—91noHall
10C3×C13×C23C2×D311yescharacteristic
11D9×D23—131nomaximal, Hall
12C2×C13×C23—91no—
13D299—91no—
14D299D911yescharacteristic, direct product factor
15D9×D13—231nomaximal, Hall
16D207—131no—
17C9×D23—131no—
18D9×C23D1311yescharacteristic, complemented
19C13×C23C2×D911yescharacteristic, complemented, Hall
20D3×D23—391no—
21D117—231no—
22C9×D13—231no—
23C13×D9D2311yescharacteristic, complemented
24C9×C23C2×D1311yescharacteristic, complemented, Hall
25D3×D13—691no—
26D69—391no—
27C3×D23—131no—
28D3×C23—31no—
29C9×C13C2×D2311yescharacteristic, complemented, Hall
30C2×D23—1171noHall
31D39—691no—
32C3×D13—231no—
33D3×C13—31no—
34C3×C23D3×D1311yescharacteristic
35C2×D13—2071noHall
36C2×C23—91no—
37D23—131no—
38D23—1171no—
39C3×C13D3×D2311yescharacteristic
40C2×D9—2991noHall
41C2×C13—91no—
42D13—231no—
43D13—2071no—
44C23D9×D1311yescharacteristic, complemented, Sylow
45C2×C9—2991no—
46D9—2991no—
47D9D29911yescharacteristic, direct product factor
48C13D9×D2311yescharacteristic, complemented, Sylow
49C2×D3—8971no—
50C9C2×D29911yescharacteristic, complemented, Sylow
51C2×C3—2991no—
52D3—31no—
53D3—8971no—
54C22—26911noSylow
55C3D3×D29911yescharacteristic
56C2—91no—
57C2—2991no—
58C2—26911no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C13×C23C22
FrattiniC3D3×D299
socleC3×C13×C23C2×D3
LCSG ▷ C9×C13×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. D2691C2semidirect
2. C13×D9×C23C2semidirect
3. C9×D299C2semidirect
5. C9×C13×C23C22semidirect
14. D299D9direct (N × H)
18. D9×C23D13semidirect
19. C13×C23C2×D9semidirect
23. C13×D9D23semidirect
24. C9×C23C2×D13semidirect
29. C9×C13C2×D23semidirect
44. C23D9×D13semidirect
47. D9D299direct (N × H)
48. C13D9×D23semidirect
50. C9C2×D299semidirect