Finite Group Databasebeta

← D117⋊D23 #24924494

Subgroups — D117⋊D23 #24924494

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D117C211yesmaximal, characteristic, complemented
2C13×D207C211yesmaximal, characteristic, complemented
3C9×D299C211yesmaximal, characteristic, complemented
4D39⋊D23—31nomaximal
5C9×C13×C23C2211yescharacteristic, complemented, Hall
6C23×D39—31no—
7C13×D69—31no—
8C3×D299D311yescharacteristic
9D13×D23—91noHall
10C3×C13×C23C2×D311yescharacteristic
11D9×D23—131nomaximal, Hall
12D299D911yescharacteristic, complemented
13C13×D23—91no—
14C23×D13—91no—
15D9×D13—231nomaximal, Hall
16D207D1311yescharacteristic, complemented
17C9×D23—131no—
18D9×C23—131no—
19C13×C23C2×D911yescharacteristic, complemented, Hall
20D3×D23—391no—
21D117D2311yescharacteristic, complemented
22C9×D13—231no—
23C13×D9—231no—
24C9×C23C2×D1311yescharacteristic, complemented, Hall
25D3×D13—691no—
26D69—31no—
27C3×D23—131no—
28D3×C23—391no—
29C9×C13C2×D2311yescharacteristic, complemented, Hall
30C2×D23—1171noHall
31D39—31no—
32C3×D13—231no—
33D3×C13—691no—
34C3×C23D3×D1311yescharacteristic
35C2×D13—2071noHall
36C2×C23—1171no—
37D23—91no—
38D23—131no—
39C3×C13D3×D2311yescharacteristic
40C2×D9—2991noHall
41C2×C13—2071no—
42D13—91no—
43D13—231no—
44C23D9×D1311yescharacteristic, complemented, Sylow
45C2×C9—2991no—
46D9—131no—
47D9—231no—
48C13D9×D2311yescharacteristic, complemented, Sylow
49C2×D3—8971no—
50C9D13×D2311yescharacteristic, complemented, Sylow
51C2×C3—2991no—
52D3—391no—
53D3—691no—
54C22—26911noSylow
55C3D39⋊D2311yescharacteristic
56C2—2991no—
57C2—1171no—
58C2—2071no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C13×C23C22
FrattiniC3D39⋊D23
socleC3×C13×C23C2×D3
LCSG ▷ C9×C13×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C23×D117C2semidirect
2. C13×D207C2semidirect
3. C9×D299C2semidirect
5. C9×C13×C23C22semidirect
12. D299D9semidirect
16. D207D13semidirect
19. C13×C23C2×D9semidirect
21. D117D23semidirect
24. C9×C23C2×D13semidirect
29. C9×C13C2×D23semidirect
44. C23D9×D13semidirect
48. C13D9×D23semidirect
50. C9D13×D23semidirect