Finite Group Databasebeta

← D23×D117 #24924490

Subgroups — D23×D117 #24924490

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D2691C211yesmaximal, characteristic, complemented
2C23×D117C211yesmaximal, characteristic, complemented
3C9×C13×D23C211yesmaximal, characteristic, complemented
4D23×D39—31nomaximal
5C9×C13×C23C2211yescharacteristic, complemented, Hall
6D897—31no—
7C23×D39—31no—
8C3×C13×D23D311yescharacteristic
9D13×D23—91noHall
10C3×C13×C23C2×D311yescharacteristic
11D9×D23—131nomaximal, Hall
12D299—91no—
13C13×D23D911yescharacteristic, complemented
14C23×D13—91no—
15C2×D117—231nomaximal, Hall
16D207—131no—
17C9×D23D1311yescharacteristic, complemented
18D9×C23—131no—
19C13×C23C2×D911yescharacteristic, complemented, Hall
20D3×D23—391no—
21C2×C9×C13—231no—
22D117—231no—
23D117D2311yescharacteristic, direct product factor
24C9×C23C2×D1311yescharacteristic, complemented, Hall
25C2×D39—691no—
26D69—391no—
27C3×D23D3911yescharacteristic
28D3×C23—391no—
29C9×C13C2×D2311yescharacteristic, complemented, Hall
30C2×D23—1171noHall
31C2×C3×C13—231no—
32D39—31no—
33D39—691no—
34C3×C23C2×D3911yescharacteristic
35C2×D13—2071noHall
36C2×C23—1171no—
37D23—1171no—
38D23D11711yescharacteristic, direct product factor
39C3×C13D3×D2311yescharacteristic
40C2×D9—2991noHall
41C2×C13—231no—
42D13—91no—
43D13—2071no—
44C23C2×D11711yescharacteristic, complemented, Sylow
45C2×C9—231no—
46D9—131no—
47D9—2991no—
48C13D9×D2311yescharacteristic, complemented, Sylow
49C2×D3—8971no—
50C9D13×D2311yescharacteristic, complemented, Sylow
51C2×C3—231no—
52D3—391no—
53D3—8971no—
54C22—26911noSylow
55C3D23×D3911yescharacteristic
56C2—231no—
57C2—1171no—
58C2—26911no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C13×C23C22
FrattiniC3D23×D39
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. C23×D117C2semidirect
3. C9×C13×D23C2semidirect
5. C9×C13×C23C22semidirect
13. C13×D23D9semidirect
17. C9×D23D13semidirect
19. C13×C23C2×D9semidirect
23. D117D23direct (N × H)
24. C9×C23C2×D13semidirect
29. C9×C13C2×D23semidirect
38. D23D117direct (N × H)
44. C23C2×D117semidirect
48. C13D9×D23semidirect
50. C9D13×D23semidirect