Finite Group Databasebeta

← C23×#11744751 #20299355

Subgroups — C23×#11744751 #20299355

Order 7232.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11744751C2114yesmaximal, direct product factor
2C23×C4×C113C211yesmaximal, characteristic
3C2×#11744751C22128yesdirect product factor
4C24×C113C411yescharacteristic
5C22×C4×C113C417yes—
6C22×C4×C113C2217yes—
7C23×C113C818yescomplemented
8C23×C113C2×C417yes—
9C2×C4×C113C2×C4121yes—
10C2×C4×C113C2317yes—
11#11744751C2318yesdirect product factor
12C22×C113C2×C8128yescomplemented
13C22×C113C22×C417yes—
14C4×C113C22×C417yes—
15C4×C113C2411yescharacteristic
16C2×C113C22×C8114yescomplemented
17C2×C113C23×C411yescharacteristic
18C113C23×C811yescharacteristic, complemented, Sylow
19C23×C8—1131nomaximal, Sylow
20C23×C4D11311yescharacteristic
21C22×C8—11314no—
22C24Dic11311yescharacteristic
23C22×C4Dic11317yes—
24C22×C4C2×D11317yes—
25C2×C8—11328no—
26C23#1174475118yesdirect product factor
27C23C2×Dic11317yes—
28C2×C4C2×Dic113121yes—
29C2×C4C22×D11317yes—
30C8—1138no—
31C22C2×#11744751128yesdirect product factor
32C22C22×Dic11317yes—
33C4C22×Dic11317yes—
34C4C23×D11311yescharacteristic
35C2C22×#11744751114yesdirect product factor
36C2C23×Dic11311yescharacteristic
subgroupG/H
center, hypercenterC23×C4D113
commutator, hypocenterC113C23×C8
FrattiniC4C23×D113
FittingC23×C4×C113C2
socleC24×C113C4
LCSG ▷ C113
UCSC1 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#11744751C2direct (N × H)
3. C2×#11744751C22direct (N × H)
7. C23×C113C8semidirect
11. #11744751C23direct (N × H)
12. C22×C113C2×C8semidirect
16. C2×C113C22×C8semidirect
18. C113C23×C8semidirect
26. C23#11744751direct (N × H)
31. C22C2×#11744751direct (N × H)
35. C2C22×#11744751direct (N × H)