Finite Group Databasebeta

← C23×Dic226 #20299422

Subgroups — C23×Dic226 #20299422

Order 7232.

850 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic226C2128yesmaximal, direct product factor
2C23×Dic113C212yesmaximal
3C23×C4×C113C211yesmaximal, characteristic
4C2×Dic226C221112yesdirect product factor
5C22×Dic113C22128yes—
6C24×C113C2211yescharacteristic
7C22×C4×C113C22114yes—
8C23×C113Q818yescomplemented
9C23×C113C2317yes—
10C2×C4×C113C23128yes—
11C2×Dic113C23156yes—
12Dic226C23164yesdirect product factor
13C22×C113C2×Q8128yescomplemented
14C22×C113C2417yes—
15C4×C113C2418yes—
16Dic113C24116yes—
17C2×C113C22×Q8114yescomplemented
18C2×C113C2511yescharacteristic
19C113C23×Q811yescharacteristic, complemented, Sylow
20C23×Q8—1131nomaximal, Sylow
21C22×Q8—11328no—
22C23×C4—1132no—
23C23×C4D11311yescharacteristic
24C24C2×D11311yescharacteristic
25C2×Q8—113112no—
26C22×C4—11328no—
27C22×C4C2×D113114yes—
28C23Dic22618yesdirect product factor
29C23C22×D11317yes—
30Q8—11364no—
31C2×C4—11356no—
32C2×C4C22×D113128yes—
33C22C2×Dic226128yesdirect product factor
34C22C23×D11317yes—
35C4—11316no—
36C4C23×D11318yes—
37C2C22×Dic226114yesdirect product factor
38C2C24×D11311yescharacteristic
subgroupG/H
centerC24C2×D113
commutatorC2×C113C25
FrattiniC2C24×D113
FittingC23×C4×C113C2
socleC24×C113C22
hypercenterC23×C4D113
hypocenterC113C23×Q8
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×Dic226C2direct (N × H)
4. C2×Dic226C22direct (N × H)
8. C23×C113Q8semidirect
12. Dic226C23direct (N × H)
13. C22×C113C2×Q8semidirect
17. C2×C113C22×Q8semidirect
19. C113C23×Q8semidirect
28. C23Dic226direct (N × H)
33. C22C2×Dic226direct (N × H)
37. C2C22×Dic226direct (N × H)