Finite Group Databasebeta

← C23×Dic254 #22550700

Subgroups — C23×Dic254 #22550700

Order 8128.

850 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic254C2128yesmaximal, direct product factor
2C23×Dic127C212yesmaximal
3C23×C4×C127C211yesmaximal, characteristic
4C2×Dic254C221112yesdirect product factor
5C22×Dic127C22128yes—
6C24×C127C2211yescharacteristic
7C22×C4×C127C22114yes—
8Dic254C23164yesdirect product factor
9C2×Dic127C23156yes—
10C23×C127Q818yescomplemented
11C23×C127C2317yes—
12C2×C4×C127C23128yes—
13C22×C127C2×Q8128yescomplemented
14C22×C127C2417yes—
15C4×C127C2418yes—
16Dic127C24116yes—
17C2×C127C22×Q8114yescomplemented
18C2×C127C2511yescharacteristic
19C127C23×Q811yescharacteristic, complemented, Sylow
20C23×Q8—1271nomaximal, Sylow
21C22×Q8—12728no—
22C23×C4—1272no—
23C23×C4D12711yescharacteristic
24C24C2×D12711yescharacteristic
25C2×Q8—127112no—
26C22×C4—12728no—
27C22×C4C2×D127114yes—
28C23Dic25418yesdirect product factor
29C23C22×D12717yes—
30Q8—12764no—
31C2×C4—12756no—
32C2×C4C22×D127128yes—
33C22C2×Dic254128yesdirect product factor
34C22C23×D12717yes—
35C4—12716no—
36C4C23×D12718yes—
37C2C22×Dic254114yesdirect product factor
38C2C24×D12711yescharacteristic
subgroupG/H
centerC24C2×D127
commutatorC2×C127C25
FrattiniC2C24×D127
FittingC23×C4×C127C2
socleC24×C127C22
hypercenterC23×C4D127
hypocenterC127C23×Q8
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×Dic254C2direct (N × H)
4. C2×Dic254C22direct (N × H)
8. Dic254C23direct (N × H)
10. C23×C127Q8semidirect
13. C22×C127C2×Q8semidirect
17. C2×C127C22×Q8semidirect
19. C127C23×Q8semidirect
28. C23Dic254direct (N × H)
33. C22C2×Dic254direct (N × H)
37. C2C22×Dic254direct (N × H)