Finite Group Databasebeta

← C23×#11717579 #20265934

Subgroups — C23×#11717579 #20265934

Order 6464.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11717579C2114yesmaximal, direct product factor
2C23×C4×C101C211yesmaximal, characteristic
3C2×#11717579C22128yesdirect product factor
4C24×C101C411yescharacteristic
5C22×C4×C101C417yes—
6C22×C4×C101C2217yes—
7C23×C101C818yescomplemented
8C23×C101C2×C417yes—
9C2×C4×C101C2×C4121yes—
10C2×C4×C101C2317yes—
11#11717579C2318yesdirect product factor
12C22×C101C2×C8128yescomplemented
13C22×C101C22×C417yes—
14C4×C101C22×C417yes—
15C4×C101C2411yescharacteristic
16C2×C101C22×C8114yescomplemented
17C2×C101C23×C411yescharacteristic
18C101C23×C811yescharacteristic, complemented, Sylow
19C23×C8—1011nomaximal, Sylow
20C23×C4D10111yescharacteristic
21C22×C8—10114no—
22C24Dic10111yescharacteristic
23C22×C4Dic10117yes—
24C22×C4C2×D10117yes—
25C2×C8—10128no—
26C23#1171757918yesdirect product factor
27C23C2×Dic10117yes—
28C2×C4C2×Dic101121yes—
29C2×C4C22×D10117yes—
30C8—1018no—
31C22C2×#11717579128yesdirect product factor
32C22C22×Dic10117yes—
33C4C22×Dic10117yes—
34C4C23×D10111yescharacteristic
35C2C22×#11717579114yesdirect product factor
36C2C23×Dic10111yescharacteristic
subgroupG/H
center, hypercenterC23×C4D101
commutator, hypocenterC101C23×C8
FrattiniC4C23×D101
FittingC23×C4×C101C2
socleC24×C101C4
LCSG ▷ C101
UCSC1 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#11717579C2direct (N × H)
3. C2×#11717579C22direct (N × H)
7. C23×C101C8semidirect
11. #11717579C23direct (N × H)
12. C22×C101C2×C8semidirect
16. C2×C101C22×C8semidirect
18. C101C23×C8semidirect
26. C23#11717579direct (N × H)
31. C22C2×#11717579direct (N × H)
35. C2C22×#11717579direct (N × H)