Finite Group Databasebeta

← C2×#19104732 #23782205

Subgroups — C2×#19104732 #23782205

Order 10432.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D652C216yesmaximal, complemented
2#19104732C218yesmaximal, direct product factor
3C2×C42×C163C211yesmaximal, characteristic, complemented
4C23×D163C2214yes—
5C2×D652—224no—
6C2×D652C22124yescomplemented
7C22×C4×C163C2213yes—
8C42×C163C2214yescomplemented
9C22×D163—224no—
10C22×D163C2318yes—
11D652—248no—
12C23×C163C2311yescharacteristic
13C2×C4×C163D4112yescomplemented
14C2×C4×C163C2316yes—
15C22×C163C2×D416yes—
16C22×C163C2411yescharacteristic
17C2×D163—224no—
18C2×D163—416no—
19C4×C163C2×D4112yescomplemented
20C2×C163#12714yescomplemented
21C2×C163C22×D413yes—
22D163—48no—
23C163C2×#12711yescharacteristic, complemented, Sylow
24C2×#127—1631nomaximal, Sylow
25C22×D4—1636no—
26#127—1638no—
27C2×C42D16311yescharacteristic, complemented
28C24—1634no—
29C2×D4—32624no—
30C2×D4—16324no—
31C22×C4C2×D16313yes—
32C42C2×D16314yescomplemented
33C23—32624no—
34C23—1638no—
35C23C22×D16311yescharacteristic
36D4—32648no—
37C2×C4D652112yescomplemented
38C2×C4C22×D16316yes—
39C22—32624no—
40C22—65216no—
41C22C2×D65216yes—
42C22C23×D16311yescharacteristic
43C4C2×D652112yescomplemented
44C2—6528no—
45C2#1910473214yesdirect product factor
46C2C22×D65213yes—
subgroupG/H
centerC23C22×D163
commutator, cosocleC22×C163C24
FrattiniC22C23×D163
FittingC2×C42×C163C2
socleC23×C163C23
hypercenterC2×C42D163
hypocenterC163C2×#127
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×D652C2semidirect
2. #19104732C2direct (N × H)
3. C2×C42×C163C2semidirect
6. C2×D652C22semidirect
8. C42×C163C22semidirect
13. C2×C4×C163D4semidirect
19. C4×C163C2×D4semidirect
20. C2×C163#127semidirect
23. C163C2×#127semidirect
27. C2×C42D163semidirect
32. C42C2×D163semidirect
37. C2×C4D652semidirect
43. C4C2×D652semidirect
45. C2#19104732direct (N × H)