Finite Group Databasebeta

← C2×#15690807 #20261275

Subgroups — C2×#15690807 #20261275

Order 6208.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D388C216yesmaximal, complemented
2#15690807C218yesmaximal, direct product factor
3C2×C42×C97C211yesmaximal, characteristic, complemented
4C23×D97C2214yes—
5C2×D388—224no—
6C2×D388C22124yescomplemented
7C22×C4×C97C2213yes—
8C42×C97C2214yescomplemented
9C23×C97C2311yescharacteristic
10C22×D97—224no—
11C22×D97C2318yes—
12C2×C4×C97D4112yescomplemented
13C2×C4×C97C2316yes—
14D388—248no—
15C22×C97C2×D416yes—
16C22×C97C2411yescharacteristic
17C2×D97—224no—
18C2×D97—416no—
19C4×C97C2×D4112yescomplemented
20C2×C97#12714yescomplemented
21C2×C97C22×D413yes—
22D97—48no—
23C97C2×#12711yescharacteristic, complemented, Sylow
24C2×#127—971nomaximal, Sylow
25C22×D4—976no—
26#127—978no—
27C2×C42D9711yescharacteristic, complemented
28C24—974no—
29C2×D4—9724no—
30C2×D4—19424no—
31C22×C4C2×D9713yes—
32C42C2×D9714yescomplemented
33C23—978no—
34C23—19424no—
35C23C22×D9711yescharacteristic
36D4—19448no—
37C2×C4D388112yescomplemented
38C2×C4C22×D9716yes—
39C22—38816no—
40C22—19424no—
41C22C2×D38816yes—
42C22C23×D9711yescharacteristic
43C4C2×D388112yescomplemented
44C2—3888no—
45C2#1569080714yesdirect product factor
46C2C22×D38813yes—
subgroupG/H
centerC23C22×D97
commutatorC22×C97C24
FrattiniC22C23×D97
FittingC2×C42×C97C2
socleC23×C97C23
hypercenterC2×C42D97
hypocenterC97C2×#127
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×D388C2semidirect
2. #15690807C2direct (N × H)
3. C2×C42×C97C2semidirect
6. C2×D388C22semidirect
8. C42×C97C22semidirect
12. C2×C4×C97D4semidirect
19. C4×C97C2×D4semidirect
20. C2×C97#127semidirect
23. C97C2×#127semidirect
27. C2×C42D97semidirect
32. C42C2×D97semidirect
37. C2×C4D388semidirect
43. C4C2×D388semidirect
45. C2#15690807direct (N × H)