Finite Group Databasebeta

← C3×C11×A4×C13 #19104241

Subgroups — C3×C11×A4×C13 #19104241

Order 5148.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C11×C13C311yesmaximal, characteristic, complemented
2C11×A4×C13C313yesmaximal, direct product factor
3C32×C11×C13—41nomaximal, Hall
4C2×C3×C11×C13—31no—
5C22×C11×C13C3211yescharacteristic, complemented, Hall
6C3×A4×C13C1111yesmaximal, characteristic, direct product factor, Hall
7C3×C11×C13—43no—
8C3×C11×C13A411yescharacteristic, direct product factor
9C3×C11×A4C1311yesmaximal, characteristic, direct product factor, Hall
10C2×C11×C13—31no—
11C22×C3×C13C3×C1111yescharacteristic, complemented
12A4×C13C3×C1113yesdirect product factor
13C11×C13C3×A411yescharacteristic, direct product factor, Hall
14C22×C3×C11C3×C1311yescharacteristic, complemented
15C11×A4C3×C1313yesdirect product factor
16C32×C13—41noHall
17C32×C11—41noHall
18C2×C3×C13—31no—
19C2×C3×C11—31no—
20C22×C13C32×C1111yescharacteristic, complemented, Hall
21C22×C11C32×C1311yescharacteristic, complemented, Hall
22C3×C13—43no—
23C3×C13C11×A411yescharacteristic, direct product factor
24C3×A4C11×C1311yescharacteristic, direct product factor, Hall
25C3×C11—43no—
26C3×C11A4×C1311yescharacteristic, direct product factor
27C2×C13—31no—
28C2×C11—31no—
29C13C3×C11×A411yescharacteristic, direct product factor, Sylow
30C22×C3C3×C11×C1311yescharacteristic, complemented
31A4C3×C11×C1313yesdirect product factor
32C11C3×A4×C1311yescharacteristic, direct product factor, Sylow
33C32—41noSylow
34C2×C3—31no—
35C22C32×C11×C1311yescharacteristic, complemented, Sylow
36C3—43no—
37C3C11×A4×C1311yescharacteristic, direct product factor
38C2—31no—
subgroupG/H
center, hypercenterC3×C11×C13A4
commutator, hypocenterC22C32×C11×C13
FrattiniC1G
Fitting, socleC22×C3×C11×C13C3
LCSG ▷ C22
UCSC1 ◁ C3×C11×C13

Complements

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

NH ≅ G/Ntype
1. C22×C3×C11×C13C3semidirect
2. C11×A4×C13C3direct (N × H)
5. C22×C11×C13C32semidirect
6. C3×A4×C13C11direct (N × H)
8. C3×C11×C13A4direct (N × H)
9. C3×C11×A4C13direct (N × H)
11. C22×C3×C13C3×C11semidirect
12. A4×C13C3×C11direct (N × H)
13. C11×C13C3×A4direct (N × H)
14. C22×C3×C11C3×C13semidirect
15. C11×A4C3×C13direct (N × H)
20. C22×C13C32×C11semidirect
21. C22×C11C32×C13semidirect
23. C3×C13C11×A4direct (N × H)
24. C3×A4C11×C13direct (N × H)
26. C3×C11A4×C13direct (N × H)
29. C13C3×C11×A4direct (N × H)
30. C22×C3C3×C11×C13semidirect
31. A4C3×C11×C13direct (N × H)
32. C11C3×A4×C13direct (N × H)
35. C22C32×C11×C13semidirect
37. C3C11×A4×C13direct (N × H)