Finite Group Databasebeta

← C22×C3×C11×C13⋊C3 #19104242

Subgroups — C22×C3×C11×C13⋊C3 #19104242

Order 5148.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C11×C13⋊C3C213yesmaximal, direct product factor
2C22×C3×C11×C13C311yesmaximal, characteristic, complemented
3C22×C11×C13⋊C3C313yesmaximal, direct product factor
4C3×C11×C13⋊C3C2211yescharacteristic, direct product factor, Hall
5C2×C3×C11×C13C2×C313yescomplemented
6C2×C11×C13⋊C3C2×C319yesdirect product factor
7C22×C11×C13C3211yescharacteristic, complemented, Hall
8C22×C3×C13⋊C3C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C11×C13C22×C311yescharacteristic, complemented
10C11×C13⋊C3C22×C313yesdirect product factor
11C22×C32×C11—131nomaximal, Hall
12C2×C11×C13C2×C3213yescomplemented
13C2×C3×C13⋊C3C2×C1113yesdirect product factor
14C2×C32×C11—133no—
15C22×C3×C13C3×C1111yescharacteristic, complemented
16C22×C13⋊C3C3×C1113yesdirect product factor
17C11×C13C22×C3211yescharacteristic, complemented, Hall
18C22×C3×C11—133no—
19C22×C3×C11C13⋊C311yescharacteristic, direct product factor
20C3×C13⋊C3C22×C1111yescharacteristic, direct product factor, Hall
21C32×C11—131noHall
22C2×C3×C13C2×C3×C1113yescomplemented
23C2×C13⋊C3C2×C3×C1119yesdirect product factor
24C2×C3×C11—139no—
25C2×C3×C11C2×C13⋊C313yesdirect product factor
26C22×C13C32×C1111yescharacteristic, complemented, Hall
27C22×C11C3×C13⋊C311yescharacteristic, direct product factor, Hall
28C3×C13C22×C3×C1111yescharacteristic, complemented
29C13⋊C3C22×C3×C1113yesdirect product factor
30C22×C32—131noHall
31C3×C11—133no—
32C3×C11C22×C13⋊C311yescharacteristic, direct product factor
33C2×C13C2×C32×C1113yescomplemented
34C2×C11C2×C3×C13⋊C313yesdirect product factor
35C2×C32—133no—
36C13C22×C32×C1111yescharacteristic, complemented, Sylow
37C22×C3—133no—
38C22×C3C11×C13⋊C311yescharacteristic, direct product factor
39C11C22×C3×C13⋊C311yescharacteristic, direct product factor, Sylow
40C32—131noSylow
41C2×C3—139no—
42C2×C3C2×C11×C13⋊C313yesdirect product factor
43C22C3×C11×C13⋊C311yescharacteristic, direct product factor, Sylow
44C3—133no—
45C3C22×C11×C13⋊C311yescharacteristic, direct product factor
46C2C2×C3×C11×C13⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C3×C11C13⋊C3
commutator, hypocenterC13C22×C32×C11
FrattiniC1G
Fitting, socleC22×C3×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C3×C11

Complements

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

NH ≅ G/Ntype
1. C2×C3×C11×C13⋊C3C2direct (N × H)
2. C22×C3×C11×C13C3semidirect
3. C22×C11×C13⋊C3C3direct (N × H)
4. C3×C11×C13⋊C3C22direct (N × H)
5. C2×C3×C11×C13C2×C3semidirect
6. C2×C11×C13⋊C3C2×C3direct (N × H)
7. C22×C11×C13C32semidirect
8. C22×C3×C13⋊C3C11direct (N × H)
9. C3×C11×C13C22×C3semidirect
10. C11×C13⋊C3C22×C3direct (N × H)
12. C2×C11×C13C2×C32semidirect
13. C2×C3×C13⋊C3C2×C11direct (N × H)
15. C22×C3×C13C3×C11semidirect
16. C22×C13⋊C3C3×C11direct (N × H)
17. C11×C13C22×C32semidirect
19. C22×C3×C11C13⋊C3direct (N × H)
20. C3×C13⋊C3C22×C11direct (N × H)
22. C2×C3×C13C2×C3×C11semidirect
23. C2×C13⋊C3C2×C3×C11direct (N × H)
25. C2×C3×C11C2×C13⋊C3direct (N × H)
26. C22×C13C32×C11semidirect
27. C22×C11C3×C13⋊C3direct (N × H)
28. C3×C13C22×C3×C11semidirect
29. C13⋊C3C22×C3×C11direct (N × H)
32. C3×C11C22×C13⋊C3direct (N × H)
33. C2×C13C2×C32×C11semidirect
34. C2×C11C2×C3×C13⋊C3direct (N × H)
36. C13C22×C32×C11semidirect
38. C22×C3C11×C13⋊C3direct (N × H)
39. C11C22×C3×C13⋊C3direct (N × H)
42. C2×C3C2×C11×C13⋊C3direct (N × H)
43. C22C3×C11×C13⋊C3direct (N × H)
45. C3C22×C11×C13⋊C3direct (N × H)
46. C2C2×C3×C11×C13⋊C3direct (N × H)