Finite Group Databasebeta

← C32×C11×C13×D7 #31825096

Subgroups — C32×C11×C13×D7 #31825096

Order 18018.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11×C13C211yesmaximal, characteristic, complemented, Hall
2C3×C11×C13×D7C314yesmaximal, direct product factor
3C3×C7×C11×C13C2×C314yescomplemented
4C2×C32×C11×C13—71nomaximal, Hall
5C11×C13×D7C3211yescharacteristic, direct product factor, Hall
6C32×C13×D7C1111yesmaximal, characteristic, direct product factor, Hall
7C32×C11×D7C1311yesmaximal, characteristic, direct product factor, Hall
8C32×C11×C13D711yescharacteristic, direct product factor, Hall
9C7×C11×C13C2×C3211yescharacteristic, complemented, Hall
10C2×C3×C11×C13—74no—
11C32×C7×C13C2×C1111yescharacteristic, complemented, Hall
12C32×C7×C11C2×C1311yescharacteristic, complemented, Hall
13C3×C13×D7C3×C1114yesdirect product factor
14C3×C11×D7C3×C1314yesdirect product factor
15C3×C11×C13C3×D714yesdirect product factor
16C2×C11×C13—71noHall
17C3×C7×C13C2×C3×C1114yescomplemented
18C2×C32×C13—71noHall
19C3×C7×C11C2×C3×C1314yescomplemented
20C2×C32×C11—71noHall
21C13×D7C32×C1111yescharacteristic, direct product factor, Hall
22C11×D7C32×C1311yescharacteristic, direct product factor, Hall
23C11×C13C32×D711yescharacteristic, direct product factor, Hall
24C32×D7C11×C1311yescharacteristic, direct product factor, Hall
25C32×C13C11×D711yescharacteristic, direct product factor, Hall
26C32×C11C13×D711yescharacteristic, direct product factor, Hall
27C7×C13C2×C32×C1111yescharacteristic, complemented, Hall
28C2×C3×C13—74no—
29C7×C11C2×C32×C1311yescharacteristic, complemented, Hall
30C2×C3×C11—74no—
31C32×C7C2×C11×C1311yescharacteristic, complemented, Hall
32C3×D7C3×C11×C1314yesdirect product factor
33C3×C13C3×C11×D714yesdirect product factor
34C3×C11C3×C13×D714yesdirect product factor
35C2×C13—71noHall
36C2×C11—71noHall
37C3×C7C2×C3×C11×C1314yescomplemented
38C2×C32—71noHall
39D7C32×C11×C1311yescharacteristic, direct product factor, Hall
40C13C32×C11×D711yescharacteristic, direct product factor, Sylow
41C11C32×C13×D711yescharacteristic, direct product factor, Sylow
42C32C11×C13×D711yescharacteristic, direct product factor, Sylow
43C7C2×C32×C11×C1311yescharacteristic, complemented, Sylow
44C2×C3—74no—
45C3C3×C11×C13×D714yesdirect product factor
46C2—71noSylow
subgroupG/H
center, hypercenterC32×C11×C13D7
commutator, cosocle, hypocenterC7C2×C32×C11×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C2
LCSG ▷ C7
UCSC1 ◁ C32×C11×C13

Complements

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

NH ≅ G/Ntype
1. C32×C7×C11×C13C2semidirect
2. C3×C11×C13×D7C3direct (N × H)
3. C3×C7×C11×C13C2×C3semidirect
5. C11×C13×D7C32direct (N × H)
6. C32×C13×D7C11direct (N × H)
7. C32×C11×D7C13direct (N × H)
8. C32×C11×C13D7direct (N × H)
9. C7×C11×C13C2×C32semidirect
11. C32×C7×C13C2×C11semidirect
12. C32×C7×C11C2×C13semidirect
13. C3×C13×D7C3×C11direct (N × H)
14. C3×C11×D7C3×C13direct (N × H)
15. C3×C11×C13C3×D7direct (N × H)
17. C3×C7×C13C2×C3×C11semidirect
19. C3×C7×C11C2×C3×C13semidirect
21. C13×D7C32×C11direct (N × H)
22. C11×D7C32×C13direct (N × H)
23. C11×C13C32×D7direct (N × H)
24. C32×D7C11×C13direct (N × H)
25. C32×C13C11×D7direct (N × H)
26. C32×C11C13×D7direct (N × H)
27. C7×C13C2×C32×C11semidirect
29. C7×C11C2×C32×C13semidirect
31. C32×C7C2×C11×C13semidirect
32. C3×D7C3×C11×C13direct (N × H)
33. C3×C13C3×C11×D7direct (N × H)
34. C3×C11C3×C13×D7direct (N × H)
37. C3×C7C2×C3×C11×C13semidirect
39. D7C32×C11×C13direct (N × H)
40. C13C32×C11×D7direct (N × H)
41. C11C32×C13×D7direct (N × H)
42. C32C11×C13×D7direct (N × H)
43. C7C2×C32×C11×C13semidirect
45. C3C3×C11×C13×D7direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×C7×C11×C132
C3×C11×C13×D73
C2×C32×C11×C137
C32×C13×D711
C32×C11×D713