Finite Group Databasebeta

← C22×C7×C11×C13⋊C3 #26046583

Subgroups — C22×C7×C11×C13⋊C3 #26046583

Order 12012.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×C11×C13⋊C3C213yesmaximal, direct product factor
2C22×C7×C11×C13C311yesmaximal, characteristic, complemented, Hall
3C7×C11×C13⋊C3C2211yescharacteristic, direct product factor, Hall
4C2×C7×C11×C13C2×C313yescomplemented
5C22×C11×C13⋊C3C711yesmaximal, characteristic, direct product factor, Hall
6C22×C7×C13⋊C3C1111yesmaximal, characteristic, direct product factor, Hall
7C7×C11×C13C22×C311yescharacteristic, complemented, Hall
8C22×C3×C7×C11—131nomaximal, Hall
9C2×C11×C13⋊C3C2×C713yesdirect product factor
10C22×C11×C13C3×C711yescharacteristic, complemented, Hall
11C2×C7×C13⋊C3C2×C1113yesdirect product factor
12C2×C3×C7×C11—133no—
13C11×C13⋊C3C22×C711yescharacteristic, direct product factor, Hall
14C22×C7×C13C3×C1111yescharacteristic, complemented, Hall
15C22×C7×C11C13⋊C311yescharacteristic, direct product factor, Hall
16C2×C11×C13C2×C3×C713yescomplemented
17C7×C13⋊C3C22×C1111yescharacteristic, direct product factor, Hall
18C3×C7×C11—131noHall
19C2×C7×C13C2×C3×C1113yescomplemented
20C22×C13⋊C3C7×C1111yescharacteristic, direct product factor, Hall
21C2×C7×C11C2×C13⋊C313yesdirect product factor
22C11×C13C22×C3×C711yescharacteristic, complemented, Hall
23C22×C3×C11—131noHall
24C7×C13C22×C3×C1111yescharacteristic, complemented, Hall
25C22×C3×C7—131noHall
26C2×C13⋊C3C2×C7×C1113yesdirect product factor
27C7×C11C22×C13⋊C311yescharacteristic, direct product factor, Hall
28C2×C3×C11—133no—
29C22×C13C3×C7×C1111yescharacteristic, complemented, Hall
30C22×C11C7×C13⋊C311yescharacteristic, direct product factor, Hall
31C2×C3×C7—133no—
32C13⋊C3C22×C7×C1111yescharacteristic, direct product factor, Hall
33C3×C11—131noHall
34C22×C7C11×C13⋊C311yescharacteristic, direct product factor, Hall
35C2×C13C2×C3×C7×C1113yescomplemented
36C2×C11C2×C7×C13⋊C313yesdirect product factor
37C3×C7—131noHall
38C2×C7C2×C11×C13⋊C313yesdirect product factor
39C13C22×C3×C7×C1111yescharacteristic, complemented, Sylow
40C22×C3—131noHall
41C11C22×C7×C13⋊C311yescharacteristic, direct product factor, Sylow
42C7C22×C11×C13⋊C311yescharacteristic, direct product factor, Sylow
43C2×C3—133no—
44C22C7×C11×C13⋊C311yescharacteristic, direct product factor, Sylow
45C3—131noSylow
46C2C2×C7×C11×C13⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C7×C11C13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C7×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C7×C11

Complements

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

NH ≅ G/Ntype
1. C2×C7×C11×C13⋊C3C2direct (N × H)
2. C22×C7×C11×C13C3semidirect
3. C7×C11×C13⋊C3C22direct (N × H)
4. C2×C7×C11×C13C2×C3semidirect
5. C22×C11×C13⋊C3C7direct (N × H)
6. C22×C7×C13⋊C3C11direct (N × H)
7. C7×C11×C13C22×C3semidirect
9. C2×C11×C13⋊C3C2×C7direct (N × H)
10. C22×C11×C13C3×C7semidirect
11. C2×C7×C13⋊C3C2×C11direct (N × H)
13. C11×C13⋊C3C22×C7direct (N × H)
14. C22×C7×C13C3×C11semidirect
15. C22×C7×C11C13⋊C3direct (N × H)
16. C2×C11×C13C2×C3×C7semidirect
17. C7×C13⋊C3C22×C11direct (N × H)
19. C2×C7×C13C2×C3×C11semidirect
20. C22×C13⋊C3C7×C11direct (N × H)
21. C2×C7×C11C2×C13⋊C3direct (N × H)
22. C11×C13C22×C3×C7semidirect
24. C7×C13C22×C3×C11semidirect
26. C2×C13⋊C3C2×C7×C11direct (N × H)
27. C7×C11C22×C13⋊C3direct (N × H)
29. C22×C13C3×C7×C11semidirect
30. C22×C11C7×C13⋊C3direct (N × H)
32. C13⋊C3C22×C7×C11direct (N × H)
34. C22×C7C11×C13⋊C3direct (N × H)
35. C2×C13C2×C3×C7×C11semidirect
36. C2×C11C2×C7×C13⋊C3direct (N × H)
38. C2×C7C2×C11×C13⋊C3direct (N × H)
39. C13C22×C3×C7×C11semidirect
41. C11C22×C7×C13⋊C3direct (N × H)
42. C7C22×C11×C13⋊C3direct (N × H)
44. C22C7×C11×C13⋊C3direct (N × H)
46. C2C2×C7×C11×C13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×C11×C13⋊C32
C22×C7×C11×C133
C22×C11×C13⋊C37
C22×C7×C13⋊C311
C22×C3×C7×C1113