Finite Group Databasebeta

← C24×C33×C29 #72190878

Subgroups — C24×C33×C29 #72190878

Order 12528.

3752 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C33×C29C2115yesmaximal, direct product factor
2C24×C32×C29C3113yesmaximal, direct product factor
3C22×C33×C29C22135yesdirect product factor
4C23×C32×C29C2×C31195yesdirect product factor
5C2×C33×C29C23115yesdirect product factor
6C24×C3×C29C32113yesdirect product factor
7C22×C32×C29C22×C31455yesdirect product factor
8C33×C29C2411yescharacteristic, direct product factor, Hall
9C23×C3×C29C2×C321195yesdirect product factor
10C2×C32×C29C23×C31195yesdirect product factor
11C24×C29C3311yescharacteristic, direct product factor, Hall
12C24×C33C2911yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C29C22×C321455yesdirect product factor
14C32×C29C24×C3113yesdirect product factor
15C23×C29C2×C33115yesdirect product factor
16C23×C33C2×C29115yesdirect product factor
17C2×C3×C29C23×C321195yesdirect product factor
18C24×C32C3×C29113yesdirect product factor
19C22×C29C22×C33135yesdirect product factor
20C22×C33C22×C29135yesdirect product factor
21C3×C29C24×C32113yesdirect product factor
22C23×C32C2×C3×C291195yesdirect product factor
23C2×C29C23×C33115yesdirect product factor
24C2×C33C23×C29115yesdirect product factor
25C24×C3C32×C29113yesdirect product factor
26C22×C32C22×C3×C291455yesdirect product factor
27C29C24×C3311yescharacteristic, direct product factor, Sylow
28C33C24×C2911yescharacteristic, direct product factor, Sylow
29C23×C3C2×C32×C291195yesdirect product factor
30C2×C32C23×C3×C291195yesdirect product factor
31C24C33×C2911yescharacteristic, direct product factor, Sylow
32C22×C3C22×C32×C291455yesdirect product factor
33C32C24×C3×C29113yesdirect product factor
34C23C2×C33×C29115yesdirect product factor
35C2×C3C23×C32×C291195yesdirect product factor
36C22C22×C33×C29135yesdirect product factor
37C3C24×C32×C29113yesdirect product factor
38C2C23×C33×C29115yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C33×C29C2direct (N × H)
2. C24×C32×C29C3direct (N × H)
3. C22×C33×C29C22direct (N × H)
4. C23×C32×C29C2×C3direct (N × H)
5. C2×C33×C29C23direct (N × H)
6. C24×C3×C29C32direct (N × H)
7. C22×C32×C29C22×C3direct (N × H)
8. C33×C29C24direct (N × H)
9. C23×C3×C29C2×C32direct (N × H)
10. C2×C32×C29C23×C3direct (N × H)
11. C24×C29C33direct (N × H)
12. C24×C33C29direct (N × H)
13. C22×C3×C29C22×C32direct (N × H)
14. C32×C29C24×C3direct (N × H)
15. C23×C29C2×C33direct (N × H)
16. C23×C33C2×C29direct (N × H)
17. C2×C3×C29C23×C32direct (N × H)
18. C24×C32C3×C29direct (N × H)
19. C22×C29C22×C33direct (N × H)
20. C22×C33C22×C29direct (N × H)
21. C3×C29C24×C32direct (N × H)
22. C23×C32C2×C3×C29direct (N × H)
23. C2×C29C23×C33direct (N × H)
24. C2×C33C23×C29direct (N × H)
25. C24×C3C32×C29direct (N × H)
26. C22×C32C22×C3×C29direct (N × H)
27. C29C24×C33direct (N × H)
28. C33C24×C29direct (N × H)
29. C23×C3C2×C32×C29direct (N × H)
30. C2×C32C23×C3×C29direct (N × H)
31. C24C33×C29direct (N × H)
32. C22×C3C22×C32×C29direct (N × H)
33. C32C24×C3×C29direct (N × H)
34. C23C2×C33×C29direct (N × H)
35. C2×C3C23×C32×C29direct (N × H)
36. C22C22×C33×C29direct (N × H)
37. C3C24×C32×C29direct (N × H)
38. C2C23×C33×C29direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C33×C292
C24×C32×C293
C24×C3329