Finite Group Databasebeta

← C24×C32×C132 #72201652

Subgroups — C24×C32×C132 #72201652

Order 24336.

6432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×C132C2115yesmaximal, direct product factor
2C24×C3×C132C314yesmaximal, direct product factor
3C23×C3×C132C2×C3160yesdirect product factor
4C24×C132C3211yescharacteristic, direct product factor, Hall
5C22×C32×C132C22135yesdirect product factor
6C2×C32×C132C23115yesdirect product factor
7C22×C3×C132C22×C31140yesdirect product factor
8C24×C32×C13C13114yesmaximal, direct product factor
9C32×C132C2411yescharacteristic, direct product factor, Hall
10C23×C132C2×C32115yesdirect product factor
11C2×C3×C132C23×C3160yesdirect product factor
12C23×C32×C13C2×C131210yesdirect product factor
13C22×C132C22×C32135yesdirect product factor
14C24×C3×C13C3×C13156yesdirect product factor
15C3×C132C24×C314yesdirect product factor
16C22×C32×C13C22×C131490yesdirect product factor
17C2×C132C23×C32115yesdirect product factor
18C23×C3×C13C2×C3×C131840yesdirect product factor
19C2×C32×C13C23×C131210yesdirect product factor
20C24×C13C32×C13114yesdirect product factor
21C132C24×C3211yescharacteristic, direct product factor, Sylow
22C22×C3×C13C22×C3×C1311960yesdirect product factor
23C24×C32C13211yescharacteristic, direct product factor, Hall
24C32×C13C24×C13114yesdirect product factor
25C23×C13C2×C32×C131210yesdirect product factor
26C2×C3×C13C23×C3×C131840yesdirect product factor
27C23×C32C2×C132115yesdirect product factor
28C22×C13C22×C32×C131490yesdirect product factor
29C24×C3C3×C13214yesdirect product factor
30C3×C13C24×C3×C13156yesdirect product factor
31C22×C32C22×C132135yesdirect product factor
32C2×C13C23×C32×C131210yesdirect product factor
33C23×C3C2×C3×C132160yesdirect product factor
34C2×C32C23×C132115yesdirect product factor
35C24C32×C13211yescharacteristic, direct product factor, Sylow
36C13C24×C32×C13114yesdirect product factor
37C22×C3C22×C3×C1321140yesdirect product factor
38C32C24×C13211yescharacteristic, direct product factor, Sylow
39C23C2×C32×C132115yesdirect product factor
40C2×C3C23×C3×C132160yesdirect product factor
41C22C22×C32×C132135yesdirect product factor
42C3C24×C3×C13214yesdirect product factor
43C2C23×C32×C132115yesdirect 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×C32×C132C2direct (N × H)
2. C24×C3×C132C3direct (N × H)
3. C23×C3×C132C2×C3direct (N × H)
4. C24×C132C32direct (N × H)
5. C22×C32×C132C22direct (N × H)
6. C2×C32×C132C23direct (N × H)
7. C22×C3×C132C22×C3direct (N × H)
8. C24×C32×C13C13direct (N × H)
9. C32×C132C24direct (N × H)
10. C23×C132C2×C32direct (N × H)
11. C2×C3×C132C23×C3direct (N × H)
12. C23×C32×C13C2×C13direct (N × H)
13. C22×C132C22×C32direct (N × H)
14. C24×C3×C13C3×C13direct (N × H)
15. C3×C132C24×C3direct (N × H)
16. C22×C32×C13C22×C13direct (N × H)
17. C2×C132C23×C32direct (N × H)
18. C23×C3×C13C2×C3×C13direct (N × H)
19. C2×C32×C13C23×C13direct (N × H)
20. C24×C13C32×C13direct (N × H)
21. C132C24×C32direct (N × H)
22. C22×C3×C13C22×C3×C13direct (N × H)
23. C24×C32C132direct (N × H)
24. C32×C13C24×C13direct (N × H)
25. C23×C13C2×C32×C13direct (N × H)
26. C2×C3×C13C23×C3×C13direct (N × H)
27. C23×C32C2×C132direct (N × H)
28. C22×C13C22×C32×C13direct (N × H)
29. C24×C3C3×C132direct (N × H)
30. C3×C13C24×C3×C13direct (N × H)
31. C22×C32C22×C132direct (N × H)
32. C2×C13C23×C32×C13direct (N × H)
33. C23×C3C2×C3×C132direct (N × H)
34. C2×C32C23×C132direct (N × H)
35. C24C32×C132direct (N × H)
36. C13C24×C32×C13direct (N × H)
37. C22×C3C22×C3×C132direct (N × H)
38. C32C24×C132direct (N × H)
39. C23C2×C32×C132direct (N × H)
40. C2×C3C23×C3×C132direct (N × H)
41. C22C22×C32×C132direct (N × H)
42. C3C24×C3×C132direct (N × H)
43. C2C23×C32×C132direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×C1322
C24×C3×C1323
C24×C32×C1313