Finite Group Databasebeta

← C24×C3×C7×C61 #72198119

Subgroups — C24×C3×C7×C61 #72198119

Order 20496.

536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C7×C61C2115yesmaximal, direct product factor
2C24×C7×C61C311yesmaximal, characteristic, direct product factor, Hall
3C23×C7×C61C2×C3115yesdirect product factor
4C24×C3×C61C711yesmaximal, characteristic, direct product factor, Hall
5C22×C3×C7×C61C22135yesdirect product factor
6C2×C3×C7×C61C23115yesdirect product factor
7C22×C7×C61C22×C3135yesdirect product factor
8C23×C3×C61C2×C7115yesdirect product factor
9C3×C7×C61C2411yescharacteristic, direct product factor, Hall
10C24×C61C3×C711yescharacteristic, direct product factor, Hall
11C2×C7×C61C23×C3115yesdirect product factor
12C22×C3×C61C22×C7135yesdirect product factor
13C23×C61C2×C3×C7115yesdirect product factor
14C7×C61C24×C311yescharacteristic, direct product factor, Hall
15C2×C3×C61C23×C7115yesdirect product factor
16C24×C3×C7C6111yesmaximal, characteristic, direct product factor, Hall
17C22×C61C22×C3×C7135yesdirect product factor
18C3×C61C24×C711yescharacteristic, direct product factor, Hall
19C23×C3×C7C2×C61115yesdirect product factor
20C2×C61C23×C3×C7115yesdirect product factor
21C24×C7C3×C6111yescharacteristic, direct product factor, Hall
22C22×C3×C7C22×C61135yesdirect product factor
23C61C24×C3×C711yescharacteristic, direct product factor, Sylow
24C23×C7C2×C3×C61115yesdirect product factor
25C24×C3C7×C6111yescharacteristic, direct product factor, Hall
26C2×C3×C7C23×C61115yesdirect product factor
27C22×C7C22×C3×C61135yesdirect product factor
28C23×C3C2×C7×C61115yesdirect product factor
29C3×C7C24×C6111yescharacteristic, direct product factor, Hall
30C24C3×C7×C6111yescharacteristic, direct product factor, Sylow
31C2×C7C23×C3×C61115yesdirect product factor
32C22×C3C22×C7×C61135yesdirect product factor
33C23C2×C3×C7×C61115yesdirect product factor
34C7C24×C3×C6111yescharacteristic, direct product factor, Sylow
35C2×C3C23×C7×C61115yesdirect product factor
36C22C22×C3×C7×C61135yesdirect product factor
37C3C24×C7×C6111yescharacteristic, direct product factor, Sylow
38C2C23×C3×C7×C61115yesdirect 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×C3×C7×C61C2direct (N × H)
2. C24×C7×C61C3direct (N × H)
3. C23×C7×C61C2×C3direct (N × H)
4. C24×C3×C61C7direct (N × H)
5. C22×C3×C7×C61C22direct (N × H)
6. C2×C3×C7×C61C23direct (N × H)
7. C22×C7×C61C22×C3direct (N × H)
8. C23×C3×C61C2×C7direct (N × H)
9. C3×C7×C61C24direct (N × H)
10. C24×C61C3×C7direct (N × H)
11. C2×C7×C61C23×C3direct (N × H)
12. C22×C3×C61C22×C7direct (N × H)
13. C23×C61C2×C3×C7direct (N × H)
14. C7×C61C24×C3direct (N × H)
15. C2×C3×C61C23×C7direct (N × H)
16. C24×C3×C7C61direct (N × H)
17. C22×C61C22×C3×C7direct (N × H)
18. C3×C61C24×C7direct (N × H)
19. C23×C3×C7C2×C61direct (N × H)
20. C2×C61C23×C3×C7direct (N × H)
21. C24×C7C3×C61direct (N × H)
22. C22×C3×C7C22×C61direct (N × H)
23. C61C24×C3×C7direct (N × H)
24. C23×C7C2×C3×C61direct (N × H)
25. C24×C3C7×C61direct (N × H)
26. C2×C3×C7C23×C61direct (N × H)
27. C22×C7C22×C3×C61direct (N × H)
28. C23×C3C2×C7×C61direct (N × H)
29. C3×C7C24×C61direct (N × H)
30. C24C3×C7×C61direct (N × H)
31. C2×C7C23×C3×C61direct (N × H)
32. C22×C3C22×C7×C61direct (N × H)
33. C23C2×C3×C7×C61direct (N × H)
34. C7C24×C3×C61direct (N × H)
35. C2×C3C23×C7×C61direct (N × H)
36. C22C22×C3×C7×C61direct (N × H)
37. C3C24×C7×C61direct (N × H)
38. C2C23×C3×C7×C61direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C7×C612
C24×C7×C613
C24×C3×C617
C24×C3×C761