Finite Group Databasebeta

← C2×C3×C7×C11×C23 #24922293

Subgroups — C2×C3×C7×C11×C23 #24922293

Order 10626.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C11×C23C211yesmaximal, characteristic, direct product factor, Hall
2C2×C7×C11×C23C311yesmaximal, characteristic, direct product factor, Hall
3C7×C11×C23C2×C311yescharacteristic, direct product factor, Hall
4C2×C3×C11×C23C711yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C7×C23C1111yesmaximal, characteristic, direct product factor, Hall
6C3×C11×C23C2×C711yescharacteristic, direct product factor, Hall
7C2×C11×C23C3×C711yescharacteristic, direct product factor, Hall
8C3×C7×C23C2×C1111yescharacteristic, direct product factor, Hall
9C2×C3×C7×C11C2311yesmaximal, characteristic, direct product factor, Hall
10C2×C7×C23C3×C1111yescharacteristic, direct product factor, Hall
11C11×C23C2×C3×C711yescharacteristic, direct product factor, Hall
12C3×C7×C11C2×C2311yescharacteristic, direct product factor, Hall
13C7×C23C2×C3×C1111yescharacteristic, direct product factor, Hall
14C2×C7×C11C3×C2311yescharacteristic, direct product factor, Hall
15C2×C3×C23C7×C1111yescharacteristic, direct product factor, Hall
16C7×C11C2×C3×C2311yescharacteristic, direct product factor, Hall
17C3×C23C2×C7×C1111yescharacteristic, direct product factor, Hall
18C2×C3×C11C7×C2311yescharacteristic, direct product factor, Hall
19C2×C23C3×C7×C1111yescharacteristic, direct product factor, Hall
20C2×C3×C7C11×C2311yescharacteristic, direct product factor, Hall
21C3×C11C2×C7×C2311yescharacteristic, direct product factor, Hall
22C23C2×C3×C7×C1111yescharacteristic, direct product factor, Sylow
23C2×C11C3×C7×C2311yescharacteristic, direct product factor, Hall
24C3×C7C2×C11×C2311yescharacteristic, direct product factor, Hall
25C2×C7C3×C11×C2311yescharacteristic, direct product factor, Hall
26C11C2×C3×C7×C2311yescharacteristic, direct product factor, Sylow
27C7C2×C3×C11×C2311yescharacteristic, direct product factor, Sylow
28C2×C3C7×C11×C2311yescharacteristic, direct product factor, Hall
29C3C2×C7×C11×C2311yescharacteristic, direct product factor, Sylow
30C2C3×C7×C11×C2311yescharacteristic, direct product factor, Sylow
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×C23C2direct (N × H)
2. C2×C7×C11×C23C3direct (N × H)
3. C7×C11×C23C2×C3direct (N × H)
4. C2×C3×C11×C23C7direct (N × H)
5. C2×C3×C7×C23C11direct (N × H)
6. C3×C11×C23C2×C7direct (N × H)
7. C2×C11×C23C3×C7direct (N × H)
8. C3×C7×C23C2×C11direct (N × H)
9. C2×C3×C7×C11C23direct (N × H)
10. C2×C7×C23C3×C11direct (N × H)
11. C11×C23C2×C3×C7direct (N × H)
12. C3×C7×C11C2×C23direct (N × H)
13. C7×C23C2×C3×C11direct (N × H)
14. C2×C7×C11C3×C23direct (N × H)
15. C2×C3×C23C7×C11direct (N × H)
16. C7×C11C2×C3×C23direct (N × H)
17. C3×C23C2×C7×C11direct (N × H)
18. C2×C3×C11C7×C23direct (N × H)
19. C2×C23C3×C7×C11direct (N × H)
20. C2×C3×C7C11×C23direct (N × H)
21. C3×C11C2×C7×C23direct (N × H)
22. C23C2×C3×C7×C11direct (N × H)
23. C2×C11C3×C7×C23direct (N × H)
24. C3×C7C2×C11×C23direct (N × H)
25. C2×C7C3×C11×C23direct (N × H)
26. C11C2×C3×C7×C23direct (N × H)
27. C7C2×C3×C11×C23direct (N × H)
28. C2×C3C7×C11×C23direct (N × H)
29. C3C2×C7×C11×C23direct (N × H)
30. C2C3×C7×C11×C23direct (N × H)