Finite Group Databasebeta

← C24×C32×C103 #72192913

Subgroups — C24×C32×C103 #72192913

Order 14832.

804 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×C103C2115yesmaximal, direct product factor
2C24×C3×C103C314yesmaximal, direct product factor
3C23×C3×C103C2×C3160yesdirect product factor
4C22×C32×C103C22135yesdirect product factor
5C2×C32×C103C23115yesdirect product factor
6C24×C103C3211yescharacteristic, direct product factor, Hall
7C22×C3×C103C22×C31140yesdirect product factor
8C32×C103C2411yescharacteristic, direct product factor, Hall
9C23×C103C2×C32115yesdirect product factor
10C2×C3×C103C23×C3160yesdirect product factor
11C22×C103C22×C32135yesdirect product factor
12C3×C103C24×C314yesdirect product factor
13C2×C103C23×C32115yesdirect product factor
14C24×C32C10311yesmaximal, characteristic, direct product factor, Hall
15C103C24×C3211yescharacteristic, direct product factor, Sylow
16C23×C32C2×C103115yesdirect product factor
17C24×C3C3×C10314yesdirect product factor
18C22×C32C22×C103135yesdirect product factor
19C23×C3C2×C3×C103160yesdirect product factor
20C2×C32C23×C103115yesdirect product factor
21C24C32×C10311yescharacteristic, direct product factor, Sylow
22C22×C3C22×C3×C1031140yesdirect product factor
23C32C24×C10311yescharacteristic, direct product factor, Sylow
24C23C2×C32×C103115yesdirect product factor
25C2×C3C23×C3×C103160yesdirect product factor
26C22C22×C32×C103135yesdirect product factor
27C3C24×C3×C10314yesdirect product factor
28C2C23×C32×C103115yesdirect 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×C103C2direct (N × H)
2. C24×C3×C103C3direct (N × H)
3. C23×C3×C103C2×C3direct (N × H)
4. C22×C32×C103C22direct (N × H)
5. C2×C32×C103C23direct (N × H)
6. C24×C103C32direct (N × H)
7. C22×C3×C103C22×C3direct (N × H)
8. C32×C103C24direct (N × H)
9. C23×C103C2×C32direct (N × H)
10. C2×C3×C103C23×C3direct (N × H)
11. C22×C103C22×C32direct (N × H)
12. C3×C103C24×C3direct (N × H)
13. C2×C103C23×C32direct (N × H)
14. C24×C32C103direct (N × H)
15. C103C24×C32direct (N × H)
16. C23×C32C2×C103direct (N × H)
17. C24×C3C3×C103direct (N × H)
18. C22×C32C22×C103direct (N × H)
19. C23×C3C2×C3×C103direct (N × H)
20. C2×C32C23×C103direct (N × H)
21. C24C32×C103direct (N × H)
22. C22×C3C22×C3×C103direct (N × H)
23. C32C24×C103direct (N × H)
24. C23C2×C32×C103direct (N × H)
25. C2×C3C23×C3×C103direct (N × H)
26. C22C22×C32×C103direct (N × H)
27. C3C24×C3×C103direct (N × H)
28. C2C23×C32×C103direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×C1032
C24×C3×C1033
C24×C32103