Finite Group Databasebeta

← C32×C7×C11×C17 #26044545

Subgroups — C32×C7×C11×C17 #26044545

Order 11781.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C11×C17C314yesmaximal, direct product factor
2C32×C11×C17C711yesmaximal, characteristic, direct product factor, Hall
3C7×C11×C17C3211yescharacteristic, direct product factor, Hall
4C32×C7×C17C1111yesmaximal, characteristic, direct product factor, Hall
5C32×C7×C11C1711yesmaximal, characteristic, direct product factor, Hall
6C3×C11×C17C3×C714yesdirect product factor
7C3×C7×C17C3×C1114yesdirect product factor
8C3×C7×C11C3×C1714yesdirect product factor
9C11×C17C32×C711yescharacteristic, direct product factor, Hall
10C32×C17C7×C1111yescharacteristic, direct product factor, Hall
11C7×C17C32×C1111yescharacteristic, direct product factor, Hall
12C32×C11C7×C1711yescharacteristic, direct product factor, Hall
13C7×C11C32×C1711yescharacteristic, direct product factor, Hall
14C32×C7C11×C1711yescharacteristic, direct product factor, Hall
15C3×C17C3×C7×C1114yesdirect product factor
16C3×C11C3×C7×C1714yesdirect product factor
17C3×C7C3×C11×C1714yesdirect product factor
18C17C32×C7×C1111yescharacteristic, direct product factor, Sylow
19C11C32×C7×C1711yescharacteristic, direct product factor, Sylow
20C32C7×C11×C1711yescharacteristic, direct product factor, Sylow
21C7C32×C11×C1711yescharacteristic, direct product factor, Sylow
22C3C3×C7×C11×C1714yesdirect 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. C3×C7×C11×C17C3direct (N × H)
2. C32×C11×C17C7direct (N × H)
3. C7×C11×C17C32direct (N × H)
4. C32×C7×C17C11direct (N × H)
5. C32×C7×C11C17direct (N × H)
6. C3×C11×C17C3×C7direct (N × H)
7. C3×C7×C17C3×C11direct (N × H)
8. C3×C7×C11C3×C17direct (N × H)
9. C11×C17C32×C7direct (N × H)
10. C32×C17C7×C11direct (N × H)
11. C7×C17C32×C11direct (N × H)
12. C32×C11C7×C17direct (N × H)
13. C7×C11C32×C17direct (N × H)
14. C32×C7C11×C17direct (N × H)
15. C3×C17C3×C7×C11direct (N × H)
16. C3×C11C3×C7×C17direct (N × H)
17. C3×C7C3×C11×C17direct (N × H)
18. C17C32×C7×C11direct (N × H)
19. C11C32×C7×C17direct (N × H)
20. C32C7×C11×C17direct (N × H)
21. C7C32×C11×C17direct (N × H)
22. C3C3×C7×C11×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×C11×C173
C32×C11×C177
C32×C7×C1711
C32×C7×C1117