Finite Group Databasebeta

← C24×C3×C499 #72201230

Subgroups — C24×C3×C499 #72201230

Order 23952.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C499C2115yesmaximal, direct product factor
2C24×C499C311yesmaximal, characteristic, direct product factor, Hall
3C22×C3×C499C22135yesdirect product factor
4C23×C499C2×C3115yesdirect product factor
5C2×C3×C499C23115yesdirect product factor
6C22×C499C22×C3135yesdirect product factor
7C3×C499C2411yescharacteristic, direct product factor, Hall
8C2×C499C23×C3115yesdirect product factor
9C499C24×C311yescharacteristic, direct product factor, Sylow
10C24×C3C49911yesmaximal, characteristic, direct product factor, Hall
11C23×C3C2×C499115yesdirect product factor
12C24C3×C49911yescharacteristic, direct product factor, Sylow
13C22×C3C22×C499135yesdirect product factor
14C23C2×C3×C499115yesdirect product factor
15C2×C3C23×C499115yesdirect product factor
16C22C22×C3×C499135yesdirect product factor
17C3C24×C49911yescharacteristic, direct product factor, Sylow
18C2C23×C3×C499115yesdirect 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×C499C2direct (N × H)
2. C24×C499C3direct (N × H)
3. C22×C3×C499C22direct (N × H)
4. C23×C499C2×C3direct (N × H)
5. C2×C3×C499C23direct (N × H)
6. C22×C499C22×C3direct (N × H)
7. C3×C499C24direct (N × H)
8. C2×C499C23×C3direct (N × H)
9. C499C24×C3direct (N × H)
10. C24×C3C499direct (N × H)
11. C23×C3C2×C499direct (N × H)
12. C24C3×C499direct (N × H)
13. C22×C3C22×C499direct (N × H)
14. C23C2×C3×C499direct (N × H)
15. C2×C3C23×C499direct (N × H)
16. C22C22×C3×C499direct (N × H)
17. C3C24×C499direct (N × H)
18. C2C23×C3×C499direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4992
C24×C4993
C24×C3499