Finite Group Databasebeta

← C23×C32×C257 #72196320

Subgroups — C23×C32×C257 #72196320

Order 18504.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C257C314yesmaximal, direct product factor
2C22×C32×C257C217yesmaximal, direct product factor
3C2×C32×C257C2217yesdirect product factor
4C22×C3×C257C2×C3128yesdirect product factor
5C32×C257C2311yescharacteristic, direct product factor, Hall
6C23×C257C3211yescharacteristic, direct product factor, Hall
7C2×C3×C257C22×C3128yesdirect product factor
8C22×C257C2×C3217yesdirect product factor
9C3×C257C23×C314yesdirect product factor
10C2×C257C22×C3217yesdirect product factor
11C257C23×C3211yescharacteristic, direct product factor, Sylow
12C23×C32C25711yesmaximal, characteristic, direct product factor, Hall
13C22×C32C2×C25717yesdirect product factor
14C23×C3C3×C25714yesdirect product factor
15C2×C32C22×C25717yesdirect product factor
16C22×C3C2×C3×C257128yesdirect product factor
17C32C23×C25711yescharacteristic, direct product factor, Sylow
18C23C32×C25711yescharacteristic, direct product factor, Sylow
19C2×C3C22×C3×C257128yesdirect product factor
20C22C2×C32×C25717yesdirect product factor
21C3C23×C3×C25714yesdirect product factor
22C2C22×C32×C25717yesdirect 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×C257C3direct (N × H)
2. C22×C32×C257C2direct (N × H)
3. C2×C32×C257C22direct (N × H)
4. C22×C3×C257C2×C3direct (N × H)
5. C32×C257C23direct (N × H)
6. C23×C257C32direct (N × H)
7. C2×C3×C257C22×C3direct (N × H)
8. C22×C257C2×C32direct (N × H)
9. C3×C257C23×C3direct (N × H)
10. C2×C257C22×C32direct (N × H)
11. C257C23×C32direct (N × H)
12. C23×C32C257direct (N × H)
13. C22×C32C2×C257direct (N × H)
14. C23×C3C3×C257direct (N × H)
15. C2×C32C22×C257direct (N × H)
16. C22×C3C2×C3×C257direct (N × H)
17. C32C23×C257direct (N × H)
18. C23C32×C257direct (N × H)
19. C2×C3C22×C3×C257direct (N × H)
20. C22C2×C32×C257direct (N × H)
21. C3C23×C3×C257direct (N × H)
22. C2C22×C32×C257direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C2573
C22×C32×C2572
C23×C32257