Finite Group Databasebeta

← C27×C7×C17 #72193261

Subgroups — C27×C7×C17 #72193261

Order 15232.

116848 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C7×C17C21127yesmaximal, direct product factor
2C25×C7×C17C2212667yesdirect product factor
3C27×C17C711yesmaximal, characteristic, direct product factor, Hall
4C24×C7×C17C23111811yesdirect product factor
5C26×C17C2×C71127yesdirect product factor
6C23×C7×C17C24111811yesdirect product factor
7C27×C7C1711yesmaximal, characteristic, direct product factor, Hall
8C25×C17C22×C712667yesdirect product factor
9C22×C7×C17C2512667yesdirect product factor
10C26×C7C2×C171127yesdirect product factor
11C24×C17C23×C7111811yesdirect product factor
12C2×C7×C17C261127yesdirect product factor
13C25×C7C22×C1712667yesdirect product factor
14C23×C17C24×C7111811yesdirect product factor
15C27C7×C1711yescharacteristic, direct product factor, Sylow
16C7×C17C2711yescharacteristic, direct product factor, Hall
17C24×C7C23×C17111811yesdirect product factor
18C22×C17C25×C712667yesdirect product factor
19C26C2×C7×C171127yesdirect product factor
20C23×C7C24×C17111811yesdirect product factor
21C2×C17C26×C71127yesdirect product factor
22C25C22×C7×C1712667yesdirect product factor
23C22×C7C25×C1712667yesdirect product factor
24C17C27×C711yescharacteristic, direct product factor, Sylow
25C24C23×C7×C17111811yesdirect product factor
26C2×C7C26×C171127yesdirect product factor
27C23C24×C7×C17111811yesdirect product factor
28C7C27×C1711yescharacteristic, direct product factor, Sylow
29C22C25×C7×C1712667yesdirect product factor
30C2C26×C7×C171127yesdirect 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. C26×C7×C17C2direct (N × H)
2. C25×C7×C17C22direct (N × H)
3. C27×C17C7direct (N × H)
4. C24×C7×C17C23direct (N × H)
5. C26×C17C2×C7direct (N × H)
6. C23×C7×C17C24direct (N × H)
7. C27×C7C17direct (N × H)
8. C25×C17C22×C7direct (N × H)
9. C22×C7×C17C25direct (N × H)
10. C26×C7C2×C17direct (N × H)
11. C24×C17C23×C7direct (N × H)
12. C2×C7×C17C26direct (N × H)
13. C25×C7C22×C17direct (N × H)
14. C23×C17C24×C7direct (N × H)
15. C27C7×C17direct (N × H)
16. C7×C17C27direct (N × H)
17. C24×C7C23×C17direct (N × H)
18. C22×C17C25×C7direct (N × H)
19. C26C2×C7×C17direct (N × H)
20. C23×C7C24×C17direct (N × H)
21. C2×C17C26×C7direct (N × H)
22. C25C22×C7×C17direct (N × H)
23. C22×C7C25×C17direct (N × H)
24. C17C27×C7direct (N × H)
25. C24C23×C7×C17direct (N × H)
26. C2×C7C26×C17direct (N × H)
27. C23C24×C7×C17direct (N × H)
28. C7C27×C17direct (N × H)
29. C22C25×C7×C17direct (N × H)
30. C2C26×C7×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C7×C172
C27×C177
C27×C717