Finite Group Databasebeta

← C27×C132 #72199170

Subgroups — C27×C132 #72199170

Order 21632.

467392 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C132C21127yesmaximal, direct product factor
2C25×C132C2212667yesdirect product factor
3C24×C132C23111811yesdirect product factor
4C27×C13C13114yesmaximal, direct product factor
5C23×C132C24111811yesdirect product factor
6C26×C13C2×C1311778yesdirect product factor
7C22×C132C2512667yesdirect product factor
8C25×C13C22×C13137338yesdirect product factor
9C2×C132C261127yesdirect product factor
10C24×C13C23×C131165354yesdirect product factor
11C132C2711yescharacteristic, direct product factor, Sylow
12C27C13211yescharacteristic, direct product factor, Sylow
13C23×C13C24×C131165354yesdirect product factor
14C26C2×C1321127yesdirect product factor
15C22×C13C25×C13137338yesdirect product factor
16C25C22×C13212667yesdirect product factor
17C2×C13C26×C1311778yesdirect product factor
18C24C23×C132111811yesdirect product factor
19C13C27×C13114yesdirect product factor
20C23C24×C132111811yesdirect product factor
21C22C25×C13212667yesdirect product factor
22C2C26×C1321127yesdirect 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×C132C2direct (N × H)
2. C25×C132C22direct (N × H)
3. C24×C132C23direct (N × H)
4. C27×C13C13direct (N × H)
5. C23×C132C24direct (N × H)
6. C26×C13C2×C13direct (N × H)
7. C22×C132C25direct (N × H)
8. C25×C13C22×C13direct (N × H)
9. C2×C132C26direct (N × H)
10. C24×C13C23×C13direct (N × H)
11. C132C27direct (N × H)
12. C27C132direct (N × H)
13. C23×C13C24×C13direct (N × H)
14. C26C2×C132direct (N × H)
15. C22×C13C25×C13direct (N × H)
16. C25C22×C132direct (N × H)
17. C2×C13C26×C13direct (N × H)
18. C24C23×C132direct (N × H)
19. C13C27×C13direct (N × H)
20. C23C24×C132direct (N × H)
21. C22C25×C132direct (N × H)
22. C2C26×C132direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C1322
C27×C1313