Finite Group Databasebeta

← C27×C181 #37531539

Subgroups — C27×C181 #37531539

Order 23168.

58424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C181C21127yesmaximal, direct product factor
2C25×C181C2212667yesdirect product factor
3C24×C181C23111811yesdirect product factor
4C23×C181C24111811yesdirect product factor
5C22×C181C2512667yesdirect product factor
6C2×C181C261127yesdirect product factor
7C181C2711yescharacteristic, direct product factor, Sylow
8C27C18111yesmaximal, characteristic, direct product factor, Sylow
9C26C2×C1811127yesdirect product factor
10C25C22×C18112667yesdirect product factor
11C24C23×C181111811yesdirect product factor
12C23C24×C181111811yesdirect product factor
13C22C25×C18112667yesdirect product factor
14C2C26×C1811127yesdirect 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×C181C2direct (N × H)
2. C25×C181C22direct (N × H)
3. C24×C181C23direct (N × H)
4. C23×C181C24direct (N × H)
5. C22×C181C25direct (N × H)
6. C2×C181C26direct (N × H)
7. C181C27direct (N × H)
8. C27C181direct (N × H)
9. C26C2×C181direct (N × H)
10. C25C22×C181direct (N × H)
11. C24C23×C181direct (N × H)
12. C23C24×C181direct (N × H)
13. C22C25×C181direct (N × H)
14. C2C26×C181direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C1812
C27181