Finite Group Databasebeta

← C28×C3×C29 #72199721

Subgroups — C28×C3×C29 #72199721

Order 22272.

1668796 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C27×C3×C29C21255yesmaximal, direct product factor
2C26×C3×C29C22110795yesdirect product factor
3C25×C3×C29C23197155yesdirect product factor
4C28×C29C311yesmaximal, characteristic, direct product factor, Hall
5C27×C29C2×C31255yesdirect product factor
6C26×C29C22×C3110795yesdirect product factor
7C24×C3×C29C241200787yesdirect product factor
8C25×C29C23×C3197155yesdirect product factor
9C28×C3C2911yesmaximal, characteristic, direct product factor, Hall
10C23×C3×C29C25197155yesdirect product factor
11C24×C29C24×C31200787yesdirect product factor
12C27×C3C2×C291255yesdirect product factor
13C22×C3×C29C26110795yesdirect product factor
14C28C3×C2911yescharacteristic, direct product factor, Sylow
15C23×C29C25×C3197155yesdirect product factor
16C26×C3C22×C29110795yesdirect product factor
17C2×C3×C29C271255yesdirect product factor
18C27C2×C3×C291255yesdirect product factor
19C22×C29C26×C3110795yesdirect product factor
20C25×C3C23×C29197155yesdirect product factor
21C3×C29C2811yescharacteristic, direct product factor, Hall
22C26C22×C3×C29110795yesdirect product factor
23C2×C29C27×C31255yesdirect product factor
24C24×C3C24×C291200787yesdirect product factor
25C25C23×C3×C29197155yesdirect product factor
26C29C28×C311yescharacteristic, direct product factor, Sylow
27C23×C3C25×C29197155yesdirect product factor
28C24C24×C3×C291200787yesdirect product factor
29C22×C3C26×C29110795yesdirect product factor
30C23C25×C3×C29197155yesdirect product factor
31C2×C3C27×C291255yesdirect product factor
32C22C26×C3×C29110795yesdirect product factor
33C3C28×C2911yescharacteristic, direct product factor, Sylow
34C2C27×C3×C291255yesdirect 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. C27×C3×C29C2direct (N × H)
2. C26×C3×C29C22direct (N × H)
3. C25×C3×C29C23direct (N × H)
4. C28×C29C3direct (N × H)
5. C27×C29C2×C3direct (N × H)
6. C26×C29C22×C3direct (N × H)
7. C24×C3×C29C24direct (N × H)
8. C25×C29C23×C3direct (N × H)
9. C28×C3C29direct (N × H)
10. C23×C3×C29C25direct (N × H)
11. C24×C29C24×C3direct (N × H)
12. C27×C3C2×C29direct (N × H)
13. C22×C3×C29C26direct (N × H)
14. C28C3×C29direct (N × H)
15. C23×C29C25×C3direct (N × H)
16. C26×C3C22×C29direct (N × H)
17. C2×C3×C29C27direct (N × H)
18. C27C2×C3×C29direct (N × H)
19. C22×C29C26×C3direct (N × H)
20. C25×C3C23×C29direct (N × H)
21. C3×C29C28direct (N × H)
22. C26C22×C3×C29direct (N × H)
23. C2×C29C27×C3direct (N × H)
24. C24×C3C24×C29direct (N × H)
25. C25C23×C3×C29direct (N × H)
26. C29C28×C3direct (N × H)
27. C23×C3C25×C29direct (N × H)
28. C24C24×C3×C29direct (N × H)
29. C22×C3C26×C29direct (N × H)
30. C23C25×C3×C29direct (N × H)
31. C2×C3C27×C29direct (N × H)
32. C22C26×C3×C29direct (N × H)
33. C3C28×C29direct (N × H)
34. C2C27×C3×C29direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C3×C292
C28×C293
C28×C329