Finite Group Databasebeta

← C23×C7×C11×C53 #72209331

Subgroups — C23×C7×C11×C53 #72209331

Order 32648.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×C53C711yesmaximal, characteristic, direct product factor, Hall
2C23×C7×C53C1111yesmaximal, characteristic, direct product factor, Hall
3C22×C7×C11×C53C217yesmaximal, direct product factor
4C2×C7×C11×C53C2217yesdirect product factor
5C7×C11×C53C2311yescharacteristic, direct product factor, Hall
6C22×C11×C53C2×C717yesdirect product factor
7C22×C7×C53C2×C1117yesdirect product factor
8C2×C11×C53C22×C717yesdirect product factor
9C2×C7×C53C22×C1117yesdirect product factor
10C23×C7×C11C5311yesmaximal, characteristic, direct product factor, Hall
11C11×C53C23×C711yescharacteristic, direct product factor, Hall
12C23×C53C7×C1111yescharacteristic, direct product factor, Hall
13C7×C53C23×C1111yescharacteristic, direct product factor, Hall
14C22×C7×C11C2×C5317yesdirect product factor
15C22×C53C2×C7×C1117yesdirect product factor
16C2×C7×C11C22×C5317yesdirect product factor
17C2×C53C22×C7×C1117yesdirect product factor
18C23×C11C7×C5311yescharacteristic, direct product factor, Hall
19C7×C11C23×C5311yescharacteristic, direct product factor, Hall
20C23×C7C11×C5311yescharacteristic, direct product factor, Hall
21C53C23×C7×C1111yescharacteristic, direct product factor, Sylow
22C22×C11C2×C7×C5317yesdirect product factor
23C22×C7C2×C11×C5317yesdirect product factor
24C2×C11C22×C7×C5317yesdirect product factor
25C2×C7C22×C11×C5317yesdirect product factor
26C11C23×C7×C5311yescharacteristic, direct product factor, Sylow
27C23C7×C11×C5311yescharacteristic, direct product factor, Sylow
28C7C23×C11×C5311yescharacteristic, direct product factor, Sylow
29C22C2×C7×C11×C5317yesdirect product factor
30C2C22×C7×C11×C5317yesdirect 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×C11×C53C7direct (N × H)
2. C23×C7×C53C11direct (N × H)
3. C22×C7×C11×C53C2direct (N × H)
4. C2×C7×C11×C53C22direct (N × H)
5. C7×C11×C53C23direct (N × H)
6. C22×C11×C53C2×C7direct (N × H)
7. C22×C7×C53C2×C11direct (N × H)
8. C2×C11×C53C22×C7direct (N × H)
9. C2×C7×C53C22×C11direct (N × H)
10. C23×C7×C11C53direct (N × H)
11. C11×C53C23×C7direct (N × H)
12. C23×C53C7×C11direct (N × H)
13. C7×C53C23×C11direct (N × H)
14. C22×C7×C11C2×C53direct (N × H)
15. C22×C53C2×C7×C11direct (N × H)
16. C2×C7×C11C22×C53direct (N × H)
17. C2×C53C22×C7×C11direct (N × H)
18. C23×C11C7×C53direct (N × H)
19. C7×C11C23×C53direct (N × H)
20. C23×C7C11×C53direct (N × H)
21. C53C23×C7×C11direct (N × H)
22. C22×C11C2×C7×C53direct (N × H)
23. C22×C7C2×C11×C53direct (N × H)
24. C2×C11C22×C7×C53direct (N × H)
25. C2×C7C22×C11×C53direct (N × H)
26. C11C23×C7×C53direct (N × H)
27. C23C7×C11×C53direct (N × H)
28. C7C23×C11×C53direct (N × H)
29. C22C2×C7×C11×C53direct (N × H)
30. C2C22×C7×C11×C53direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×C537
C23×C7×C5311
C22×C7×C11×C532
C23×C7×C1153