Finite Group Databasebeta

← C22×C32×C11×C67 #40997649

Subgroups — C22×C32×C11×C67 #40997649

Order 26532.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C11×C67C213yesmaximal, direct product factor
2C22×C3×C11×C67C314yesmaximal, direct product factor
3C32×C11×C67C2211yescharacteristic, direct product factor, Hall
4C2×C3×C11×C67C2×C3112yesdirect product factor
5C22×C11×C67C3211yescharacteristic, direct product factor, Hall
6C22×C32×C67C1111yesmaximal, characteristic, direct product factor, Hall
7C3×C11×C67C22×C314yesdirect product factor
8C2×C11×C67C2×C3213yesdirect product factor
9C2×C32×C67C2×C1113yesdirect product factor
10C22×C3×C67C3×C1114yesdirect product factor
11C11×C67C22×C3211yescharacteristic, direct product factor, Hall
12C32×C67C22×C1111yescharacteristic, direct product factor, Hall
13C2×C3×C67C2×C3×C11112yesdirect product factor
14C22×C32×C11C6711yesmaximal, characteristic, direct product factor, Hall
15C22×C67C32×C1111yescharacteristic, direct product factor, Hall
16C3×C67C22×C3×C1114yesdirect product factor
17C2×C32×C11C2×C6713yesdirect product factor
18C2×C67C2×C32×C1113yesdirect product factor
19C22×C3×C11C3×C6714yesdirect product factor
20C32×C11C22×C6711yescharacteristic, direct product factor, Hall
21C67C22×C32×C1111yescharacteristic, direct product factor, Sylow
22C2×C3×C11C2×C3×C67112yesdirect product factor
23C22×C11C32×C6711yescharacteristic, direct product factor, Hall
24C22×C32C11×C6711yescharacteristic, direct product factor, Hall
25C3×C11C22×C3×C6714yesdirect product factor
26C2×C11C2×C32×C6713yesdirect product factor
27C2×C32C2×C11×C6713yesdirect product factor
28C22×C3C3×C11×C6714yesdirect product factor
29C11C22×C32×C6711yescharacteristic, direct product factor, Sylow
30C32C22×C11×C6711yescharacteristic, direct product factor, Sylow
31C2×C3C2×C3×C11×C67112yesdirect product factor
32C22C32×C11×C6711yescharacteristic, direct product factor, Sylow
33C3C22×C3×C11×C6714yesdirect product factor
34C2C2×C32×C11×C6713yesdirect 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. C2×C32×C11×C67C2direct (N × H)
2. C22×C3×C11×C67C3direct (N × H)
3. C32×C11×C67C22direct (N × H)
4. C2×C3×C11×C67C2×C3direct (N × H)
5. C22×C11×C67C32direct (N × H)
6. C22×C32×C67C11direct (N × H)
7. C3×C11×C67C22×C3direct (N × H)
8. C2×C11×C67C2×C32direct (N × H)
9. C2×C32×C67C2×C11direct (N × H)
10. C22×C3×C67C3×C11direct (N × H)
11. C11×C67C22×C32direct (N × H)
12. C32×C67C22×C11direct (N × H)
13. C2×C3×C67C2×C3×C11direct (N × H)
14. C22×C32×C11C67direct (N × H)
15. C22×C67C32×C11direct (N × H)
16. C3×C67C22×C3×C11direct (N × H)
17. C2×C32×C11C2×C67direct (N × H)
18. C2×C67C2×C32×C11direct (N × H)
19. C22×C3×C11C3×C67direct (N × H)
20. C32×C11C22×C67direct (N × H)
21. C67C22×C32×C11direct (N × H)
22. C2×C3×C11C2×C3×C67direct (N × H)
23. C22×C11C32×C67direct (N × H)
24. C22×C32C11×C67direct (N × H)
25. C3×C11C22×C3×C67direct (N × H)
26. C2×C11C2×C32×C67direct (N × H)
27. C2×C32C2×C11×C67direct (N × H)
28. C22×C3C3×C11×C67direct (N × H)
29. C11C22×C32×C67direct (N × H)
30. C32C22×C11×C67direct (N × H)
31. C2×C3C2×C3×C11×C67direct (N × H)
32. C22C32×C11×C67direct (N × H)
33. C3C22×C3×C11×C67direct (N × H)
34. C2C2×C32×C11×C67direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C11×C672
C22×C3×C11×C673
C22×C32×C6711
C22×C32×C1167