Finite Group Databasebeta

← C2×C34×C7×C11 #72190819

Subgroups — C2×C34×C7×C11 #72190819

Order 12474.

1696 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C34×C7×C11C211yesmaximal, characteristic, direct product factor, Hall
2C2×C33×C7×C11C3140yesmaximal, direct product factor
3C33×C7×C11C2×C3140yesdirect product factor
4C2×C34×C11C711yesmaximal, characteristic, direct product factor, Hall
5C2×C32×C7×C11C321130yesdirect product factor
6C2×C34×C7C1111yesmaximal, characteristic, direct product factor, Hall
7C34×C11C2×C711yescharacteristic, direct product factor, Hall
8C32×C7×C11C2×C321130yesdirect product factor
9C2×C33×C11C3×C7140yesdirect product factor
10C34×C7C2×C1111yescharacteristic, direct product factor, Hall
11C2×C3×C7×C11C33140yesdirect product factor
12C2×C33×C7C3×C11140yesdirect product factor
13C33×C11C2×C3×C7140yesdirect product factor
14C3×C7×C11C2×C33140yesdirect product factor
15C2×C32×C11C32×C71130yesdirect product factor
16C33×C7C2×C3×C11140yesdirect product factor
17C2×C34C7×C1111yescharacteristic, direct product factor, Hall
18C2×C7×C11C3411yescharacteristic, direct product factor, Hall
19C2×C32×C7C32×C111130yesdirect product factor
20C32×C11C2×C32×C71130yesdirect product factor
21C34C2×C7×C1111yescharacteristic, direct product factor, Sylow
22C7×C11C2×C3411yescharacteristic, direct product factor, Hall
23C2×C3×C11C33×C7140yesdirect product factor
24C32×C7C2×C32×C111130yesdirect product factor
25C2×C33C3×C7×C11140yesdirect product factor
26C2×C3×C7C33×C11140yesdirect product factor
27C3×C11C2×C33×C7140yesdirect product factor
28C33C2×C3×C7×C11140yesdirect product factor
29C2×C11C34×C711yescharacteristic, direct product factor, Hall
30C3×C7C2×C33×C11140yesdirect product factor
31C2×C32C32×C7×C111130yesdirect product factor
32C2×C7C34×C1111yescharacteristic, direct product factor, Hall
33C11C2×C34×C711yescharacteristic, direct product factor, Sylow
34C32C2×C32×C7×C111130yesdirect product factor
35C7C2×C34×C1111yescharacteristic, direct product factor, Sylow
36C2×C3C33×C7×C11140yesdirect product factor
37C3C2×C33×C7×C11140yesdirect product factor
38C2C34×C7×C1111yescharacteristic, direct product factor, Sylow
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C34×C7×C11C2direct (N × H)
2. C2×C33×C7×C11C3direct (N × H)
3. C33×C7×C11C2×C3direct (N × H)
4. C2×C34×C11C7direct (N × H)
5. C2×C32×C7×C11C32direct (N × H)
6. C2×C34×C7C11direct (N × H)
7. C34×C11C2×C7direct (N × H)
8. C32×C7×C11C2×C32direct (N × H)
9. C2×C33×C11C3×C7direct (N × H)
10. C34×C7C2×C11direct (N × H)
11. C2×C3×C7×C11C33direct (N × H)
12. C2×C33×C7C3×C11direct (N × H)
13. C33×C11C2×C3×C7direct (N × H)
14. C3×C7×C11C2×C33direct (N × H)
15. C2×C32×C11C32×C7direct (N × H)
16. C33×C7C2×C3×C11direct (N × H)
17. C2×C34C7×C11direct (N × H)
18. C2×C7×C11C34direct (N × H)
19. C2×C32×C7C32×C11direct (N × H)
20. C32×C11C2×C32×C7direct (N × H)
21. C34C2×C7×C11direct (N × H)
22. C7×C11C2×C34direct (N × H)
23. C2×C3×C11C33×C7direct (N × H)
24. C32×C7C2×C32×C11direct (N × H)
25. C2×C33C3×C7×C11direct (N × H)
26. C2×C3×C7C33×C11direct (N × H)
27. C3×C11C2×C33×C7direct (N × H)
28. C33C2×C3×C7×C11direct (N × H)
29. C2×C11C34×C7direct (N × H)
30. C3×C7C2×C33×C11direct (N × H)
31. C2×C32C32×C7×C11direct (N × H)
32. C2×C7C34×C11direct (N × H)
33. C11C2×C34×C7direct (N × H)
34. C32C2×C32×C7×C11direct (N × H)
35. C7C2×C34×C11direct (N × H)
36. C2×C3C33×C7×C11direct (N × H)
37. C3C2×C33×C7×C11direct (N × H)
38. C2C34×C7×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C34×C7×C112
C2×C33×C7×C113
C2×C34×C117
C2×C34×C711