Finite Group Databasebeta

← C2×C3×C9×C11×C37 #72199459

Subgroups — C2×C3×C9×C11×C37 #72199459

Order 21978.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×C11×C37C211yesmaximal, characteristic, direct product factor, Hall
2C2×C32×C11×C37C311yesmaximal, characteristic
3C2×C9×C11×C37C313yesmaximal, direct product factor
4C32×C11×C37C2×C311yescharacteristic
5C9×C11×C37C2×C313yesdirect product factor
6C2×C3×C11×C37C913yesdirect product factor
7C2×C3×C11×C37C3211yescharacteristic
8C2×C3×C9×C37C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C11×C37C2×C913yesdirect product factor
10C3×C11×C37C2×C3211yescharacteristic
11C3×C9×C37C2×C1111yescharacteristic, direct product factor, Hall
12C2×C11×C37C3×C911yescharacteristic, direct product factor, Hall
13C2×C32×C37C3×C1111yescharacteristic
14C2×C9×C37C3×C1113yesdirect product factor
15C2×C3×C9×C11C3711yesmaximal, characteristic, direct product factor, Hall
16C11×C37C2×C3×C911yescharacteristic, direct product factor, Hall
17C32×C37C2×C3×C1111yescharacteristic
18C9×C37C2×C3×C1113yesdirect product factor
19C3×C9×C11C2×C3711yescharacteristic, direct product factor, Hall
20C2×C3×C37C9×C1113yesdirect product factor
21C2×C3×C37C32×C1111yescharacteristic
22C2×C32×C11C3×C3711yescharacteristic
23C2×C9×C11C3×C3713yesdirect product factor
24C3×C37C2×C9×C1113yesdirect product factor
25C3×C37C2×C32×C1111yescharacteristic
26C32×C11C2×C3×C3711yescharacteristic
27C9×C11C2×C3×C3713yesdirect product factor
28C2×C37C3×C9×C1111yescharacteristic, direct product factor, Hall
29C2×C3×C11C9×C3713yesdirect product factor
30C2×C3×C11C32×C3711yescharacteristic
31C2×C3×C9C11×C3711yescharacteristic, direct product factor, Hall
32C37C2×C3×C9×C1111yescharacteristic, direct product factor, Sylow
33C3×C11C2×C9×C3713yesdirect product factor
34C3×C11C2×C32×C3711yescharacteristic
35C3×C9C2×C11×C3711yescharacteristic, direct product factor, Sylow
36C2×C11C3×C9×C3711yescharacteristic, direct product factor, Hall
37C2×C32C3×C11×C3711yescharacteristic
38C2×C9C3×C11×C3713yesdirect product factor
39C11C2×C3×C9×C3711yescharacteristic, direct product factor, Sylow
40C32C2×C3×C11×C3711yescharacteristic
41C9C2×C3×C11×C3713yesdirect product factor
42C2×C3C9×C11×C3713yesdirect product factor
43C2×C3C32×C11×C3711yescharacteristic
44C3C2×C9×C11×C3713yesdirect product factor
45C3C2×C32×C11×C3711yescharacteristic
46C2C3×C9×C11×C3711yescharacteristic, direct product factor, Sylow
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C2×C32×C11×C37
socle, prime radicalC2×C32×C11×C37C3
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C9×C11×C37C2direct (N × H)
3. C2×C9×C11×C37C3direct (N × H)
5. C9×C11×C37C2×C3direct (N × H)
6. C2×C3×C11×C37C9direct (N × H)
8. C2×C3×C9×C37C11direct (N × H)
9. C3×C11×C37C2×C9direct (N × H)
11. C3×C9×C37C2×C11direct (N × H)
12. C2×C11×C37C3×C9direct (N × H)
14. C2×C9×C37C3×C11direct (N × H)
15. C2×C3×C9×C11C37direct (N × H)
16. C11×C37C2×C3×C9direct (N × H)
18. C9×C37C2×C3×C11direct (N × H)
19. C3×C9×C11C2×C37direct (N × H)
20. C2×C3×C37C9×C11direct (N × H)
23. C2×C9×C11C3×C37direct (N × H)
24. C3×C37C2×C9×C11direct (N × H)
27. C9×C11C2×C3×C37direct (N × H)
28. C2×C37C3×C9×C11direct (N × H)
29. C2×C3×C11C9×C37direct (N × H)
31. C2×C3×C9C11×C37direct (N × H)
32. C37C2×C3×C9×C11direct (N × H)
33. C3×C11C2×C9×C37direct (N × H)
35. C3×C9C2×C11×C37direct (N × H)
36. C2×C11C3×C9×C37direct (N × H)
38. C2×C9C3×C11×C37direct (N × H)
39. C11C2×C3×C9×C37direct (N × H)
41. C9C2×C3×C11×C37direct (N × H)
42. C2×C3C9×C11×C37direct (N × H)
44. C3C2×C9×C11×C37direct (N × H)
46. C2C3×C9×C11×C37direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×C11×C372
C2×C32×C11×C373
C2×C9×C11×C373
C2×C3×C9×C3711
C2×C3×C9×C1137