Finite Group Databasebeta

← C2×C3×C9×C11×C29 #72195097

Subgroups — C2×C3×C9×C11×C29 #72195097

Order 17226.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×C11×C29C211yesmaximal, characteristic, direct product factor, Hall
2C2×C32×C11×C29C311yesmaximal, characteristic
3C2×C9×C11×C29C313yesmaximal, direct product factor
4C32×C11×C29C2×C311yescharacteristic
5C9×C11×C29C2×C313yesdirect product factor
6C2×C3×C11×C29C913yesdirect product factor
7C2×C3×C11×C29C3211yescharacteristic
8C2×C3×C9×C29C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C11×C29C2×C913yesdirect product factor
10C3×C11×C29C2×C3211yescharacteristic
11C3×C9×C29C2×C1111yescharacteristic, direct product factor, Hall
12C2×C11×C29C3×C911yescharacteristic, direct product factor, Hall
13C2×C3×C9×C11C2911yesmaximal, characteristic, direct product factor, Hall
14C2×C32×C29C3×C1111yescharacteristic
15C2×C9×C29C3×C1113yesdirect product factor
16C11×C29C2×C3×C911yescharacteristic, direct product factor, Hall
17C3×C9×C11C2×C2911yescharacteristic, direct product factor, Hall
18C32×C29C2×C3×C1111yescharacteristic
19C9×C29C2×C3×C1113yesdirect product factor
20C2×C32×C11C3×C2911yescharacteristic
21C2×C9×C11C3×C2913yesdirect product factor
22C2×C3×C29C9×C1113yesdirect product factor
23C2×C3×C29C32×C1111yescharacteristic
24C32×C11C2×C3×C2911yescharacteristic
25C9×C11C2×C3×C2913yesdirect product factor
26C3×C29C2×C9×C1113yesdirect product factor
27C3×C29C2×C32×C1111yescharacteristic
28C2×C3×C11C9×C2913yesdirect product factor
29C2×C3×C11C32×C2911yescharacteristic
30C2×C29C3×C9×C1111yescharacteristic, direct product factor, Hall
31C2×C3×C9C11×C2911yescharacteristic, direct product factor, Hall
32C3×C11C2×C9×C2913yesdirect product factor
33C3×C11C2×C32×C2911yescharacteristic
34C29C2×C3×C9×C1111yescharacteristic, direct product factor, Sylow
35C3×C9C2×C11×C2911yescharacteristic, direct product factor, Sylow
36C2×C11C3×C9×C2911yescharacteristic, direct product factor, Hall
37C2×C32C3×C11×C2911yescharacteristic
38C2×C9C3×C11×C2913yesdirect product factor
39C11C2×C3×C9×C2911yescharacteristic, direct product factor, Sylow
40C32C2×C3×C11×C2911yescharacteristic
41C9C2×C3×C11×C2913yesdirect product factor
42C2×C3C9×C11×C2913yesdirect product factor
43C2×C3C32×C11×C2911yescharacteristic
44C3C2×C9×C11×C2913yesdirect product factor
45C3C2×C32×C11×C2911yescharacteristic
46C2C3×C9×C11×C2911yescharacteristic, direct product factor, Sylow
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C2×C32×C11×C29
socle, prime radicalC2×C32×C11×C29C3
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C9×C11×C29C2direct (N × H)
3. C2×C9×C11×C29C3direct (N × H)
5. C9×C11×C29C2×C3direct (N × H)
6. C2×C3×C11×C29C9direct (N × H)
8. C2×C3×C9×C29C11direct (N × H)
9. C3×C11×C29C2×C9direct (N × H)
11. C3×C9×C29C2×C11direct (N × H)
12. C2×C11×C29C3×C9direct (N × H)
13. C2×C3×C9×C11C29direct (N × H)
15. C2×C9×C29C3×C11direct (N × H)
16. C11×C29C2×C3×C9direct (N × H)
17. C3×C9×C11C2×C29direct (N × H)
19. C9×C29C2×C3×C11direct (N × H)
21. C2×C9×C11C3×C29direct (N × H)
22. C2×C3×C29C9×C11direct (N × H)
25. C9×C11C2×C3×C29direct (N × H)
26. C3×C29C2×C9×C11direct (N × H)
28. C2×C3×C11C9×C29direct (N × H)
30. C2×C29C3×C9×C11direct (N × H)
31. C2×C3×C9C11×C29direct (N × H)
32. C3×C11C2×C9×C29direct (N × H)
34. C29C2×C3×C9×C11direct (N × H)
35. C3×C9C2×C11×C29direct (N × H)
36. C2×C11C3×C9×C29direct (N × H)
38. C2×C9C3×C11×C29direct (N × H)
39. C11C2×C3×C9×C29direct (N × H)
41. C9C2×C3×C11×C29direct (N × H)
42. C2×C3C9×C11×C29direct (N × H)
44. C3C2×C9×C11×C29direct (N × H)
46. C2C3×C9×C11×C29direct (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×C292
C2×C32×C11×C293
C2×C9×C11×C293
C2×C3×C9×C2911
C2×C3×C9×C1129