Finite Group Databasebeta

← C22×C3×C9×C11×C23 #72204376

Subgroups — C22×C3×C9×C11×C23 #72204376

Order 27324.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C9×C11×C23C213yesmaximal, direct product factor
2C3×C9×C11×C23C2211yescharacteristic, direct product factor, Hall
3C22×C3×C9×C23C1111yesmaximal, characteristic, direct product factor, Hall
4C22×C32×C11×C23C311yesmaximal, characteristic
5C22×C9×C11×C23C313yesmaximal, direct product factor
6C2×C32×C11×C23C2×C313yes—
7C2×C9×C11×C23C2×C319yesdirect product factor
8C22×C3×C11×C23C913yesdirect product factor
9C22×C3×C11×C23C3211yescharacteristic
10C32×C11×C23C22×C311yescharacteristic
11C9×C11×C23C22×C313yesdirect product factor
12C2×C3×C11×C23C2×C919yesdirect product factor
13C2×C3×C11×C23C2×C3213yes—
14C2×C3×C9×C23C2×C1113yesdirect product factor
15C22×C3×C9×C11C2311yesmaximal, characteristic, direct product factor, Hall
16C22×C11×C23C3×C911yescharacteristic, direct product factor, Hall
17C22×C32×C23C3×C1111yescharacteristic
18C22×C9×C23C3×C1113yesdirect product factor
19C3×C11×C23C22×C913yesdirect product factor
20C3×C11×C23C22×C3211yescharacteristic
21C3×C9×C23C22×C1111yescharacteristic, direct product factor, Hall
22C2×C3×C9×C11C2×C2313yesdirect product factor
23C2×C11×C23C2×C3×C913yesdirect product factor
24C2×C32×C23C2×C3×C1113yes—
25C2×C9×C23C2×C3×C1119yesdirect product factor
26C22×C32×C11C3×C2311yescharacteristic
27C22×C9×C11C3×C2313yesdirect product factor
28C3×C9×C11C22×C2311yescharacteristic, direct product factor, Hall
29C22×C3×C23C9×C1113yesdirect product factor
30C22×C3×C23C32×C1111yescharacteristic
31C11×C23C22×C3×C911yescharacteristic, direct product factor, Hall
32C32×C23C22×C3×C1111yescharacteristic
33C9×C23C22×C3×C1113yesdirect product factor
34C2×C32×C11C2×C3×C2313yes—
35C2×C9×C11C2×C3×C2319yesdirect product factor
36C2×C3×C23C2×C9×C1119yesdirect product factor
37C2×C3×C23C2×C32×C1113yes—
38C22×C3×C11C9×C2313yesdirect product factor
39C22×C3×C11C32×C2311yescharacteristic
40C22×C3×C9C11×C2311yescharacteristic, direct product factor, Hall
41C32×C11C22×C3×C2311yescharacteristic
42C9×C11C22×C3×C2313yesdirect product factor
43C22×C23C3×C9×C1111yescharacteristic, direct product factor, Hall
44C3×C23C22×C9×C1113yesdirect product factor
45C3×C23C22×C32×C1111yescharacteristic
46C2×C3×C11C2×C9×C2319yesdirect product factor
47C2×C3×C11C2×C32×C2313yes—
48C2×C3×C9C2×C11×C2313yesdirect product factor
49C2×C23C2×C3×C9×C1113yesdirect product factor
50C22×C11C3×C9×C2311yescharacteristic, direct product factor, Hall
51C22×C32C3×C11×C2311yescharacteristic
52C22×C9C3×C11×C2313yesdirect product factor
53C3×C11C22×C9×C2313yesdirect product factor
54C3×C11C22×C32×C2311yescharacteristic
55C3×C9C22×C11×C2311yescharacteristic, direct product factor, Sylow
56C23C22×C3×C9×C1111yescharacteristic, direct product factor, Sylow
57C2×C11C2×C3×C9×C2313yesdirect product factor
58C2×C32C2×C3×C11×C2313yes—
59C2×C9C2×C3×C11×C2319yesdirect product factor
60C22×C3C9×C11×C2313yesdirect product factor
61C22×C3C32×C11×C2311yescharacteristic
62C11C22×C3×C9×C2311yescharacteristic, direct product factor, Sylow
63C32C22×C3×C11×C2311yescharacteristic
64C9C22×C3×C11×C2313yesdirect product factor
65C2×C3C2×C9×C11×C2319yesdirect product factor
66C2×C3C2×C32×C11×C2313yes—
67C22C3×C9×C11×C2311yescharacteristic, direct product factor, Sylow
68C3C22×C9×C11×C2313yesdirect product factor
69C3C22×C32×C11×C2311yescharacteristic
70C2C2×C3×C9×C11×C2313yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C22×C32×C11×C23
socle, prime radicalC22×C32×C11×C23C3
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9×C11×C23C2direct (N × H)
2. C3×C9×C11×C23C22direct (N × H)
3. C22×C3×C9×C23C11direct (N × H)
5. C22×C9×C11×C23C3direct (N × H)
7. C2×C9×C11×C23C2×C3direct (N × H)
8. C22×C3×C11×C23C9direct (N × H)
11. C9×C11×C23C22×C3direct (N × H)
12. C2×C3×C11×C23C2×C9direct (N × H)
14. C2×C3×C9×C23C2×C11direct (N × H)
15. C22×C3×C9×C11C23direct (N × H)
16. C22×C11×C23C3×C9direct (N × H)
18. C22×C9×C23C3×C11direct (N × H)
19. C3×C11×C23C22×C9direct (N × H)
21. C3×C9×C23C22×C11direct (N × H)
22. C2×C3×C9×C11C2×C23direct (N × H)
23. C2×C11×C23C2×C3×C9direct (N × H)
25. C2×C9×C23C2×C3×C11direct (N × H)
27. C22×C9×C11C3×C23direct (N × H)
28. C3×C9×C11C22×C23direct (N × H)
29. C22×C3×C23C9×C11direct (N × H)
31. C11×C23C22×C3×C9direct (N × H)
33. C9×C23C22×C3×C11direct (N × H)
35. C2×C9×C11C2×C3×C23direct (N × H)
36. C2×C3×C23C2×C9×C11direct (N × H)
38. C22×C3×C11C9×C23direct (N × H)
40. C22×C3×C9C11×C23direct (N × H)
42. C9×C11C22×C3×C23direct (N × H)
43. C22×C23C3×C9×C11direct (N × H)
44. C3×C23C22×C9×C11direct (N × H)
46. C2×C3×C11C2×C9×C23direct (N × H)
48. C2×C3×C9C2×C11×C23direct (N × H)
49. C2×C23C2×C3×C9×C11direct (N × H)
50. C22×C11C3×C9×C23direct (N × H)
52. C22×C9C3×C11×C23direct (N × H)
53. C3×C11C22×C9×C23direct (N × H)
55. C3×C9C22×C11×C23direct (N × H)
56. C23C22×C3×C9×C11direct (N × H)
57. C2×C11C2×C3×C9×C23direct (N × H)
59. C2×C9C2×C3×C11×C23direct (N × H)
60. C22×C3C9×C11×C23direct (N × H)
62. C11C22×C3×C9×C23direct (N × H)
64. C9C22×C3×C11×C23direct (N × H)
65. C2×C3C2×C9×C11×C23direct (N × H)
67. C22C3×C9×C11×C23direct (N × H)
68. C3C22×C9×C11×C23direct (N × H)
70. C2C2×C3×C9×C11×C23direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9×C11×C232
C22×C3×C9×C2311
C22×C32×C11×C233
C22×C9×C11×C233
C22×C3×C9×C1123