Finite Group Databasebeta

← C2×C32×C4×C11×C31 #72201795

Subgroups — C2×C32×C4×C11×C31 #72201795

Order 24552.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C11×C31C314yesmaximal, direct product factor
2C2×C4×C11×C31C3211yescharacteristic, direct product factor, Hall
3C2×C32×C4×C31C1111yesmaximal, characteristic, direct product factor, Hall
4C22×C32×C11×C31C211yesmaximal, characteristic
5C32×C4×C11×C31C212yesmaximal, direct product factor
6C2×C32×C11×C31C412yesdirect product factor
7C2×C32×C11×C31C2211yescharacteristic
8C22×C3×C11×C31C2×C314yes—
9C3×C4×C11×C31C2×C318yesdirect product factor
10C32×C11×C31C2×C411yescharacteristic, direct product factor, Hall
11C2×C3×C11×C31C3×C418yesdirect product factor
12C2×C3×C11×C31C22×C314yes—
13C22×C11×C31C2×C3211yescharacteristic
14C4×C11×C31C2×C3212yesdirect product factor
15C22×C32×C31C2×C1111yescharacteristic
16C32×C4×C31C2×C1112yesdirect product factor
17C3×C11×C31C2×C3×C414yesdirect product factor
18C2×C32×C4×C11C3111yesmaximal, characteristic, direct product factor, Hall
19C2×C3×C4×C31C3×C1114yesdirect product factor
20C2×C11×C31C32×C412yesdirect product factor
21C2×C11×C31C22×C3211yescharacteristic
22C2×C32×C31C4×C1112yesdirect product factor
23C2×C32×C31C22×C1111yescharacteristic
24C22×C32×C11C2×C3111yescharacteristic
25C32×C4×C11C2×C3112yesdirect product factor
26C22×C3×C31C2×C3×C1114yes—
27C3×C4×C31C2×C3×C1118yesdirect product factor
28C11×C31C2×C32×C411yescharacteristic, direct product factor, Hall
29C32×C31C2×C4×C1111yescharacteristic, direct product factor, Hall
30C2×C3×C4×C11C3×C3114yesdirect product factor
31C2×C4×C31C32×C1111yescharacteristic, direct product factor, Hall
32C2×C32×C11C4×C3112yesdirect product factor
33C2×C32×C11C22×C3111yescharacteristic
34C2×C3×C31C3×C4×C1118yesdirect product factor
35C2×C3×C31C22×C3×C1114yes—
36C22×C3×C11C2×C3×C3114yes—
37C3×C4×C11C2×C3×C3118yesdirect product factor
38C22×C31C2×C32×C1111yescharacteristic
39C4×C31C2×C32×C1112yesdirect product factor
40C32×C11C2×C4×C3111yescharacteristic, direct product factor, Hall
41C3×C31C2×C3×C4×C1114yesdirect product factor
42C2×C4×C11C32×C3111yescharacteristic, direct product factor, Hall
43C2×C32×C4C11×C3111yescharacteristic, direct product factor, Hall
44C2×C3×C11C3×C4×C3118yesdirect product factor
45C2×C3×C11C22×C3×C3114yes—
46C2×C31C32×C4×C1112yesdirect product factor
47C2×C31C22×C32×C1111yescharacteristic
48C22×C11C2×C32×C3111yescharacteristic
49C4×C11C2×C32×C3112yesdirect product factor
50C22×C32C2×C11×C3111yescharacteristic
51C32×C4C2×C11×C3112yesdirect product factor
52C3×C11C2×C3×C4×C3114yesdirect product factor
53C31C2×C32×C4×C1111yescharacteristic, direct product factor, Sylow
54C2×C3×C4C3×C11×C3114yesdirect product factor
55C2×C11C32×C4×C3112yesdirect product factor
56C2×C11C22×C32×C3111yescharacteristic
57C2×C32C4×C11×C3112yesdirect product factor
58C2×C32C22×C11×C3111yescharacteristic
59C22×C3C2×C3×C11×C3114yes—
60C3×C4C2×C3×C11×C3118yesdirect product factor
61C11C2×C32×C4×C3111yescharacteristic, direct product factor, Sylow
62C32C2×C4×C11×C3111yescharacteristic, direct product factor, Sylow
63C2×C4C32×C11×C3111yescharacteristic, direct product factor, Sylow
64C2×C3C3×C4×C11×C3118yesdirect product factor
65C2×C3C22×C3×C11×C3114yes—
66C22C2×C32×C11×C3111yescharacteristic
67C4C2×C32×C11×C3112yesdirect product factor
68C3C2×C3×C4×C11×C3114yesdirect product factor
69C2C32×C4×C11×C3112yesdirect product factor
70C2C22×C32×C11×C3111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C32×C11×C31
socle, prime radicalC22×C32×C11×C31C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C11×C31C3direct (N × H)
2. C2×C4×C11×C31C32direct (N × H)
3. C2×C32×C4×C31C11direct (N × H)
5. C32×C4×C11×C31C2direct (N × H)
6. C2×C32×C11×C31C4direct (N × H)
9. C3×C4×C11×C31C2×C3direct (N × H)
10. C32×C11×C31C2×C4direct (N × H)
11. C2×C3×C11×C31C3×C4direct (N × H)
14. C4×C11×C31C2×C32direct (N × H)
16. C32×C4×C31C2×C11direct (N × H)
17. C3×C11×C31C2×C3×C4direct (N × H)
18. C2×C32×C4×C11C31direct (N × H)
19. C2×C3×C4×C31C3×C11direct (N × H)
20. C2×C11×C31C32×C4direct (N × H)
22. C2×C32×C31C4×C11direct (N × H)
25. C32×C4×C11C2×C31direct (N × H)
27. C3×C4×C31C2×C3×C11direct (N × H)
28. C11×C31C2×C32×C4direct (N × H)
29. C32×C31C2×C4×C11direct (N × H)
30. C2×C3×C4×C11C3×C31direct (N × H)
31. C2×C4×C31C32×C11direct (N × H)
32. C2×C32×C11C4×C31direct (N × H)
34. C2×C3×C31C3×C4×C11direct (N × H)
37. C3×C4×C11C2×C3×C31direct (N × H)
39. C4×C31C2×C32×C11direct (N × H)
40. C32×C11C2×C4×C31direct (N × H)
41. C3×C31C2×C3×C4×C11direct (N × H)
42. C2×C4×C11C32×C31direct (N × H)
43. C2×C32×C4C11×C31direct (N × H)
44. C2×C3×C11C3×C4×C31direct (N × H)
46. C2×C31C32×C4×C11direct (N × H)
49. C4×C11C2×C32×C31direct (N × H)
51. C32×C4C2×C11×C31direct (N × H)
52. C3×C11C2×C3×C4×C31direct (N × H)
53. C31C2×C32×C4×C11direct (N × H)
54. C2×C3×C4C3×C11×C31direct (N × H)
55. C2×C11C32×C4×C31direct (N × H)
57. C2×C32C4×C11×C31direct (N × H)
60. C3×C4C2×C3×C11×C31direct (N × H)
61. C11C2×C32×C4×C31direct (N × H)
62. C32C2×C4×C11×C31direct (N × H)
63. C2×C4C32×C11×C31direct (N × H)
64. C2×C3C3×C4×C11×C31direct (N × H)
67. C4C2×C32×C11×C31direct (N × H)
68. C3C2×C3×C4×C11×C31direct (N × H)
69. C2C32×C4×C11×C31direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C11×C313
C2×C32×C4×C3111
C22×C32×C11×C312
C32×C4×C11×C312
C2×C32×C4×C1131