Finite Group Databasebeta

← C23×C32×C4×C11 #72182913

Subgroups — C23×C32×C4×C11 #72182913

Order 3168.

1416 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C32×C11C211yesmaximal, characteristic
2C22×C32×C4×C11C2114yesmaximal, direct product factor
3C23×C3×C4×C11C314yesmaximal, direct product factor
4C23×C32×C11C418yesdirect product factor
5C23×C32×C11C2217yes—
6C2×C32×C4×C11C22128yesdirect product factor
7C24×C3×C11C2×C314yes—
8C22×C3×C4×C11C2×C3156yesdirect product factor
9C22×C32×C11C2×C4128yesdirect product factor
10C22×C32×C11C2317yes—
11C32×C4×C11C2318yesdirect product factor
12C23×C4×C11C3211yescharacteristic, direct product factor, Hall
13C23×C32×C4C1111yesmaximal, characteristic, direct product factor, Hall
14C23×C3×C11C3×C4132yesdirect product factor
15C23×C3×C11C22×C3128yes—
16C2×C3×C4×C11C22×C31112yesdirect product factor
17C2×C32×C11C22×C4114yesdirect product factor
18C2×C32×C11C2411yescharacteristic
19C24×C11C2×C3211yescharacteristic
20C22×C4×C11C2×C32114yesdirect product factor
21C24×C32C2×C1111yescharacteristic
22C22×C32×C4C2×C11114yesdirect product factor
23C22×C3×C11C2×C3×C41112yesdirect product factor
24C22×C3×C11C23×C3128yes—
25C3×C4×C11C23×C3132yesdirect product factor
26C32×C11C23×C411yescharacteristic, direct product factor, Hall
27C23×C3×C4C3×C1114yesdirect product factor
28C23×C11C32×C418yesdirect product factor
29C23×C11C22×C3217yes—
30C2×C4×C11C22×C32128yesdirect product factor
31C23×C32C4×C1118yesdirect product factor
32C23×C32C22×C1117yes—
33C2×C32×C4C22×C11128yesdirect product factor
34C2×C3×C11C22×C3×C4156yesdirect product factor
35C2×C3×C11C24×C314yes—
36C24×C3C2×C3×C1114yes—
37C22×C3×C4C2×C3×C11156yesdirect product factor
38C22×C11C2×C32×C4128yesdirect product factor
39C22×C11C23×C3217yes—
40C4×C11C23×C3218yesdirect product factor
41C22×C32C2×C4×C11128yesdirect product factor
42C22×C32C23×C1117yes—
43C32×C4C23×C1118yesdirect product factor
44C3×C11C23×C3×C414yesdirect product factor
45C23×C4C32×C1111yescharacteristic, direct product factor, Sylow
46C23×C3C3×C4×C11132yesdirect product factor
47C23×C3C22×C3×C11128yes—
48C2×C3×C4C22×C3×C111112yesdirect product factor
49C2×C11C22×C32×C4114yesdirect product factor
50C2×C11C24×C3211yescharacteristic
51C2×C32C22×C4×C11114yesdirect product factor
52C2×C32C24×C1111yescharacteristic
53C24C2×C32×C1111yescharacteristic
54C22×C4C2×C32×C11114yesdirect product factor
55C22×C3C2×C3×C4×C111112yesdirect product factor
56C22×C3C23×C3×C11128yes—
57C3×C4C23×C3×C11132yesdirect product factor
58C11C23×C32×C411yescharacteristic, direct product factor, Sylow
59C32C23×C4×C1111yescharacteristic, direct product factor, Sylow
60C23C32×C4×C1118yesdirect product factor
61C23C22×C32×C1117yes—
62C2×C4C22×C32×C11128yesdirect product factor
63C2×C3C22×C3×C4×C11156yesdirect product factor
64C2×C3C24×C3×C1114yes—
65C22C2×C32×C4×C11128yesdirect product factor
66C22C23×C32×C1117yes—
67C4C23×C32×C1118yesdirect product factor
68C3C23×C3×C4×C1114yesdirect product factor
69C2C22×C32×C4×C11114yesdirect product factor
70C2C24×C32×C1111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C32×C11
socle, prime radicalC24×C32×C11C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C32×C4×C11C2direct (N × H)
3. C23×C3×C4×C11C3direct (N × H)
4. C23×C32×C11C4direct (N × H)
6. C2×C32×C4×C11C22direct (N × H)
8. C22×C3×C4×C11C2×C3direct (N × H)
9. C22×C32×C11C2×C4direct (N × H)
11. C32×C4×C11C23direct (N × H)
12. C23×C4×C11C32direct (N × H)
13. C23×C32×C4C11direct (N × H)
14. C23×C3×C11C3×C4direct (N × H)
16. C2×C3×C4×C11C22×C3direct (N × H)
17. C2×C32×C11C22×C4direct (N × H)
20. C22×C4×C11C2×C32direct (N × H)
22. C22×C32×C4C2×C11direct (N × H)
23. C22×C3×C11C2×C3×C4direct (N × H)
25. C3×C4×C11C23×C3direct (N × H)
26. C32×C11C23×C4direct (N × H)
27. C23×C3×C4C3×C11direct (N × H)
28. C23×C11C32×C4direct (N × H)
30. C2×C4×C11C22×C32direct (N × H)
31. C23×C32C4×C11direct (N × H)
33. C2×C32×C4C22×C11direct (N × H)
34. C2×C3×C11C22×C3×C4direct (N × H)
37. C22×C3×C4C2×C3×C11direct (N × H)
38. C22×C11C2×C32×C4direct (N × H)
40. C4×C11C23×C32direct (N × H)
41. C22×C32C2×C4×C11direct (N × H)
43. C32×C4C23×C11direct (N × H)
44. C3×C11C23×C3×C4direct (N × H)
45. C23×C4C32×C11direct (N × H)
46. C23×C3C3×C4×C11direct (N × H)
48. C2×C3×C4C22×C3×C11direct (N × H)
49. C2×C11C22×C32×C4direct (N × H)
51. C2×C32C22×C4×C11direct (N × H)
54. C22×C4C2×C32×C11direct (N × H)
55. C22×C3C2×C3×C4×C11direct (N × H)
57. C3×C4C23×C3×C11direct (N × H)
58. C11C23×C32×C4direct (N × H)
59. C32C23×C4×C11direct (N × H)
60. C23C32×C4×C11direct (N × H)
62. C2×C4C22×C32×C11direct (N × H)
63. C2×C3C22×C3×C4×C11direct (N × H)
65. C22C2×C32×C4×C11direct (N × H)
67. C4C23×C32×C11direct (N × H)
68. C3C23×C3×C4×C11direct (N × H)
69. C2C22×C32×C4×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C32×C112
C22×C32×C4×C112
C23×C3×C4×C113
C23×C32×C411