Finite Group Databasebeta

← C23×C3×C4×C112 #72190058

Subgroups — C23×C3×C4×C112 #72190058

Order 11616.

3304 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×C112C211yesmaximal, characteristic
2C22×C3×C4×C112C2114yesmaximal, direct product factor
3C23×C4×C112C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C112C418yesdirect product factor
5C23×C3×C112C2217yes—
6C2×C3×C4×C112C22128yesdirect product factor
7C24×C112C2×C311yescharacteristic
8C22×C4×C112C2×C3114yesdirect product factor
9C22×C3×C112C2×C4128yesdirect product factor
10C22×C3×C112C2317yes—
11C3×C4×C112C2318yesdirect product factor
12C23×C3×C4×C11C11112yesmaximal, direct product factor
13C23×C112C3×C418yesdirect product factor
14C23×C112C22×C317yes—
15C2×C4×C112C22×C3128yesdirect product factor
16C2×C3×C112C22×C4114yesdirect product factor
17C2×C3×C112C2411yescharacteristic
18C24×C3×C11C2×C11112yes—
19C22×C3×C4×C11C2×C111168yesdirect product factor
20C22×C112C2×C3×C4128yesdirect product factor
21C22×C112C23×C317yes—
22C4×C112C23×C318yesdirect product factor
23C3×C112C23×C411yescharacteristic, direct product factor, Hall
24C23×C4×C11C3×C11112yesdirect product factor
25C23×C3×C11C4×C11196yesdirect product factor
26C23×C3×C11C22×C11184yes—
27C2×C3×C4×C11C22×C111336yesdirect product factor
28C2×C112C22×C3×C4114yesdirect product factor
29C2×C112C24×C311yescharacteristic
30C24×C11C2×C3×C11112yes—
31C22×C4×C11C2×C3×C111168yesdirect product factor
32C22×C3×C11C2×C4×C111336yesdirect product factor
33C22×C3×C11C23×C11184yes—
34C3×C4×C11C23×C11196yesdirect product factor
35C112C23×C3×C411yescharacteristic, direct product factor, Sylow
36C23×C3×C4C11211yescharacteristic, direct product factor, Hall
37C23×C11C3×C4×C11196yesdirect product factor
38C23×C11C22×C3×C11184yes—
39C2×C4×C11C22×C3×C111336yesdirect product factor
40C2×C3×C11C22×C4×C111168yesdirect product factor
41C2×C3×C11C24×C11112yes—
42C24×C3C2×C11211yescharacteristic
43C22×C3×C4C2×C112114yesdirect product factor
44C22×C11C2×C3×C4×C111336yesdirect product factor
45C22×C11C23×C3×C11184yes—
46C4×C11C23×C3×C11196yesdirect product factor
47C3×C11C23×C4×C11112yesdirect product factor
48C23×C4C3×C11211yescharacteristic, direct product factor, Sylow
49C23×C3C4×C11218yesdirect product factor
50C23×C3C22×C11217yes—
51C2×C3×C4C22×C112128yesdirect product factor
52C2×C11C22×C3×C4×C111168yesdirect product factor
53C2×C11C24×C3×C11112yes—
54C24C2×C3×C11211yescharacteristic
55C22×C4C2×C3×C112114yesdirect product factor
56C22×C3C2×C4×C112128yesdirect product factor
57C22×C3C23×C11217yes—
58C3×C4C23×C11218yesdirect product factor
59C11C23×C3×C4×C11112yesdirect product factor
60C23C3×C4×C11218yesdirect product factor
61C23C22×C3×C11217yes—
62C2×C4C22×C3×C112128yesdirect product factor
63C2×C3C22×C4×C112114yesdirect product factor
64C2×C3C24×C11211yescharacteristic
65C22C2×C3×C4×C112128yesdirect product factor
66C22C23×C3×C11217yes—
67C4C23×C3×C11218yesdirect product factor
68C3C23×C4×C11211yescharacteristic, direct product factor, Sylow
69C2C22×C3×C4×C112114yesdirect product factor
70C2C24×C3×C11211yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C3×C112
socle, prime radicalC24×C3×C112C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×C112C2direct (N × H)
3. C23×C4×C112C3direct (N × H)
4. C23×C3×C112C4direct (N × H)
6. C2×C3×C4×C112C22direct (N × H)
8. C22×C4×C112C2×C3direct (N × H)
9. C22×C3×C112C2×C4direct (N × H)
11. C3×C4×C112C23direct (N × H)
12. C23×C3×C4×C11C11direct (N × H)
13. C23×C112C3×C4direct (N × H)
15. C2×C4×C112C22×C3direct (N × H)
16. C2×C3×C112C22×C4direct (N × H)
19. C22×C3×C4×C11C2×C11direct (N × H)
20. C22×C112C2×C3×C4direct (N × H)
22. C4×C112C23×C3direct (N × H)
23. C3×C112C23×C4direct (N × H)
24. C23×C4×C11C3×C11direct (N × H)
25. C23×C3×C11C4×C11direct (N × H)
27. C2×C3×C4×C11C22×C11direct (N × H)
28. C2×C112C22×C3×C4direct (N × H)
31. C22×C4×C11C2×C3×C11direct (N × H)
32. C22×C3×C11C2×C4×C11direct (N × H)
34. C3×C4×C11C23×C11direct (N × H)
35. C112C23×C3×C4direct (N × H)
36. C23×C3×C4C112direct (N × H)
37. C23×C11C3×C4×C11direct (N × H)
39. C2×C4×C11C22×C3×C11direct (N × H)
40. C2×C3×C11C22×C4×C11direct (N × H)
43. C22×C3×C4C2×C112direct (N × H)
44. C22×C11C2×C3×C4×C11direct (N × H)
46. C4×C11C23×C3×C11direct (N × H)
47. C3×C11C23×C4×C11direct (N × H)
48. C23×C4C3×C112direct (N × H)
49. C23×C3C4×C112direct (N × H)
51. C2×C3×C4C22×C112direct (N × H)
52. C2×C11C22×C3×C4×C11direct (N × H)
55. C22×C4C2×C3×C112direct (N × H)
56. C22×C3C2×C4×C112direct (N × H)
58. C3×C4C23×C112direct (N × H)
59. C11C23×C3×C4×C11direct (N × H)
60. C23C3×C4×C112direct (N × H)
62. C2×C4C22×C3×C112direct (N × H)
63. C2×C3C22×C4×C112direct (N × H)
65. C22C2×C3×C4×C112direct (N × H)
67. C4C23×C3×C112direct (N × H)
68. C3C23×C4×C112direct (N × H)
69. C2C22×C3×C4×C112direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×C1122
C22×C3×C4×C1122
C23×C4×C1123
C23×C3×C4×C1111