Finite Group Databasebeta

← C22×C3×C4×C13×C23 #72192513

Subgroups — C22×C3×C4×C13×C23 #72192513

Order 14352.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C13×C23C211yesmaximal, characteristic
2C2×C3×C4×C13×C23C216yesmaximal, direct product factor
3C22×C4×C13×C23C311yesmaximal, characteristic, direct product factor, Hall
4C23×C13×C23C2×C311yescharacteristic
5C2×C4×C13×C23C2×C316yesdirect product factor
6C22×C3×C13×C23C414yesdirect product factor
7C22×C3×C13×C23C2213yes—
8C3×C4×C13×C23C2214yesdirect product factor
9C2×C3×C13×C23C2×C416yesdirect product factor
10C2×C3×C13×C23C2311yescharacteristic
11C22×C13×C23C3×C414yesdirect product factor
12C22×C13×C23C22×C313yes—
13C4×C13×C23C22×C314yesdirect product factor
14C22×C3×C4×C23C1311yesmaximal, characteristic, direct product factor, Hall
15C3×C13×C23C22×C411yescharacteristic, direct product factor, Hall
16C22×C3×C4×C13C2311yesmaximal, characteristic, direct product factor, Hall
17C2×C13×C23C2×C3×C416yesdirect product factor
18C2×C13×C23C23×C311yescharacteristic
19C23×C3×C23C2×C1311yescharacteristic
20C2×C3×C4×C23C2×C1316yesdirect product factor
21C22×C4×C23C3×C1311yescharacteristic, direct product factor, Hall
22C23×C3×C13C2×C2311yescharacteristic
23C2×C3×C4×C13C2×C2316yesdirect product factor
24C13×C23C22×C3×C411yescharacteristic, direct product factor, Hall
25C22×C3×C23C4×C1314yesdirect product factor
26C22×C3×C23C22×C1313yes—
27C3×C4×C23C22×C1314yesdirect product factor
28C22×C4×C13C3×C2311yescharacteristic, direct product factor, Hall
29C23×C23C2×C3×C1311yescharacteristic
30C2×C4×C23C2×C3×C1316yesdirect product factor
31C22×C3×C13C4×C2314yesdirect product factor
32C22×C3×C13C22×C2313yes—
33C3×C4×C13C22×C2314yesdirect product factor
34C2×C3×C23C2×C4×C1316yesdirect product factor
35C2×C3×C23C23×C1311yescharacteristic
36C23×C13C2×C3×C2311yescharacteristic
37C2×C4×C13C2×C3×C2316yesdirect product factor
38C22×C23C3×C4×C1314yesdirect product factor
39C22×C23C22×C3×C1313yes—
40C4×C23C22×C3×C1314yesdirect product factor
41C2×C3×C13C2×C4×C2316yesdirect product factor
42C2×C3×C13C23×C2311yescharacteristic
43C3×C23C22×C4×C1311yescharacteristic, direct product factor, Hall
44C22×C13C3×C4×C2314yesdirect product factor
45C22×C13C22×C3×C2313yes—
46C4×C13C22×C3×C2314yesdirect product factor
47C22×C3×C4C13×C2311yescharacteristic, direct product factor, Hall
48C2×C23C2×C3×C4×C1316yesdirect product factor
49C2×C23C23×C3×C1311yescharacteristic
50C3×C13C22×C4×C2311yescharacteristic, direct product factor, Hall
51C2×C13C2×C3×C4×C2316yesdirect product factor
52C2×C13C23×C3×C2311yescharacteristic
53C23×C3C2×C13×C2311yescharacteristic
54C2×C3×C4C2×C13×C2316yesdirect product factor
55C23C22×C3×C4×C1311yescharacteristic, direct product factor, Sylow
56C22×C4C3×C13×C2311yescharacteristic, direct product factor, Sylow
57C13C22×C3×C4×C2311yescharacteristic, direct product factor, Sylow
58C22×C3C4×C13×C2314yesdirect product factor
59C22×C3C22×C13×C2313yes—
60C3×C4C22×C13×C2314yesdirect product factor
61C23C2×C3×C13×C2311yescharacteristic
62C2×C4C2×C3×C13×C2316yesdirect product factor
63C2×C3C2×C4×C13×C2316yesdirect product factor
64C2×C3C23×C13×C2311yescharacteristic
65C22C3×C4×C13×C2314yesdirect product factor
66C22C22×C3×C13×C2313yes—
67C4C22×C3×C13×C2314yesdirect product factor
68C3C22×C4×C13×C2311yescharacteristic, direct product factor, Sylow
69C2C2×C3×C4×C13×C2316yesdirect product factor
70C2C23×C3×C13×C2311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C13×C23
socle, prime radicalC23×C3×C13×C23C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C13×C23C2direct (N × H)
3. C22×C4×C13×C23C3direct (N × H)
5. C2×C4×C13×C23C2×C3direct (N × H)
6. C22×C3×C13×C23C4direct (N × H)
8. C3×C4×C13×C23C22direct (N × H)
9. C2×C3×C13×C23C2×C4direct (N × H)
11. C22×C13×C23C3×C4direct (N × H)
13. C4×C13×C23C22×C3direct (N × H)
14. C22×C3×C4×C23C13direct (N × H)
15. C3×C13×C23C22×C4direct (N × H)
16. C22×C3×C4×C13C23direct (N × H)
17. C2×C13×C23C2×C3×C4direct (N × H)
20. C2×C3×C4×C23C2×C13direct (N × H)
21. C22×C4×C23C3×C13direct (N × H)
23. C2×C3×C4×C13C2×C23direct (N × H)
24. C13×C23C22×C3×C4direct (N × H)
25. C22×C3×C23C4×C13direct (N × H)
27. C3×C4×C23C22×C13direct (N × H)
28. C22×C4×C13C3×C23direct (N × H)
30. C2×C4×C23C2×C3×C13direct (N × H)
31. C22×C3×C13C4×C23direct (N × H)
33. C3×C4×C13C22×C23direct (N × H)
34. C2×C3×C23C2×C4×C13direct (N × H)
37. C2×C4×C13C2×C3×C23direct (N × H)
38. C22×C23C3×C4×C13direct (N × H)
40. C4×C23C22×C3×C13direct (N × H)
41. C2×C3×C13C2×C4×C23direct (N × H)
43. C3×C23C22×C4×C13direct (N × H)
44. C22×C13C3×C4×C23direct (N × H)
46. C4×C13C22×C3×C23direct (N × H)
47. C22×C3×C4C13×C23direct (N × H)
48. C2×C23C2×C3×C4×C13direct (N × H)
50. C3×C13C22×C4×C23direct (N × H)
51. C2×C13C2×C3×C4×C23direct (N × H)
54. C2×C3×C4C2×C13×C23direct (N × H)
55. C23C22×C3×C4×C13direct (N × H)
56. C22×C4C3×C13×C23direct (N × H)
57. C13C22×C3×C4×C23direct (N × H)
58. C22×C3C4×C13×C23direct (N × H)
60. C3×C4C22×C13×C23direct (N × H)
62. C2×C4C2×C3×C13×C23direct (N × H)
63. C2×C3C2×C4×C13×C23direct (N × H)
65. C22C3×C4×C13×C23direct (N × H)
67. C4C22×C3×C13×C23direct (N × H)
68. C3C22×C4×C13×C23direct (N × H)
69. C2C2×C3×C4×C13×C23direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C13×C232
C2×C3×C4×C13×C232
C22×C4×C13×C233
C22×C3×C4×C2313
C22×C3×C4×C1323