Finite Group Databasebeta

← C22×C4×C112×C13 #72202425

Subgroups — C22×C4×C112×C13 #72202425

Order 25168.

756 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C112×C13C211yesmaximal, characteristic
2C2×C4×C112×C13C216yesmaximal, direct product factor
3C22×C4×C11×C13C11112yesmaximal, direct product factor
4C22×C112×C13C414yesdirect product factor
5C22×C112×C13C2213yes—
6C4×C112×C13C2214yesdirect product factor
7C2×C112×C13C2×C416yesdirect product factor
8C2×C112×C13C2311yescharacteristic
9C22×C4×C112C1311yesmaximal, characteristic, direct product factor, Hall
10C112×C13C22×C411yescharacteristic, direct product factor, Hall
11C23×C11×C13C2×C11112yes—
12C2×C4×C11×C13C2×C11172yesdirect product factor
13C23×C112C2×C1311yescharacteristic
14C2×C4×C112C2×C1316yesdirect product factor
15C22×C11×C13C4×C11148yesdirect product factor
16C22×C11×C13C22×C11136yes—
17C4×C11×C13C22×C11148yesdirect product factor
18C22×C112C4×C1314yesdirect product factor
19C22×C112C22×C1313yes—
20C4×C112C22×C1314yesdirect product factor
21C2×C11×C13C2×C4×C11172yesdirect product factor
22C2×C11×C13C23×C11112yes—
23C2×C112C2×C4×C1316yesdirect product factor
24C2×C112C23×C1311yescharacteristic
25C22×C4×C13C11211yescharacteristic, direct product factor, Hall
26C22×C4×C11C11×C13112yesdirect product factor
27C11×C13C22×C4×C11112yesdirect product factor
28C112C22×C4×C1311yescharacteristic, direct product factor, Sylow
29C23×C13C2×C11211yescharacteristic
30C2×C4×C13C2×C11216yesdirect product factor
31C23×C11C2×C11×C13112yes—
32C2×C4×C11C2×C11×C13172yesdirect product factor
33C22×C13C4×C11214yesdirect product factor
34C22×C13C22×C11213yes—
35C4×C13C22×C11214yesdirect product factor
36C22×C11C4×C11×C13148yesdirect product factor
37C22×C11C22×C11×C13136yes—
38C4×C11C22×C11×C13148yesdirect product factor
39C2×C13C2×C4×C11216yesdirect product factor
40C2×C13C23×C11211yescharacteristic
41C2×C11C2×C4×C11×C13172yesdirect product factor
42C2×C11C23×C11×C13112yes—
43C22×C4C112×C1311yescharacteristic, direct product factor, Sylow
44C13C22×C4×C11211yescharacteristic, direct product factor, Sylow
45C11C22×C4×C11×C13112yesdirect product factor
46C23C2×C112×C1311yescharacteristic
47C2×C4C2×C112×C1316yesdirect product factor
48C22C4×C112×C1314yesdirect product factor
49C22C22×C112×C1313yes—
50C4C22×C112×C1314yesdirect product factor
51C2C2×C4×C112×C1316yesdirect product factor
52C2C23×C112×C1311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C112×C13
socle, prime radicalC23×C112×C13C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C112×C13C2direct (N × H)
3. C22×C4×C11×C13C11direct (N × H)
4. C22×C112×C13C4direct (N × H)
6. C4×C112×C13C22direct (N × H)
7. C2×C112×C13C2×C4direct (N × H)
9. C22×C4×C112C13direct (N × H)
10. C112×C13C22×C4direct (N × H)
12. C2×C4×C11×C13C2×C11direct (N × H)
14. C2×C4×C112C2×C13direct (N × H)
15. C22×C11×C13C4×C11direct (N × H)
17. C4×C11×C13C22×C11direct (N × H)
18. C22×C112C4×C13direct (N × H)
20. C4×C112C22×C13direct (N × H)
21. C2×C11×C13C2×C4×C11direct (N × H)
23. C2×C112C2×C4×C13direct (N × H)
25. C22×C4×C13C112direct (N × H)
26. C22×C4×C11C11×C13direct (N × H)
27. C11×C13C22×C4×C11direct (N × H)
28. C112C22×C4×C13direct (N × H)
30. C2×C4×C13C2×C112direct (N × H)
32. C2×C4×C11C2×C11×C13direct (N × H)
33. C22×C13C4×C112direct (N × H)
35. C4×C13C22×C112direct (N × H)
36. C22×C11C4×C11×C13direct (N × H)
38. C4×C11C22×C11×C13direct (N × H)
39. C2×C13C2×C4×C112direct (N × H)
41. C2×C11C2×C4×C11×C13direct (N × H)
43. C22×C4C112×C13direct (N × H)
44. C13C22×C4×C112direct (N × H)
45. C11C22×C4×C11×C13direct (N × H)
47. C2×C4C2×C112×C13direct (N × H)
48. C22C4×C112×C13direct (N × H)
50. C4C22×C112×C13direct (N × H)
51. C2C2×C4×C112×C13direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C112×C132
C2×C4×C112×C132
C22×C4×C11×C1311
C22×C4×C11213