Finite Group Databasebeta

← C23×C4×C11×C53 #72196449

Subgroups — C23×C4×C11×C53 #72196449

Order 18656.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C11×C53C211yesmaximal, characteristic
2C22×C4×C11×C53C2114yesmaximal, direct product factor
3C23×C11×C53C418yesdirect product factor
4C23×C11×C53C2217yes—
5C2×C4×C11×C53C22128yesdirect product factor
6C22×C11×C53C2×C4128yesdirect product factor
7C22×C11×C53C2317yes—
8C4×C11×C53C2318yesdirect product factor
9C23×C4×C53C1111yesmaximal, characteristic, direct product factor, Hall
10C2×C11×C53C22×C4114yesdirect product factor
11C2×C11×C53C2411yescharacteristic
12C24×C53C2×C1111yescharacteristic
13C22×C4×C53C2×C11114yesdirect product factor
14C11×C53C23×C411yescharacteristic, direct product factor, Hall
15C23×C53C4×C1118yesdirect product factor
16C23×C53C22×C1117yes—
17C2×C4×C53C22×C11128yesdirect product factor
18C23×C4×C11C5311yesmaximal, characteristic, direct product factor, Hall
19C22×C53C2×C4×C11128yesdirect product factor
20C22×C53C23×C1117yes—
21C4×C53C23×C1118yesdirect product factor
22C24×C11C2×C5311yescharacteristic
23C22×C4×C11C2×C53114yesdirect product factor
24C2×C53C22×C4×C11114yesdirect product factor
25C2×C53C24×C1111yescharacteristic
26C23×C11C4×C5318yesdirect product factor
27C23×C11C22×C5317yes—
28C2×C4×C11C22×C53128yesdirect product factor
29C53C23×C4×C1111yescharacteristic, direct product factor, Sylow
30C22×C11C2×C4×C53128yesdirect product factor
31C22×C11C23×C5317yes—
32C4×C11C23×C5318yesdirect product factor
33C23×C4C11×C5311yescharacteristic, direct product factor, Sylow
34C2×C11C22×C4×C53114yesdirect product factor
35C2×C11C24×C5311yescharacteristic
36C24C2×C11×C5311yescharacteristic
37C22×C4C2×C11×C53114yesdirect product factor
38C11C23×C4×C5311yescharacteristic, direct product factor, Sylow
39C23C4×C11×C5318yesdirect product factor
40C23C22×C11×C5317yes—
41C2×C4C22×C11×C53128yesdirect product factor
42C22C2×C4×C11×C53128yesdirect product factor
43C22C23×C11×C5317yes—
44C4C23×C11×C5318yesdirect product factor
45C2C22×C4×C11×C53114yesdirect product factor
46C2C24×C11×C5311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C11×C53
socle, prime radicalC24×C11×C53C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×C11×C53C2direct (N × H)
3. C23×C11×C53C4direct (N × H)
5. C2×C4×C11×C53C22direct (N × H)
6. C22×C11×C53C2×C4direct (N × H)
8. C4×C11×C53C23direct (N × H)
9. C23×C4×C53C11direct (N × H)
10. C2×C11×C53C22×C4direct (N × H)
13. C22×C4×C53C2×C11direct (N × H)
14. C11×C53C23×C4direct (N × H)
15. C23×C53C4×C11direct (N × H)
17. C2×C4×C53C22×C11direct (N × H)
18. C23×C4×C11C53direct (N × H)
19. C22×C53C2×C4×C11direct (N × H)
21. C4×C53C23×C11direct (N × H)
23. C22×C4×C11C2×C53direct (N × H)
24. C2×C53C22×C4×C11direct (N × H)
26. C23×C11C4×C53direct (N × H)
28. C2×C4×C11C22×C53direct (N × H)
29. C53C23×C4×C11direct (N × H)
30. C22×C11C2×C4×C53direct (N × H)
32. C4×C11C23×C53direct (N × H)
33. C23×C4C11×C53direct (N × H)
34. C2×C11C22×C4×C53direct (N × H)
37. C22×C4C2×C11×C53direct (N × H)
38. C11C23×C4×C53direct (N × H)
39. C23C4×C11×C53direct (N × H)
41. C2×C4C22×C11×C53direct (N × H)
42. C22C2×C4×C11×C53direct (N × H)
44. C4C23×C11×C53direct (N × H)
45. C2C22×C4×C11×C53direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C11×C532
C22×C4×C11×C532
C23×C4×C5311
C23×C4×C1153