Finite Group Databasebeta

← C23×C4×C17×C41 #72199751

Subgroups — C23×C4×C17×C41 #72199751

Order 22304.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C17×C41C211yesmaximal, characteristic
2C22×C4×C17×C41C2114yesmaximal, direct product factor
3C23×C17×C41C418yesdirect product factor
4C23×C17×C41C2217yes—
5C2×C4×C17×C41C22128yesdirect product factor
6C22×C17×C41C2×C4128yesdirect product factor
7C22×C17×C41C2317yes—
8C4×C17×C41C2318yesdirect product factor
9C2×C17×C41C22×C4114yesdirect product factor
10C2×C17×C41C2411yescharacteristic
11C23×C4×C41C1711yesmaximal, characteristic, direct product factor, Hall
12C17×C41C23×C411yescharacteristic, direct product factor, Hall
13C24×C41C2×C1711yescharacteristic
14C22×C4×C41C2×C17114yesdirect product factor
15C23×C4×C17C4111yesmaximal, characteristic, direct product factor, Hall
16C23×C41C4×C1718yesdirect product factor
17C23×C41C22×C1717yes—
18C2×C4×C41C22×C17128yesdirect product factor
19C24×C17C2×C4111yescharacteristic
20C22×C4×C17C2×C41114yesdirect product factor
21C22×C41C2×C4×C17128yesdirect product factor
22C22×C41C23×C1717yes—
23C4×C41C23×C1718yesdirect product factor
24C23×C17C4×C4118yesdirect product factor
25C23×C17C22×C4117yes—
26C2×C4×C17C22×C41128yesdirect product factor
27C2×C41C22×C4×C17114yesdirect product factor
28C2×C41C24×C1711yescharacteristic
29C22×C17C2×C4×C41128yesdirect product factor
30C22×C17C23×C4117yes—
31C4×C17C23×C4118yesdirect product factor
32C41C23×C4×C1711yescharacteristic, direct product factor, Sylow
33C2×C17C22×C4×C41114yesdirect product factor
34C2×C17C24×C4111yescharacteristic
35C23×C4C17×C4111yescharacteristic, direct product factor, Sylow
36C17C23×C4×C4111yescharacteristic, direct product factor, Sylow
37C24C2×C17×C4111yescharacteristic
38C22×C4C2×C17×C41114yesdirect product factor
39C23C4×C17×C4118yesdirect product factor
40C23C22×C17×C4117yes—
41C2×C4C22×C17×C41128yesdirect product factor
42C22C2×C4×C17×C41128yesdirect product factor
43C22C23×C17×C4117yes—
44C4C23×C17×C4118yesdirect product factor
45C2C22×C4×C17×C41114yesdirect product factor
46C2C24×C17×C4111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C17×C41
socle, prime radicalC24×C17×C41C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×C17×C41C2direct (N × H)
3. C23×C17×C41C4direct (N × H)
5. C2×C4×C17×C41C22direct (N × H)
6. C22×C17×C41C2×C4direct (N × H)
8. C4×C17×C41C23direct (N × H)
9. C2×C17×C41C22×C4direct (N × H)
11. C23×C4×C41C17direct (N × H)
12. C17×C41C23×C4direct (N × H)
14. C22×C4×C41C2×C17direct (N × H)
15. C23×C4×C17C41direct (N × H)
16. C23×C41C4×C17direct (N × H)
18. C2×C4×C41C22×C17direct (N × H)
20. C22×C4×C17C2×C41direct (N × H)
21. C22×C41C2×C4×C17direct (N × H)
23. C4×C41C23×C17direct (N × H)
24. C23×C17C4×C41direct (N × H)
26. C2×C4×C17C22×C41direct (N × H)
27. C2×C41C22×C4×C17direct (N × H)
29. C22×C17C2×C4×C41direct (N × H)
31. C4×C17C23×C41direct (N × H)
32. C41C23×C4×C17direct (N × H)
33. C2×C17C22×C4×C41direct (N × H)
35. C23×C4C17×C41direct (N × H)
36. C17C23×C4×C41direct (N × H)
38. C22×C4C2×C17×C41direct (N × H)
39. C23C4×C17×C41direct (N × H)
41. C2×C4C22×C17×C41direct (N × H)
42. C22C2×C4×C17×C41direct (N × H)
44. C4C23×C17×C41direct (N × H)
45. C2C22×C4×C17×C41direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C17×C412
C22×C4×C17×C412
C23×C4×C4117
C23×C4×C1741