Finite Group Databasebeta

← C23×C4×C17×C23 #72190861

Subgroups — C23×C4×C17×C23 #72190861

Order 12512.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C17×C23C211yesmaximal, characteristic
2C22×C4×C17×C23C2114yesmaximal, direct product factor
3C23×C17×C23C418yesdirect product factor
4C23×C17×C23C2217yes—
5C2×C4×C17×C23C22128yesdirect product factor
6C22×C17×C23C2×C4128yesdirect product factor
7C22×C17×C23C2317yes—
8C4×C17×C23C2318yesdirect product factor
9C2×C17×C23C22×C4114yesdirect product factor
10C2×C17×C23C2411yescharacteristic
11C23×C4×C23C1711yesmaximal, characteristic, direct product factor, Hall
12C23×C4×C17C2311yesmaximal, characteristic, direct product factor, Hall
13C17×C23C23×C411yescharacteristic, direct product factor, Hall
14C24×C23C2×C1711yescharacteristic
15C22×C4×C23C2×C17114yesdirect product factor
16C24×C17C2×C2311yescharacteristic
17C22×C4×C17C2×C23114yesdirect product factor
18C23×C23C4×C1718yesdirect product factor
19C23×C23C22×C1717yes—
20C2×C4×C23C22×C17128yesdirect product factor
21C23×C17C4×C2318yesdirect product factor
22C23×C17C22×C2317yes—
23C2×C4×C17C22×C23128yesdirect product factor
24C22×C23C2×C4×C17128yesdirect product factor
25C22×C23C23×C1717yes—
26C4×C23C23×C1718yesdirect product factor
27C22×C17C2×C4×C23128yesdirect product factor
28C22×C17C23×C2317yes—
29C4×C17C23×C2318yesdirect product factor
30C2×C23C22×C4×C17114yesdirect product factor
31C2×C23C24×C1711yescharacteristic
32C2×C17C22×C4×C23114yesdirect product factor
33C2×C17C24×C2311yescharacteristic
34C23×C4C17×C2311yescharacteristic, direct product factor, Sylow
35C23C23×C4×C1711yescharacteristic, direct product factor, Sylow
36C17C23×C4×C2311yescharacteristic, direct product factor, Sylow
37C24C2×C17×C2311yescharacteristic
38C22×C4C2×C17×C23114yesdirect product factor
39C23C4×C17×C2318yesdirect product factor
40C23C22×C17×C2317yes—
41C2×C4C22×C17×C23128yesdirect product factor
42C22C2×C4×C17×C23128yesdirect product factor
43C22C23×C17×C2317yes—
44C4C23×C17×C2318yesdirect product factor
45C2C22×C4×C17×C23114yesdirect product factor
46C2C24×C17×C2311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C17×C23
socle, prime radicalC24×C17×C23C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×C17×C23C2direct (N × H)
3. C23×C17×C23C4direct (N × H)
5. C2×C4×C17×C23C22direct (N × H)
6. C22×C17×C23C2×C4direct (N × H)
8. C4×C17×C23C23direct (N × H)
9. C2×C17×C23C22×C4direct (N × H)
11. C23×C4×C23C17direct (N × H)
12. C23×C4×C17C23direct (N × H)
13. C17×C23C23×C4direct (N × H)
15. C22×C4×C23C2×C17direct (N × H)
17. C22×C4×C17C2×C23direct (N × H)
18. C23×C23C4×C17direct (N × H)
20. C2×C4×C23C22×C17direct (N × H)
21. C23×C17C4×C23direct (N × H)
23. C2×C4×C17C22×C23direct (N × H)
24. C22×C23C2×C4×C17direct (N × H)
26. C4×C23C23×C17direct (N × H)
27. C22×C17C2×C4×C23direct (N × H)
29. C4×C17C23×C23direct (N × H)
30. C2×C23C22×C4×C17direct (N × H)
32. C2×C17C22×C4×C23direct (N × H)
34. C23×C4C17×C23direct (N × H)
35. C23C23×C4×C17direct (N × H)
36. C17C23×C4×C23direct (N × H)
38. C22×C4C2×C17×C23direct (N × H)
39. C23C4×C17×C23direct (N × H)
41. C2×C4C22×C17×C23direct (N × H)
42. C22C2×C4×C17×C23direct (N × H)
44. C4C23×C17×C23direct (N × H)
45. C2C22×C4×C17×C23direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C17×C232
C22×C4×C17×C232
C23×C4×C2317
C23×C4×C1723