Finite Group Databasebeta

← C23×C3×C4×C293 #72205124

Subgroups — C23×C3×C4×C293 #72205124

Order 28128.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×C293C211yesmaximal, characteristic
2C22×C3×C4×C293C2114yesmaximal, direct product factor
3C23×C3×C293C418yesdirect product factor
4C23×C3×C293C2217yes—
5C2×C3×C4×C293C22128yesdirect product factor
6C23×C4×C293C311yesmaximal, characteristic, direct product factor, Hall
7C24×C293C2×C311yescharacteristic
8C22×C4×C293C2×C3114yesdirect product factor
9C22×C3×C293C2×C4128yesdirect product factor
10C22×C3×C293C2317yes—
11C3×C4×C293C2318yesdirect product factor
12C23×C293C3×C418yesdirect product factor
13C23×C293C22×C317yes—
14C2×C4×C293C22×C3128yesdirect product factor
15C2×C3×C293C22×C4114yesdirect product factor
16C2×C3×C293C2411yescharacteristic
17C22×C293C2×C3×C4128yesdirect product factor
18C22×C293C23×C317yes—
19C4×C293C23×C318yesdirect product factor
20C3×C293C23×C411yescharacteristic, direct product factor, Hall
21C2×C293C22×C3×C4114yesdirect product factor
22C2×C293C24×C311yescharacteristic
23C293C23×C3×C411yescharacteristic, direct product factor, Sylow
24C23×C3×C4C29311yesmaximal, characteristic, direct product factor, Hall
25C24×C3C2×C29311yescharacteristic
26C22×C3×C4C2×C293114yesdirect product factor
27C23×C4C3×C29311yescharacteristic, direct product factor, Sylow
28C23×C3C4×C29318yesdirect product factor
29C23×C3C22×C29317yes—
30C2×C3×C4C22×C293128yesdirect product factor
31C24C2×C3×C29311yescharacteristic
32C22×C4C2×C3×C293114yesdirect product factor
33C22×C3C2×C4×C293128yesdirect product factor
34C22×C3C23×C29317yes—
35C3×C4C23×C29318yesdirect product factor
36C23C3×C4×C29318yesdirect product factor
37C23C22×C3×C29317yes—
38C2×C4C22×C3×C293128yesdirect product factor
39C2×C3C22×C4×C293114yesdirect product factor
40C2×C3C24×C29311yescharacteristic
41C22C2×C3×C4×C293128yesdirect product factor
42C22C23×C3×C29317yes—
43C4C23×C3×C29318yesdirect product factor
44C3C23×C4×C29311yescharacteristic, direct product factor, Sylow
45C2C22×C3×C4×C293114yesdirect product factor
46C2C24×C3×C29311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C3×C293
socle, prime radicalC24×C3×C293C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×C293C2direct (N × H)
3. C23×C3×C293C4direct (N × H)
5. C2×C3×C4×C293C22direct (N × H)
6. C23×C4×C293C3direct (N × H)
8. C22×C4×C293C2×C3direct (N × H)
9. C22×C3×C293C2×C4direct (N × H)
11. C3×C4×C293C23direct (N × H)
12. C23×C293C3×C4direct (N × H)
14. C2×C4×C293C22×C3direct (N × H)
15. C2×C3×C293C22×C4direct (N × H)
17. C22×C293C2×C3×C4direct (N × H)
19. C4×C293C23×C3direct (N × H)
20. C3×C293C23×C4direct (N × H)
21. C2×C293C22×C3×C4direct (N × H)
23. C293C23×C3×C4direct (N × H)
24. C23×C3×C4C293direct (N × H)
26. C22×C3×C4C2×C293direct (N × H)
27. C23×C4C3×C293direct (N × H)
28. C23×C3C4×C293direct (N × H)
30. C2×C3×C4C22×C293direct (N × H)
32. C22×C4C2×C3×C293direct (N × H)
33. C22×C3C2×C4×C293direct (N × H)
35. C3×C4C23×C293direct (N × H)
36. C23C3×C4×C293direct (N × H)
38. C2×C4C22×C3×C293direct (N × H)
39. C2×C3C22×C4×C293direct (N × H)
41. C22C2×C3×C4×C293direct (N × H)
43. C4C23×C3×C293direct (N × H)
44. C3C23×C4×C293direct (N × H)
45. C2C22×C3×C4×C293direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×C2932
C22×C3×C4×C2932
C23×C4×C2933
C23×C3×C4293