Finite Group Databasebeta

← C23×C4×C7×C47 #72189136

Subgroups — C23×C4×C7×C47 #72189136

Order 10528.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×C47C2114yesmaximal, direct product factor
2C24×C7×C47C211yesmaximal, characteristic
3C2×C4×C7×C47C22128yesdirect product factor
4C23×C7×C47C418yesdirect product factor
5C23×C7×C47C2217yes—
6C23×C4×C47C711yesmaximal, characteristic, direct product factor, Hall
7C22×C7×C47C2×C4128yesdirect product factor
8C22×C7×C47C2317yes—
9C4×C7×C47C2318yesdirect product factor
10C24×C47C2×C711yescharacteristic
11C22×C4×C47C2×C7114yesdirect product factor
12C2×C7×C47C22×C4114yesdirect product factor
13C2×C7×C47C2411yescharacteristic
14C23×C47C4×C718yesdirect product factor
15C23×C47C22×C717yes—
16C2×C4×C47C22×C7128yesdirect product factor
17C7×C47C23×C411yescharacteristic, direct product factor, Hall
18C23×C4×C7C4711yesmaximal, characteristic, direct product factor, Hall
19C22×C47C2×C4×C7128yesdirect product factor
20C22×C47C23×C717yes—
21C4×C47C23×C718yesdirect product factor
22C24×C7C2×C4711yescharacteristic
23C22×C4×C7C2×C47114yesdirect product factor
24C2×C47C22×C4×C7114yesdirect product factor
25C2×C47C24×C711yescharacteristic
26C23×C7C4×C4718yesdirect product factor
27C23×C7C22×C4717yes—
28C2×C4×C7C22×C47128yesdirect product factor
29C47C23×C4×C711yescharacteristic, direct product factor, Sylow
30C23×C4C7×C4711yescharacteristic, direct product factor, Sylow
31C22×C7C2×C4×C47128yesdirect product factor
32C22×C7C23×C4717yes—
33C4×C7C23×C4718yesdirect product factor
34C24C2×C7×C4711yescharacteristic
35C22×C4C2×C7×C47114yesdirect product factor
36C2×C7C22×C4×C47114yesdirect product factor
37C2×C7C24×C4711yescharacteristic
38C23C4×C7×C4718yesdirect product factor
39C23C22×C7×C4717yes—
40C2×C4C22×C7×C47128yesdirect product factor
41C7C23×C4×C4711yescharacteristic, direct product factor, Sylow
42C22C23×C7×C4717yes—
43C22C2×C4×C7×C47128yesdirect product factor
44C4C23×C7×C4718yesdirect product factor
45C2C24×C7×C4711yescharacteristic
46C2C22×C4×C7×C47114yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C7×C47
socle, prime radicalC24×C7×C47C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×C47C2direct (N × H)
3. C2×C4×C7×C47C22direct (N × H)
4. C23×C7×C47C4direct (N × H)
6. C23×C4×C47C7direct (N × H)
7. C22×C7×C47C2×C4direct (N × H)
9. C4×C7×C47C23direct (N × H)
11. C22×C4×C47C2×C7direct (N × H)
12. C2×C7×C47C22×C4direct (N × H)
14. C23×C47C4×C7direct (N × H)
16. C2×C4×C47C22×C7direct (N × H)
17. C7×C47C23×C4direct (N × H)
18. C23×C4×C7C47direct (N × H)
19. C22×C47C2×C4×C7direct (N × H)
21. C4×C47C23×C7direct (N × H)
23. C22×C4×C7C2×C47direct (N × H)
24. C2×C47C22×C4×C7direct (N × H)
26. C23×C7C4×C47direct (N × H)
28. C2×C4×C7C22×C47direct (N × H)
29. C47C23×C4×C7direct (N × H)
30. C23×C4C7×C47direct (N × H)
31. C22×C7C2×C4×C47direct (N × H)
33. C4×C7C23×C47direct (N × H)
35. C22×C4C2×C7×C47direct (N × H)
36. C2×C7C22×C4×C47direct (N × H)
38. C23C4×C7×C47direct (N × H)
40. C2×C4C22×C7×C47direct (N × H)
41. C7C23×C4×C47direct (N × H)
43. C22C2×C4×C7×C47direct (N × H)
44. C4C23×C7×C47direct (N × H)
46. C2C22×C4×C7×C47direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×C472
C24×C7×C472
C23×C4×C477
C23×C4×C747