Finite Group Databasebeta

← C23×C7×C9×C47 #72201039

Subgroups — C23×C7×C9×C47 #72201039

Order 23688.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C7×C47C311yesmaximal, characteristic
2C23×C9×C47C711yesmaximal, characteristic, direct product factor, Hall
3C23×C7×C47C911yescharacteristic, direct product factor, Hall
4C22×C7×C9×C47C217yesmaximal, direct product factor
5C2×C7×C9×C47C2217yesdirect product factor
6C22×C3×C7×C47C2×C317yes—
7C7×C9×C47C2311yescharacteristic, direct product factor, Hall
8C2×C3×C7×C47C22×C317yes—
9C22×C9×C47C2×C717yesdirect product factor
10C22×C7×C47C2×C917yesdirect product factor
11C23×C3×C47C3×C711yescharacteristic
12C3×C7×C47C23×C311yescharacteristic
13C2×C9×C47C22×C717yesdirect product factor
14C2×C7×C47C22×C917yesdirect product factor
15C22×C3×C47C2×C3×C717yes—
16C23×C7×C9C4711yesmaximal, characteristic, direct product factor, Hall
17C9×C47C23×C711yescharacteristic, direct product factor, Hall
18C23×C47C7×C911yescharacteristic, direct product factor, Hall
19C7×C47C23×C911yescharacteristic, direct product factor, Hall
20C2×C3×C47C22×C3×C717yes—
21C22×C7×C9C2×C4717yesdirect product factor
22C22×C47C2×C7×C917yesdirect product factor
23C23×C3×C7C3×C4711yescharacteristic
24C3×C47C23×C3×C711yescharacteristic
25C2×C7×C9C22×C4717yesdirect product factor
26C2×C47C22×C7×C917yesdirect product factor
27C22×C3×C7C2×C3×C4717yes—
28C23×C9C7×C4711yescharacteristic, direct product factor, Hall
29C7×C9C23×C4711yescharacteristic, direct product factor, Hall
30C23×C7C9×C4711yescharacteristic, direct product factor, Hall
31C47C23×C7×C911yescharacteristic, direct product factor, Sylow
32C2×C3×C7C22×C3×C4717yes—
33C22×C9C2×C7×C4717yesdirect product factor
34C22×C7C2×C9×C4717yesdirect product factor
35C23×C3C3×C7×C4711yescharacteristic
36C3×C7C23×C3×C4711yescharacteristic
37C2×C9C22×C7×C4717yesdirect product factor
38C2×C7C22×C9×C4717yesdirect product factor
39C22×C3C2×C3×C7×C4717yes—
40C9C23×C7×C4711yescharacteristic, direct product factor, Sylow
41C23C7×C9×C4711yescharacteristic, direct product factor, Sylow
42C7C23×C9×C4711yescharacteristic, direct product factor, Sylow
43C2×C3C22×C3×C7×C4717yes—
44C22C2×C7×C9×C4717yesdirect product factor
45C3C23×C3×C7×C4711yescharacteristic
46C2C22×C7×C9×C4717yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C23×C3×C7×C47
socle, prime radicalC23×C3×C7×C47C3
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C9×C47C7direct (N × H)
3. C23×C7×C47C9direct (N × H)
4. C22×C7×C9×C47C2direct (N × H)
5. C2×C7×C9×C47C22direct (N × H)
7. C7×C9×C47C23direct (N × H)
9. C22×C9×C47C2×C7direct (N × H)
10. C22×C7×C47C2×C9direct (N × H)
13. C2×C9×C47C22×C7direct (N × H)
14. C2×C7×C47C22×C9direct (N × H)
16. C23×C7×C9C47direct (N × H)
17. C9×C47C23×C7direct (N × H)
18. C23×C47C7×C9direct (N × H)
19. C7×C47C23×C9direct (N × H)
21. C22×C7×C9C2×C47direct (N × H)
22. C22×C47C2×C7×C9direct (N × H)
25. C2×C7×C9C22×C47direct (N × H)
26. C2×C47C22×C7×C9direct (N × H)
28. C23×C9C7×C47direct (N × H)
29. C7×C9C23×C47direct (N × H)
30. C23×C7C9×C47direct (N × H)
31. C47C23×C7×C9direct (N × H)
33. C22×C9C2×C7×C47direct (N × H)
34. C22×C7C2×C9×C47direct (N × H)
37. C2×C9C22×C7×C47direct (N × H)
38. C2×C7C22×C9×C47direct (N × H)
40. C9C23×C7×C47direct (N × H)
41. C23C7×C9×C47direct (N × H)
42. C7C23×C9×C47direct (N × H)
44. C22C2×C7×C9×C47direct (N × H)
46. C2C22×C7×C9×C47direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C7×C473
C23×C9×C477
C22×C7×C9×C472
C23×C7×C947