Finite Group Databasebeta

← C23×C5×C11×C49 #72199065

Subgroups — C23×C5×C11×C49 #72199065

Order 21560.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×C49C511yesmaximal, characteristic, direct product factor, Hall
2C23×C5×C7×C11C711yesmaximal, characteristic
3C22×C5×C11×C49C217yesmaximal, direct product factor
4C2×C5×C11×C49C2217yesdirect product factor
5C5×C11×C49C2311yescharacteristic, direct product factor, Hall
6C22×C11×C49C2×C517yesdirect product factor
7C23×C5×C49C1111yesmaximal, characteristic, direct product factor, Hall
8C22×C5×C7×C11C2×C717yes—
9C2×C11×C49C22×C517yesdirect product factor
10C22×C5×C49C2×C1117yesdirect product factor
11C2×C5×C7×C11C22×C717yes—
12C23×C7×C11C5×C711yescharacteristic
13C11×C49C23×C511yescharacteristic, direct product factor, Hall
14C2×C5×C49C22×C1117yesdirect product factor
15C23×C5×C11C4911yescharacteristic, direct product factor, Hall
16C23×C49C5×C1111yescharacteristic, direct product factor, Hall
17C5×C7×C11C23×C711yescharacteristic
18C22×C7×C11C2×C5×C717yes—
19C23×C5×C7C7×C1111yescharacteristic
20C5×C49C23×C1111yescharacteristic, direct product factor, Hall
21C22×C5×C11C2×C4917yesdirect product factor
22C22×C49C2×C5×C1117yesdirect product factor
23C2×C7×C11C22×C5×C717yes—
24C22×C5×C7C2×C7×C1117yes—
25C2×C5×C11C22×C4917yesdirect product factor
26C2×C49C22×C5×C1117yesdirect product factor
27C23×C11C5×C4911yescharacteristic, direct product factor, Hall
28C7×C11C23×C5×C711yescharacteristic
29C2×C5×C7C22×C7×C1117yes—
30C23×C7C5×C7×C1111yescharacteristic
31C5×C11C23×C4911yescharacteristic, direct product factor, Hall
32C49C23×C5×C1111yescharacteristic, direct product factor, Sylow
33C22×C11C2×C5×C4917yesdirect product factor
34C23×C5C11×C4911yescharacteristic, direct product factor, Hall
35C5×C7C23×C7×C1111yescharacteristic
36C22×C7C2×C5×C7×C1117yes—
37C2×C11C22×C5×C4917yesdirect product factor
38C22×C5C2×C11×C4917yesdirect product factor
39C2×C7C22×C5×C7×C1117yes—
40C11C23×C5×C4911yescharacteristic, direct product factor, Sylow
41C2×C5C22×C11×C4917yesdirect product factor
42C23C5×C11×C4911yescharacteristic, direct product factor, Sylow
43C7C23×C5×C7×C1111yescharacteristic
44C5C23×C11×C4911yescharacteristic, direct product factor, Sylow
45C22C2×C5×C11×C4917yesdirect product factor
46C2C22×C5×C11×C4917yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C23×C5×C7×C11
socle, prime radicalC23×C5×C7×C11C7
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C11×C49C5direct (N × H)
3. C22×C5×C11×C49C2direct (N × H)
4. C2×C5×C11×C49C22direct (N × H)
5. C5×C11×C49C23direct (N × H)
6. C22×C11×C49C2×C5direct (N × H)
7. C23×C5×C49C11direct (N × H)
9. C2×C11×C49C22×C5direct (N × H)
10. C22×C5×C49C2×C11direct (N × H)
13. C11×C49C23×C5direct (N × H)
14. C2×C5×C49C22×C11direct (N × H)
15. C23×C5×C11C49direct (N × H)
16. C23×C49C5×C11direct (N × H)
20. C5×C49C23×C11direct (N × H)
21. C22×C5×C11C2×C49direct (N × H)
22. C22×C49C2×C5×C11direct (N × H)
25. C2×C5×C11C22×C49direct (N × H)
26. C2×C49C22×C5×C11direct (N × H)
27. C23×C11C5×C49direct (N × H)
31. C5×C11C23×C49direct (N × H)
32. C49C23×C5×C11direct (N × H)
33. C22×C11C2×C5×C49direct (N × H)
34. C23×C5C11×C49direct (N × H)
37. C2×C11C22×C5×C49direct (N × H)
38. C22×C5C2×C11×C49direct (N × H)
40. C11C23×C5×C49direct (N × H)
41. C2×C5C22×C11×C49direct (N × H)
42. C23C5×C11×C49direct (N × H)
44. C5C23×C11×C49direct (N × H)
45. C22C2×C5×C11×C49direct (N × H)
46. C2C22×C5×C11×C49direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×C495
C23×C5×C7×C117
C22×C5×C11×C492
C23×C5×C4911