Finite Group Databasebeta

← C24×C4×C7×C31 #72192111

Subgroups — C24×C4×C7×C31 #72192111

Order 13888.

2724 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C7×C31C2130yesmaximal, direct product factor
2C25×C7×C31C211yesmaximal, characteristic
3C24×C7×C31C4116yesdirect product factor
4C24×C7×C31C22115yes—
5C22×C4×C7×C31C221140yesdirect product factor
6C24×C4×C31C711yesmaximal, characteristic, direct product factor, Hall
7C23×C7×C31C2×C41120yesdirect product factor
8C23×C7×C31C23135yes—
9C2×C4×C7×C31C231120yesdirect product factor
10C25×C31C2×C711yescharacteristic
11C23×C4×C31C2×C7130yesdirect product factor
12C22×C7×C31C22×C41140yesdirect product factor
13C22×C7×C31C24115yes—
14C4×C7×C31C24116yesdirect product factor
15C24×C31C4×C7116yesdirect product factor
16C24×C31C22×C7115yes—
17C22×C4×C31C22×C71140yesdirect product factor
18C24×C4×C7C3111yesmaximal, characteristic, direct product factor, Hall
19C2×C7×C31C23×C4130yesdirect product factor
20C2×C7×C31C2511yescharacteristic
21C23×C31C2×C4×C71120yesdirect product factor
22C23×C31C23×C7135yes—
23C2×C4×C31C23×C71120yesdirect product factor
24C25×C7C2×C3111yescharacteristic
25C23×C4×C7C2×C31130yesdirect product factor
26C7×C31C24×C411yescharacteristic, direct product factor, Hall
27C22×C31C22×C4×C71140yesdirect product factor
28C22×C31C24×C7115yes—
29C4×C31C24×C7116yesdirect product factor
30C24×C7C4×C31116yesdirect product factor
31C24×C7C22×C31115yes—
32C22×C4×C7C22×C311140yesdirect product factor
33C24×C4C7×C3111yescharacteristic, direct product factor, Sylow
34C2×C31C23×C4×C7130yesdirect product factor
35C2×C31C25×C711yescharacteristic
36C23×C7C2×C4×C311120yesdirect product factor
37C23×C7C23×C31135yes—
38C2×C4×C7C23×C311120yesdirect product factor
39C25C2×C7×C3111yescharacteristic
40C23×C4C2×C7×C31130yesdirect product factor
41C31C24×C4×C711yescharacteristic, direct product factor, Sylow
42C22×C7C22×C4×C311140yesdirect product factor
43C22×C7C24×C31115yes—
44C4×C7C24×C31116yesdirect product factor
45C24C4×C7×C31116yesdirect product factor
46C24C22×C7×C31115yes—
47C22×C4C22×C7×C311140yesdirect product factor
48C2×C7C23×C4×C31130yesdirect product factor
49C2×C7C25×C3111yescharacteristic
50C23C2×C4×C7×C311120yesdirect product factor
51C23C23×C7×C31135yes—
52C2×C4C23×C7×C311120yesdirect product factor
53C7C24×C4×C3111yescharacteristic, direct product factor, Sylow
54C22C22×C4×C7×C311140yesdirect product factor
55C22C24×C7×C31115yes—
56C4C24×C7×C31116yesdirect product factor
57C2C25×C7×C3111yescharacteristic
58C2C23×C4×C7×C31130yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C7×C31
socle, prime radicalC25×C7×C31C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C4×C7×C31C2direct (N × H)
3. C24×C7×C31C4direct (N × H)
5. C22×C4×C7×C31C22direct (N × H)
6. C24×C4×C31C7direct (N × H)
7. C23×C7×C31C2×C4direct (N × H)
9. C2×C4×C7×C31C23direct (N × H)
11. C23×C4×C31C2×C7direct (N × H)
12. C22×C7×C31C22×C4direct (N × H)
14. C4×C7×C31C24direct (N × H)
15. C24×C31C4×C7direct (N × H)
17. C22×C4×C31C22×C7direct (N × H)
18. C24×C4×C7C31direct (N × H)
19. C2×C7×C31C23×C4direct (N × H)
21. C23×C31C2×C4×C7direct (N × H)
23. C2×C4×C31C23×C7direct (N × H)
25. C23×C4×C7C2×C31direct (N × H)
26. C7×C31C24×C4direct (N × H)
27. C22×C31C22×C4×C7direct (N × H)
29. C4×C31C24×C7direct (N × H)
30. C24×C7C4×C31direct (N × H)
32. C22×C4×C7C22×C31direct (N × H)
33. C24×C4C7×C31direct (N × H)
34. C2×C31C23×C4×C7direct (N × H)
36. C23×C7C2×C4×C31direct (N × H)
38. C2×C4×C7C23×C31direct (N × H)
40. C23×C4C2×C7×C31direct (N × H)
41. C31C24×C4×C7direct (N × H)
42. C22×C7C22×C4×C31direct (N × H)
44. C4×C7C24×C31direct (N × H)
45. C24C4×C7×C31direct (N × H)
47. C22×C4C22×C7×C31direct (N × H)
48. C2×C7C23×C4×C31direct (N × H)
50. C23C2×C4×C7×C31direct (N × H)
52. C2×C4C23×C7×C31direct (N × H)
53. C7C24×C4×C31direct (N × H)
54. C22C22×C4×C7×C31direct (N × H)
56. C4C24×C7×C31direct (N × H)
58. C2C23×C4×C7×C31direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×C7×C312
C25×C7×C312
C24×C4×C317
C24×C4×C731