Finite Group Databasebeta

← C26×C32×C72 #72205249

Subgroups — C26×C32×C72 #72205249

Order 28224.

169500 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C32×C72C2163yesmaximal, direct product factor
2C26×C3×C72C314yesmaximal, direct product factor
3C24×C32×C72C221651yesdirect product factor
4C25×C3×C72C2×C31252yesdirect product factor
5C26×C32×C7C718yesmaximal, direct product factor
6C23×C32×C72C2311395yesdirect product factor
7C26×C72C3211yescharacteristic, direct product factor, Hall
8C24×C3×C72C22×C312604yesdirect product factor
9C25×C32×C7C2×C71504yesdirect product factor
10C22×C32×C72C241651yesdirect product factor
11C25×C72C2×C32163yesdirect product factor
12C26×C3×C7C3×C7132yesdirect product factor
13C23×C3×C72C23×C315580yesdirect product factor
14C24×C32×C7C22×C715208yesdirect product factor
15C2×C32×C72C25163yesdirect product factor
16C24×C72C22×C321651yesdirect product factor
17C25×C3×C7C2×C3×C712016yesdirect product factor
18C22×C3×C72C24×C312604yesdirect product factor
19C26×C32C7211yescharacteristic, direct product factor, Hall
20C23×C32×C7C23×C7111160yesdirect product factor
21C26×C7C32×C718yesdirect product factor
22C32×C72C2611yescharacteristic, direct product factor, Hall
23C23×C72C23×C3211395yesdirect product factor
24C24×C3×C7C22×C3×C7120832yesdirect product factor
25C2×C3×C72C25×C31252yesdirect product factor
26C25×C32C2×C72163yesdirect product factor
27C22×C32×C7C24×C715208yesdirect product factor
28C25×C7C2×C32×C71504yesdirect product factor
29C22×C72C24×C321651yesdirect product factor
30C26×C3C3×C7214yesdirect product factor
31C23×C3×C7C23×C3×C7144640yesdirect product factor
32C3×C72C26×C314yesdirect product factor
33C24×C32C22×C721651yesdirect product factor
34C2×C32×C7C25×C71504yesdirect product factor
35C24×C7C22×C32×C715208yesdirect product factor
36C2×C72C25×C32163yesdirect product factor
37C25×C3C2×C3×C721252yesdirect product factor
38C22×C3×C7C24×C3×C7120832yesdirect product factor
39C23×C32C23×C7211395yesdirect product factor
40C26C32×C7211yescharacteristic, direct product factor, Sylow
41C32×C7C26×C718yesdirect product factor
42C23×C7C23×C32×C7111160yesdirect product factor
43C72C26×C3211yescharacteristic, direct product factor, Sylow
44C24×C3C22×C3×C7212604yesdirect product factor
45C2×C3×C7C25×C3×C712016yesdirect product factor
46C22×C32C24×C721651yesdirect product factor
47C25C2×C32×C72163yesdirect product factor
48C22×C7C24×C32×C715208yesdirect product factor
49C23×C3C23×C3×C7215580yesdirect product factor
50C3×C7C26×C3×C7132yesdirect product factor
51C2×C32C25×C72163yesdirect product factor
52C24C22×C32×C721651yesdirect product factor
53C2×C7C25×C32×C71504yesdirect product factor
54C22×C3C24×C3×C7212604yesdirect product factor
55C32C26×C7211yescharacteristic, direct product factor, Sylow
56C23C23×C32×C7211395yesdirect product factor
57C7C26×C32×C718yesdirect product factor
58C2×C3C25×C3×C721252yesdirect product factor
59C22C24×C32×C721651yesdirect product factor
60C3C26×C3×C7214yesdirect product factor
61C2C25×C32×C72163yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C25×C32×C72C2direct (N × H)
2. C26×C3×C72C3direct (N × H)
3. C24×C32×C72C22direct (N × H)
4. C25×C3×C72C2×C3direct (N × H)
5. C26×C32×C7C7direct (N × H)
6. C23×C32×C72C23direct (N × H)
7. C26×C72C32direct (N × H)
8. C24×C3×C72C22×C3direct (N × H)
9. C25×C32×C7C2×C7direct (N × H)
10. C22×C32×C72C24direct (N × H)
11. C25×C72C2×C32direct (N × H)
12. C26×C3×C7C3×C7direct (N × H)
13. C23×C3×C72C23×C3direct (N × H)
14. C24×C32×C7C22×C7direct (N × H)
15. C2×C32×C72C25direct (N × H)
16. C24×C72C22×C32direct (N × H)
17. C25×C3×C7C2×C3×C7direct (N × H)
18. C22×C3×C72C24×C3direct (N × H)
19. C26×C32C72direct (N × H)
20. C23×C32×C7C23×C7direct (N × H)
21. C26×C7C32×C7direct (N × H)
22. C32×C72C26direct (N × H)
23. C23×C72C23×C32direct (N × H)
24. C24×C3×C7C22×C3×C7direct (N × H)
25. C2×C3×C72C25×C3direct (N × H)
26. C25×C32C2×C72direct (N × H)
27. C22×C32×C7C24×C7direct (N × H)
28. C25×C7C2×C32×C7direct (N × H)
29. C22×C72C24×C32direct (N × H)
30. C26×C3C3×C72direct (N × H)
31. C23×C3×C7C23×C3×C7direct (N × H)
32. C3×C72C26×C3direct (N × H)
33. C24×C32C22×C72direct (N × H)
34. C2×C32×C7C25×C7direct (N × H)
35. C24×C7C22×C32×C7direct (N × H)
36. C2×C72C25×C32direct (N × H)
37. C25×C3C2×C3×C72direct (N × H)
38. C22×C3×C7C24×C3×C7direct (N × H)
39. C23×C32C23×C72direct (N × H)
40. C26C32×C72direct (N × H)
41. C32×C7C26×C7direct (N × H)
42. C23×C7C23×C32×C7direct (N × H)
43. C72C26×C32direct (N × H)
44. C24×C3C22×C3×C72direct (N × H)
45. C2×C3×C7C25×C3×C7direct (N × H)
46. C22×C32C24×C72direct (N × H)
47. C25C2×C32×C72direct (N × H)
48. C22×C7C24×C32×C7direct (N × H)
49. C23×C3C23×C3×C72direct (N × H)
50. C3×C7C26×C3×C7direct (N × H)
51. C2×C32C25×C72direct (N × H)
52. C24C22×C32×C72direct (N × H)
53. C2×C7C25×C32×C7direct (N × H)
54. C22×C3C24×C3×C72direct (N × H)
55. C32C26×C72direct (N × H)
56. C23C23×C32×C72direct (N × H)
57. C7C26×C32×C7direct (N × H)
58. C2×C3C25×C3×C72direct (N × H)
59. C22C24×C32×C72direct (N × H)
60. C3C26×C3×C72direct (N × H)
61. C2C25×C32×C72direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C32×C722
C26×C3×C723
C26×C32×C77