Finite Group Databasebeta

← C26×C3×C7×C23 #72207672

Subgroups — C26×C3×C7×C23 #72207672

Order 30912.

22600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C3×C7×C23C2163yesmaximal, direct product factor
2C26×C7×C23C311yesmaximal, characteristic, direct product factor, Hall
3C24×C3×C7×C23C221651yesdirect product factor
4C25×C7×C23C2×C3163yesdirect product factor
5C26×C3×C23C711yesmaximal, characteristic, direct product factor, Hall
6C23×C3×C7×C23C2311395yesdirect product factor
7C24×C7×C23C22×C31651yesdirect product factor
8C25×C3×C23C2×C7163yesdirect product factor
9C22×C3×C7×C23C241651yesdirect product factor
10C26×C23C3×C711yescharacteristic, direct product factor, Hall
11C26×C3×C7C2311yesmaximal, characteristic, direct product factor, Hall
12C23×C7×C23C23×C311395yesdirect product factor
13C24×C3×C23C22×C71651yesdirect product factor
14C2×C3×C7×C23C25163yesdirect product factor
15C25×C23C2×C3×C7163yesdirect product factor
16C25×C3×C7C2×C23163yesdirect product factor
17C22×C7×C23C24×C31651yesdirect product factor
18C23×C3×C23C23×C711395yesdirect product factor
19C3×C7×C23C2611yescharacteristic, direct product factor, Hall
20C26×C7C3×C2311yescharacteristic, direct product factor, Hall
21C24×C23C22×C3×C71651yesdirect product factor
22C24×C3×C7C22×C231651yesdirect product factor
23C2×C7×C23C25×C3163yesdirect product factor
24C22×C3×C23C24×C71651yesdirect product factor
25C25×C7C2×C3×C23163yesdirect product factor
26C26×C3C7×C2311yescharacteristic, direct product factor, Hall
27C23×C23C23×C3×C711395yesdirect product factor
28C23×C3×C7C23×C2311395yesdirect product factor
29C7×C23C26×C311yescharacteristic, direct product factor, Hall
30C2×C3×C23C25×C7163yesdirect product factor
31C24×C7C22×C3×C231651yesdirect product factor
32C25×C3C2×C7×C23163yesdirect product factor
33C22×C23C24×C3×C71651yesdirect product factor
34C22×C3×C7C24×C231651yesdirect product factor
35C3×C23C26×C711yescharacteristic, direct product factor, Hall
36C26C3×C7×C2311yescharacteristic, direct product factor, Sylow
37C23×C7C23×C3×C2311395yesdirect product factor
38C24×C3C22×C7×C231651yesdirect product factor
39C2×C23C25×C3×C7163yesdirect product factor
40C2×C3×C7C25×C23163yesdirect product factor
41C25C2×C3×C7×C23163yesdirect product factor
42C22×C7C24×C3×C231651yesdirect product factor
43C23×C3C23×C7×C2311395yesdirect product factor
44C23C26×C3×C711yescharacteristic, direct product factor, Sylow
45C3×C7C26×C2311yescharacteristic, direct product factor, Hall
46C24C22×C3×C7×C231651yesdirect product factor
47C2×C7C25×C3×C23163yesdirect product factor
48C22×C3C24×C7×C231651yesdirect product factor
49C23C23×C3×C7×C2311395yesdirect product factor
50C7C26×C3×C2311yescharacteristic, direct product factor, Sylow
51C2×C3C25×C7×C23163yesdirect product factor
52C22C24×C3×C7×C231651yesdirect product factor
53C3C26×C7×C2311yescharacteristic, direct product factor, Sylow
54C2C25×C3×C7×C23163yesdirect 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×C3×C7×C23C2direct (N × H)
2. C26×C7×C23C3direct (N × H)
3. C24×C3×C7×C23C22direct (N × H)
4. C25×C7×C23C2×C3direct (N × H)
5. C26×C3×C23C7direct (N × H)
6. C23×C3×C7×C23C23direct (N × H)
7. C24×C7×C23C22×C3direct (N × H)
8. C25×C3×C23C2×C7direct (N × H)
9. C22×C3×C7×C23C24direct (N × H)
10. C26×C23C3×C7direct (N × H)
11. C26×C3×C7C23direct (N × H)
12. C23×C7×C23C23×C3direct (N × H)
13. C24×C3×C23C22×C7direct (N × H)
14. C2×C3×C7×C23C25direct (N × H)
15. C25×C23C2×C3×C7direct (N × H)
16. C25×C3×C7C2×C23direct (N × H)
17. C22×C7×C23C24×C3direct (N × H)
18. C23×C3×C23C23×C7direct (N × H)
19. C3×C7×C23C26direct (N × H)
20. C26×C7C3×C23direct (N × H)
21. C24×C23C22×C3×C7direct (N × H)
22. C24×C3×C7C22×C23direct (N × H)
23. C2×C7×C23C25×C3direct (N × H)
24. C22×C3×C23C24×C7direct (N × H)
25. C25×C7C2×C3×C23direct (N × H)
26. C26×C3C7×C23direct (N × H)
27. C23×C23C23×C3×C7direct (N × H)
28. C23×C3×C7C23×C23direct (N × H)
29. C7×C23C26×C3direct (N × H)
30. C2×C3×C23C25×C7direct (N × H)
31. C24×C7C22×C3×C23direct (N × H)
32. C25×C3C2×C7×C23direct (N × H)
33. C22×C23C24×C3×C7direct (N × H)
34. C22×C3×C7C24×C23direct (N × H)
35. C3×C23C26×C7direct (N × H)
36. C26C3×C7×C23direct (N × H)
37. C23×C7C23×C3×C23direct (N × H)
38. C24×C3C22×C7×C23direct (N × H)
39. C2×C23C25×C3×C7direct (N × H)
40. C2×C3×C7C25×C23direct (N × H)
41. C25C2×C3×C7×C23direct (N × H)
42. C22×C7C24×C3×C23direct (N × H)
43. C23×C3C23×C7×C23direct (N × H)
44. C23C26×C3×C7direct (N × H)
45. C3×C7C26×C23direct (N × H)
46. C24C22×C3×C7×C23direct (N × H)
47. C2×C7C25×C3×C23direct (N × H)
48. C22×C3C24×C7×C23direct (N × H)
49. C23C23×C3×C7×C23direct (N × H)
50. C7C26×C3×C23direct (N × H)
51. C2×C3C25×C7×C23direct (N × H)
52. C22C24×C3×C7×C23direct (N × H)
53. C3C26×C7×C23direct (N × H)
54. C2C25×C3×C7×C23direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C3×C7×C232
C26×C7×C233
C26×C3×C237
C26×C3×C723