Finite Group Databasebeta

← C27×C3×C7×C11 #72206451

Subgroups — C27×C3×C7×C11 #72206451

Order 29568.

233696 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C3×C7×C11C21127yesmaximal, direct product factor
2C27×C7×C11C311yesmaximal, characteristic, direct product factor, Hall
3C25×C3×C7×C11C2212667yesdirect product factor
4C26×C7×C11C2×C31127yesdirect product factor
5C27×C3×C11C711yesmaximal, characteristic, direct product factor, Hall
6C24×C3×C7×C11C23111811yesdirect product factor
7C27×C3×C7C1111yesmaximal, characteristic, direct product factor, Hall
8C25×C7×C11C22×C312667yesdirect product factor
9C26×C3×C11C2×C71127yesdirect product factor
10C23×C3×C7×C11C24111811yesdirect product factor
11C27×C11C3×C711yescharacteristic, direct product factor, Hall
12C26×C3×C7C2×C111127yesdirect product factor
13C24×C7×C11C23×C3111811yesdirect product factor
14C25×C3×C11C22×C712667yesdirect product factor
15C22×C3×C7×C11C2512667yesdirect product factor
16C27×C7C3×C1111yescharacteristic, direct product factor, Hall
17C26×C11C2×C3×C71127yesdirect product factor
18C25×C3×C7C22×C1112667yesdirect product factor
19C23×C7×C11C24×C3111811yesdirect product factor
20C24×C3×C11C23×C7111811yesdirect product factor
21C2×C3×C7×C11C261127yesdirect product factor
22C26×C7C2×C3×C111127yesdirect product factor
23C27×C3C7×C1111yescharacteristic, direct product factor, Hall
24C25×C11C22×C3×C712667yesdirect product factor
25C24×C3×C7C23×C11111811yesdirect product factor
26C22×C7×C11C25×C312667yesdirect product factor
27C23×C3×C11C24×C7111811yesdirect product factor
28C3×C7×C11C2711yescharacteristic, direct product factor, Hall
29C25×C7C22×C3×C1112667yesdirect product factor
30C26×C3C2×C7×C111127yesdirect product factor
31C24×C11C23×C3×C7111811yesdirect product factor
32C23×C3×C7C24×C11111811yesdirect product factor
33C2×C7×C11C26×C31127yesdirect product factor
34C22×C3×C11C25×C712667yesdirect product factor
35C27C3×C7×C1111yescharacteristic, direct product factor, Sylow
36C24×C7C23×C3×C11111811yesdirect product factor
37C25×C3C22×C7×C1112667yesdirect product factor
38C23×C11C24×C3×C7111811yesdirect product factor
39C22×C3×C7C25×C1112667yesdirect product factor
40C7×C11C27×C311yescharacteristic, direct product factor, Hall
41C2×C3×C11C26×C71127yesdirect product factor
42C26C2×C3×C7×C111127yesdirect product factor
43C23×C7C24×C3×C11111811yesdirect product factor
44C24×C3C23×C7×C11111811yesdirect product factor
45C22×C11C25×C3×C712667yesdirect product factor
46C2×C3×C7C26×C111127yesdirect product factor
47C3×C11C27×C711yescharacteristic, direct product factor, Hall
48C25C22×C3×C7×C1112667yesdirect product factor
49C22×C7C25×C3×C1112667yesdirect product factor
50C23×C3C24×C7×C11111811yesdirect product factor
51C2×C11C26×C3×C71127yesdirect product factor
52C3×C7C27×C1111yescharacteristic, direct product factor, Hall
53C24C23×C3×C7×C11111811yesdirect product factor
54C2×C7C26×C3×C111127yesdirect product factor
55C22×C3C25×C7×C1112667yesdirect product factor
56C11C27×C3×C711yescharacteristic, direct product factor, Sylow
57C23C24×C3×C7×C11111811yesdirect product factor
58C7C27×C3×C1111yescharacteristic, direct product factor, Sylow
59C2×C3C26×C7×C111127yesdirect product factor
60C22C25×C3×C7×C1112667yesdirect product factor
61C3C27×C7×C1111yescharacteristic, direct product factor, Sylow
62C2C26×C3×C7×C111127yesdirect 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. C26×C3×C7×C11C2direct (N × H)
2. C27×C7×C11C3direct (N × H)
3. C25×C3×C7×C11C22direct (N × H)
4. C26×C7×C11C2×C3direct (N × H)
5. C27×C3×C11C7direct (N × H)
6. C24×C3×C7×C11C23direct (N × H)
7. C27×C3×C7C11direct (N × H)
8. C25×C7×C11C22×C3direct (N × H)
9. C26×C3×C11C2×C7direct (N × H)
10. C23×C3×C7×C11C24direct (N × H)
11. C27×C11C3×C7direct (N × H)
12. C26×C3×C7C2×C11direct (N × H)
13. C24×C7×C11C23×C3direct (N × H)
14. C25×C3×C11C22×C7direct (N × H)
15. C22×C3×C7×C11C25direct (N × H)
16. C27×C7C3×C11direct (N × H)
17. C26×C11C2×C3×C7direct (N × H)
18. C25×C3×C7C22×C11direct (N × H)
19. C23×C7×C11C24×C3direct (N × H)
20. C24×C3×C11C23×C7direct (N × H)
21. C2×C3×C7×C11C26direct (N × H)
22. C26×C7C2×C3×C11direct (N × H)
23. C27×C3C7×C11direct (N × H)
24. C25×C11C22×C3×C7direct (N × H)
25. C24×C3×C7C23×C11direct (N × H)
26. C22×C7×C11C25×C3direct (N × H)
27. C23×C3×C11C24×C7direct (N × H)
28. C3×C7×C11C27direct (N × H)
29. C25×C7C22×C3×C11direct (N × H)
30. C26×C3C2×C7×C11direct (N × H)
31. C24×C11C23×C3×C7direct (N × H)
32. C23×C3×C7C24×C11direct (N × H)
33. C2×C7×C11C26×C3direct (N × H)
34. C22×C3×C11C25×C7direct (N × H)
35. C27C3×C7×C11direct (N × H)
36. C24×C7C23×C3×C11direct (N × H)
37. C25×C3C22×C7×C11direct (N × H)
38. C23×C11C24×C3×C7direct (N × H)
39. C22×C3×C7C25×C11direct (N × H)
40. C7×C11C27×C3direct (N × H)
41. C2×C3×C11C26×C7direct (N × H)
42. C26C2×C3×C7×C11direct (N × H)
43. C23×C7C24×C3×C11direct (N × H)
44. C24×C3C23×C7×C11direct (N × H)
45. C22×C11C25×C3×C7direct (N × H)
46. C2×C3×C7C26×C11direct (N × H)
47. C3×C11C27×C7direct (N × H)
48. C25C22×C3×C7×C11direct (N × H)
49. C22×C7C25×C3×C11direct (N × H)
50. C23×C3C24×C7×C11direct (N × H)
51. C2×C11C26×C3×C7direct (N × H)
52. C3×C7C27×C11direct (N × H)
53. C24C23×C3×C7×C11direct (N × H)
54. C2×C7C26×C3×C11direct (N × H)
55. C22×C3C25×C7×C11direct (N × H)
56. C11C27×C3×C7direct (N × H)
57. C23C24×C3×C7×C11direct (N × H)
58. C7C27×C3×C11direct (N × H)
59. C2×C3C26×C7×C11direct (N × H)
60. C22C25×C3×C7×C11direct (N × H)
61. C3C27×C7×C11direct (N × H)
62. C2C26×C3×C7×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C3×C7×C112
C27×C7×C113
C27×C3×C117
C27×C3×C711