Finite Group Databasebeta

← C22×C3×C5×C72×C11 #44568539

Subgroups — C22×C3×C5×C72×C11 #44568539

Order 32340.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C72×C11C213yesmaximal, direct product factor
2C22×C5×C72×C11C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C72×C11C2211yescharacteristic, direct product factor, Hall
4C22×C3×C72×C11C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C72×C11C2×C313yesdirect product factor
6C22×C3×C5×C7×C11C718yesmaximal, direct product factor
7C2×C3×C72×C11C2×C513yesdirect product factor
8C22×C3×C5×C72C1111yesmaximal, characteristic, direct product factor, Hall
9C5×C72×C11C22×C311yescharacteristic, direct product factor, Hall
10C2×C3×C5×C7×C11C2×C7124yesdirect product factor
11C22×C72×C11C3×C511yescharacteristic, direct product factor, Hall
12C3×C72×C11C22×C511yescharacteristic, direct product factor, Hall
13C22×C5×C7×C11C3×C718yesdirect product factor
14C2×C3×C5×C72C2×C1113yesdirect product factor
15C3×C5×C7×C11C22×C718yesdirect product factor
16C2×C72×C11C2×C3×C513yesdirect product factor
17C22×C5×C72C3×C1111yescharacteristic, direct product factor, Hall
18C22×C3×C7×C11C5×C718yesdirect product factor
19C2×C5×C7×C11C2×C3×C7124yesdirect product factor
20C3×C5×C72C22×C1111yescharacteristic, direct product factor, Hall
21C22×C3×C5×C11C7211yescharacteristic, direct product factor, Hall
22C22×C3×C72C5×C1111yescharacteristic, direct product factor, Hall
23C72×C11C22×C3×C511yescharacteristic, direct product factor, Hall
24C2×C5×C72C2×C3×C1113yesdirect product factor
25C2×C3×C7×C11C2×C5×C7124yesdirect product factor
26C22×C3×C5×C7C7×C1118yesdirect product factor
27C5×C7×C11C22×C3×C718yesdirect product factor
28C2×C3×C5×C11C2×C7213yesdirect product factor
29C22×C7×C11C3×C5×C718yesdirect product factor
30C2×C3×C72C2×C5×C1113yesdirect product factor
31C5×C72C22×C3×C1111yescharacteristic, direct product factor, Hall
32C3×C7×C11C22×C5×C718yesdirect product factor
33C22×C5×C11C3×C7211yescharacteristic, direct product factor, Hall
34C2×C3×C5×C7C2×C7×C11124yesdirect product factor
35C22×C72C3×C5×C1111yescharacteristic, direct product factor, Hall
36C3×C5×C11C22×C7211yescharacteristic, direct product factor, Hall
37C2×C7×C11C2×C3×C5×C7124yesdirect product factor
38C3×C72C22×C5×C1111yescharacteristic, direct product factor, Hall
39C22×C5×C7C3×C7×C1118yesdirect product factor
40C22×C3×C11C5×C7211yescharacteristic, direct product factor, Hall
41C2×C5×C11C2×C3×C7213yesdirect product factor
42C3×C5×C7C22×C7×C1118yesdirect product factor
43C2×C72C2×C3×C5×C1113yesdirect product factor
44C22×C3×C7C5×C7×C1118yesdirect product factor
45C7×C11C22×C3×C5×C718yesdirect product factor
46C2×C5×C7C2×C3×C7×C11124yesdirect product factor
47C2×C3×C11C2×C5×C7213yesdirect product factor
48C22×C3×C5C72×C1111yescharacteristic, direct product factor, Hall
49C5×C11C22×C3×C7211yescharacteristic, direct product factor, Hall
50C72C22×C3×C5×C1111yescharacteristic, direct product factor, Sylow
51C22×C11C3×C5×C7211yescharacteristic, direct product factor, Hall
52C2×C3×C7C2×C5×C7×C11124yesdirect product factor
53C5×C7C22×C3×C7×C1118yesdirect product factor
54C3×C11C22×C5×C7211yescharacteristic, direct product factor, Hall
55C2×C3×C5C2×C72×C1113yesdirect product factor
56C22×C7C3×C5×C7×C1118yesdirect product factor
57C2×C11C2×C3×C5×C7213yesdirect product factor
58C3×C7C22×C5×C7×C1118yesdirect product factor
59C22×C5C3×C72×C1111yescharacteristic, direct product factor, Hall
60C3×C5C22×C72×C1111yescharacteristic, direct product factor, Hall
61C2×C7C2×C3×C5×C7×C11124yesdirect product factor
62C22×C3C5×C72×C1111yescharacteristic, direct product factor, Hall
63C11C22×C3×C5×C7211yescharacteristic, direct product factor, Sylow
64C2×C5C2×C3×C72×C1113yesdirect product factor
65C7C22×C3×C5×C7×C1118yesdirect product factor
66C2×C3C2×C5×C72×C1113yesdirect product factor
67C5C22×C3×C72×C1111yescharacteristic, direct product factor, Sylow
68C22C3×C5×C72×C1111yescharacteristic, direct product factor, Sylow
69C3C22×C5×C72×C1111yescharacteristic, direct product factor, Sylow
70C2C2×C3×C5×C72×C1113yesdirect 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. C2×C3×C5×C72×C11C2direct (N × H)
2. C22×C5×C72×C11C3direct (N × H)
3. C3×C5×C72×C11C22direct (N × H)
4. C22×C3×C72×C11C5direct (N × H)
5. C2×C5×C72×C11C2×C3direct (N × H)
6. C22×C3×C5×C7×C11C7direct (N × H)
7. C2×C3×C72×C11C2×C5direct (N × H)
8. C22×C3×C5×C72C11direct (N × H)
9. C5×C72×C11C22×C3direct (N × H)
10. C2×C3×C5×C7×C11C2×C7direct (N × H)
11. C22×C72×C11C3×C5direct (N × H)
12. C3×C72×C11C22×C5direct (N × H)
13. C22×C5×C7×C11C3×C7direct (N × H)
14. C2×C3×C5×C72C2×C11direct (N × H)
15. C3×C5×C7×C11C22×C7direct (N × H)
16. C2×C72×C11C2×C3×C5direct (N × H)
17. C22×C5×C72C3×C11direct (N × H)
18. C22×C3×C7×C11C5×C7direct (N × H)
19. C2×C5×C7×C11C2×C3×C7direct (N × H)
20. C3×C5×C72C22×C11direct (N × H)
21. C22×C3×C5×C11C72direct (N × H)
22. C22×C3×C72C5×C11direct (N × H)
23. C72×C11C22×C3×C5direct (N × H)
24. C2×C5×C72C2×C3×C11direct (N × H)
25. C2×C3×C7×C11C2×C5×C7direct (N × H)
26. C22×C3×C5×C7C7×C11direct (N × H)
27. C5×C7×C11C22×C3×C7direct (N × H)
28. C2×C3×C5×C11C2×C72direct (N × H)
29. C22×C7×C11C3×C5×C7direct (N × H)
30. C2×C3×C72C2×C5×C11direct (N × H)
31. C5×C72C22×C3×C11direct (N × H)
32. C3×C7×C11C22×C5×C7direct (N × H)
33. C22×C5×C11C3×C72direct (N × H)
34. C2×C3×C5×C7C2×C7×C11direct (N × H)
35. C22×C72C3×C5×C11direct (N × H)
36. C3×C5×C11C22×C72direct (N × H)
37. C2×C7×C11C2×C3×C5×C7direct (N × H)
38. C3×C72C22×C5×C11direct (N × H)
39. C22×C5×C7C3×C7×C11direct (N × H)
40. C22×C3×C11C5×C72direct (N × H)
41. C2×C5×C11C2×C3×C72direct (N × H)
42. C3×C5×C7C22×C7×C11direct (N × H)
43. C2×C72C2×C3×C5×C11direct (N × H)
44. C22×C3×C7C5×C7×C11direct (N × H)
45. C7×C11C22×C3×C5×C7direct (N × H)
46. C2×C5×C7C2×C3×C7×C11direct (N × H)
47. C2×C3×C11C2×C5×C72direct (N × H)
48. C22×C3×C5C72×C11direct (N × H)
49. C5×C11C22×C3×C72direct (N × H)
50. C72C22×C3×C5×C11direct (N × H)
51. C22×C11C3×C5×C72direct (N × H)
52. C2×C3×C7C2×C5×C7×C11direct (N × H)
53. C5×C7C22×C3×C7×C11direct (N × H)
54. C3×C11C22×C5×C72direct (N × H)
55. C2×C3×C5C2×C72×C11direct (N × H)
56. C22×C7C3×C5×C7×C11direct (N × H)
57. C2×C11C2×C3×C5×C72direct (N × H)
58. C3×C7C22×C5×C7×C11direct (N × H)
59. C22×C5C3×C72×C11direct (N × H)
60. C3×C5C22×C72×C11direct (N × H)
61. C2×C7C2×C3×C5×C7×C11direct (N × H)
62. C22×C3C5×C72×C11direct (N × H)
63. C11C22×C3×C5×C72direct (N × H)
64. C2×C5C2×C3×C72×C11direct (N × H)
65. C7C22×C3×C5×C7×C11direct (N × H)
66. C2×C3C2×C5×C72×C11direct (N × H)
67. C5C22×C3×C72×C11direct (N × H)
68. C22C3×C5×C72×C11direct (N × H)
69. C3C22×C5×C72×C11direct (N × H)
70. C2C2×C3×C5×C72×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C72×C112
C22×C5×C72×C113
C22×C3×C72×C115
C22×C3×C5×C7×C117
C22×C3×C5×C7211