Finite Group Databasebeta

← C2×C3×C4×C72×C11 #72191237

Subgroups — C2×C3×C4×C72×C11 #72191237

Order 12936.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C72×C11C311yesmaximal, characteristic, direct product factor, Hall
2C22×C3×C72×C11C211yesmaximal, characteristic
3C3×C4×C72×C11C212yesmaximal, direct product factor
4C2×C3×C72×C11C412yesdirect product factor
5C2×C3×C72×C11C2211yescharacteristic
6C22×C72×C11C2×C311yescharacteristic
7C4×C72×C11C2×C312yesdirect product factor
8C2×C3×C4×C7×C11C718yesmaximal, direct product factor
9C3×C72×C11C2×C411yescharacteristic, direct product factor, Hall
10C2×C3×C4×C72C1111yesmaximal, characteristic, direct product factor, Hall
11C2×C72×C11C3×C412yesdirect product factor
12C2×C72×C11C22×C311yescharacteristic
13C22×C3×C7×C11C2×C718yes—
14C3×C4×C7×C11C2×C7116yesdirect product factor
15C2×C4×C7×C11C3×C718yesdirect product factor
16C22×C3×C72C2×C1111yescharacteristic
17C3×C4×C72C2×C1112yesdirect product factor
18C72×C11C2×C3×C411yescharacteristic, direct product factor, Hall
19C2×C3×C7×C11C4×C7116yesdirect product factor
20C2×C3×C7×C11C22×C718yes—
21C2×C4×C72C3×C1111yescharacteristic, direct product factor, Hall
22C22×C7×C11C2×C3×C718yes—
23C4×C7×C11C2×C3×C7116yesdirect product factor
24C2×C3×C72C4×C1112yesdirect product factor
25C2×C3×C72C22×C1111yescharacteristic
26C2×C3×C4×C11C7211yescharacteristic, direct product factor, Hall
27C3×C7×C11C2×C4×C718yesdirect product factor
28C22×C72C2×C3×C1111yescharacteristic
29C4×C72C2×C3×C1112yesdirect product factor
30C2×C3×C4×C7C7×C1118yesdirect product factor
31C2×C7×C11C3×C4×C7116yesdirect product factor
32C2×C7×C11C22×C3×C718yes—
33C3×C72C2×C4×C1111yescharacteristic, direct product factor, Hall
34C22×C3×C11C2×C7211yescharacteristic
35C3×C4×C11C2×C7212yesdirect product factor
36C2×C72C3×C4×C1112yesdirect product factor
37C2×C72C22×C3×C1111yescharacteristic
38C2×C4×C11C3×C7211yescharacteristic, direct product factor, Hall
39C22×C3×C7C2×C7×C1118yes—
40C3×C4×C7C2×C7×C11116yesdirect product factor
41C7×C11C2×C3×C4×C718yesdirect product factor
42C2×C3×C11C4×C7212yesdirect product factor
43C2×C3×C11C22×C7211yescharacteristic
44C2×C4×C7C3×C7×C1118yesdirect product factor
45C72C2×C3×C4×C1111yescharacteristic, direct product factor, Sylow
46C22×C11C2×C3×C7211yescharacteristic
47C4×C11C2×C3×C7212yesdirect product factor
48C2×C3×C7C4×C7×C11116yesdirect product factor
49C2×C3×C7C22×C7×C1118yes—
50C3×C11C2×C4×C7211yescharacteristic, direct product factor, Hall
51C22×C7C2×C3×C7×C1118yes—
52C4×C7C2×C3×C7×C11116yesdirect product factor
53C2×C3×C4C72×C1111yescharacteristic, direct product factor, Hall
54C2×C11C3×C4×C7212yesdirect product factor
55C2×C11C22×C3×C7211yescharacteristic
56C3×C7C2×C4×C7×C1118yesdirect product factor
57C2×C7C3×C4×C7×C11116yesdirect product factor
58C2×C7C22×C3×C7×C1118yes—
59C22×C3C2×C72×C1111yescharacteristic
60C3×C4C2×C72×C1112yesdirect product factor
61C11C2×C3×C4×C7211yescharacteristic, direct product factor, Sylow
62C2×C4C3×C72×C1111yescharacteristic, direct product factor, Sylow
63C7C2×C3×C4×C7×C1118yesdirect product factor
64C2×C3C4×C72×C1112yesdirect product factor
65C2×C3C22×C72×C1111yescharacteristic
66C22C2×C3×C72×C1111yescharacteristic
67C4C2×C3×C72×C1112yesdirect product factor
68C3C2×C4×C72×C1111yescharacteristic, direct product factor, Sylow
69C2C3×C4×C72×C1112yesdirect product factor
70C2C22×C3×C72×C1111yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C72×C11
socle, prime radicalC22×C3×C72×C11C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×C72×C11C3direct (N × H)
3. C3×C4×C72×C11C2direct (N × H)
4. C2×C3×C72×C11C4direct (N × H)
7. C4×C72×C11C2×C3direct (N × H)
8. C2×C3×C4×C7×C11C7direct (N × H)
9. C3×C72×C11C2×C4direct (N × H)
10. C2×C3×C4×C72C11direct (N × H)
11. C2×C72×C11C3×C4direct (N × H)
14. C3×C4×C7×C11C2×C7direct (N × H)
15. C2×C4×C7×C11C3×C7direct (N × H)
17. C3×C4×C72C2×C11direct (N × H)
18. C72×C11C2×C3×C4direct (N × H)
19. C2×C3×C7×C11C4×C7direct (N × H)
21. C2×C4×C72C3×C11direct (N × H)
23. C4×C7×C11C2×C3×C7direct (N × H)
24. C2×C3×C72C4×C11direct (N × H)
26. C2×C3×C4×C11C72direct (N × H)
27. C3×C7×C11C2×C4×C7direct (N × H)
29. C4×C72C2×C3×C11direct (N × H)
30. C2×C3×C4×C7C7×C11direct (N × H)
31. C2×C7×C11C3×C4×C7direct (N × H)
33. C3×C72C2×C4×C11direct (N × H)
35. C3×C4×C11C2×C72direct (N × H)
36. C2×C72C3×C4×C11direct (N × H)
38. C2×C4×C11C3×C72direct (N × H)
40. C3×C4×C7C2×C7×C11direct (N × H)
41. C7×C11C2×C3×C4×C7direct (N × H)
42. C2×C3×C11C4×C72direct (N × H)
44. C2×C4×C7C3×C7×C11direct (N × H)
45. C72C2×C3×C4×C11direct (N × H)
47. C4×C11C2×C3×C72direct (N × H)
48. C2×C3×C7C4×C7×C11direct (N × H)
50. C3×C11C2×C4×C72direct (N × H)
52. C4×C7C2×C3×C7×C11direct (N × H)
53. C2×C3×C4C72×C11direct (N × H)
54. C2×C11C3×C4×C72direct (N × H)
56. C3×C7C2×C4×C7×C11direct (N × H)
57. C2×C7C3×C4×C7×C11direct (N × H)
60. C3×C4C2×C72×C11direct (N × H)
61. C11C2×C3×C4×C72direct (N × H)
62. C2×C4C3×C72×C11direct (N × H)
63. C7C2×C3×C4×C7×C11direct (N × H)
64. C2×C3C4×C72×C11direct (N × H)
67. C4C2×C3×C72×C11direct (N × H)
68. C3C2×C4×C72×C11direct (N × H)
69. C2C3×C4×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×C4×C72×C113
C22×C3×C72×C112
C3×C4×C72×C112
C2×C3×C4×C7×C117
C2×C3×C4×C7211