Finite Group Databasebeta

← C2×C3×C4×C7×C132 #72205342

Subgroups — C2×C3×C4×C7×C132 #72205342

Order 28392.

512 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C132C311yesmaximal, characteristic, direct product factor, Hall
2C2×C3×C4×C132C711yesmaximal, characteristic, direct product factor, Hall
3C2×C3×C4×C7×C13C13114yesmaximal, direct product factor
4C22×C3×C7×C132C211yesmaximal, characteristic
5C3×C4×C7×C132C212yesmaximal, direct product factor
6C2×C3×C7×C132C412yesdirect product factor
7C2×C3×C7×C132C2211yescharacteristic
8C22×C7×C132C2×C311yescharacteristic
9C4×C7×C132C2×C312yesdirect product factor
10C3×C7×C132C2×C411yescharacteristic, direct product factor, Hall
11C2×C7×C132C3×C412yesdirect product factor
12C2×C7×C132C22×C311yescharacteristic
13C22×C3×C132C2×C711yescharacteristic
14C3×C4×C132C2×C712yesdirect product factor
15C2×C4×C132C3×C711yescharacteristic, direct product factor, Hall
16C7×C132C2×C3×C411yescharacteristic, direct product factor, Hall
17C22×C3×C7×C13C2×C13114yes—
18C3×C4×C7×C13C2×C13128yesdirect product factor
19C2×C3×C132C4×C712yesdirect product factor
20C2×C3×C132C22×C711yescharacteristic
21C2×C4×C7×C13C3×C13114yesdirect product factor
22C22×C132C2×C3×C711yescharacteristic
23C4×C132C2×C3×C712yesdirect product factor
24C2×C3×C7×C13C4×C13128yesdirect product factor
25C2×C3×C7×C13C22×C13114yes—
26C3×C132C2×C4×C711yescharacteristic, direct product factor, Hall
27C22×C7×C13C2×C3×C13114yes—
28C4×C7×C13C2×C3×C13128yesdirect product factor
29C2×C132C3×C4×C712yesdirect product factor
30C2×C132C22×C3×C711yescharacteristic
31C2×C3×C4×C13C7×C13114yesdirect product factor
32C3×C7×C13C2×C4×C13114yesdirect product factor
33C2×C7×C13C3×C4×C13128yesdirect product factor
34C2×C7×C13C22×C3×C13114yes—
35C132C2×C3×C4×C711yescharacteristic, direct product factor, Sylow
36C2×C3×C4×C7C13211yescharacteristic, direct product factor, Hall
37C22×C3×C13C2×C7×C13114yes—
38C3×C4×C13C2×C7×C13128yesdirect product factor
39C2×C4×C13C3×C7×C13114yesdirect product factor
40C7×C13C2×C3×C4×C13114yesdirect product factor
41C22×C3×C7C2×C13211yescharacteristic
42C3×C4×C7C2×C13212yesdirect product factor
43C2×C3×C13C4×C7×C13128yesdirect product factor
44C2×C3×C13C22×C7×C13114yes—
45C2×C4×C7C3×C13211yescharacteristic, direct product factor, Hall
46C22×C13C2×C3×C7×C13114yes—
47C4×C13C2×C3×C7×C13128yesdirect product factor
48C2×C3×C7C4×C13212yesdirect product factor
49C2×C3×C7C22×C13211yescharacteristic
50C3×C13C2×C4×C7×C13114yesdirect product factor
51C22×C7C2×C3×C13211yescharacteristic
52C4×C7C2×C3×C13212yesdirect product factor
53C2×C13C3×C4×C7×C13128yesdirect product factor
54C2×C13C22×C3×C7×C13114yes—
55C2×C3×C4C7×C13211yescharacteristic, direct product factor, Hall
56C3×C7C2×C4×C13211yescharacteristic, direct product factor, Hall
57C2×C7C3×C4×C13212yesdirect product factor
58C2×C7C22×C3×C13211yescharacteristic
59C13C2×C3×C4×C7×C13114yesdirect product factor
60C22×C3C2×C7×C13211yescharacteristic
61C3×C4C2×C7×C13212yesdirect product factor
62C2×C4C3×C7×C13211yescharacteristic, direct product factor, Sylow
63C7C2×C3×C4×C13211yescharacteristic, direct product factor, Sylow
64C2×C3C4×C7×C13212yesdirect product factor
65C2×C3C22×C7×C13211yescharacteristic
66C22C2×C3×C7×C13211yescharacteristic
67C4C2×C3×C7×C13212yesdirect product factor
68C3C2×C4×C7×C13211yescharacteristic, direct product factor, Sylow
69C2C3×C4×C7×C13212yesdirect product factor
70C2C22×C3×C7×C13211yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C7×C132
socle, prime radicalC22×C3×C7×C132C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C132C3direct (N × H)
2. C2×C3×C4×C132C7direct (N × H)
3. C2×C3×C4×C7×C13C13direct (N × H)
5. C3×C4×C7×C132C2direct (N × H)
6. C2×C3×C7×C132C4direct (N × H)
9. C4×C7×C132C2×C3direct (N × H)
10. C3×C7×C132C2×C4direct (N × H)
11. C2×C7×C132C3×C4direct (N × H)
14. C3×C4×C132C2×C7direct (N × H)
15. C2×C4×C132C3×C7direct (N × H)
16. C7×C132C2×C3×C4direct (N × H)
18. C3×C4×C7×C13C2×C13direct (N × H)
19. C2×C3×C132C4×C7direct (N × H)
21. C2×C4×C7×C13C3×C13direct (N × H)
23. C4×C132C2×C3×C7direct (N × H)
24. C2×C3×C7×C13C4×C13direct (N × H)
26. C3×C132C2×C4×C7direct (N × H)
28. C4×C7×C13C2×C3×C13direct (N × H)
29. C2×C132C3×C4×C7direct (N × H)
31. C2×C3×C4×C13C7×C13direct (N × H)
32. C3×C7×C13C2×C4×C13direct (N × H)
33. C2×C7×C13C3×C4×C13direct (N × H)
35. C132C2×C3×C4×C7direct (N × H)
36. C2×C3×C4×C7C132direct (N × H)
38. C3×C4×C13C2×C7×C13direct (N × H)
39. C2×C4×C13C3×C7×C13direct (N × H)
40. C7×C13C2×C3×C4×C13direct (N × H)
42. C3×C4×C7C2×C132direct (N × H)
43. C2×C3×C13C4×C7×C13direct (N × H)
45. C2×C4×C7C3×C132direct (N × H)
47. C4×C13C2×C3×C7×C13direct (N × H)
48. C2×C3×C7C4×C132direct (N × H)
50. C3×C13C2×C4×C7×C13direct (N × H)
52. C4×C7C2×C3×C132direct (N × H)
53. C2×C13C3×C4×C7×C13direct (N × H)
55. C2×C3×C4C7×C132direct (N × H)
56. C3×C7C2×C4×C132direct (N × H)
57. C2×C7C3×C4×C132direct (N × H)
59. C13C2×C3×C4×C7×C13direct (N × H)
61. C3×C4C2×C7×C132direct (N × H)
62. C2×C4C3×C7×C132direct (N × H)
63. C7C2×C3×C4×C132direct (N × H)
64. C2×C3C4×C7×C132direct (N × H)
67. C4C2×C3×C7×C132direct (N × H)
68. C3C2×C4×C7×C132direct (N × H)
69. C2C3×C4×C7×C132direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×C1323
C2×C3×C4×C1327
C2×C3×C4×C7×C1313
C22×C3×C7×C1322
C3×C4×C7×C1322