Finite Group Databasebeta

← C2×C32×C4×C73 #72202001

Subgroups — C2×C32×C4×C73 #72202001

Order 24696.

5568 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C73C211yesmaximal, characteristic
2C32×C4×C73C212yesmaximal, direct product factor
3C2×C3×C4×C73C314yesmaximal, direct product factor
4C2×C32×C73C412yesdirect product factor
5C2×C32×C73C2211yescharacteristic
6C22×C3×C73C2×C314yes—
7C3×C4×C73C2×C318yesdirect product factor
8C2×C32×C4×C72C7157yesmaximal, direct product factor
9C32×C73C2×C411yescharacteristic, direct product factor, Hall
10C2×C4×C73C3211yescharacteristic, direct product factor, Hall
11C2×C3×C73C3×C418yesdirect product factor
12C2×C3×C73C22×C314yes—
13C22×C32×C72C2×C7157yes—
14C32×C4×C72C2×C71114yesdirect product factor
15C22×C73C2×C3211yescharacteristic
16C4×C73C2×C3212yesdirect product factor
17C2×C3×C4×C72C3×C71228yesdirect product factor
18C3×C73C2×C3×C414yesdirect product factor
19C2×C32×C72C4×C71114yesdirect product factor
20C2×C32×C72C22×C7157yes—
21C2×C73C32×C412yesdirect product factor
22C2×C73C22×C3211yescharacteristic
23C22×C3×C72C2×C3×C71228yes—
24C3×C4×C72C2×C3×C71456yesdirect product factor
25C2×C32×C4×C7C72157yesdirect product factor
26C32×C72C2×C4×C7157yesdirect product factor
27C2×C4×C72C32×C7157yesdirect product factor
28C73C2×C32×C411yescharacteristic, direct product factor, Sylow
29C2×C3×C72C3×C4×C71456yesdirect product factor
30C2×C3×C72C22×C3×C71228yes—
31C22×C32×C7C2×C72157yes—
32C32×C4×C7C2×C721114yesdirect product factor
33C22×C72C2×C32×C7157yes—
34C4×C72C2×C32×C71114yesdirect product factor
35C2×C3×C4×C7C3×C721228yesdirect product factor
36C3×C72C2×C3×C4×C71228yesdirect product factor
37C2×C32×C7C4×C721114yesdirect product factor
38C2×C32×C7C22×C72157yes—
39C2×C72C32×C4×C71114yesdirect product factor
40C2×C72C22×C32×C7157yes—
41C22×C3×C7C2×C3×C721228yes—
42C3×C4×C7C2×C3×C721456yesdirect product factor
43C2×C32×C4C7311yescharacteristic, direct product factor, Hall
44C32×C7C2×C4×C72157yesdirect product factor
45C2×C4×C7C32×C72157yesdirect product factor
46C72C2×C32×C4×C7157yesdirect product factor
47C2×C3×C7C3×C4×C721456yesdirect product factor
48C2×C3×C7C22×C3×C721228yes—
49C22×C32C2×C7311yescharacteristic
50C32×C4C2×C7312yesdirect product factor
51C22×C7C2×C32×C72157yes—
52C4×C7C2×C32×C721114yesdirect product factor
53C2×C3×C4C3×C7314yesdirect product factor
54C3×C7C2×C3×C4×C721228yesdirect product factor
55C2×C32C4×C7312yesdirect product factor
56C2×C32C22×C7311yescharacteristic
57C2×C7C32×C4×C721114yesdirect product factor
58C2×C7C22×C32×C72157yes—
59C22×C3C2×C3×C7314yes—
60C3×C4C2×C3×C7318yesdirect product factor
61C32C2×C4×C7311yescharacteristic, direct product factor, Sylow
62C2×C4C32×C7311yescharacteristic, direct product factor, Sylow
63C7C2×C32×C4×C72157yesdirect product factor
64C2×C3C3×C4×C7318yesdirect product factor
65C2×C3C22×C3×C7314yes—
66C22C2×C32×C7311yescharacteristic
67C4C2×C32×C7312yesdirect product factor
68C3C2×C3×C4×C7314yesdirect product factor
69C2C32×C4×C7312yesdirect product factor
70C2C22×C32×C7311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C32×C73
socle, prime radicalC22×C32×C73C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C32×C4×C73C2direct (N × H)
3. C2×C3×C4×C73C3direct (N × H)
4. C2×C32×C73C4direct (N × H)
7. C3×C4×C73C2×C3direct (N × H)
8. C2×C32×C4×C72C7direct (N × H)
9. C32×C73C2×C4direct (N × H)
10. C2×C4×C73C32direct (N × H)
11. C2×C3×C73C3×C4direct (N × H)
14. C32×C4×C72C2×C7direct (N × H)
16. C4×C73C2×C32direct (N × H)
17. C2×C3×C4×C72C3×C7direct (N × H)
18. C3×C73C2×C3×C4direct (N × H)
19. C2×C32×C72C4×C7direct (N × H)
21. C2×C73C32×C4direct (N × H)
24. C3×C4×C72C2×C3×C7direct (N × H)
25. C2×C32×C4×C7C72direct (N × H)
26. C32×C72C2×C4×C7direct (N × H)
27. C2×C4×C72C32×C7direct (N × H)
28. C73C2×C32×C4direct (N × H)
29. C2×C3×C72C3×C4×C7direct (N × H)
32. C32×C4×C7C2×C72direct (N × H)
34. C4×C72C2×C32×C7direct (N × H)
35. C2×C3×C4×C7C3×C72direct (N × H)
36. C3×C72C2×C3×C4×C7direct (N × H)
37. C2×C32×C7C4×C72direct (N × H)
39. C2×C72C32×C4×C7direct (N × H)
42. C3×C4×C7C2×C3×C72direct (N × H)
43. C2×C32×C4C73direct (N × H)
44. C32×C7C2×C4×C72direct (N × H)
45. C2×C4×C7C32×C72direct (N × H)
46. C72C2×C32×C4×C7direct (N × H)
47. C2×C3×C7C3×C4×C72direct (N × H)
50. C32×C4C2×C73direct (N × H)
52. C4×C7C2×C32×C72direct (N × H)
53. C2×C3×C4C3×C73direct (N × H)
54. C3×C7C2×C3×C4×C72direct (N × H)
55. C2×C32C4×C73direct (N × H)
57. C2×C7C32×C4×C72direct (N × H)
60. C3×C4C2×C3×C73direct (N × H)
61. C32C2×C4×C73direct (N × H)
62. C2×C4C32×C73direct (N × H)
63. C7C2×C32×C4×C72direct (N × H)
64. C2×C3C3×C4×C73direct (N × H)
67. C4C2×C32×C73direct (N × H)
68. C3C2×C3×C4×C73direct (N × H)
69. C2C32×C4×C73direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C732
C32×C4×C732
C2×C3×C4×C733
C2×C32×C4×C727