Finite Group Databasebeta

← C22×C3×C4×C7×C73 #72201783

Subgroups — C22×C3×C4×C7×C73 #72201783

Order 24528.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C7×C73C211yesmaximal, characteristic
2C2×C3×C4×C7×C73C216yesmaximal, direct product factor
3C22×C4×C7×C73C311yesmaximal, characteristic, direct product factor, Hall
4C23×C7×C73C2×C311yescharacteristic
5C2×C4×C7×C73C2×C316yesdirect product factor
6C22×C3×C4×C73C711yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C7×C73C414yesdirect product factor
8C22×C3×C7×C73C2213yes—
9C3×C4×C7×C73C2214yesdirect product factor
10C2×C3×C7×C73C2×C416yesdirect product factor
11C2×C3×C7×C73C2311yescharacteristic
12C22×C7×C73C3×C414yesdirect product factor
13C22×C7×C73C22×C313yes—
14C4×C7×C73C22×C314yesdirect product factor
15C23×C3×C73C2×C711yescharacteristic
16C2×C3×C4×C73C2×C716yesdirect product factor
17C3×C7×C73C22×C411yescharacteristic, direct product factor, Hall
18C22×C4×C73C3×C711yescharacteristic, direct product factor, Hall
19C2×C7×C73C2×C3×C416yesdirect product factor
20C2×C7×C73C23×C311yescharacteristic
21C22×C3×C73C4×C714yesdirect product factor
22C22×C3×C73C22×C713yes—
23C3×C4×C73C22×C714yesdirect product factor
24C23×C73C2×C3×C711yescharacteristic
25C2×C4×C73C2×C3×C716yesdirect product factor
26C7×C73C22×C3×C411yescharacteristic, direct product factor, Hall
27C2×C3×C73C2×C4×C716yesdirect product factor
28C2×C3×C73C23×C711yescharacteristic
29C22×C3×C4×C7C7311yesmaximal, characteristic, direct product factor, Hall
30C22×C73C3×C4×C714yesdirect product factor
31C22×C73C22×C3×C713yes—
32C4×C73C22×C3×C714yesdirect product factor
33C3×C73C22×C4×C711yescharacteristic, direct product factor, Hall
34C23×C3×C7C2×C7311yescharacteristic
35C2×C3×C4×C7C2×C7316yesdirect product factor
36C2×C73C2×C3×C4×C716yesdirect product factor
37C2×C73C23×C3×C711yescharacteristic
38C22×C4×C7C3×C7311yescharacteristic, direct product factor, Hall
39C22×C3×C7C4×C7314yesdirect product factor
40C22×C3×C7C22×C7313yes—
41C3×C4×C7C22×C7314yesdirect product factor
42C73C22×C3×C4×C711yescharacteristic, direct product factor, Sylow
43C23×C7C2×C3×C7311yescharacteristic
44C2×C4×C7C2×C3×C7316yesdirect product factor
45C22×C3×C4C7×C7311yescharacteristic, direct product factor, Hall
46C2×C3×C7C2×C4×C7316yesdirect product factor
47C2×C3×C7C23×C7311yescharacteristic
48C22×C7C3×C4×C7314yesdirect product factor
49C22×C7C22×C3×C7313yes—
50C4×C7C22×C3×C7314yesdirect product factor
51C23×C3C2×C7×C7311yescharacteristic
52C2×C3×C4C2×C7×C7316yesdirect product factor
53C3×C7C22×C4×C7311yescharacteristic, direct product factor, Hall
54C22×C4C3×C7×C7311yescharacteristic, direct product factor, Sylow
55C2×C7C2×C3×C4×C7316yesdirect product factor
56C2×C7C23×C3×C7311yescharacteristic
57C22×C3C4×C7×C7314yesdirect product factor
58C22×C3C22×C7×C7313yes—
59C3×C4C22×C7×C7314yesdirect product factor
60C23C2×C3×C7×C7311yescharacteristic
61C2×C4C2×C3×C7×C7316yesdirect product factor
62C7C22×C3×C4×C7311yescharacteristic, direct product factor, Sylow
63C2×C3C2×C4×C7×C7316yesdirect product factor
64C2×C3C23×C7×C7311yescharacteristic
65C22C3×C4×C7×C7314yesdirect product factor
66C22C22×C3×C7×C7313yes—
67C4C22×C3×C7×C7314yesdirect product factor
68C3C22×C4×C7×C7311yescharacteristic, direct product factor, Sylow
69C2C2×C3×C4×C7×C7316yesdirect product factor
70C2C23×C3×C7×C7311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C7×C73
socle, prime radicalC23×C3×C7×C73C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C7×C73C2direct (N × H)
3. C22×C4×C7×C73C3direct (N × H)
5. C2×C4×C7×C73C2×C3direct (N × H)
6. C22×C3×C4×C73C7direct (N × H)
7. C22×C3×C7×C73C4direct (N × H)
9. C3×C4×C7×C73C22direct (N × H)
10. C2×C3×C7×C73C2×C4direct (N × H)
12. C22×C7×C73C3×C4direct (N × H)
14. C4×C7×C73C22×C3direct (N × H)
16. C2×C3×C4×C73C2×C7direct (N × H)
17. C3×C7×C73C22×C4direct (N × H)
18. C22×C4×C73C3×C7direct (N × H)
19. C2×C7×C73C2×C3×C4direct (N × H)
21. C22×C3×C73C4×C7direct (N × H)
23. C3×C4×C73C22×C7direct (N × H)
25. C2×C4×C73C2×C3×C7direct (N × H)
26. C7×C73C22×C3×C4direct (N × H)
27. C2×C3×C73C2×C4×C7direct (N × H)
29. C22×C3×C4×C7C73direct (N × H)
30. C22×C73C3×C4×C7direct (N × H)
32. C4×C73C22×C3×C7direct (N × H)
33. C3×C73C22×C4×C7direct (N × H)
35. C2×C3×C4×C7C2×C73direct (N × H)
36. C2×C73C2×C3×C4×C7direct (N × H)
38. C22×C4×C7C3×C73direct (N × H)
39. C22×C3×C7C4×C73direct (N × H)
41. C3×C4×C7C22×C73direct (N × H)
42. C73C22×C3×C4×C7direct (N × H)
44. C2×C4×C7C2×C3×C73direct (N × H)
45. C22×C3×C4C7×C73direct (N × H)
46. C2×C3×C7C2×C4×C73direct (N × H)
48. C22×C7C3×C4×C73direct (N × H)
50. C4×C7C22×C3×C73direct (N × H)
52. C2×C3×C4C2×C7×C73direct (N × H)
53. C3×C7C22×C4×C73direct (N × H)
54. C22×C4C3×C7×C73direct (N × H)
55. C2×C7C2×C3×C4×C73direct (N × H)
57. C22×C3C4×C7×C73direct (N × H)
59. C3×C4C22×C7×C73direct (N × H)
61. C2×C4C2×C3×C7×C73direct (N × H)
62. C7C22×C3×C4×C73direct (N × H)
63. C2×C3C2×C4×C7×C73direct (N × H)
65. C22C3×C4×C7×C73direct (N × H)
67. C4C22×C3×C7×C73direct (N × H)
68. C3C22×C4×C7×C73direct (N × H)
69. C2C2×C3×C4×C7×C73direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C7×C732
C2×C3×C4×C7×C732
C22×C4×C7×C733
C22×C3×C4×C737
C22×C3×C4×C773