Finite Group Databasebeta

← C22×C4×C7×C13×C17 #72202039

Subgroups — C22×C4×C7×C13×C17 #72202039

Order 24752.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C13×C17C211yesmaximal, characteristic
2C2×C4×C7×C13×C17C216yesmaximal, direct product factor
3C22×C4×C13×C17C711yesmaximal, characteristic, direct product factor, Hall
4C22×C7×C13×C17C414yesdirect product factor
5C22×C7×C13×C17C2213yes—
6C4×C7×C13×C17C2214yesdirect product factor
7C2×C7×C13×C17C2×C416yesdirect product factor
8C2×C7×C13×C17C2311yescharacteristic
9C22×C4×C7×C17C1311yesmaximal, characteristic, direct product factor, Hall
10C23×C13×C17C2×C711yescharacteristic
11C2×C4×C13×C17C2×C716yesdirect product factor
12C7×C13×C17C22×C411yescharacteristic, direct product factor, Hall
13C22×C4×C7×C13C1711yesmaximal, characteristic, direct product factor, Hall
14C23×C7×C17C2×C1311yescharacteristic
15C2×C4×C7×C17C2×C1316yesdirect product factor
16C22×C13×C17C4×C714yesdirect product factor
17C22×C13×C17C22×C713yes—
18C4×C13×C17C22×C714yesdirect product factor
19C23×C7×C13C2×C1711yescharacteristic
20C2×C4×C7×C13C2×C1716yesdirect product factor
21C22×C7×C17C4×C1314yesdirect product factor
22C22×C7×C17C22×C1313yes—
23C4×C7×C17C22×C1314yesdirect product factor
24C2×C13×C17C2×C4×C716yesdirect product factor
25C2×C13×C17C23×C711yescharacteristic
26C22×C7×C13C4×C1714yesdirect product factor
27C22×C7×C13C22×C1713yes—
28C4×C7×C13C22×C1714yesdirect product factor
29C22×C4×C17C7×C1311yescharacteristic, direct product factor, Hall
30C2×C7×C17C2×C4×C1316yesdirect product factor
31C2×C7×C17C23×C1311yescharacteristic
32C13×C17C22×C4×C711yescharacteristic, direct product factor, Hall
33C22×C4×C13C7×C1711yescharacteristic, direct product factor, Hall
34C2×C7×C13C2×C4×C1716yesdirect product factor
35C2×C7×C13C23×C1711yescharacteristic
36C23×C17C2×C7×C1311yescharacteristic
37C2×C4×C17C2×C7×C1316yesdirect product factor
38C7×C17C22×C4×C1311yescharacteristic, direct product factor, Hall
39C22×C4×C7C13×C1711yescharacteristic, direct product factor, Hall
40C23×C13C2×C7×C1711yescharacteristic
41C2×C4×C13C2×C7×C1716yesdirect product factor
42C7×C13C22×C4×C1711yescharacteristic, direct product factor, Hall
43C22×C17C4×C7×C1314yesdirect product factor
44C22×C17C22×C7×C1313yes—
45C4×C17C22×C7×C1314yesdirect product factor
46C23×C7C2×C13×C1711yescharacteristic
47C2×C4×C7C2×C13×C1716yesdirect product factor
48C22×C13C4×C7×C1714yesdirect product factor
49C22×C13C22×C7×C1713yes—
50C4×C13C22×C7×C1714yesdirect product factor
51C2×C17C2×C4×C7×C1316yesdirect product factor
52C2×C17C23×C7×C1311yescharacteristic
53C22×C7C4×C13×C1714yesdirect product factor
54C22×C7C22×C13×C1713yes—
55C4×C7C22×C13×C1714yesdirect product factor
56C2×C13C2×C4×C7×C1716yesdirect product factor
57C2×C13C23×C7×C1711yescharacteristic
58C17C22×C4×C7×C1311yescharacteristic, direct product factor, Sylow
59C22×C4C7×C13×C1711yescharacteristic, direct product factor, Sylow
60C2×C7C2×C4×C13×C1716yesdirect product factor
61C2×C7C23×C13×C1711yescharacteristic
62C13C22×C4×C7×C1711yescharacteristic, direct product factor, Sylow
63C23C2×C7×C13×C1711yescharacteristic
64C2×C4C2×C7×C13×C1716yesdirect product factor
65C7C22×C4×C13×C1711yescharacteristic, direct product factor, Sylow
66C22C4×C7×C13×C1714yesdirect product factor
67C22C22×C7×C13×C1713yes—
68C4C22×C7×C13×C1714yesdirect product factor
69C2C2×C4×C7×C13×C1716yesdirect product factor
70C2C23×C7×C13×C1711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C7×C13×C17
socle, prime radicalC23×C7×C13×C17C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C13×C17C2direct (N × H)
3. C22×C4×C13×C17C7direct (N × H)
4. C22×C7×C13×C17C4direct (N × H)
6. C4×C7×C13×C17C22direct (N × H)
7. C2×C7×C13×C17C2×C4direct (N × H)
9. C22×C4×C7×C17C13direct (N × H)
11. C2×C4×C13×C17C2×C7direct (N × H)
12. C7×C13×C17C22×C4direct (N × H)
13. C22×C4×C7×C13C17direct (N × H)
15. C2×C4×C7×C17C2×C13direct (N × H)
16. C22×C13×C17C4×C7direct (N × H)
18. C4×C13×C17C22×C7direct (N × H)
20. C2×C4×C7×C13C2×C17direct (N × H)
21. C22×C7×C17C4×C13direct (N × H)
23. C4×C7×C17C22×C13direct (N × H)
24. C2×C13×C17C2×C4×C7direct (N × H)
26. C22×C7×C13C4×C17direct (N × H)
28. C4×C7×C13C22×C17direct (N × H)
29. C22×C4×C17C7×C13direct (N × H)
30. C2×C7×C17C2×C4×C13direct (N × H)
32. C13×C17C22×C4×C7direct (N × H)
33. C22×C4×C13C7×C17direct (N × H)
34. C2×C7×C13C2×C4×C17direct (N × H)
37. C2×C4×C17C2×C7×C13direct (N × H)
38. C7×C17C22×C4×C13direct (N × H)
39. C22×C4×C7C13×C17direct (N × H)
41. C2×C4×C13C2×C7×C17direct (N × H)
42. C7×C13C22×C4×C17direct (N × H)
43. C22×C17C4×C7×C13direct (N × H)
45. C4×C17C22×C7×C13direct (N × H)
47. C2×C4×C7C2×C13×C17direct (N × H)
48. C22×C13C4×C7×C17direct (N × H)
50. C4×C13C22×C7×C17direct (N × H)
51. C2×C17C2×C4×C7×C13direct (N × H)
53. C22×C7C4×C13×C17direct (N × H)
55. C4×C7C22×C13×C17direct (N × H)
56. C2×C13C2×C4×C7×C17direct (N × H)
58. C17C22×C4×C7×C13direct (N × H)
59. C22×C4C7×C13×C17direct (N × H)
60. C2×C7C2×C4×C13×C17direct (N × H)
62. C13C22×C4×C7×C17direct (N × H)
64. C2×C4C2×C7×C13×C17direct (N × H)
65. C7C22×C4×C13×C17direct (N × H)
66. C22C4×C7×C13×C17direct (N × H)
68. C4C22×C7×C13×C17direct (N × H)
69. C2C2×C4×C7×C13×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C13×C172
C2×C4×C7×C13×C172
C22×C4×C13×C177
C22×C4×C7×C1713
C22×C4×C7×C1317