Finite Group Databasebeta

← C32×C4×C5×C11×C17 #46777953

Subgroups — C32×C4×C5×C11×C17 #46777953

Order 33660.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C5×C11×C17C211yesmaximal, characteristic
2C3×C4×C5×C11×C17C314yesmaximal, direct product factor
3C32×C5×C11×C17C411yescharacteristic, direct product factor, Hall
4C32×C4×C11×C17C511yesmaximal, characteristic, direct product factor, Hall
5C2×C3×C5×C11×C17C2×C314yes—
6C4×C5×C11×C17C3211yescharacteristic, direct product factor, Hall
7C2×C32×C11×C17C2×C511yescharacteristic
8C32×C4×C5×C17C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C11×C17C3×C414yesdirect product factor
10C3×C4×C11×C17C3×C514yesdirect product factor
11C32×C4×C5×C11C1711yesmaximal, characteristic, direct product factor, Hall
12C2×C5×C11×C17C2×C3211yescharacteristic
13C32×C11×C17C4×C511yescharacteristic, direct product factor, Hall
14C2×C32×C5×C17C2×C1111yescharacteristic
15C2×C3×C11×C17C2×C3×C514yes—
16C3×C4×C5×C17C3×C1114yesdirect product factor
17C2×C32×C5×C11C2×C1711yescharacteristic
18C5×C11×C17C32×C411yescharacteristic, direct product factor, Hall
19C32×C5×C17C4×C1111yescharacteristic, direct product factor, Hall
20C4×C11×C17C32×C511yescharacteristic, direct product factor, Hall
21C3×C4×C5×C11C3×C1714yesdirect product factor
22C32×C4×C17C5×C1111yescharacteristic, direct product factor, Hall
23C3×C11×C17C3×C4×C514yesdirect product factor
24C2×C3×C5×C17C2×C3×C1114yes—
25C32×C5×C11C4×C1711yescharacteristic, direct product factor, Hall
26C32×C4×C11C5×C1711yescharacteristic, direct product factor, Hall
27C2×C11×C17C2×C32×C511yescharacteristic
28C4×C5×C17C32×C1111yescharacteristic, direct product factor, Hall
29C2×C3×C5×C11C2×C3×C1714yes—
30C2×C32×C17C2×C5×C1111yescharacteristic
31C3×C5×C17C3×C4×C1114yesdirect product factor
32C4×C5×C11C32×C1711yescharacteristic, direct product factor, Hall
33C3×C4×C17C3×C5×C1114yesdirect product factor
34C2×C32×C11C2×C5×C1711yescharacteristic
35C11×C17C32×C4×C511yescharacteristic, direct product factor, Hall
36C32×C4×C5C11×C1711yescharacteristic, direct product factor, Hall
37C2×C5×C17C2×C32×C1111yescharacteristic
38C3×C5×C11C3×C4×C1714yesdirect product factor
39C32×C17C4×C5×C1111yescharacteristic, direct product factor, Hall
40C3×C4×C11C3×C5×C1714yesdirect product factor
41C2×C5×C11C2×C32×C1711yescharacteristic
42C2×C3×C17C2×C3×C5×C1114yes—
43C32×C11C4×C5×C1711yescharacteristic, direct product factor, Hall
44C2×C32×C5C2×C11×C1711yescharacteristic
45C5×C17C32×C4×C1111yescharacteristic, direct product factor, Hall
46C4×C17C32×C5×C1111yescharacteristic, direct product factor, Hall
47C2×C3×C11C2×C3×C5×C1714yes—
48C3×C4×C5C3×C11×C1714yesdirect product factor
49C5×C11C32×C4×C1711yescharacteristic, direct product factor, Hall
50C3×C17C3×C4×C5×C1114yesdirect product factor
51C32×C5C4×C11×C1711yescharacteristic, direct product factor, Hall
52C4×C11C32×C5×C1711yescharacteristic, direct product factor, Hall
53C32×C4C5×C11×C1711yescharacteristic, direct product factor, Hall
54C2×C17C2×C32×C5×C1111yescharacteristic
55C3×C11C3×C4×C5×C1714yesdirect product factor
56C2×C3×C5C2×C3×C11×C1714yes—
57C2×C11C2×C32×C5×C1711yescharacteristic
58C4×C5C32×C11×C1711yescharacteristic, direct product factor, Hall
59C2×C32C2×C5×C11×C1711yescharacteristic
60C17C32×C4×C5×C1111yescharacteristic, direct product factor, Sylow
61C3×C5C3×C4×C11×C1714yesdirect product factor
62C3×C4C3×C5×C11×C1714yesdirect product factor
63C11C32×C4×C5×C1711yescharacteristic, direct product factor, Sylow
64C2×C5C2×C32×C11×C1711yescharacteristic
65C32C4×C5×C11×C1711yescharacteristic, direct product factor, Sylow
66C2×C3C2×C3×C5×C11×C1714yes—
67C5C32×C4×C11×C1711yescharacteristic, direct product factor, Sylow
68C4C32×C5×C11×C1711yescharacteristic, direct product factor, Sylow
69C3C3×C4×C5×C11×C1714yesdirect product factor
70C2C2×C32×C5×C11×C1711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C32×C5×C11×C17
socle, prime radicalC2×C32×C5×C11×C17C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×C11×C17C3direct (N × H)
3. C32×C5×C11×C17C4direct (N × H)
4. C32×C4×C11×C17C5direct (N × H)
6. C4×C5×C11×C17C32direct (N × H)
8. C32×C4×C5×C17C11direct (N × H)
9. C3×C5×C11×C17C3×C4direct (N × H)
10. C3×C4×C11×C17C3×C5direct (N × H)
11. C32×C4×C5×C11C17direct (N × H)
13. C32×C11×C17C4×C5direct (N × H)
16. C3×C4×C5×C17C3×C11direct (N × H)
18. C5×C11×C17C32×C4direct (N × H)
19. C32×C5×C17C4×C11direct (N × H)
20. C4×C11×C17C32×C5direct (N × H)
21. C3×C4×C5×C11C3×C17direct (N × H)
22. C32×C4×C17C5×C11direct (N × H)
23. C3×C11×C17C3×C4×C5direct (N × H)
25. C32×C5×C11C4×C17direct (N × H)
26. C32×C4×C11C5×C17direct (N × H)
28. C4×C5×C17C32×C11direct (N × H)
31. C3×C5×C17C3×C4×C11direct (N × H)
32. C4×C5×C11C32×C17direct (N × H)
33. C3×C4×C17C3×C5×C11direct (N × H)
35. C11×C17C32×C4×C5direct (N × H)
36. C32×C4×C5C11×C17direct (N × H)
38. C3×C5×C11C3×C4×C17direct (N × H)
39. C32×C17C4×C5×C11direct (N × H)
40. C3×C4×C11C3×C5×C17direct (N × H)
43. C32×C11C4×C5×C17direct (N × H)
45. C5×C17C32×C4×C11direct (N × H)
46. C4×C17C32×C5×C11direct (N × H)
48. C3×C4×C5C3×C11×C17direct (N × H)
49. C5×C11C32×C4×C17direct (N × H)
50. C3×C17C3×C4×C5×C11direct (N × H)
51. C32×C5C4×C11×C17direct (N × H)
52. C4×C11C32×C5×C17direct (N × H)
53. C32×C4C5×C11×C17direct (N × H)
55. C3×C11C3×C4×C5×C17direct (N × H)
58. C4×C5C32×C11×C17direct (N × H)
60. C17C32×C4×C5×C11direct (N × H)
61. C3×C5C3×C4×C11×C17direct (N × H)
62. C3×C4C3×C5×C11×C17direct (N × H)
63. C11C32×C4×C5×C17direct (N × H)
65. C32C4×C5×C11×C17direct (N × H)
67. C5C32×C4×C11×C17direct (N × H)
68. C4C32×C5×C11×C17direct (N × H)
69. C3C3×C4×C5×C11×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×C11×C172
C3×C4×C5×C11×C173
C32×C4×C11×C175
C32×C4×C5×C1711
C32×C4×C5×C1117