Finite Group Databasebeta

← C23×C33×C4×C17 #72192804

Subgroups — C23×C33×C4×C17 #72192804

Order 14688.

6608 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C33×C17C211yesmaximal, characteristic
2C22×C33×C4×C17C2114yesmaximal, direct product factor
3C23×C32×C4×C17C3113yesmaximal, direct product factor
4C23×C33×C17C418yesdirect product factor
5C23×C33×C17C2217yes—
6C2×C33×C4×C17C22128yesdirect product factor
7C24×C32×C17C2×C3113yes—
8C22×C32×C4×C17C2×C31182yesdirect product factor
9C22×C33×C17C2×C4128yesdirect product factor
10C22×C33×C17C2317yes—
11C33×C4×C17C2318yesdirect product factor
12C23×C3×C4×C17C32113yesdirect product factor
13C23×C32×C17C3×C41104yesdirect product factor
14C23×C32×C17C22×C3191yes—
15C2×C32×C4×C17C22×C31364yesdirect product factor
16C2×C33×C17C22×C4114yesdirect product factor
17C2×C33×C17C2411yescharacteristic
18C23×C33×C4C1711yesmaximal, characteristic, direct product factor, Hall
19C24×C3×C17C2×C32113yes—
20C22×C3×C4×C17C2×C321182yesdirect product factor
21C22×C32×C17C2×C3×C41364yesdirect product factor
22C22×C32×C17C23×C3191yes—
23C32×C4×C17C23×C31104yesdirect product factor
24C23×C4×C17C3311yescharacteristic, direct product factor, Hall
25C33×C17C23×C411yescharacteristic, direct product factor, Hall
26C24×C33C2×C1711yescharacteristic
27C22×C33×C4C2×C17114yesdirect product factor
28C23×C3×C17C32×C41104yesdirect product factor
29C23×C3×C17C22×C32191yes—
30C2×C3×C4×C17C22×C321364yesdirect product factor
31C2×C32×C17C22×C3×C41182yesdirect product factor
32C2×C32×C17C24×C3113yes—
33C23×C32×C4C3×C17113yesdirect product factor
34C24×C17C2×C3311yescharacteristic
35C22×C4×C17C2×C33114yesdirect product factor
36C23×C33C4×C1718yesdirect product factor
37C23×C33C22×C1717yes—
38C2×C33×C4C22×C17128yesdirect product factor
39C22×C3×C17C2×C32×C41364yesdirect product factor
40C22×C3×C17C23×C32191yes—
41C3×C4×C17C23×C321104yesdirect product factor
42C32×C17C23×C3×C4113yesdirect product factor
43C24×C32C2×C3×C17113yes—
44C22×C32×C4C2×C3×C171182yesdirect product factor
45C23×C17C33×C418yesdirect product factor
46C23×C17C22×C3317yes—
47C2×C4×C17C22×C33128yesdirect product factor
48C22×C33C2×C4×C17128yesdirect product factor
49C22×C33C23×C1717yes—
50C33×C4C23×C1718yesdirect product factor
51C2×C3×C17C22×C32×C41182yesdirect product factor
52C2×C3×C17C24×C32113yes—
53C23×C3×C4C32×C17113yesdirect product factor
54C23×C32C3×C4×C171104yesdirect product factor
55C23×C32C22×C3×C17191yes—
56C2×C32×C4C22×C3×C171364yesdirect product factor
57C22×C17C2×C33×C4128yesdirect product factor
58C22×C17C23×C3317yes—
59C4×C17C23×C3318yesdirect product factor
60C2×C33C22×C4×C17114yesdirect product factor
61C2×C33C24×C1711yescharacteristic
62C3×C17C23×C32×C4113yesdirect product factor
63C24×C3C2×C32×C17113yes—
64C22×C3×C4C2×C32×C171182yesdirect product factor
65C22×C32C2×C3×C4×C171364yesdirect product factor
66C22×C32C23×C3×C17191yes—
67C32×C4C23×C3×C171104yesdirect product factor
68C2×C17C22×C33×C4114yesdirect product factor
69C2×C17C24×C3311yescharacteristic
70C23×C4C33×C1711yescharacteristic, direct product factor, Sylow
71C33C23×C4×C1711yescharacteristic, direct product factor, Sylow
72C23×C3C32×C4×C171104yesdirect product factor
73C23×C3C22×C32×C17191yes—
74C2×C3×C4C22×C32×C171364yesdirect product factor
75C2×C32C22×C3×C4×C171182yesdirect product factor
76C2×C32C24×C3×C17113yes—
77C17C23×C33×C411yescharacteristic, direct product factor, Sylow
78C24C2×C33×C1711yescharacteristic
79C22×C4C2×C33×C17114yesdirect product factor
80C22×C3C2×C32×C4×C171364yesdirect product factor
81C22×C3C23×C32×C17191yes—
82C3×C4C23×C32×C171104yesdirect product factor
83C32C23×C3×C4×C17113yesdirect product factor
84C23C33×C4×C1718yesdirect product factor
85C23C22×C33×C1717yes—
86C2×C4C22×C33×C17128yesdirect product factor
87C2×C3C22×C32×C4×C171182yesdirect product factor
88C2×C3C24×C32×C17113yes—
89C22C2×C33×C4×C17128yesdirect product factor
90C22C23×C33×C1717yes—
91C4C23×C33×C1718yesdirect product factor
92C3C23×C32×C4×C17113yesdirect product factor
93C2C22×C33×C4×C17114yesdirect product factor
94C2C24×C33×C1711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C33×C17
socle, prime radicalC24×C33×C17C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C33×C4×C17C2direct (N × H)
3. C23×C32×C4×C17C3direct (N × H)
4. C23×C33×C17C4direct (N × H)
6. C2×C33×C4×C17C22direct (N × H)
8. C22×C32×C4×C17C2×C3direct (N × H)
9. C22×C33×C17C2×C4direct (N × H)
11. C33×C4×C17C23direct (N × H)
12. C23×C3×C4×C17C32direct (N × H)
13. C23×C32×C17C3×C4direct (N × H)
15. C2×C32×C4×C17C22×C3direct (N × H)
16. C2×C33×C17C22×C4direct (N × H)
18. C23×C33×C4C17direct (N × H)
20. C22×C3×C4×C17C2×C32direct (N × H)
21. C22×C32×C17C2×C3×C4direct (N × H)
23. C32×C4×C17C23×C3direct (N × H)
24. C23×C4×C17C33direct (N × H)
25. C33×C17C23×C4direct (N × H)
27. C22×C33×C4C2×C17direct (N × H)
28. C23×C3×C17C32×C4direct (N × H)
30. C2×C3×C4×C17C22×C32direct (N × H)
31. C2×C32×C17C22×C3×C4direct (N × H)
33. C23×C32×C4C3×C17direct (N × H)
35. C22×C4×C17C2×C33direct (N × H)
36. C23×C33C4×C17direct (N × H)
38. C2×C33×C4C22×C17direct (N × H)
39. C22×C3×C17C2×C32×C4direct (N × H)
41. C3×C4×C17C23×C32direct (N × H)
42. C32×C17C23×C3×C4direct (N × H)
44. C22×C32×C4C2×C3×C17direct (N × H)
45. C23×C17C33×C4direct (N × H)
47. C2×C4×C17C22×C33direct (N × H)
48. C22×C33C2×C4×C17direct (N × H)
50. C33×C4C23×C17direct (N × H)
51. C2×C3×C17C22×C32×C4direct (N × H)
53. C23×C3×C4C32×C17direct (N × H)
54. C23×C32C3×C4×C17direct (N × H)
56. C2×C32×C4C22×C3×C17direct (N × H)
57. C22×C17C2×C33×C4direct (N × H)
59. C4×C17C23×C33direct (N × H)
60. C2×C33C22×C4×C17direct (N × H)
62. C3×C17C23×C32×C4direct (N × H)
64. C22×C3×C4C2×C32×C17direct (N × H)
65. C22×C32C2×C3×C4×C17direct (N × H)
67. C32×C4C23×C3×C17direct (N × H)
68. C2×C17C22×C33×C4direct (N × H)
70. C23×C4C33×C17direct (N × H)
71. C33C23×C4×C17direct (N × H)
72. C23×C3C32×C4×C17direct (N × H)
74. C2×C3×C4C22×C32×C17direct (N × H)
75. C2×C32C22×C3×C4×C17direct (N × H)
77. C17C23×C33×C4direct (N × H)
79. C22×C4C2×C33×C17direct (N × H)
80. C22×C3C2×C32×C4×C17direct (N × H)
82. C3×C4C23×C32×C17direct (N × H)
83. C32C23×C3×C4×C17direct (N × H)
84. C23C33×C4×C17direct (N × H)
86. C2×C4C22×C33×C17direct (N × H)
87. C2×C3C22×C32×C4×C17direct (N × H)
89. C22C2×C33×C4×C17direct (N × H)
91. C4C23×C33×C17direct (N × H)
92. C3C23×C32×C4×C17direct (N × H)
93. C2C22×C33×C4×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C33×C172
C22×C33×C4×C172
C23×C32×C4×C173
C23×C33×C417