Finite Group Databasebeta

← C23×C33×C4×C37 #72208702

Subgroups — C23×C33×C4×C37 #72208702

Order 31968.

6608 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C33×C37C211yesmaximal, characteristic
2C22×C33×C4×C37C2114yesmaximal, direct product factor
3C23×C32×C4×C37C3113yesmaximal, direct product factor
4C23×C33×C37C418yesdirect product factor
5C23×C33×C37C2217yes—
6C2×C33×C4×C37C22128yesdirect product factor
7C24×C32×C37C2×C3113yes—
8C22×C32×C4×C37C2×C31182yesdirect product factor
9C22×C33×C37C2×C4128yesdirect product factor
10C22×C33×C37C2317yes—
11C33×C4×C37C2318yesdirect product factor
12C23×C3×C4×C37C32113yesdirect product factor
13C23×C32×C37C3×C41104yesdirect product factor
14C23×C32×C37C22×C3191yes—
15C2×C32×C4×C37C22×C31364yesdirect product factor
16C2×C33×C37C22×C4114yesdirect product factor
17C2×C33×C37C2411yescharacteristic
18C24×C3×C37C2×C32113yes—
19C22×C3×C4×C37C2×C321182yesdirect product factor
20C22×C32×C37C2×C3×C41364yesdirect product factor
21C22×C32×C37C23×C3191yes—
22C32×C4×C37C23×C31104yesdirect product factor
23C23×C4×C37C3311yescharacteristic, direct product factor, Hall
24C33×C37C23×C411yescharacteristic, direct product factor, Hall
25C23×C3×C37C32×C41104yesdirect product factor
26C23×C3×C37C22×C32191yes—
27C2×C3×C4×C37C22×C321364yesdirect product factor
28C23×C33×C4C3711yesmaximal, characteristic, direct product factor, Hall
29C2×C32×C37C22×C3×C41182yesdirect product factor
30C2×C32×C37C24×C3113yes—
31C24×C37C2×C3311yescharacteristic
32C22×C4×C37C2×C33114yesdirect product factor
33C22×C3×C37C2×C32×C41364yesdirect product factor
34C22×C3×C37C23×C32191yes—
35C3×C4×C37C23×C321104yesdirect product factor
36C24×C33C2×C3711yescharacteristic
37C22×C33×C4C2×C37114yesdirect product factor
38C32×C37C23×C3×C4113yesdirect product factor
39C23×C37C33×C418yesdirect product factor
40C23×C37C22×C3317yes—
41C2×C4×C37C22×C33128yesdirect product factor
42C23×C32×C4C3×C37113yesdirect product factor
43C2×C3×C37C22×C32×C41182yesdirect product factor
44C2×C3×C37C24×C32113yes—
45C23×C33C4×C3718yesdirect product factor
46C23×C33C22×C3717yes—
47C2×C33×C4C22×C37128yesdirect product factor
48C22×C37C2×C33×C4128yesdirect product factor
49C22×C37C23×C3317yes—
50C4×C37C23×C3318yesdirect product factor
51C24×C32C2×C3×C37113yes—
52C22×C32×C4C2×C3×C371182yesdirect product factor
53C3×C37C23×C32×C4113yesdirect product factor
54C22×C33C2×C4×C37128yesdirect product factor
55C22×C33C23×C3717yes—
56C33×C4C23×C3718yesdirect product factor
57C23×C3×C4C32×C37113yesdirect product factor
58C2×C37C22×C33×C4114yesdirect product factor
59C2×C37C24×C3311yescharacteristic
60C23×C32C3×C4×C371104yesdirect product factor
61C23×C32C22×C3×C37191yes—
62C2×C32×C4C22×C3×C371364yesdirect product factor
63C2×C33C22×C4×C37114yesdirect product factor
64C2×C33C24×C3711yescharacteristic
65C24×C3C2×C32×C37113yes—
66C22×C3×C4C2×C32×C371182yesdirect product factor
67C37C23×C33×C411yescharacteristic, direct product factor, Sylow
68C22×C32C2×C3×C4×C371364yesdirect product factor
69C22×C32C23×C3×C37191yes—
70C32×C4C23×C3×C371104yesdirect product factor
71C23×C4C33×C3711yescharacteristic, direct product factor, Sylow
72C33C23×C4×C3711yescharacteristic, direct product factor, Sylow
73C23×C3C32×C4×C371104yesdirect product factor
74C23×C3C22×C32×C37191yes—
75C2×C3×C4C22×C32×C371364yesdirect product factor
76C2×C32C22×C3×C4×C371182yesdirect product factor
77C2×C32C24×C3×C37113yes—
78C24C2×C33×C3711yescharacteristic
79C22×C4C2×C33×C37114yesdirect product factor
80C22×C3C2×C32×C4×C371364yesdirect product factor
81C22×C3C23×C32×C37191yes—
82C3×C4C23×C32×C371104yesdirect product factor
83C32C23×C3×C4×C37113yesdirect product factor
84C23C33×C4×C3718yesdirect product factor
85C23C22×C33×C3717yes—
86C2×C4C22×C33×C37128yesdirect product factor
87C2×C3C22×C32×C4×C371182yesdirect product factor
88C2×C3C24×C32×C37113yes—
89C22C2×C33×C4×C37128yesdirect product factor
90C22C23×C33×C3717yes—
91C4C23×C33×C3718yesdirect product factor
92C3C23×C32×C4×C37113yesdirect product factor
93C2C22×C33×C4×C37114yesdirect product factor
94C2C24×C33×C3711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C33×C37
socle, prime radicalC24×C33×C37C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C33×C4×C37C2direct (N × H)
3. C23×C32×C4×C37C3direct (N × H)
4. C23×C33×C37C4direct (N × H)
6. C2×C33×C4×C37C22direct (N × H)
8. C22×C32×C4×C37C2×C3direct (N × H)
9. C22×C33×C37C2×C4direct (N × H)
11. C33×C4×C37C23direct (N × H)
12. C23×C3×C4×C37C32direct (N × H)
13. C23×C32×C37C3×C4direct (N × H)
15. C2×C32×C4×C37C22×C3direct (N × H)
16. C2×C33×C37C22×C4direct (N × H)
19. C22×C3×C4×C37C2×C32direct (N × H)
20. C22×C32×C37C2×C3×C4direct (N × H)
22. C32×C4×C37C23×C3direct (N × H)
23. C23×C4×C37C33direct (N × H)
24. C33×C37C23×C4direct (N × H)
25. C23×C3×C37C32×C4direct (N × H)
27. C2×C3×C4×C37C22×C32direct (N × H)
28. C23×C33×C4C37direct (N × H)
29. C2×C32×C37C22×C3×C4direct (N × H)
32. C22×C4×C37C2×C33direct (N × H)
33. C22×C3×C37C2×C32×C4direct (N × H)
35. C3×C4×C37C23×C32direct (N × H)
37. C22×C33×C4C2×C37direct (N × H)
38. C32×C37C23×C3×C4direct (N × H)
39. C23×C37C33×C4direct (N × H)
41. C2×C4×C37C22×C33direct (N × H)
42. C23×C32×C4C3×C37direct (N × H)
43. C2×C3×C37C22×C32×C4direct (N × H)
45. C23×C33C4×C37direct (N × H)
47. C2×C33×C4C22×C37direct (N × H)
48. C22×C37C2×C33×C4direct (N × H)
50. C4×C37C23×C33direct (N × H)
52. C22×C32×C4C2×C3×C37direct (N × H)
53. C3×C37C23×C32×C4direct (N × H)
54. C22×C33C2×C4×C37direct (N × H)
56. C33×C4C23×C37direct (N × H)
57. C23×C3×C4C32×C37direct (N × H)
58. C2×C37C22×C33×C4direct (N × H)
60. C23×C32C3×C4×C37direct (N × H)
62. C2×C32×C4C22×C3×C37direct (N × H)
63. C2×C33C22×C4×C37direct (N × H)
66. C22×C3×C4C2×C32×C37direct (N × H)
67. C37C23×C33×C4direct (N × H)
68. C22×C32C2×C3×C4×C37direct (N × H)
70. C32×C4C23×C3×C37direct (N × H)
71. C23×C4C33×C37direct (N × H)
72. C33C23×C4×C37direct (N × H)
73. C23×C3C32×C4×C37direct (N × H)
75. C2×C3×C4C22×C32×C37direct (N × H)
76. C2×C32C22×C3×C4×C37direct (N × H)
79. C22×C4C2×C33×C37direct (N × H)
80. C22×C3C2×C32×C4×C37direct (N × H)
82. C3×C4C23×C32×C37direct (N × H)
83. C32C23×C3×C4×C37direct (N × H)
84. C23C33×C4×C37direct (N × H)
86. C2×C4C22×C33×C37direct (N × H)
87. C2×C3C22×C32×C4×C37direct (N × H)
89. C22C2×C33×C4×C37direct (N × H)
91. C4C23×C33×C37direct (N × H)
92. C3C23×C32×C4×C37direct (N × H)
93. C2C22×C33×C4×C37direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C33×C372
C22×C33×C4×C372
C23×C32×C4×C373
C23×C33×C437