Finite Group Databasebeta

← C23×C33×C4×C7 #72185235

Subgroups — C23×C33×C4×C7 #72185235

Order 6048.

6608 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C33×C7C211yesmaximal, characteristic
2C22×C33×C4×C7C2114yesmaximal, direct product factor
3C23×C32×C4×C7C3113yesmaximal, direct product factor
4C23×C33×C7C418yesdirect product factor
5C23×C33×C7C2217yes—
6C2×C33×C4×C7C22128yesdirect product factor
7C24×C32×C7C2×C3113yes—
8C22×C32×C4×C7C2×C31182yesdirect product factor
9C23×C33×C4C711yesmaximal, characteristic, direct product factor, Hall
10C22×C33×C7C2×C4128yesdirect product factor
11C22×C33×C7C2317yes—
12C33×C4×C7C2318yesdirect product factor
13C23×C3×C4×C7C32113yesdirect product factor
14C23×C32×C7C3×C41104yesdirect product factor
15C23×C32×C7C22×C3191yes—
16C2×C32×C4×C7C22×C31364yesdirect product factor
17C24×C33C2×C711yescharacteristic
18C22×C33×C4C2×C7114yesdirect product factor
19C2×C33×C7C22×C4114yesdirect product factor
20C2×C33×C7C2411yescharacteristic
21C24×C3×C7C2×C32113yes—
22C22×C3×C4×C7C2×C321182yesdirect product factor
23C23×C32×C4C3×C7113yesdirect product factor
24C22×C32×C7C2×C3×C41364yesdirect product factor
25C22×C32×C7C23×C3191yes—
26C32×C4×C7C23×C31104yesdirect product factor
27C23×C4×C7C3311yescharacteristic, direct product factor, Hall
28C23×C33C4×C718yesdirect product factor
29C23×C33C22×C717yes—
30C2×C33×C4C22×C7128yesdirect product factor
31C33×C7C23×C411yescharacteristic, direct product factor, Hall
32C23×C3×C7C32×C41104yesdirect product factor
33C23×C3×C7C22×C32191yes—
34C2×C3×C4×C7C22×C321364yesdirect product factor
35C24×C32C2×C3×C7113yes—
36C22×C32×C4C2×C3×C71182yesdirect product factor
37C2×C32×C7C22×C3×C41182yesdirect product factor
38C2×C32×C7C24×C3113yes—
39C24×C7C2×C3311yescharacteristic
40C22×C4×C7C2×C33114yesdirect product factor
41C22×C33C2×C4×C7128yesdirect product factor
42C22×C33C23×C717yes—
43C33×C4C23×C718yesdirect product factor
44C23×C3×C4C32×C7113yesdirect product factor
45C22×C3×C7C2×C32×C41364yesdirect product factor
46C22×C3×C7C23×C32191yes—
47C3×C4×C7C23×C321104yesdirect product factor
48C23×C32C3×C4×C71104yesdirect product factor
49C23×C32C22×C3×C7191yes—
50C2×C32×C4C22×C3×C71364yesdirect product factor
51C32×C7C23×C3×C4113yesdirect product factor
52C23×C7C33×C418yesdirect product factor
53C23×C7C22×C3317yes—
54C2×C4×C7C22×C33128yesdirect product factor
55C2×C33C22×C4×C7114yesdirect product factor
56C2×C33C24×C711yescharacteristic
57C24×C3C2×C32×C7113yes—
58C22×C3×C4C2×C32×C71182yesdirect product factor
59C2×C3×C7C22×C32×C41182yesdirect product factor
60C2×C3×C7C24×C32113yes—
61C22×C32C2×C3×C4×C71364yesdirect product factor
62C22×C32C23×C3×C7191yes—
63C32×C4C23×C3×C71104yesdirect product factor
64C23×C4C33×C711yescharacteristic, direct product factor, Sylow
65C22×C7C2×C33×C4128yesdirect product factor
66C22×C7C23×C3317yes—
67C4×C7C23×C3318yesdirect product factor
68C33C23×C4×C711yescharacteristic, direct product factor, Sylow
69C23×C3C32×C4×C71104yesdirect product factor
70C23×C3C22×C32×C7191yes—
71C2×C3×C4C22×C32×C71364yesdirect product factor
72C3×C7C23×C32×C4113yesdirect product factor
73C2×C32C22×C3×C4×C71182yesdirect product factor
74C2×C32C24×C3×C7113yes—
75C24C2×C33×C711yescharacteristic
76C22×C4C2×C33×C7114yesdirect product factor
77C2×C7C22×C33×C4114yesdirect product factor
78C2×C7C24×C3311yescharacteristic
79C22×C3C2×C32×C4×C71364yesdirect product factor
80C22×C3C23×C32×C7191yes—
81C3×C4C23×C32×C71104yesdirect product factor
82C32C23×C3×C4×C7113yesdirect product factor
83C23C33×C4×C718yesdirect product factor
84C23C22×C33×C717yes—
85C2×C4C22×C33×C7128yesdirect product factor
86C7C23×C33×C411yescharacteristic, direct product factor, Sylow
87C2×C3C22×C32×C4×C71182yesdirect product factor
88C2×C3C24×C32×C7113yes—
89C22C2×C33×C4×C7128yesdirect product factor
90C22C23×C33×C717yes—
91C4C23×C33×C718yesdirect product factor
92C3C23×C32×C4×C7113yesdirect product factor
93C2C22×C33×C4×C7114yesdirect product factor
94C2C24×C33×C711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C33×C7
socle, prime radicalC24×C33×C7C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C33×C4×C7C2direct (N × H)
3. C23×C32×C4×C7C3direct (N × H)
4. C23×C33×C7C4direct (N × H)
6. C2×C33×C4×C7C22direct (N × H)
8. C22×C32×C4×C7C2×C3direct (N × H)
9. C23×C33×C4C7direct (N × H)
10. C22×C33×C7C2×C4direct (N × H)
12. C33×C4×C7C23direct (N × H)
13. C23×C3×C4×C7C32direct (N × H)
14. C23×C32×C7C3×C4direct (N × H)
16. C2×C32×C4×C7C22×C3direct (N × H)
18. C22×C33×C4C2×C7direct (N × H)
19. C2×C33×C7C22×C4direct (N × H)
22. C22×C3×C4×C7C2×C32direct (N × H)
23. C23×C32×C4C3×C7direct (N × H)
24. C22×C32×C7C2×C3×C4direct (N × H)
26. C32×C4×C7C23×C3direct (N × H)
27. C23×C4×C7C33direct (N × H)
28. C23×C33C4×C7direct (N × H)
30. C2×C33×C4C22×C7direct (N × H)
31. C33×C7C23×C4direct (N × H)
32. C23×C3×C7C32×C4direct (N × H)
34. C2×C3×C4×C7C22×C32direct (N × H)
36. C22×C32×C4C2×C3×C7direct (N × H)
37. C2×C32×C7C22×C3×C4direct (N × H)
40. C22×C4×C7C2×C33direct (N × H)
41. C22×C33C2×C4×C7direct (N × H)
43. C33×C4C23×C7direct (N × H)
44. C23×C3×C4C32×C7direct (N × H)
45. C22×C3×C7C2×C32×C4direct (N × H)
47. C3×C4×C7C23×C32direct (N × H)
48. C23×C32C3×C4×C7direct (N × H)
50. C2×C32×C4C22×C3×C7direct (N × H)
51. C32×C7C23×C3×C4direct (N × H)
52. C23×C7C33×C4direct (N × H)
54. C2×C4×C7C22×C33direct (N × H)
55. C2×C33C22×C4×C7direct (N × H)
58. C22×C3×C4C2×C32×C7direct (N × H)
59. C2×C3×C7C22×C32×C4direct (N × H)
61. C22×C32C2×C3×C4×C7direct (N × H)
63. C32×C4C23×C3×C7direct (N × H)
64. C23×C4C33×C7direct (N × H)
65. C22×C7C2×C33×C4direct (N × H)
67. C4×C7C23×C33direct (N × H)
68. C33C23×C4×C7direct (N × H)
69. C23×C3C32×C4×C7direct (N × H)
71. C2×C3×C4C22×C32×C7direct (N × H)
72. C3×C7C23×C32×C4direct (N × H)
73. C2×C32C22×C3×C4×C7direct (N × H)
76. C22×C4C2×C33×C7direct (N × H)
77. C2×C7C22×C33×C4direct (N × H)
79. C22×C3C2×C32×C4×C7direct (N × H)
81. C3×C4C23×C32×C7direct (N × H)
82. C32C23×C3×C4×C7direct (N × H)
83. C23C33×C4×C7direct (N × H)
85. C2×C4C22×C33×C7direct (N × H)
86. C7C23×C33×C4direct (N × H)
87. C2×C3C22×C32×C4×C7direct (N × H)
89. C22C2×C33×C4×C7direct (N × H)
91. C4C23×C33×C7direct (N × H)
92. C3C23×C32×C4×C7direct (N × H)
93. C2C22×C33×C4×C7direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C33×C72
C22×C33×C4×C72
C23×C32×C4×C73
C23×C33×C47