Finite Group Databasebeta

← C23×C3×C4×C7×C47 #72208331

Subgroups — C23×C3×C4×C7×C47 #72208331

Order 31584.

944 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×C7×C47C211yesmaximal, characteristic
2C22×C3×C4×C7×C47C2114yesmaximal, direct product factor
3C23×C4×C7×C47C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C7×C47C418yesdirect product factor
5C23×C3×C7×C47C2217yes—
6C2×C3×C4×C7×C47C22128yesdirect product factor
7C22×C4×C7×C47C2×C3114yesdirect product factor
8C24×C7×C47C2×C311yescharacteristic
9C23×C3×C4×C47C711yesmaximal, characteristic, direct product factor, Hall
10C2×C4×C7×C47C22×C3128yesdirect product factor
11C23×C7×C47C3×C418yesdirect product factor
12C23×C7×C47C22×C317yes—
13C24×C3×C47C2×C711yescharacteristic
14C22×C3×C4×C47C2×C7114yesdirect product factor
15C22×C3×C7×C47C2×C4128yesdirect product factor
16C22×C3×C7×C47C2317yes—
17C3×C4×C7×C47C2318yesdirect product factor
18C2×C3×C7×C47C22×C4114yesdirect product factor
19C2×C3×C7×C47C2411yescharacteristic
20C23×C4×C47C3×C711yescharacteristic, direct product factor, Hall
21C22×C7×C47C2×C3×C4128yesdirect product factor
22C22×C7×C47C23×C317yes—
23C4×C7×C47C23×C318yesdirect product factor
24C23×C3×C47C4×C718yesdirect product factor
25C23×C3×C47C22×C717yes—
26C2×C3×C4×C47C22×C7128yesdirect product factor
27C3×C7×C47C23×C411yescharacteristic, direct product factor, Hall
28C24×C47C2×C3×C711yescharacteristic
29C22×C4×C47C2×C3×C7114yesdirect product factor
30C23×C3×C4×C7C4711yesmaximal, characteristic, direct product factor, Hall
31C2×C7×C47C22×C3×C4114yesdirect product factor
32C2×C7×C47C24×C311yescharacteristic
33C22×C3×C47C2×C4×C7128yesdirect product factor
34C22×C3×C47C23×C717yes—
35C3×C4×C47C23×C718yesdirect product factor
36C23×C47C3×C4×C718yesdirect product factor
37C23×C47C22×C3×C717yes—
38C2×C4×C47C22×C3×C7128yesdirect product factor
39C24×C3×C7C2×C4711yescharacteristic
40C22×C3×C4×C7C2×C47114yesdirect product factor
41C7×C47C23×C3×C411yescharacteristic, direct product factor, Hall
42C2×C3×C47C22×C4×C7114yesdirect product factor
43C2×C3×C47C24×C711yescharacteristic
44C23×C4×C7C3×C4711yescharacteristic, direct product factor, Hall
45C22×C47C2×C3×C4×C7128yesdirect product factor
46C22×C47C23×C3×C717yes—
47C4×C47C23×C3×C718yesdirect product factor
48C23×C3×C7C4×C4718yesdirect product factor
49C23×C3×C7C22×C4717yes—
50C2×C3×C4×C7C22×C47128yesdirect product factor
51C3×C47C23×C4×C711yescharacteristic, direct product factor, Hall
52C24×C7C2×C3×C4711yescharacteristic
53C22×C4×C7C2×C3×C47114yesdirect product factor
54C23×C3×C4C7×C4711yescharacteristic, direct product factor, Hall
55C2×C47C22×C3×C4×C7114yesdirect product factor
56C2×C47C24×C3×C711yescharacteristic
57C22×C3×C7C2×C4×C47128yesdirect product factor
58C22×C3×C7C23×C4717yes—
59C3×C4×C7C23×C4718yesdirect product factor
60C23×C7C3×C4×C4718yesdirect product factor
61C23×C7C22×C3×C4717yes—
62C2×C4×C7C22×C3×C47128yesdirect product factor
63C24×C3C2×C7×C4711yescharacteristic
64C22×C3×C4C2×C7×C47114yesdirect product factor
65C47C23×C3×C4×C711yescharacteristic, direct product factor, Sylow
66C2×C3×C7C22×C4×C47114yesdirect product factor
67C2×C3×C7C24×C4711yescharacteristic
68C23×C4C3×C7×C4711yescharacteristic, direct product factor, Sylow
69C22×C7C2×C3×C4×C47128yesdirect product factor
70C22×C7C23×C3×C4717yes—
71C4×C7C23×C3×C4718yesdirect product factor
72C23×C3C4×C7×C4718yesdirect product factor
73C23×C3C22×C7×C4717yes—
74C2×C3×C4C22×C7×C47128yesdirect product factor
75C3×C7C23×C4×C4711yescharacteristic, direct product factor, Hall
76C24C2×C3×C7×C4711yescharacteristic
77C22×C4C2×C3×C7×C47114yesdirect product factor
78C2×C7C22×C3×C4×C47114yesdirect product factor
79C2×C7C24×C3×C4711yescharacteristic
80C22×C3C23×C7×C4717yes—
81C22×C3C2×C4×C7×C47128yesdirect product factor
82C3×C4C23×C7×C4718yesdirect product factor
83C23C3×C4×C7×C4718yesdirect product factor
84C23C22×C3×C7×C4717yes—
85C2×C4C22×C3×C7×C47128yesdirect product factor
86C7C23×C3×C4×C4711yescharacteristic, direct product factor, Sylow
87C2×C3C24×C7×C4711yescharacteristic
88C2×C3C22×C4×C7×C47114yesdirect product factor
89C22C2×C3×C4×C7×C47128yesdirect product factor
90C22C23×C3×C7×C4717yes—
91C4C23×C3×C7×C4718yesdirect product factor
92C3C23×C4×C7×C4711yescharacteristic, direct product factor, Sylow
93C2C22×C3×C4×C7×C47114yesdirect product factor
94C2C24×C3×C7×C4711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C3×C7×C47
socle, prime radicalC24×C3×C7×C47C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×C7×C47C2direct (N × H)
3. C23×C4×C7×C47C3direct (N × H)
4. C23×C3×C7×C47C4direct (N × H)
6. C2×C3×C4×C7×C47C22direct (N × H)
7. C22×C4×C7×C47C2×C3direct (N × H)
9. C23×C3×C4×C47C7direct (N × H)
10. C2×C4×C7×C47C22×C3direct (N × H)
11. C23×C7×C47C3×C4direct (N × H)
14. C22×C3×C4×C47C2×C7direct (N × H)
15. C22×C3×C7×C47C2×C4direct (N × H)
17. C3×C4×C7×C47C23direct (N × H)
18. C2×C3×C7×C47C22×C4direct (N × H)
20. C23×C4×C47C3×C7direct (N × H)
21. C22×C7×C47C2×C3×C4direct (N × H)
23. C4×C7×C47C23×C3direct (N × H)
24. C23×C3×C47C4×C7direct (N × H)
26. C2×C3×C4×C47C22×C7direct (N × H)
27. C3×C7×C47C23×C4direct (N × H)
29. C22×C4×C47C2×C3×C7direct (N × H)
30. C23×C3×C4×C7C47direct (N × H)
31. C2×C7×C47C22×C3×C4direct (N × H)
33. C22×C3×C47C2×C4×C7direct (N × H)
35. C3×C4×C47C23×C7direct (N × H)
36. C23×C47C3×C4×C7direct (N × H)
38. C2×C4×C47C22×C3×C7direct (N × H)
40. C22×C3×C4×C7C2×C47direct (N × H)
41. C7×C47C23×C3×C4direct (N × H)
42. C2×C3×C47C22×C4×C7direct (N × H)
44. C23×C4×C7C3×C47direct (N × H)
45. C22×C47C2×C3×C4×C7direct (N × H)
47. C4×C47C23×C3×C7direct (N × H)
48. C23×C3×C7C4×C47direct (N × H)
50. C2×C3×C4×C7C22×C47direct (N × H)
51. C3×C47C23×C4×C7direct (N × H)
53. C22×C4×C7C2×C3×C47direct (N × H)
54. C23×C3×C4C7×C47direct (N × H)
55. C2×C47C22×C3×C4×C7direct (N × H)
57. C22×C3×C7C2×C4×C47direct (N × H)
59. C3×C4×C7C23×C47direct (N × H)
60. C23×C7C3×C4×C47direct (N × H)
62. C2×C4×C7C22×C3×C47direct (N × H)
64. C22×C3×C4C2×C7×C47direct (N × H)
65. C47C23×C3×C4×C7direct (N × H)
66. C2×C3×C7C22×C4×C47direct (N × H)
68. C23×C4C3×C7×C47direct (N × H)
69. C22×C7C2×C3×C4×C47direct (N × H)
71. C4×C7C23×C3×C47direct (N × H)
72. C23×C3C4×C7×C47direct (N × H)
74. C2×C3×C4C22×C7×C47direct (N × H)
75. C3×C7C23×C4×C47direct (N × H)
77. C22×C4C2×C3×C7×C47direct (N × H)
78. C2×C7C22×C3×C4×C47direct (N × H)
81. C22×C3C2×C4×C7×C47direct (N × H)
82. C3×C4C23×C7×C47direct (N × H)
83. C23C3×C4×C7×C47direct (N × H)
85. C2×C4C22×C3×C7×C47direct (N × H)
86. C7C23×C3×C4×C47direct (N × H)
88. C2×C3C22×C4×C7×C47direct (N × H)
89. C22C2×C3×C4×C7×C47direct (N × H)
91. C4C23×C3×C7×C47direct (N × H)
92. C3C23×C4×C7×C47direct (N × H)
93. C2C22×C3×C4×C7×C47direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×C7×C472
C22×C3×C4×C7×C472
C23×C4×C7×C473
C23×C3×C4×C477
C23×C3×C4×C747