Finite Group Databasebeta

← C24×C8×C11×C17 #72201217

Subgroups — C24×C8×C11×C17 #72201217

Order 23936.

3952 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×C11×C17C211yesmaximal, characteristic
2C23×C8×C11×C17C2130yesmaximal, direct product factor
3C23×C4×C11×C17C4115yes—
4C23×C4×C11×C17C22115yes—
5C25×C11×C17C411yescharacteristic
6C22×C8×C11×C17C221140yesdirect product factor
7C24×C11×C17C8116yesdirect product factor
8C24×C11×C17C2×C4115yes—
9C22×C4×C11×C17C2×C41105yes—
10C22×C4×C11×C17C23135yes—
11C2×C8×C11×C17C231120yesdirect product factor
12C24×C8×C17C1111yesmaximal, characteristic, direct product factor, Hall
13C23×C11×C17C2×C81120yesdirect product factor
14C23×C11×C17C22×C4135yes—
15C2×C4×C11×C17C22×C41105yes—
16C2×C4×C11×C17C24115yes—
17C8×C11×C17C24116yesdirect product factor
18C24×C8×C11C1711yesmaximal, characteristic, direct product factor, Hall
19C24×C4×C17C2×C1111yescharacteristic
20C23×C8×C17C2×C11130yesdirect product factor
21C22×C11×C17C22×C81140yesdirect product factor
22C22×C11×C17C23×C4115yes—
23C4×C11×C17C23×C4115yes—
24C4×C11×C17C2511yescharacteristic
25C24×C4×C11C2×C1711yescharacteristic
26C23×C8×C11C2×C17130yesdirect product factor
27C25×C17C4×C1111yescharacteristic
28C23×C4×C17C4×C11115yes—
29C23×C4×C17C22×C11115yes—
30C22×C8×C17C22×C111140yesdirect product factor
31C2×C11×C17C23×C8130yesdirect product factor
32C2×C11×C17C24×C411yescharacteristic
33C25×C11C4×C1711yescharacteristic
34C23×C4×C11C4×C17115yes—
35C23×C4×C11C22×C17115yes—
36C22×C8×C11C22×C171140yesdirect product factor
37C24×C17C8×C11116yesdirect product factor
38C24×C17C2×C4×C11115yes—
39C22×C4×C17C2×C4×C111105yes—
40C22×C4×C17C23×C11135yes—
41C2×C8×C17C23×C111120yesdirect product factor
42C11×C17C24×C811yescharacteristic, direct product factor, Hall
43C24×C11C8×C17116yesdirect product factor
44C24×C11C2×C4×C17115yes—
45C22×C4×C11C2×C4×C171105yes—
46C22×C4×C11C23×C17135yes—
47C2×C8×C11C23×C171120yesdirect product factor
48C23×C17C2×C8×C111120yesdirect product factor
49C23×C17C22×C4×C11135yes—
50C2×C4×C17C22×C4×C111105yes—
51C2×C4×C17C24×C11115yes—
52C8×C17C24×C11116yesdirect product factor
53C24×C8C11×C1711yescharacteristic, direct product factor, Sylow
54C23×C11C2×C8×C171120yesdirect product factor
55C23×C11C22×C4×C17135yes—
56C2×C4×C11C22×C4×C171105yes—
57C2×C4×C11C24×C17115yes—
58C8×C11C24×C17116yesdirect product factor
59C22×C17C22×C8×C111140yesdirect product factor
60C22×C17C23×C4×C11115yes—
61C4×C17C23×C4×C11115yes—
62C4×C17C25×C1111yescharacteristic
63C24×C4C2×C11×C1711yescharacteristic
64C23×C8C2×C11×C17130yesdirect product factor
65C22×C11C22×C8×C171140yesdirect product factor
66C22×C11C23×C4×C17115yes—
67C4×C11C23×C4×C17115yes—
68C4×C11C25×C1711yescharacteristic
69C2×C17C23×C8×C11130yesdirect product factor
70C2×C17C24×C4×C1111yescharacteristic
71C25C4×C11×C1711yescharacteristic
72C23×C4C4×C11×C17115yes—
73C23×C4C22×C11×C17115yes—
74C22×C8C22×C11×C171140yesdirect product factor
75C2×C11C23×C8×C17130yesdirect product factor
76C2×C11C24×C4×C1711yescharacteristic
77C17C24×C8×C1111yescharacteristic, direct product factor, Sylow
78C24C8×C11×C17116yesdirect product factor
79C24C2×C4×C11×C17115yes—
80C22×C4C2×C4×C11×C171105yes—
81C22×C4C23×C11×C17135yes—
82C2×C8C23×C11×C171120yesdirect product factor
83C11C24×C8×C1711yescharacteristic, direct product factor, Sylow
84C23C2×C8×C11×C171120yesdirect product factor
85C23C22×C4×C11×C17135yes—
86C2×C4C22×C4×C11×C171105yes—
87C2×C4C24×C11×C17115yes—
88C8C24×C11×C17116yesdirect product factor
89C22C22×C8×C11×C171140yesdirect product factor
90C22C23×C4×C11×C17115yes—
91C4C25×C11×C1711yescharacteristic
92C4C23×C4×C11×C17115yes—
93C2C23×C8×C11×C17130yesdirect product factor
94C2C24×C4×C11×C1711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C25×C11×C17
socle, prime radicalC25×C11×C17C4
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C8×C11×C17C2direct (N × H)
6. C22×C8×C11×C17C22direct (N × H)
7. C24×C11×C17C8direct (N × H)
11. C2×C8×C11×C17C23direct (N × H)
12. C24×C8×C17C11direct (N × H)
13. C23×C11×C17C2×C8direct (N × H)
17. C8×C11×C17C24direct (N × H)
18. C24×C8×C11C17direct (N × H)
20. C23×C8×C17C2×C11direct (N × H)
21. C22×C11×C17C22×C8direct (N × H)
26. C23×C8×C11C2×C17direct (N × H)
30. C22×C8×C17C22×C11direct (N × H)
31. C2×C11×C17C23×C8direct (N × H)
36. C22×C8×C11C22×C17direct (N × H)
37. C24×C17C8×C11direct (N × H)
41. C2×C8×C17C23×C11direct (N × H)
42. C11×C17C24×C8direct (N × H)
43. C24×C11C8×C17direct (N × H)
47. C2×C8×C11C23×C17direct (N × H)
48. C23×C17C2×C8×C11direct (N × H)
52. C8×C17C24×C11direct (N × H)
53. C24×C8C11×C17direct (N × H)
54. C23×C11C2×C8×C17direct (N × H)
58. C8×C11C24×C17direct (N × H)
59. C22×C17C22×C8×C11direct (N × H)
64. C23×C8C2×C11×C17direct (N × H)
65. C22×C11C22×C8×C17direct (N × H)
69. C2×C17C23×C8×C11direct (N × H)
74. C22×C8C22×C11×C17direct (N × H)
75. C2×C11C23×C8×C17direct (N × H)
77. C17C24×C8×C11direct (N × H)
78. C24C8×C11×C17direct (N × H)
82. C2×C8C23×C11×C17direct (N × H)
83. C11C24×C8×C17direct (N × H)
84. C23C2×C8×C11×C17direct (N × H)
88. C8C24×C11×C17direct (N × H)
89. C22C22×C8×C11×C17direct (N × H)
93. C2C23×C8×C11×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×C11×C172
C23×C8×C11×C172
C24×C8×C1711
C24×C8×C1117