Finite Group Databasebeta

← C23×C42×C11×C17 #72201220

Subgroups — C23×C42×C11×C17 #72201220

Order 23936.

6000 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×C11×C17C213yesmaximal
2C22×C42×C11×C17C2128yesmaximal, direct product factor
3C23×C4×C11×C17C4148yesdirect product factor
4C23×C4×C11×C17C22142yes—
5C25×C11×C17C2211yescharacteristic
6C2×C42×C11×C17C221112yesdirect product factor
7C24×C11×C17C2×C4124yes—
8C24×C11×C17C2317yes—
9C22×C4×C11×C17C2×C41336yesdirect product factor
10C22×C4×C11×C17C23184yes—
11C42×C11×C17C23164yesdirect product factor
12C23×C42×C17C1111yesmaximal, characteristic, direct product factor, Hall
13C23×C11×C17C42164yesdirect product factor
14C23×C11×C17C22×C4184yes—
15C23×C11×C17C2417yes—
16C2×C4×C11×C17C22×C41336yesdirect product factor
17C2×C4×C11×C17C24124yes—
18C23×C42×C11C1711yesmaximal, characteristic, direct product factor, Hall
19C24×C4×C17C2×C1113yes—
20C22×C42×C17C2×C11128yesdirect product factor
21C22×C11×C17C2×C421112yesdirect product factor
22C22×C11×C17C23×C4142yes—
23C22×C11×C17C2511yescharacteristic
24C4×C11×C17C23×C4148yesdirect product factor
25C24×C4×C11C2×C1713yes—
26C22×C42×C11C2×C17128yesdirect product factor
27C25×C17C22×C1111yescharacteristic
28C23×C4×C17C4×C11148yesdirect product factor
29C23×C4×C17C22×C11142yes—
30C2×C42×C17C22×C111112yesdirect product factor
31C2×C11×C17C22×C42128yesdirect product factor
32C2×C11×C17C24×C413yes—
33C25×C11C22×C1711yescharacteristic
34C23×C4×C11C4×C17148yesdirect product factor
35C23×C4×C11C22×C17142yes—
36C2×C42×C11C22×C171112yesdirect product factor
37C24×C17C2×C4×C11124yes—
38C24×C17C23×C1117yes—
39C22×C4×C17C2×C4×C111336yesdirect product factor
40C22×C4×C17C23×C11184yes—
41C42×C17C23×C11164yesdirect product factor
42C11×C17C23×C4211yescharacteristic, direct product factor, Hall
43C24×C11C2×C4×C17124yes—
44C24×C11C23×C1717yes—
45C22×C4×C11C2×C4×C171336yesdirect product factor
46C22×C4×C11C23×C17184yes—
47C42×C11C23×C17164yesdirect product factor
48C23×C17C42×C11164yesdirect product factor
49C23×C17C22×C4×C11184yes—
50C23×C17C24×C1117yes—
51C2×C4×C17C22×C4×C111336yesdirect product factor
52C2×C4×C17C24×C11124yes—
53C23×C42C11×C1711yescharacteristic, direct product factor, Sylow
54C23×C11C42×C17164yesdirect product factor
55C23×C11C22×C4×C17184yes—
56C23×C11C24×C1717yes—
57C2×C4×C11C22×C4×C171336yesdirect product factor
58C2×C4×C11C24×C17124yes—
59C22×C17C2×C42×C111112yesdirect product factor
60C22×C17C23×C4×C11142yes—
61C22×C17C25×C1111yescharacteristic
62C4×C17C23×C4×C11148yesdirect product factor
63C24×C4C2×C11×C1713yes—
64C22×C42C2×C11×C17128yesdirect product factor
65C22×C11C2×C42×C171112yesdirect product factor
66C22×C11C23×C4×C17142yes—
67C22×C11C25×C1711yescharacteristic
68C4×C11C23×C4×C17148yesdirect product factor
69C2×C17C22×C42×C11128yesdirect product factor
70C2×C17C24×C4×C1113yes—
71C25C22×C11×C1711yescharacteristic
72C23×C4C4×C11×C17148yesdirect product factor
73C23×C4C22×C11×C17142yes—
74C2×C42C22×C11×C171112yesdirect product factor
75C2×C11C22×C42×C17128yesdirect product factor
76C2×C11C24×C4×C1713yes—
77C17C23×C42×C1111yescharacteristic, direct product factor, Sylow
78C24C2×C4×C11×C17124yes—
79C24C23×C11×C1717yes—
80C22×C4C2×C4×C11×C171336yesdirect product factor
81C22×C4C23×C11×C17184yes—
82C42C23×C11×C17164yesdirect product factor
83C11C23×C42×C1711yescharacteristic, direct product factor, Sylow
84C23C42×C11×C17164yesdirect product factor
85C23C22×C4×C11×C17184yes—
86C23C24×C11×C1717yes—
87C2×C4C22×C4×C11×C171336yesdirect product factor
88C2×C4C24×C11×C17124yes—
89C22C2×C42×C11×C171112yesdirect product factor
90C22C25×C11×C1711yescharacteristic
91C22C23×C4×C11×C17142yes—
92C4C23×C4×C11×C17148yesdirect product factor
93C2C22×C42×C11×C17128yesdirect product factor
94C2C24×C4×C11×C1713yes—
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C25×C11×C17
socle, prime radicalC25×C11×C17C22
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C42×C11×C17C2direct (N × H)
3. C23×C4×C11×C17C4direct (N × H)
6. C2×C42×C11×C17C22direct (N × H)
9. C22×C4×C11×C17C2×C4direct (N × H)
11. C42×C11×C17C23direct (N × H)
12. C23×C42×C17C11direct (N × H)
13. C23×C11×C17C42direct (N × H)
16. C2×C4×C11×C17C22×C4direct (N × H)
18. C23×C42×C11C17direct (N × H)
20. C22×C42×C17C2×C11direct (N × H)
21. C22×C11×C17C2×C42direct (N × H)
24. C4×C11×C17C23×C4direct (N × H)
26. C22×C42×C11C2×C17direct (N × H)
28. C23×C4×C17C4×C11direct (N × H)
30. C2×C42×C17C22×C11direct (N × H)
31. C2×C11×C17C22×C42direct (N × H)
34. C23×C4×C11C4×C17direct (N × H)
36. C2×C42×C11C22×C17direct (N × H)
39. C22×C4×C17C2×C4×C11direct (N × H)
41. C42×C17C23×C11direct (N × H)
42. C11×C17C23×C42direct (N × H)
45. C22×C4×C11C2×C4×C17direct (N × H)
47. C42×C11C23×C17direct (N × H)
48. C23×C17C42×C11direct (N × H)
51. C2×C4×C17C22×C4×C11direct (N × H)
53. C23×C42C11×C17direct (N × H)
54. C23×C11C42×C17direct (N × H)
57. C2×C4×C11C22×C4×C17direct (N × H)
59. C22×C17C2×C42×C11direct (N × H)
62. C4×C17C23×C4×C11direct (N × H)
64. C22×C42C2×C11×C17direct (N × H)
65. C22×C11C2×C42×C17direct (N × H)
68. C4×C11C23×C4×C17direct (N × H)
69. C2×C17C22×C42×C11direct (N × H)
72. C23×C4C4×C11×C17direct (N × H)
74. C2×C42C22×C11×C17direct (N × H)
75. C2×C11C22×C42×C17direct (N × H)
77. C17C23×C42×C11direct (N × H)
80. C22×C4C2×C4×C11×C17direct (N × H)
82. C42C23×C11×C17direct (N × H)
83. C11C23×C42×C17direct (N × H)
84. C23C42×C11×C17direct (N × H)
87. C2×C4C22×C4×C11×C17direct (N × H)
89. C22C2×C42×C11×C17direct (N × H)
92. C4C23×C4×C11×C17direct (N × H)
93. C2C22×C42×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
C22×C42×C11×C172
C23×C42×C1711
C23×C42×C1117