Finite Group Databasebeta

← C23×C11×C16×C17 #72201214

Subgroups — C23×C11×C16×C17 #72201214

Order 23936.

880 conjugacy classes of subgroups.

The subgroup lattice has 104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×C11×C17C211yesmaximal, characteristic
2C22×C11×C16×C17C2114yesmaximal, direct product factor
3C23×C4×C11×C17C411yescharacteristic
4C22×C8×C11×C17C417yes—
5C22×C8×C11×C17C2217yes—
6C2×C11×C16×C17C22128yesdirect product factor
7C24×C11×C17C811yescharacteristic
8C22×C4×C11×C17C817yes—
9C22×C4×C11×C17C2×C417yes—
10C2×C8×C11×C17C2×C4121yes—
11C2×C8×C11×C17C2317yes—
12C11×C16×C17C2318yesdirect product factor
13C23×C16×C17C1111yesmaximal, characteristic, direct product factor, Hall
14C23×C11×C17C1618yesdirect product factor
15C23×C11×C17C2×C817yes—
16C2×C4×C11×C17C2×C8121yes—
17C2×C4×C11×C17C22×C417yes—
18C8×C11×C17C22×C417yes—
19C8×C11×C17C2411yescharacteristic
20C23×C11×C16C1711yesmaximal, characteristic, direct product factor, Hall
21C23×C8×C17C2×C1111yescharacteristic
22C22×C16×C17C2×C11114yesdirect product factor
23C22×C11×C17C2×C16128yesdirect product factor
24C22×C11×C17C22×C817yes—
25C4×C11×C17C22×C817yes—
26C4×C11×C17C23×C411yescharacteristic
27C23×C8×C11C2×C1711yescharacteristic
28C22×C11×C16C2×C17114yesdirect product factor
29C23×C4×C17C4×C1111yescharacteristic
30C22×C8×C17C4×C1117yes—
31C22×C8×C17C22×C1117yes—
32C2×C16×C17C22×C11128yesdirect product factor
33C2×C11×C17C22×C16114yesdirect product factor
34C2×C11×C17C23×C811yescharacteristic
35C23×C4×C11C4×C1711yescharacteristic
36C22×C8×C11C4×C1717yes—
37C22×C8×C11C22×C1717yes—
38C2×C11×C16C22×C17128yesdirect product factor
39C24×C17C8×C1111yescharacteristic
40C22×C4×C17C8×C1117yes—
41C22×C4×C17C2×C4×C1117yes—
42C2×C8×C17C2×C4×C11121yes—
43C2×C8×C17C23×C1117yes—
44C16×C17C23×C1118yesdirect product factor
45C11×C17C23×C1611yescharacteristic, direct product factor, Hall
46C24×C11C8×C1711yescharacteristic
47C22×C4×C11C8×C1717yes—
48C22×C4×C11C2×C4×C1717yes—
49C2×C8×C11C2×C4×C17121yes—
50C2×C8×C11C23×C1717yes—
51C11×C16C23×C1718yesdirect product factor
52C23×C17C11×C1618yesdirect product factor
53C23×C17C2×C8×C1117yes—
54C2×C4×C17C2×C8×C11121yes—
55C2×C4×C17C22×C4×C1117yes—
56C8×C17C22×C4×C1117yes—
57C8×C17C24×C1111yescharacteristic
58C23×C16C11×C1711yescharacteristic, direct product factor, Sylow
59C23×C11C16×C1718yesdirect product factor
60C23×C11C2×C8×C1717yes—
61C2×C4×C11C2×C8×C17121yes—
62C2×C4×C11C22×C4×C1717yes—
63C8×C11C22×C4×C1717yes—
64C8×C11C24×C1711yescharacteristic
65C22×C17C2×C11×C16128yesdirect product factor
66C22×C17C22×C8×C1117yes—
67C4×C17C22×C8×C1117yes—
68C4×C17C23×C4×C1111yescharacteristic
69C23×C8C2×C11×C1711yescharacteristic
70C22×C16C2×C11×C17114yesdirect product factor
71C22×C11C2×C16×C17128yesdirect product factor
72C22×C11C22×C8×C1717yes—
73C4×C11C22×C8×C1717yes—
74C4×C11C23×C4×C1711yescharacteristic
75C2×C17C22×C11×C16114yesdirect product factor
76C2×C17C23×C8×C1111yescharacteristic
77C23×C4C4×C11×C1711yescharacteristic
78C22×C8C4×C11×C1717yes—
79C22×C8C22×C11×C1717yes—
80C2×C16C22×C11×C17128yesdirect product factor
81C2×C11C22×C16×C17114yesdirect product factor
82C2×C11C23×C8×C1711yescharacteristic
83C17C23×C11×C1611yescharacteristic, direct product factor, Sylow
84C24C8×C11×C1711yescharacteristic
85C22×C4C8×C11×C1717yes—
86C22×C4C2×C4×C11×C1717yes—
87C2×C8C2×C4×C11×C17121yes—
88C2×C8C23×C11×C1717yes—
89C16C23×C11×C1718yesdirect product factor
90C11C23×C16×C1711yescharacteristic, direct product factor, Sylow
91C23C11×C16×C1718yesdirect product factor
92C23C2×C8×C11×C1717yes—
93C2×C4C2×C8×C11×C17121yes—
94C2×C4C22×C4×C11×C1717yes—
95C8C22×C4×C11×C1717yes—
96C8C24×C11×C1711yescharacteristic
97C22C2×C11×C16×C17128yesdirect product factor
98C22C22×C8×C11×C1717yes—
99C4C22×C8×C11×C1717yes—
100C4C23×C4×C11×C1711yescharacteristic
101C2C22×C11×C16×C17114yesdirect product factor
102C2C23×C8×C11×C1711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C24×C11×C17
socle, prime radicalC24×C11×C17C8
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×C16×C17C2direct (N × H)
6. C2×C11×C16×C17C22direct (N × H)
12. C11×C16×C17C23direct (N × H)
13. C23×C16×C17C11direct (N × H)
14. C23×C11×C17C16direct (N × H)
20. C23×C11×C16C17direct (N × H)
22. C22×C16×C17C2×C11direct (N × H)
23. C22×C11×C17C2×C16direct (N × H)
28. C22×C11×C16C2×C17direct (N × H)
32. C2×C16×C17C22×C11direct (N × H)
33. C2×C11×C17C22×C16direct (N × H)
38. C2×C11×C16C22×C17direct (N × H)
44. C16×C17C23×C11direct (N × H)
45. C11×C17C23×C16direct (N × H)
51. C11×C16C23×C17direct (N × H)
52. C23×C17C11×C16direct (N × H)
58. C23×C16C11×C17direct (N × H)
59. C23×C11C16×C17direct (N × H)
65. C22×C17C2×C11×C16direct (N × H)
70. C22×C16C2×C11×C17direct (N × H)
71. C22×C11C2×C16×C17direct (N × H)
75. C2×C17C22×C11×C16direct (N × H)
80. C2×C16C22×C11×C17direct (N × H)
81. C2×C11C22×C16×C17direct (N × H)
83. C17C23×C11×C16direct (N × H)
89. C16C23×C11×C17direct (N × H)
90. C11C23×C16×C17direct (N × H)
91. C23C11×C16×C17direct (N × H)
97. C22C2×C11×C16×C17direct (N × H)
101. C2C22×C11×C16×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×C11×C172
C22×C11×C16×C172
C23×C16×C1711
C23×C11×C1617