Finite Group Databasebeta

← #23782138

Subgroups — #23782138

Order 10432.

338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊D163C211yesmaximal, characteristic
2C4×C22⋊D163C214yesmaximal, complemented
3(C22⋊D163)⋊C4C214yesmaximal, complemented
4#19104691C212yesmaximal, complemented
5C2×C22⋊Dic163C211yesmaximal, characteristic, complemented
6C22⋊C4×D163C212yesmaximal, complemented
7C2×C22⋊C4×C163C211yesmaximal, characteristic, complemented
8C23×D163C2211yescharacteristic
9C2×C22⋊D163C418yescomplemented
10C2×C22⋊D163C2212yes—
11C2×C22⋊D163C2212yes—
12C22×Dic163C2211yescharacteristic
13C22×Dic163C2212yescomplemented
14C2×C4×D163C2214yescomplemented
15Dic163⋊C4C2214yescomplemented
16C22⋊Dic163C2212yes—
17C22⋊Dic163C2212yescomplemented
18(C2×D163)⋊C4C2214yescomplemented
19C4×Dic163C2214yescomplemented
20C24×C163C2211yescharacteristic
21C22×C4×C163C2212yescomplemented
22C22⋊C4×C163C2212yes—
23C22⋊C4×C163C2212yescomplemented
24C22×D163—42no—
25C22×D163C2×C414yescomplemented
26C22×D163C2312yes—
27C22⋊D163C2×C418yescomplemented
28C22⋊D163C2×C418yescomplemented
29C2×Dic163—42no—
30C2×Dic163C2×C414yescomplemented
31C2×Dic163C2314yes—
32C2×Dic163C2312yes—
33C4×D163—44no—
34C23×C163—42no—
35C23×C163C2×C414yescomplemented
36C23×C163C2311yescharacteristic
37C23×C163C2311yescharacteristic
38C23×C163C2311yescharacteristic
39C2×C4×C163—42no—
40C2×C4×C163C2314yes—
41C22×C163—22no—
42C22×C163—22no—
43C22×C163—22no—
44C22×C163—44no—
45C22×C163C22×C412yes—
46C22×C163C22×C412yes—
47C22×C163C22×C412yes—
48C22×C163C2411yescharacteristic
49C2×D163—24no—
50C2×D163—44no—
51C2×D163C22×C414yes—
52C4×C163—24no—
53Dic163—24no—
54Dic163C22×C414yes—
55C2×C163—22no—
56C2×C163—22no—
57C2×C163—22no—
58C2×C163C23×C411yescharacteristic
59C2×C163H(5,𝔽2)12yes—
60D163—24no—
61C163#51811yescharacteristic, complemented, Sylow
62#518—1631nomaximal, Sylow
63C22×D4—1631no—
64C4×D4—1634no—
65C4×D4—1634no—
66#117—1632no—
67C2×C22⋊C4—1631no—
68C2×C22⋊C4—1632no—
69C2×C22⋊C4D16311yescharacteristic, complemented
70C24—1631no—
71C24C2×D16311yescharacteristic
72C2×D4—1638no—
73C2×D4—1632no—
74C2×D4—1632no—
75C22×C4—1632no—
76C22×C4—1634no—
77C22×C4—1631no—
78C22×C4C2×D16312yescomplemented
79C4⋊C4—1634no—
80C22⋊C4—1632no—
81C22⋊C4—1632no—
82C22⋊C4—1634no—
83C22⋊C4C2×D16312yes—
84C22⋊C4C2×D16312yescomplemented
85C42—1634no—
86C23—42no—
87C23—6522no—
88C23—1632no—
89C23—1634no—
90C23C4×D16314yescomplemented
91C23C22×D16311yescharacteristic
92C23C22×D16311yescharacteristic
93C23C22×D16311yescharacteristic
94D4—1638no—
95D4—1638no—
96C2×C4—42no—
97C2×C4—6524no—
98C2×C4—6522no—
99C2×C4—1634no—
100C2×C4—1634no—
101C2×C4—1632no—
102C2×C4C22×D16314yes—
103C22—22no—
104C22—22no—
105C22—22no—
106C22—44no—
107C22—3264no—
108C22—6524no—
109C22—1634no—
110C22C2×C4×D16312yes—
111C22C2×C4×D16312yes—
112C22C2×C4×D16312yes—
113C22C23×D16311yescharacteristic
114C4—24no—
115C4—3264no—
116C4—1634no—
117C2—22no—
118C2—22no—
119C2—22no—
120C2—3264no—
121C2C22×C4×D16311yescharacteristic
122C2#1910478012yes—
subgroupG/H
center, FrattiniC22C23×D163
commutatorC2×C163C23×C4
FittingC2×C22⋊C4×C163C2
socle, cosocleC22×C163C24
prime radicalC22×C22⋊D163C2
hypercenterC2×C22⋊C4D163
hypocenterC163#518
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊D163C2semidirect
3. (C22⋊D163)⋊C4C2semidirect
4. #19104691C2semidirect
5. C2×C22⋊Dic163C2semidirect
6. C22⋊C4×D163C2semidirect
7. C2×C22⋊C4×C163C2semidirect
9. C2×C22⋊D163C4semidirect
13. C22×Dic163C22semidirect
14. C2×C4×D163C22semidirect
15. Dic163⋊C4C22semidirect
17. C22⋊Dic163C22semidirect
18. (C2×D163)⋊C4C22semidirect
19. C4×Dic163C22semidirect
21. C22×C4×C163C22semidirect
23. C22⋊C4×C163C22semidirect
25. C22×D163C2×C4semidirect
27. C22⋊D163C2×C4semidirect
28. C22⋊D163C2×C4semidirect
30. C2×Dic163C2×C4semidirect
35. C23×C163C2×C4semidirect
61. C163#518semidirect
69. C2×C22⋊C4D163semidirect
78. C22×C4C2×D163semidirect
84. C22⋊C4C2×D163semidirect
90. C23C4×D163semidirect