Finite Group Databasebeta

← #23782225

Subgroups — #23782225

Order 10432.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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, complemented
2C2×D4×D163C211yesmaximal, characteristic, complemented
3#19104719C211yesmaximal, characteristic, complemented
4#19104717C212yesmaximal, complemented
5#19104716C211yesmaximal, characteristic, complemented
6#19104708C212yesmaximal, complemented
7#19104706C212yesmaximal, complemented
8#19104704C211yesmaximal, characteristic, complemented
9#19104703C212yesmaximal, complemented
10C22⋊C4×D163C211yesmaximal, characteristic, complemented
11#120×C163C211yesmaximal, characteristic, complemented
12C23×D163C2211yescharacteristic
13C23×D163C2211yescharacteristic, complemented
14C2×D652C2211yescharacteristic, complemented
15C2×C22⋊D163—24no—
16C2×C22⋊D163C2211yescharacteristic
17C2×C22⋊D163C2212yes—
18C2×C22⋊D163C2211yescharacteristic, complemented
19C2×C22⋊D163C2212yescomplemented
20C2×C22⋊D163C2212yescomplemented
21D4×D163—24no—
22C22×Dic163C2211yescharacteristic, complemented
23C2×C4×D163C2211yescharacteristic, complemented
24C2×C4×D163C2212yescomplemented
25C4⋊Dic163C2212yescomplemented
26Dic163⋊C4C2212yescomplemented
27C22⋊Dic163C2211yescharacteristic, complemented
28C22⋊Dic163C2212yescomplemented
29C22⋊Dic163C2212yescomplemented
30(C2×D163)⋊C4C2212yescomplemented
31(C2×D163)⋊C4C2212yescomplemented
32C24×C163C2211yescharacteristic, complemented
33C2×D4×C163C2211yescharacteristic
34C2×D4×C163C2212yescomplemented
35C22⋊C4×C163C2211yescharacteristic, complemented
36C22⋊C4×C163C2212yescomplemented
37C22×D163—22no—
38C22×D163—42no—
39C22×D163—42no—
40C22×D163D414yescomplemented
41C22×D163C2311yescharacteristic
42C22×D163C2311yescharacteristic
43C22×D163C2311yescharacteristic
44D652—22no—
45C22⋊D163—22no—
46C22⋊D163—22no—
47C22⋊D163—24no—
48C22⋊D163—24no—
49C22⋊D163—42no—
50C2×Dic163—22no—
51C2×Dic163C2312yes—
52C2×Dic163C2312yes—
53C2×Dic163C2311yescharacteristic
54C4×D163—22no—
55C4×D163—42no—
56C23×C163—22no—
57C23×C163—42no—
58C23×C163C2312yes—
59C23×C163C2311yescharacteristic
60C23×C163C2311yescharacteristic
61D4×C163—22no—
62D4×C163—42no—
63C2×C4×C163C2311yescharacteristic
64C2×C4×C163C2312yes—
65C22×C163—22no—
66C22×C163—21no—
67C22×C163—22no—
68C22×C163—22no—
69C22×C163—22no—
70C22×C163—22no—
71C22×C163—44no—
72C22×C163C2×D412yes—
73C22×C163C2411yescharacteristic
74C2×D163—22no—
75C2×D163—22no—
76C2×D163—21no—
77C2×D163—22no—
78C2×D163—44no—
79C2×D163—44no—
80C2×D163C2×D412yes—
81C2×D163C2×D412yes—
82C4×C163—21no—
83C4×C163—22no—
84Dic163—21no—
85Dic163—22no—
86Dic163—22no—
87C2×C163—22no—
88C2×C163—41no—
89C2×C163—42no—
90C2×C163C22×D411yescharacteristic
91C2×C163H(5,𝔽2)12yes—
92D163—22no—
93D163—22no—
94D163—41no—
95C163#53411yescharacteristic, complemented, Sylow
96#534—1631nomaximal, Sylow
97C22×D4—1631no—
98C22×D4—1631no—
99#123—1631no—
100#123—1632no—
101#123—1631no—
102#121—1632no—
103#121—1632no—
104#120—1631no—
105#120—1632no—
106#120D16311yescharacteristic, complemented
107C2×C22⋊C4—1631no—
108C24—1631no—
109C24—1631no—
110C24C2×D16311yescharacteristic, complemented
111C2×D4—3264no—
112C2×D4—3264no—
113C2×D4—1632no—
114C2×D4—1631no—
115C2×D4—1631no—
116C2×D4—1632no—
117C2×D4—1632no—
118C2×D4—1631no—
119C2×D4C2×D16311yescharacteristic
120C2×D4C2×D16312yescomplemented
121C22×C4—1631no—
122C22×C4—1631no—
123C22×C4—1632no—
124C4⋊C4—1632no—
125C4⋊C4—1632no—
126C22⋊C4—1631no—
127C22⋊C4—1632no—
128C22⋊C4—1632no—
129C22⋊C4—1632no—
130C22⋊C4—1632no—
131C22⋊C4C2×D16311yescharacteristic, complemented
132C22⋊C4C2×D16312yescomplemented
133C23—22no—
134C23—42no—
135C23—3262no—
136C23—6522no—
137C23—6522no—
138C23—1631no—
139C23—1631no—
140C23—1631no—
141C23—1634no—
142C23C22×D16311yescharacteristic
143C23C22×D16312yes—
144C23C22×D16311yescharacteristic
145D4—22no—
146D4—42no—
147D4—3262no—
148D4—3262no—
149D4—3264no—
150D4—3264no—
151D4—3262no—
152D4—6522no—
153C2×C4—3262no—
154C2×C4—3262no—
155C2×C4—6522no—
156C2×C4—1632no—
157C2×C4—1631no—
158C2×C4—1632no—
159C2×C4C22×D16312yes—
160C2×C4C22×D16311yescharacteristic
161C22—22no—
162C22—21no—
163C22—22no—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—3262no—
169C22—3262no—
170C22—3261no—
171C22—3262no—
172C22—6524no—
173C22—6524no—
174C22—1632no—
175C22—1632no—
176C22D4×D16312yes—
177C22C23×D16311yescharacteristic
178C4—21no—
179C4—22no—
180C4—3261no—
181C4—3262no—
182C4—3262no—
183C2—22no—
184C2—42no—
185C2—41no—
186C2—3262no—
187C2—3262no—
188C2—6521no—
189C2C2×D4×D16311yescharacteristic
190C2#1910478012yes—
subgroupG/H
center, FrattiniC22C23×D163
commutator, socle, cosocleC22×C163C24
Fitting#120×C163C2
hypercenter#120D163
hypocenterC163#534
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D163C2semidirect
2. C2×D4×D163C2semidirect
3. #19104719C2semidirect
4. #19104717C2semidirect
5. #19104716C2semidirect
6. #19104708C2semidirect
7. #19104706C2semidirect
8. #19104704C2semidirect
9. #19104703C2semidirect
10. C22⋊C4×D163C2semidirect
11. #120×C163C2semidirect
13. C23×D163C22semidirect
14. C2×D652C22semidirect
18. C2×C22⋊D163C22semidirect
19. C2×C22⋊D163C22semidirect
20. C2×C22⋊D163C22semidirect
22. C22×Dic163C22semidirect
23. C2×C4×D163C22semidirect
24. C2×C4×D163C22semidirect
25. C4⋊Dic163C22semidirect
26. Dic163⋊C4C22semidirect
27. C22⋊Dic163C22semidirect
28. C22⋊Dic163C22semidirect
29. C22⋊Dic163C22semidirect
30. (C2×D163)⋊C4C22semidirect
31. (C2×D163)⋊C4C22semidirect
32. C24×C163C22semidirect
34. C2×D4×C163C22semidirect
35. C22⋊C4×C163C22semidirect
36. C22⋊C4×C163C22semidirect
40. C22×D163D4semidirect
95. C163#534semidirect
106. #120D163semidirect
110. C24C2×D163semidirect
120. C2×D4C2×D163semidirect
131. C22⋊C4C2×D163semidirect
132. C22⋊C4C2×D163semidirect