Finite Group Databasebeta

← #34094718

Subgroups — #34094718

Order 20032.

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

normal subgroups only

This group has 334 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
1C2×#19097561C211yesmaximal, characteristic, complemented
2C2×D4×D313C211yesmaximal, characteristic, complemented
3#23756493C212yesmaximal, complemented
4#23756483C212yesmaximal, complemented
5#23756472C211yesmaximal, characteristic, complemented
6#23756471C211yesmaximal, characteristic, complemented
7#23756468C211yesmaximal, characteristic, complemented
8#23756467C212yesmaximal, complemented
9#23756465C212yesmaximal, complemented
10#23756455C211yesmaximal, characteristic, complemented
11#121×C313C211yesmaximal, characteristic, complemented
12C23×D313C2212yes—
13#19097561—24no—
14C2×Dic626C2211yescharacteristic, complemented
15C2×D1252C2211yescharacteristic
16C2×D1252C2211yescharacteristic
17C2×D1252C2212yescomplemented
18C2×C22⋊D313C2211yescharacteristic
19C2×C22⋊D313C2212yes—
20C2×C22⋊D313C2211yescharacteristic, complemented
21C2×C22⋊D313C2212yescomplemented
22C2×C22⋊D313C2212yescomplemented
23D4×D313—24no—
24C2×C4×D313C2211yescharacteristic
25C2×C4×D313C2211yescharacteristic, complemented
26C4⋊Dic313C2211yescharacteristic, complemented
27C22⋊Dic313C2212yescomplemented
28#19097538C2212yes—
29#19097538C2212yescomplemented
30#19097538C2212yescomplemented
31C4×Dic313C2212yescomplemented
32C2×D4×C313C2211yescharacteristic
33C2×D4×C313C2212yescomplemented
34C22×C4×C313C2211yescharacteristic, complemented
35C4⋊C4×C313C2211yescharacteristic, complemented
36C22⋊C4×C313C2212yescomplemented
37C22×D313—24no—
38C22×D313—42no—
39C22×D313—42no—
40C22×D313C2312yes—
41C22×D313C2311yescharacteristic
42C22×D313C2311yescharacteristic
43Dic626—22no—
44D1252—22no—
45D1252—22no—
46D1252—42no—
47C22⋊D313—22no—
48C22⋊D313—24no—
49C22⋊D313—22no—
50C22⋊D313—42no—
51C22⋊D313—42no—
52C2×Dic313C2312yes—
53C2×Dic313C2311yescharacteristic
54C2×Dic313C2311yescharacteristic
55C4×D313—22no—
56C4×D313D414yescomplemented
57C23×C313C2312yes—
58C23×C313C2311yescharacteristic
59D4×C313—22no—
60D4×C313—42no—
61C2×C4×C313—22no—
62C2×C4×C313C2311yescharacteristic
63C2×C4×C313C2312yes—
64C2×C4×C313C2311yescharacteristic
65C22×C313—21no—
66C22×C313—22no—
67C22×C313—21no—
68C22×C313—22no—
69C22×C313—21no—
70C22×C313—22no—
71C22×C313C2411yescharacteristic
72C2×D313—21no—
73C2×D313—21no—
74C2×D313—21no—
75C2×D313—22no—
76C2×D313—21no—
77C2×D313—22no—
78C2×D313—21no—
79C2×D313—22no—
80C2×D313—48no—
81C2×D313C2×D412yes—
82C4×C313—21no—
83C4×C313—22no—
84C4×C313C2×D412yes—
85Dic313—21no—
86Dic313—22no—
87Dic313C2×D412yes—
88C2×C313—42no—
89C2×C313—41no—
90C2×C313C22×D411yescharacteristic
91C2×C313H(5,𝔽2)11yescharacteristic
92C2×C313H(5,𝔽2)11yescharacteristic
93D313—22no—
94D313—41no—
95D313—42no—
96C313#53511yescharacteristic, complemented, Sylow
97#535—3131nomaximal, Sylow
98C2×#41—3131no—
99C22×D4—3131no—
100#127—3132no—
101#124—3132no—
102#121—3131no—
103#121—3131no—
104#121—3131no—
105#121D31311yescharacteristic, complemented
106#120—3132no—
107#120—3132no—
108#117—3131no—
109C24—3132no—
110#41—6264no—
111C2×Q8—3131no—
112C2×D4—3131no—
113C2×D4—3132no—
114C2×D4—3131no—
115C2×D4—3132no—
116C2×D4—3132no—
117C2×D4—3131no—
118C2×D4—3131no—
119C2×D4—3132no—
120C2×D4—6264no—
121C2×D4C2×D31311yescharacteristic
122C2×D4C2×D31312yescomplemented
123C22×C4—3131no—
124C22×C4—3131no—
125C22×C4C2×D31311yescharacteristic, complemented
126C4⋊C4—3131no—
127C4⋊C4C2×D31311yescharacteristic, complemented
128C22⋊C4—3132no—
129C22⋊C4—3132no—
130C22⋊C4—3132no—
131C22⋊C4—3132no—
132C22⋊C4C2×D31312yescomplemented
133C42—3132no—
134C23—3131no—
135C23—3132no—
136C23—3131no—
137C23—6264no—
138C23—12522no—
139C23—12522no—
140C23C22×D31312yes—
141C23C22×D31311yescharacteristic
142Q8—6262no—
143D4—22no—
144D4—42no—
145D4—6262no—
146D4—6264no—
147D4—6262no—
148D4—6262no—
149D4—6262no—
150D4—12522no—
151D4—12522no—
152D4—12522no—
153C2×C4—22no—
154C2×C4—3131no—
155C2×C4—3134no—
156C2×C4—3132no—
157C2×C4—3131no—
158C2×C4—6262no—
159C2×C4C22×D31312yes—
160C2×C4C22×D31311yescharacteristic
161C2×C4C22×D31311yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—3132no—
169C22—6261no—
170C22—6261no—
171C22—6261no—
172C22—6262no—
173C22—6261no—
174C22—6262no—
175C22—6261no—
176C22—6262no—
177C22—12528no—
178C22C23×D31311yescharacteristic
179C4—21no—
180C4—22no—
181C4—3132no—
182C4—6261no—
183C4—6262no—
184C4D4×D31312yes—
185C2—42no—
186C2—41no—
187C2—6262no—
188C2—12522no—
189C2—12521no—
190C2C2×D4×D31311yescharacteristic
191C2#2375654211yescharacteristic
192C2#2375654311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D313
commutator, socle, cosocleC22×C313C24
Fitting#121×C313C2
hypercenter#121D313
hypocenterC313#535
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#19097561C2semidirect
2. C2×D4×D313C2semidirect
3. #23756493C2semidirect
4. #23756483C2semidirect
5. #23756472C2semidirect
6. #23756471C2semidirect
7. #23756468C2semidirect
8. #23756467C2semidirect
9. #23756465C2semidirect
10. #23756455C2semidirect
11. #121×C313C2semidirect
14. C2×Dic626C22semidirect
17. C2×D1252C22semidirect
20. C2×C22⋊D313C22semidirect
21. C2×C22⋊D313C22semidirect
22. C2×C22⋊D313C22semidirect
25. C2×C4×D313C22semidirect
26. C4⋊Dic313C22semidirect
27. C22⋊Dic313C22semidirect
29. #19097538C22semidirect
30. #19097538C22semidirect
31. C4×Dic313C22semidirect
33. C2×D4×C313C22semidirect
34. C22×C4×C313C22semidirect
35. C4⋊C4×C313C22semidirect
36. C22⋊C4×C313C22semidirect
56. C4×D313D4semidirect
96. C313#535semidirect
105. #121D313semidirect
122. C2×D4C2×D313semidirect
125. C22×C4C2×D313semidirect
127. C4⋊C4C2×D313semidirect
132. C22⋊C4C2×D313semidirect

Maximal subgroups

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

subgroupindex
C2×#190975612
C2×D4×D3132
#237564932
#237564832
#237564722
#237564712
#237564682
#237564672
#237564652
#237564552
#121×C3132
#535313