Finite Group Databasebeta

← #34094717

Subgroups — #34094717

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×#19097560C211yesmaximal, characteristic, complemented
2C22×C22⋊D313C211yesmaximal, characteristic, complemented
3#23756493C212yesmaximal, complemented
4#23756483C212yesmaximal, complemented
5#23756470C212yesmaximal, complemented
6#23756469C212yesmaximal, complemented
7#23756467C211yesmaximal, characteristic, complemented
8#23756466C211yesmaximal, characteristic, complemented
9#23756465C211yesmaximal, characteristic, complemented
10#23756453C211yesmaximal, characteristic, complemented
11#120×C313C211yesmaximal, characteristic, complemented
12C23×D313C2211yescharacteristic
13#19097560—24no—
14C2×Dic626C2211yescharacteristic, complemented
15C2×D1252C2212yescomplemented
16C2×C22⋊D313—24no—
17C2×C22⋊D313C2211yescharacteristic
18C2×C22⋊D313C2212yes—
19C2×C22⋊D313C2212yes—
20C2×C22⋊D313C2211yescharacteristic, complemented
21C2×C22⋊D313C2212yescomplemented
22C2×C22⋊D313C2212yescomplemented
23C22×Dic313C2211yescharacteristic
24C22×Dic313C2211yescharacteristic, complemented
25C2×C4×D313C2211yescharacteristic, complemented
26#19097540C2212yescomplemented
27C22⋊Dic313C2211yescharacteristic
28C22⋊Dic313C2212yescomplemented
29#19097538C2212yescomplemented
30#19097538C2212yescomplemented
31C4×Dic313C2212yescomplemented
32C24×C313C2211yescharacteristic
33C2×D4×C313C2211yescharacteristic
34C2×D4×C313C2212yescomplemented
35C22⋊C4×C313C2211yescharacteristic
36C22⋊C4×C313C2212yescomplemented
37C22×D313—22no—
38C22×D313—42no—
39C22×D313C2312yes—
40C22×D313C2311yescharacteristic
41Dic626—22no—
42D1252—42no—
43C22⋊D313—22no—
44C22⋊D313—24no—
45C22⋊D313—24no—
46C22⋊D313—22no—
47C22⋊D313—42no—
48C22⋊D313—42no—
49C2×Dic313—22no—
50C2×Dic313D414yescomplemented
51C2×Dic313C2312yes—
52C2×Dic313C2311yescharacteristic
53C2×Dic313C2311yescharacteristic
54C2×Dic313C2311yescharacteristic
55C4×D313—22no—
56C23×C313—22no—
57C23×C313—42no—
58C23×C313C2312yes—
59C23×C313C2311yescharacteristic
60C23×C313C2311yescharacteristic
61D4×C313—22no—
62D4×C313—42no—
63C2×C4×C313C2312yes—
64C2×C4×C313C2311yescharacteristic
65C22×C313—22no—
66C22×C313—21no—
67C22×C313—22no—
68C22×C313—22no—
69C22×C313—22no—
70C22×C313—22no—
71C22×C313—44no—
72C22×C313C2×D412yes—
73C22×C313C2411yescharacteristic
74C2×D313—21no—
75C2×D313—22no—
76C2×D313—22no—
77C2×D313—22no—
78C2×D313—22no—
79C2×D313—44no—
80C4×C313—21no—
81C4×C313—22no—
82Dic313—21no—
83Dic313—22no—
84Dic313C2×D412yes—
85Dic313C2×D412yes—
86C2×C313—22no—
87C2×C313—41no—
88C2×C313—42no—
89C2×C313C22×D411yescharacteristic
90C2×C313H(5,𝔽2)12yes—
91D313—41no—
92D313—42no—
93C313#53511yescharacteristic, complemented, Sylow
94#535—3131nomaximal, Sylow
95C2×#41—3131no—
96C22×D4—3131no—
97#127—3132no—
98#124—3132no—
99#121—3132no—
100#121—3132no—
101#120—3131no—
102#120—3131no—
103#120—3131no—
104#120D31311yescharacteristic, complemented
105#117—3131no—
106C24—3131no—
107C24C2×D31311yescharacteristic
108#41—6264no—
109C2×Q8—3131no—
110C2×D4—3131no—
111C2×D4—3132no—
112C2×D4—3132no—
113C2×D4—3131no—
114C2×D4—3132no—
115C2×D4—3132no—
116C2×D4—3132no—
117C2×D4—6264no—
118C2×D4C2×D31311yescharacteristic
119C2×D4C2×D31312yescomplemented
120C22×C4—3131no—
121C22×C4—3131no—
122C22×C4—3131no—
123C4⋊C4—3132no—
124C22⋊C4—3131no—
125C22⋊C4—3132no—
126C22⋊C4—3132no—
127C22⋊C4—3132no—
128C22⋊C4C2×D31311yescharacteristic
129C22⋊C4C2×D31312yescomplemented
130C42—3132no—
131C23—22no—
132C23—42no—
133C23—3132no—
134C23—3131no—
135C23—6262no—
136C23—12522no—
137C23C22×D31312yes—
138C23C22×D31311yescharacteristic
139C23C22×D31311yescharacteristic
140Q8—6262no—
141D4—22no—
142D4—42no—
143D4—6264no—
144D4—6264no—
145D4—6262no—
146D4—6262no—
147D4—12522no—
148D4—12522no—
149D4—12522no—
150C2×C4—3134no—
151C2×C4—3131no—
152C2×C4—3131no—
153C2×C4—3132no—
154C2×C4—3131no—
155C2×C4—6262no—
156C2×C4—6262no—
157C2×C4C22×D31312yes—
158C2×C4C22×D31311yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—6261no—
167C22—6262no—
168C22—6262no—
169C22—6262no—
170C22—6262no—
171C22—12524no—
172C22D4×D31312yes—
173C22C23×D31311yescharacteristic
174C4—21no—
175C4—22no—
176C4—3132no—
177C4—3132no—
178C4—6261no—
179C4—6262no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—12522no—
184C2—12521no—
185C2C2×D4×D31311yescharacteristic
186C2#2375654212yes—
subgroupG/H
center, FrattiniC22C23×D313
commutator, socle, cosocleC22×C313C24
Fitting#120×C313C2
hypercenter#120D313
hypocenterC313#535
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#19097560C2semidirect
2. C22×C22⋊D313C2semidirect
3. #23756493C2semidirect
4. #23756483C2semidirect
5. #23756470C2semidirect
6. #23756469C2semidirect
7. #23756467C2semidirect
8. #23756466C2semidirect
9. #23756465C2semidirect
10. #23756453C2semidirect
11. #120×C313C2semidirect
14. C2×Dic626C22semidirect
15. C2×D1252C22semidirect
20. C2×C22⋊D313C22semidirect
21. C2×C22⋊D313C22semidirect
22. C2×C22⋊D313C22semidirect
24. C22×Dic313C22semidirect
25. C2×C4×D313C22semidirect
26. #19097540C22semidirect
28. C22⋊Dic313C22semidirect
29. #19097538C22semidirect
30. #19097538C22semidirect
31. C4×Dic313C22semidirect
34. C2×D4×C313C22semidirect
36. C22⋊C4×C313C22semidirect
50. C2×Dic313D4semidirect
93. C313#535semidirect
104. #120D313semidirect
119. C2×D4C2×D313semidirect
129. C22⋊C4C2×D313semidirect

Maximal subgroups

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

subgroupindex
C2×#190975602
C22×C22⋊D3132
#237564932
#237564832
#237564702
#237564692
#237564672
#237564662
#237564652
#237564532
#120×C3132
#535313