Finite Group Databasebeta

← #34094713

Subgroups — #34094713

Order 20032.

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×D1252C211yesmaximal, characteristic, complemented
2C2×D4×D313C211yesmaximal, characteristic, complemented
3#23756482C212yesmaximal, complemented
4#23756480C211yesmaximal, characteristic, complemented
5#23756472C212yesmaximal, complemented
6#23756470C212yesmaximal, complemented
7#23756467C211yesmaximal, characteristic, complemented
8#23756467C212yesmaximal, complemented
9#23756465C211yesmaximal, characteristic, complemented
10C22⋊C4×D313C211yesmaximal, characteristic, complemented
11#123×C313C211yesmaximal, characteristic, complemented
12C23×D313C2211yescharacteristic
13C23×D313C2211yescharacteristic, complemented
14C23×D313C2211yescharacteristic, complemented
15C2×D1252—24no—
16C2×D1252C2212yes—
17C2×D1252C2212yescomplemented
18C2×D1252C2211yescharacteristic, complemented
19C2×D1252C2212yescomplemented
20C2×C22⋊D313C2211yescharacteristic
21C2×C22⋊D313C2211yescharacteristic, complemented
22C2×C22⋊D313C2212yescomplemented
23D4×D313—24no—
24C2×C4×D313C2211yescharacteristic, complemented
25C2×C4×D313C2212yescomplemented
26#19097540C2212yescomplemented
27C22⋊Dic313C2211yescharacteristic, complemented
28#19097538C2212yescomplemented
29#19097538C2212yescomplemented
30#19097538C2212yescomplemented
31#19097538C2212yescomplemented
32C2×D4×C313C2211yescharacteristic
33C22×C4×C313C2211yescharacteristic, complemented
34C4⋊C4×C313C2212yescomplemented
35C22⋊C4×C313C2211yescharacteristic, complemented
36C22⋊C4×C313C2212yescomplemented
37C22×D313—22no—
38C22×D313—22no—
39C22×D313—42no—
40C22×D313—42no—
41C22×D313—42no—
42C22×D313D414yescomplemented
43C22×D313C2311yescharacteristic
44C22×D313C2312yes—
45C22×D313C2311yescharacteristic
46C22×D313C2311yescharacteristic
47D1252—22no—
48D1252—24no—
49D1252—24no—
50D1252—42no—
51C22⋊D313—22no—
52C22⋊D313—22no—
53C22⋊D313—42no—
54C2×Dic313C2312yes—
55C2×Dic313C2311yescharacteristic
56C4×D313—22no—
57C4×D313—42no—
58C23×C313C2311yescharacteristic
59C23×C313C2311yescharacteristic
60D4×C313—22no—
61C2×C4×C313—22no—
62C2×C4×C313C2312yes—
63C2×C4×C313C2312yes—
64C2×C4×C313C2311yescharacteristic
65C22×C313—22no—
66C22×C313—21no—
67C22×C313—22no—
68C22×C313C2×D412yes—
69C22×C313C2411yescharacteristic
70C2×D313—22no—
71C2×D313—22no—
72C2×D313—21no—
73C2×D313—22no—
74C2×D313—22no—
75C2×D313—22no—
76C2×D313—22no—
77C2×D313—44no—
78C2×D313—44no—
79C2×D313—44no—
80C2×D313C2×D412yes—
81C2×D313C2×D412yes—
82C4×C313—22no—
83C4×C313—21no—
84C4×C313—22no—
85Dic313—21no—
86Dic313—22no—
87C2×C313—22no—
88C2×C313—41no—
89C2×C313C22×D411yescharacteristic
90C2×C313H(5,𝔽2)12yes—
91D313—22no—
92D313—22no—
93D313—41no—
94D313—42no—
95C313#53411yescharacteristic, complemented, Sylow
96#534—3131nomaximal, Sylow
97C22×D4—3131no—
98C22×D4—3131no—
99#123—3131no—
100#123—3132no—
101#123D31311yescharacteristic, complemented
102#121—3132no—
103#121—3132no—
104#120—3131no—
105#120—3132no—
106#120—3131no—
107C2×C22⋊C4—3131no—
108C24—3131no—
109C24—3131no—
110C24—3131no—
111C2×D4—3131no—
112C2×D4—3131no—
113C2×D4—3132no—
114C2×D4—3132no—
115C2×D4—3131no—
116C2×D4—3132no—
117C2×D4—3132no—
118C2×D4—6264no—
119C2×D4—6264no—
120C2×D4C2×D31311yescharacteristic
121C22×C4—3131no—
122C22×C4—3132no—
123C22×C4C2×D31311yescharacteristic, complemented
124C4⋊C4—3132no—
125C4⋊C4C2×D31312yescomplemented
126C22⋊C4—3131no—
127C22⋊C4—3132no—
128C22⋊C4—3132no—
129C22⋊C4—3132no—
130C22⋊C4—3132no—
131C22⋊C4C2×D31311yescharacteristic, complemented
132C22⋊C4C2×D31312yescomplemented
133C23—3131no—
134C23—3131no—
135C23—3134no—
136C23—3131no—
137C23—3132no—
138C23—6262no—
139C23—6262no—
140C23—12522no—
141C23—12522no—
142C23—12522no—
143C23C22×D31311yescharacteristic
144C23C22×D31311yescharacteristic
145D4—22no—
146D4—6264no—
147D4—6264no—
148D4—6262no—
149D4—6262no—
150D4—6262no—
151D4—12522no—
152D4—12522no—
153C2×C4—22no—
154C2×C4—3132no—
155C2×C4—3131no—
156C2×C4—6262no—
157C2×C4—12522no—
158C2×C4C22×D31312yes—
159C2×C4C22×D31311yescharacteristic
160C2×C4C22×D31312yes—
161C22—22no—
162C22—21no—
163C22—22no—
164C22—3132no—
165C22—3132no—
166C22—6262no—
167C22—6262no—
168C22—6262no—
169C22—6261no—
170C22—6262no—
171C22—6262no—
172C22—6262no—
173C22—12524no—
174C22—12524no—
175C22—12524no—
176C22D4×D31312yes—
177C22C23×D31311yescharacteristic
178C4—22no—
179C4—21no—
180C4—22no—
181C4—6261no—
182C4—6262no—
183C2—22no—
184C2—41no—
185C2—6262no—
186C2—6262no—
187C2—12522no—
188C2—12521no—
189C2C2×D4×D31311yescharacteristic
190C2#2375654312yes—
subgroupG/H
center, FrattiniC22C23×D313
commutator, socle, cosocleC22×C313C24
Fitting#123×C313C2
hypercenter#123D313
hypocenterC313#534
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C22×D1252C2semidirect
2. C2×D4×D313C2semidirect
3. #23756482C2semidirect
4. #23756480C2semidirect
5. #23756472C2semidirect
6. #23756470C2semidirect
7. #23756467C2semidirect
8. #23756467C2semidirect
9. #23756465C2semidirect
10. C22⋊C4×D313C2semidirect
11. #123×C313C2semidirect
13. C23×D313C22semidirect
14. C23×D313C22semidirect
17. C2×D1252C22semidirect
18. C2×D1252C22semidirect
19. C2×D1252C22semidirect
21. C2×C22⋊D313C22semidirect
22. C2×C22⋊D313C22semidirect
24. C2×C4×D313C22semidirect
25. C2×C4×D313C22semidirect
26. #19097540C22semidirect
27. C22⋊Dic313C22semidirect
28. #19097538C22semidirect
29. #19097538C22semidirect
30. #19097538C22semidirect
31. #19097538C22semidirect
33. C22×C4×C313C22semidirect
34. C4⋊C4×C313C22semidirect
35. C22⋊C4×C313C22semidirect
36. C22⋊C4×C313C22semidirect
42. C22×D313D4semidirect
95. C313#534semidirect
101. #123D313semidirect
123. C22×C4C2×D313semidirect
125. C4⋊C4C2×D313semidirect
131. C22⋊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
C22×D12522
C2×D4×D3132
#237564822
#237564802
#237564722
#237564702
#237564672
#237564652
C22⋊C4×D3132
#123×C3132
#534313