Finite Group Databasebeta

← #20261296

Subgroups — #20261296

Order 6208.

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×D388C211yesmaximal, characteristic, complemented
2C2×D4×D97C211yesmaximal, characteristic, complemented
3#15690795C212yesmaximal, complemented
4#15690793C211yesmaximal, characteristic, complemented
5#15690785C212yesmaximal, complemented
6#15690783C212yesmaximal, complemented
7#15690780C211yesmaximal, characteristic, complemented
8#15690780C212yesmaximal, complemented
9#15690778C211yesmaximal, characteristic, complemented
10C22⋊C4×D97C211yesmaximal, characteristic, complemented
11#123×C97C211yesmaximal, characteristic, complemented
12C23×D97C2211yescharacteristic
13C23×D97C2211yescharacteristic, complemented
14C23×D97C2211yescharacteristic, complemented
15C2×D388—24no—
16C2×D388C2212yes—
17C2×D388C2212yescomplemented
18C2×D388C2211yescharacteristic, complemented
19C2×D388C2212yescomplemented
20C2×C22⋊D97C2211yescharacteristic
21C2×C22⋊D97C2211yescharacteristic, complemented
22C2×C22⋊D97C2212yescomplemented
23D4×D97—24no—
24C2×C4×D97C2211yescharacteristic, complemented
25C2×C4×D97C2212yescomplemented
26#13095490C2212yescomplemented
27C22⋊Dic97C2211yescharacteristic, complemented
28#13095488C2212yescomplemented
29#13095488C2212yescomplemented
30#13095488C2212yescomplemented
31#13095488C2212yescomplemented
32C2×D4×C97C2211yescharacteristic
33C22×C4×C97C2211yescharacteristic, complemented
34C4⋊C4×C97C2212yescomplemented
35C22⋊C4×C97C2211yescharacteristic, complemented
36C22⋊C4×C97C2212yescomplemented
37C23×C97C2311yescharacteristic
38C23×C97C2311yescharacteristic
39C22×D97—22no—
40C22×D97—22no—
41C22×D97—42no—
42C22×D97—42no—
43C22×D97—42no—
44C22×D97D414yescomplemented
45C22×D97C2311yescharacteristic
46C22×D97C2312yes—
47C22×D97C2311yescharacteristic
48C22×D97C2311yescharacteristic
49D4×C97—22no—
50C2×C4×C97—22no—
51C2×C4×C97C2312yes—
52C2×C4×C97C2312yes—
53C2×C4×C97C2311yescharacteristic
54C22⋊D97—22no—
55C22⋊D97—22no—
56C22⋊D97—42no—
57C2×Dic97C2312yes—
58C2×Dic97C2311yescharacteristic
59D388—22no—
60D388—24no—
61D388—24no—
62D388—42no—
63C4×D97—22no—
64C4×D97—42no—
65C22×C97—22no—
66C22×C97—21no—
67C22×C97—22no—
68C22×C97C2×D412yes—
69C22×C97C2411yescharacteristic
70C2×D97—22no—
71C2×D97—22no—
72C2×D97—22no—
73C2×D97—21no—
74C2×D97—22no—
75C2×D97—22no—
76C2×D97—22no—
77C2×D97—44no—
78C2×D97—44no—
79C2×D97—44no—
80C2×D97C2×D412yes—
81C2×D97C2×D412yes—
82C4×C97—21no—
83C4×C97—22no—
84C4×C97—22no—
85Dic97—21no—
86Dic97—22no—
87C2×C97—22no—
88C2×C97—41no—
89C2×C97C22×D411yescharacteristic
90C2×C97H(5,𝔽2)12yes—
91D97—22no—
92D97—22no—
93D97—42no—
94D97—41no—
95C97#53411yescharacteristic, complemented, Sylow
96#534—971nomaximal, Sylow
97C22×D4—971no—
98C22×D4—971no—
99#123—971no—
100#123—972no—
101#123D9711yescharacteristic, complemented
102#121—972no—
103#121—972no—
104#120—971no—
105#120—972no—
106#120—971no—
107C2×C22⋊C4—971no—
108C24—971no—
109C24—971no—
110C24—971no—
111C2×D4—972no—
112C2×D4—971no—
113C2×D4—971no—
114C2×D4—972no—
115C2×D4—972no—
116C2×D4—971no—
117C2×D4—972no—
118C2×D4—1944no—
119C2×D4—1944no—
120C2×D4C2×D9711yescharacteristic
121C22×C4—972no—
122C22×C4—971no—
123C22×C4C2×D9711yescharacteristic, complemented
124C4⋊C4—972no—
125C4⋊C4C2×D9712yescomplemented
126C22⋊C4—971no—
127C22⋊C4—972no—
128C22⋊C4—972no—
129C22⋊C4—972no—
130C22⋊C4—972no—
131C22⋊C4C2×D9711yescharacteristic, complemented
132C22⋊C4C2×D9712yescomplemented
133C23—974no—
134C23—971no—
135C23—971no—
136C23—972no—
137C23—971no—
138C23—3882no—
139C23—3882no—
140C23—3882no—
141C23—1942no—
142C23—1942no—
143C23C22×D9711yescharacteristic
144C23C22×D9711yescharacteristic
145D4—22no—
146D4—3882no—
147D4—3882no—
148D4—1944no—
149D4—1944no—
150D4—1942no—
151D4—1942no—
152D4—1942no—
153C2×C4—22no—
154C2×C4—972no—
155C2×C4—971no—
156C2×C4—3882no—
157C2×C4—1942no—
158C2×C4C22×D9712yes—
159C2×C4C22×D9711yescharacteristic
160C2×C4C22×D9712yes—
161C22—22no—
162C22—21no—
163C22—22no—
164C22—972no—
165C22—972no—
166C22—3884no—
167C22—3884no—
168C22—3884no—
169C22—1942no—
170C22—1941no—
171C22—1942no—
172C22—1942no—
173C22—1942no—
174C22—1942no—
175C22—1942no—
176C22D4×D9712yes—
177C22C23×D9711yescharacteristic
178C4—22no—
179C4—21no—
180C4—22no—
181C4—1941no—
182C4—1942no—
183C2—22no—
184C2—41no—
185C2—3882no—
186C2—3881no—
187C2—1942no—
188C2—1942no—
189C2C2×D4×D9711yescharacteristic
190C2#1569085612yes—
subgroupG/H
center, FrattiniC22C23×D97
commutator, socleC22×C97C24
Fitting#123×C97C2
hypercenter#123D97
hypocenterC97#534
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C22×D388C2semidirect
2. C2×D4×D97C2semidirect
3. #15690795C2semidirect
4. #15690793C2semidirect
5. #15690785C2semidirect
6. #15690783C2semidirect
7. #15690780C2semidirect
8. #15690780C2semidirect
9. #15690778C2semidirect
10. C22⋊C4×D97C2semidirect
11. #123×C97C2semidirect
13. C23×D97C22semidirect
14. C23×D97C22semidirect
17. C2×D388C22semidirect
18. C2×D388C22semidirect
19. C2×D388C22semidirect
21. C2×C22⋊D97C22semidirect
22. C2×C22⋊D97C22semidirect
24. C2×C4×D97C22semidirect
25. C2×C4×D97C22semidirect
26. #13095490C22semidirect
27. C22⋊Dic97C22semidirect
28. #13095488C22semidirect
29. #13095488C22semidirect
30. #13095488C22semidirect
31. #13095488C22semidirect
33. C22×C4×C97C22semidirect
34. C4⋊C4×C97C22semidirect
35. C22⋊C4×C97C22semidirect
36. C22⋊C4×C97C22semidirect
44. C22×D97D4semidirect
95. C97#534semidirect
101. #123D97semidirect
123. C22×C4C2×D97semidirect
125. C4⋊C4C2×D97semidirect
131. C22⋊C4C2×D97semidirect
132. C22⋊C4C2×D97semidirect