Finite Group Databasebeta

← #20261369

Subgroups — #20261369

Order 6208.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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×D97C212yesmaximal, complemented
3C2×D4×D97C211yesmaximal, characteristic, complemented
4#15690806C211yesmaximal, characteristic, complemented
5#15690785C211yesmaximal, characteristic, complemented
6#15690783C212yesmaximal, complemented
7#15690780C212yesmaximal, complemented
8#15690778C212yesmaximal, complemented
9#15690772C211yesmaximal, characteristic, complemented
10C4×C22⋊D97C211yesmaximal, characteristic, complemented
11#121×C97C211yesmaximal, characteristic, complemented
12C23×D97C2212yescomplemented
13C23×D97C2212yescomplemented
14C2×D388—24no—
15C2×D388C2211yescharacteristic
16C2×D388C2212yescomplemented
17C2×D388C2212yescomplemented
18C2×D388C2211yescharacteristic, complemented
19C2×C22⋊D97C2211yescharacteristic
20C2×C22⋊D97C2212yescomplemented
21C2×C22⋊D97C2212yescomplemented
22C2×C22⋊D97C2212yescomplemented
23D4×D97—28no—
24D4×D97—24no—
25C2×C4×D97C2211yescharacteristic, complemented
26C2×C4×D97C2212yescomplemented
27#13095490C2211yescharacteristic, complemented
28C22⋊Dic97C2211yescharacteristic, complemented
29#13095488C2211yescharacteristic, complemented
30#13095488C2212yescomplemented
31#13095488C2212yescomplemented
32C4×Dic97C2211yescharacteristic, complemented
33C2×D4×C97C2212yescomplemented
34C2×D4×C97C2211yescharacteristic, complemented
35C22×C4×C97C2211yescharacteristic, complemented
36C4⋊C4×C97C2211yescharacteristic, complemented
37C22⋊C4×C97C2212yescomplemented
38C23×C97C2312yes—
39C23×C97C2311yescharacteristic
40C22×D97—24no—
41C22×D97—24no—
42C22×D97—24no—
43C22×D97—24no—
44C22×D97—42no—
45C22×D97—42no—
46C22×D97C2312yes—
47C22×D97C2311yescharacteristic
48C22×D97C2312yes—
49D4×C97—24no—
50D4×C97—22no—
51C2×C4×C97—22no—
52C2×C4×C97C2311yescharacteristic
53C2×C4×C97C2312yes—
54C2×C4×C97C2311yescharacteristic
55C22⋊D97—24no—
56C22⋊D97—24no—
57C22⋊D97—42no—
58C22⋊D97D414yescomplemented
59C2×Dic97C2311yescharacteristic
60C2×Dic97C2311yescharacteristic
61C2×Dic97C2311yescharacteristic
62D388—24no—
63D388—24no—
64D388—22no—
65D388D414yescomplemented
66C4×D97—22no—
67C4×D97—24no—
68C22×C97—21no—
69C22×C97—21no—
70C22×C97—22no—
71C22×C97—22no—
72C22×C97—22no—
73C22×C97C2×D412yescomplemented
74C22×C97C2411yescharacteristic
75C2×D97—21no—
76C2×D97—22no—
77C2×D97—21no—
78C2×D97—22no—
79C2×D97—22no—
80C2×D97—22no—
81C2×D97—22no—
82C2×D97—48no—
83C2×D97—48no—
84C2×D97C2×D412yescomplemented
85C2×D97C2×D414yescomplemented
86C4×C97—22no—
87C4×C97—21no—
88C4×C97C2×D412yescomplemented
89Dic97—21no—
90Dic97—21no—
91Dic97C2×D412yescomplemented
92C2×C97—22no—
93C2×C97—42no—
94C2×C97C22×D411yescharacteristic
95C2×C97C22×D411yescharacteristic
96C2×C97H(5,𝔽2)11yescharacteristic
97D97—22no—
98D97—24no—
99D97—42no—
100C97D4211yescharacteristic, complemented, Sylow
101D42—971nomaximal, Sylow
102C22×D4—972no—
103C22×D4—971no—
104C22×D4—971no—
105#127—971no—
106#121—971no—
107#121—972no—
108#121D9711yescharacteristic, complemented
109#120—972no—
110#120—972no—
111C4×D4—971no—
112C4×D4—971no—
113C24—972no—
114C24—972no—
115C2×D4—971no—
116C2×D4—972no—
117C2×D4—972no—
118C2×D4—972no—
119C2×D4—971no—
120C2×D4—972no—
121C2×D4—972no—
122C2×D4—971no—
123C2×D4—1944no—
124C2×D4—1948no—
125C2×D4—1944no—
126C2×D4C2×D9712yescomplemented
127C2×D4C2×D9711yescharacteristic, complemented
128C22×C4—972no—
129C22×C4—971no—
130C22×C4C2×D9711yescharacteristic, complemented
131C4⋊C4—971no—
132C4⋊C4C2×D9711yescharacteristic, complemented
133C22⋊C4—971no—
134C22⋊C4—972no—
135C22⋊C4—971no—
136C22⋊C4—972no—
137C22⋊C4C2×D9712yescomplemented
138C42—971no—
139C23—971no—
140C23—972no—
141C23—972no—
142C23—3882no—
143C23—3882no—
144C23—1944no—
145C23—1944no—
146C23—1944no—
147C23—1944no—
148C23C22×D9712yes—
149C23C22×D9711yescharacteristic
150D4—24no—
151D4—22no—
152D4—974no—
153D4—974no—
154D4—3882no—
155D4—1944no—
156D4—1944no—
157D4—1944no—
158D4—1944no—
159D4—1942no—
160C2×C4—22no—
161C2×C4—971no—
162C2×C4—971no—
163C2×C4—971no—
164C2×C4—1944no—
165C2×C4—1942no—
166C2×C4C22×D9712yes—
167C2×C4C22×D9711yescharacteristic
168C2×C4C22×D9711yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—972no—
175C22—974no—
176C22—3888no—
177C22—3888no—
178C22—1942no—
179C22—1942no—
180C22—1942no—
181C22—1942no—
182C22—1941no—
183C22—1942no—
184C22—1941no—
185C22D4×D9712yescomplemented
186C22C23×D9711yescharacteristic
187C4—21no—
188C4—22no—
189C4—972no—
190C4—1941no—
191C4—1941no—
192C4D4×D9712yescomplemented
193C2—22no—
194C2—42no—
195C2—3882no—
196C2—1944no—
197C2—1942no—
198C2C2×D4×D9711yescharacteristic
199C2C2×D4×D9711yescharacteristic
200C2#1569085611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D97
commutator, socleC22×C97C24
Fitting#121×C97C2
hypercenter#121D97
hypocenterC97D42
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D388C2semidirect
2. C2×D4×D97C2semidirect
3. C2×D4×D97C2semidirect
4. #15690806C2semidirect
5. #15690785C2semidirect
6. #15690783C2semidirect
7. #15690780C2semidirect
8. #15690778C2semidirect
9. #15690772C2semidirect
10. C4×C22⋊D97C2semidirect
11. #121×C97C2semidirect
12. C23×D97C22semidirect
13. C23×D97C22semidirect
16. C2×D388C22semidirect
17. C2×D388C22semidirect
18. C2×D388C22semidirect
20. C2×C22⋊D97C22semidirect
21. C2×C22⋊D97C22semidirect
22. C2×C22⋊D97C22semidirect
25. C2×C4×D97C22semidirect
26. C2×C4×D97C22semidirect
27. #13095490C22semidirect
28. C22⋊Dic97C22semidirect
29. #13095488C22semidirect
30. #13095488C22semidirect
31. #13095488C22semidirect
32. C4×Dic97C22semidirect
33. C2×D4×C97C22semidirect
34. C2×D4×C97C22semidirect
35. C22×C4×C97C22semidirect
36. C4⋊C4×C97C22semidirect
37. C22⋊C4×C97C22semidirect
58. C22⋊D97D4semidirect
65. D388D4semidirect
73. C22×C97C2×D4semidirect
84. C2×D97C2×D4semidirect
85. C2×D97C2×D4semidirect
88. C4×C97C2×D4semidirect
91. Dic97C2×D4semidirect
100. C97D42semidirect
108. #121D97semidirect
126. C2×D4C2×D97semidirect
127. C2×D4C2×D97semidirect
130. C22×C4C2×D97semidirect
132. C4⋊C4C2×D97semidirect
137. C22⋊C4C2×D97semidirect
185. C22D4×D97semidirect
192. C4D4×D97semidirect