Finite Group Databasebeta

← #121×D97 #20261223

Subgroups — #121×D97 #20261223

Order 6208.

426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 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×D4×D97C211yesmaximal, characteristic, complemented
2C2×D4×D97C212yesmaximal, complemented
3C22×C4×D97C211yesmaximal, characteristic, complemented
4#15690785C211yesmaximal, characteristic, complemented
5#15690784C211yesmaximal, characteristic, complemented
6#15690783C212yesmaximal, complemented
7#15690782C212yesmaximal, complemented
8#15690781C211yesmaximal, characteristic, complemented
9C4⋊C4×D97C211yesmaximal, characteristic, complemented
10C22⋊C4×D97C212yesmaximal, complemented
11#121×C97C211yesmaximal, characteristic, complemented
12C23×D97C2212yes—
13C23×D97C2211yescharacteristic
14C2×D388C2212yescomplemented
15C2×D388C2211yescharacteristic, complemented
16C2×C22⋊D97C2212yescomplemented
17C2×C22⋊D97C2212yescomplemented
18C2×C22⋊D97C2212yescomplemented
19D4×D97—28no—
20D4×D97—24no—
21C22×Dic97C2211yescharacteristic, complemented
22C2×C4×D97—24no—
23C2×C4×D97C2211yescharacteristic
24C2×C4×D97C2212yes—
25C2×C4×D97C2211yescharacteristic
26C2×C4×D97C2211yescharacteristic, complemented
27C2×C4×D97C2211yescharacteristic, complemented
28C4⋊Dic97C2211yescharacteristic, complemented
29#13095490C2212yescomplemented
30C22⋊Dic97C2212yescomplemented
31#13095488C2212yescomplemented
32#13095488C2212yescomplemented
33C2×D4×C97C2211yescharacteristic, complemented
34C2×D4×C97C2212yescomplemented
35C22×C4×C97C2211yescharacteristic, complemented
36C4⋊C4×C97C2211yescharacteristic, complemented
37C22⋊C4×C97C2212yescomplemented
38C23×C97C2312yes—
39C23×C97C2311yescharacteristic
40C22×D97—22no—
41C22×D97—22no—
42C22×D97—24no—
43C22×D97—24no—
44C22×D97—24no—
45C22×D97D414yescomplemented
46C22×D97C2312yes—
47C22×D97C2311yescharacteristic
48C22×D97C2311yescharacteristic
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—24no—
58C2×Dic97—22no—
59C2×Dic97C2311yescharacteristic
60C2×Dic97C2312yes—
61C2×Dic97C2311yescharacteristic
62D388—24no—
63D388—22no—
64C4×D97—22no—
65C4×D97—24no—
66C4×D97—22no—
67C4×D97—22no—
68C4×D97D414yescomplemented
69C22×C97—21no—
70C22×C97—21no—
71C22×C97—22no—
72C22×C97—22no—
73C22×C97—22no—
74C22×C97C2×D412yescomplemented
75C22×C97C2411yescharacteristic
76C2×D97—21no—
77C2×D97—21no—
78C2×D97—28no—
79C2×D97—22no—
80C2×D97—22no—
81C2×D97—22no—
82C2×D97—48no—
83C2×D97C2×D412yes—
84C2×D97C2×D412yes—
85C2×D97C2×D412yescomplemented
86C2×D97#4112yes—
87C4×C97—21no—
88C4×C97—22no—
89C4×C97C2×D412yescomplemented
90Dic97—21no—
91Dic97—22no—
92Dic97C2×D412yescomplemented
93C2×C97—22no—
94C2×C97—42no—
95C2×C97C22×D411yescharacteristic
96C2×C97C22×D411yescharacteristic
97C2×C97C2×#4111yescharacteristic
98D97—22no—
99D97—42no—
100D97#12114yesdirect product factor
101C97C2×#12111yescharacteristic, complemented, Sylow
102C2×#121—971nomaximal, Sylow
103C22×D4—971no—
104C22×D4—972no—
105C23×C4—971no—
106#121—971no—
107#121—972no—
108#121—971no—
109#121—971no—
110#121—972no—
111#121D9711yescharacteristic, direct product factor
112C2×C4⋊C4—971no—
113C2×C22⋊C4—972no—
114C24—971no—
115C24—972no—
116C2×D4—972no—
117C2×D4—972no—
118C2×D4—972no—
119C2×D4—972no—
120C2×D4—971no—
121C2×D4—1944no—
122C2×D4—1948no—
123C2×D4C2×D9712yescomplemented
124C2×D4C2×D9711yescharacteristic, complemented
125C22×C4—971no—
126C22×C4—971no—
127C22×C4—971no—
128C22×C4—972no—
129C22×C4—971no—
130C22×C4—971no—
131C22×C4—1944no—
132C22×C4C2×D9711yescharacteristic, complemented
133C4⋊C4—972no—
134C4⋊C4—971no—
135C4⋊C4C2×D9711yescharacteristic, complemented
136C22⋊C4—972no—
137C22⋊C4—972no—
138C22⋊C4—972no—
139C22⋊C4C2×D9712yescomplemented
140C23—971no—
141C23—974no—
142C23—971no—
143C23—972no—
144C23—1944no—
145C23—1944no—
146C23—1944no—
147C23—1942no—
148C23—1942no—
149C23C22×D9712yes—
150C23C22×D9711yescharacteristic
151D4—24no—
152D4—22no—
153D4—1944no—
154D4—1944no—
155D4—1944no—
156D4—1944no—
157D4—1942no—
158C2×C4—22no—
159C2×C4—971no—
160C2×C4—974no—
161C2×C4—971no—
162C2×C4—972no—
163C2×C4—1942no—
164C2×C4—1942no—
165C2×C4—1944no—
166C2×C4—1942no—
167C2×C4—1942no—
168C2×C4C22×D9711yescharacteristic
169C2×C4C22×D9712yes—
170C2×C4C22×D9711yescharacteristic
171C22—21no—
172C22—21no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—972no—
177C22—972no—
178C22—972no—
179C22—972no—
180C22—3888no—
181C22—1948no—
182C22—1942no—
183C22—1942no—
184C22—1942no—
185C22—1941no—
186C22—1941no—
187C22D4×D9712yescomplemented
188C22C23×D9711yescharacteristic
189C4—21no—
190C4—22no—
191C4—972no—
192C4—1941no—
193C4—1942no—
194C4D4×D9712yescomplemented
195C2—22no—
196C2—42no—
197C2—974no—
198C2—3882no—
199C2—1942no—
200C2C2×D4×D9711yescharacteristic
201C2C2×D4×D9711yescharacteristic
202C2#41×D9711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D97
commutator, socleC22×C97C24
Fitting#121×C97C2
hypercenter#121D97
hypocenterC97C2×#121
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D97C2semidirect
2. C2×D4×D97C2semidirect
3. C22×C4×D97C2semidirect
4. #15690785C2semidirect
5. #15690784C2semidirect
6. #15690783C2semidirect
7. #15690782C2semidirect
8. #15690781C2semidirect
9. C4⋊C4×D97C2semidirect
10. C22⋊C4×D97C2semidirect
11. #121×C97C2semidirect
14. C2×D388C22semidirect
15. C2×D388C22semidirect
16. C2×C22⋊D97C22semidirect
17. C2×C22⋊D97C22semidirect
18. C2×C22⋊D97C22semidirect
21. C22×Dic97C22semidirect
26. C2×C4×D97C22semidirect
27. C2×C4×D97C22semidirect
28. C4⋊Dic97C22semidirect
29. #13095490C22semidirect
30. C22⋊Dic97C22semidirect
31. #13095488C22semidirect
32. #13095488C22semidirect
33. C2×D4×C97C22semidirect
34. C2×D4×C97C22semidirect
35. C22×C4×C97C22semidirect
36. C4⋊C4×C97C22semidirect
37. C22⋊C4×C97C22semidirect
45. C22×D97D4semidirect
68. C4×D97D4semidirect
74. C22×C97C2×D4semidirect
85. C2×D97C2×D4semidirect
89. C4×C97C2×D4semidirect
92. Dic97C2×D4semidirect
100. D97#121direct (N × H)
101. C97C2×#121semidirect
111. #121D97direct (N × H)
123. C2×D4C2×D97semidirect
124. C2×D4C2×D97semidirect
132. C22×C4C2×D97semidirect
135. C4⋊C4C2×D97semidirect
139. C22⋊C4C2×D97semidirect
187. C22D4×D97semidirect
194. C4D4×D97semidirect