Finite Group Databasebeta

← #21452154

Subgroups — #21452154

Order 7808.

1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519747C214yesmaximal, complemented
2C2×#14519745C212yesmaximal, complemented
3#16839679C212yesmaximal, complemented
4#16839678C214yesmaximal, complemented
5#16839664C212yesmaximal, complemented
6C61×#390C211yesmaximal, characteristic, complemented
7C24×D61C2212yescomplemented
8C22×D244C2212yes—
9C22×D244C2212yes—
10C22×C22⋊D61C2214yes—
11#14519747—216no—
12#14519745—28no—
13C2×C4⋊Dic61C2212yescomplemented
14C2×C22⋊Dic61C2212yescomplemented
15C2×#11758198C2214yescomplemented
16C2×#11758198C2214yescomplemented
17C2×#11758198C2214yescomplemented
18#14519684C2212yescomplemented
19C22×D4×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic, complemented
21C2×C22⋊C4×C61C2214yescomplemented
22C2×C42×C61C2211yescharacteristic, complemented
23C24×C61C2312yes—
24C23×D61—24no—
25C23×D61—28no—
26C23×D61—42no—
27C23×D61—42no—
28C23×D61—44no—
29C23×D61C2314yes—
30C2×D4×C61—41no—
31C2×D4×C61—41no—
32C2×D4×C61D414yescomplemented
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—28no—
37C2×C22⋊D61—28no—
38C2×C22⋊D61—44no—
39C22×Dic61C2314yes—
40C2×D244—28no—
41C2×D244—42no—
42C2×D244—42no—
43C2×D244—42no—
44C2×D244D418yescomplemented
45C4⋊C4×C61—41no—
46C22⋊C4×C61—28no—
47C42×C61—41no—
48C22⋊Dic61—24no—
49#11758198—28no—
50#11758198—28no—
51#11758198—28no—
52C4⋊Dic61—42no—
53C23×C61—24no—
54C23×C61—24no—
55C23×C61—22no—
56C23×C61—22no—
57C23×C61C2×D414yes—
58C23×C61C2411yescharacteristic
59C22×D61—24no—
60C22×D61—24no—
61C22×D61—24no—
62C22×D61—24no—
63C22×D61—24no—
64C22×D61—24no—
65C22×D61—48no—
66C22×D61—416no—
67C22×D61—416no—
68C22×D61—48no—
69C22×D61—48no—
70C22×D61C2×D418yes—
71D4×C61—44no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—24no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D414yes—
80C22⋊D61—416no—
81C2×Dic61—24no—
82C2×Dic61—24no—
83C2×Dic61—24no—
84D244—48no—
85D244—48no—
86C22×C61—24no—
87C22×C61—28no—
88C22×C61—44no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61C22×D412yes—
92C22×C61C22×D411yescharacteristic
93C22×C61H(5,𝔽2)11yescharacteristic
94C22×C61H(5,𝔽2)11yescharacteristic
95C22×C61H(5,𝔽2)12yes—
96C2×D61—28no—
97C2×D61—28no—
98C2×D61—28no—
99C2×D61—432no—
100C2×D61—44no—
101C2×D61—44no—
102C2×D61—44no—
103C2×D61—44no—
104C4×C61—24no—
105C4×C61—22no—
106C4×C61—42no—
107Dic61—44no—
108#2679—611nomaximal, Sylow
109C2×C61—44no—
110C2×C61#53412yes—
111C2×C61#53411yescharacteristic
112C2×C61D4211yescharacteristic
113C2×C61D4212yes—
114C2×C61H(3,𝔽4)11yescharacteristic
115D61—48no—
116C2×#120—612no—
117C2×#120—614no—
118#394—612no—
119#394—614no—
120#390—612no—
121#390D6111yescharacteristic, complemented
122C61#267911yescharacteristic, complemented, Sylow
123C25—612no—
124C22×D4—614no—
125C22×D4—612no—
126C22×D4—612no—
127C22×D4C2×D6111yescharacteristic
128#120—12216no—
129#120—1228no—
130C2×C4⋊C4—612no—
131C2×C4⋊C4C2×D6111yescharacteristic, complemented
132C2×C22⋊C4—612no—
133C2×C22⋊C4—614no—
134C2×C22⋊C4—614no—
135C2×C22⋊C4—614no—
136C2×C22⋊C4C2×D6114yescomplemented
137C2×C42C2×D6111yescharacteristic, complemented
138#95—612no—
139C24—614no—
140C24—1228no—
141C24—1224no—
142C24—2442no—
143C24—2442no—
144C24—2444no—
145C24C22×D6112yes—
146C2×D4—41no—
147C2×D4—41no—
148C2×D4—618no—
149C2×D4—1228no—
150C2×D4—1228no—
151C2×D4—1228no—
152C2×D4—2442no—
153C2×D4—2442no—
154C2×D4—2442no—
155C2×D4—2444no—
156C2×D4D24414yescomplemented
157C22×C4—614no—
158C22×C4C22×D6112yes—
159C22×C4C22×D6111yescharacteristic
160C22×C4C22×D6112yes—
161C4⋊C4—41no—
162C4⋊C4—2442no—
163C22⋊C4—28no—
164C22⋊C4—1228no—
165C22⋊C4—1224no—
166C22⋊C4—1228no—
167C22⋊C4—1228no—
168C42—41no—
169C23—24no—
170C23—22no—
171C23—22no—
172C23—24no—
173C23—618no—
174C23—1224no—
175C23—1224no—
176C23—1224no—
177C23—1224no—
178C23—1224no—
179C23—1224no—
180C23—24416no—
181C23—2448no—
182C23—2448no—
183C23—24416no—
184C23—2448no—
185C23C2×D24414yes—
186C23C23×D6111yescharacteristic
187D4—44no—
188D4—2448no—
189D4—2448no—
190D4—24416no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—22no—
197C2×C4—1224no—
198C2×C4—1224no—
199C2×C4—1224no—
200C2×C4C2×D24412yes—
201C2×C4D4×D6114yes—
202C22—24no—
203C22—28no—
204C22—42no—
205C22—44no—
206C22—42no—
207C22—1228no—
208C22—1228no—
209C22—1228no—
210C22—24432no—
211C22—2444no—
212C22—2444no—
213C22—2444no—
214C22—2444no—
215C22C2×D4×D6112yes—
216C22C22×D24411yescharacteristic
217C22#1451982211yescharacteristic
218C22#1451982211yescharacteristic
219C22#1451982312yes—
220C4—24no—
221C4—22no—
222C4—42no—
223C4—2444no—
224C2—44no—
225C2—2448no—
226C2#1684032012yes—
227C2#1684032411yescharacteristic
228C2#1684039711yescharacteristic
229C2D4×D24412yes—
230C2#1684050411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2679
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14519747C2semidirect
2. C2×#14519745C2semidirect
3. #16839679C2semidirect
4. #16839678C2semidirect
5. #16839664C2semidirect
6. C61×#390C2semidirect
7. C24×D61C22semidirect
13. C2×C4⋊Dic61C22semidirect
14. C2×C22⋊Dic61C22semidirect
15. C2×#11758198C22semidirect
16. C2×#11758198C22semidirect
17. C2×#11758198C22semidirect
18. #14519684C22semidirect
20. C2×C4⋊C4×C61C22semidirect
21. C2×C22⋊C4×C61C22semidirect
22. C2×C42×C61C22semidirect
32. C2×D4×C61D4semidirect
44. C2×D244D4semidirect
121. #390D61semidirect
122. C61#2679semidirect
131. C2×C4⋊C4C2×D61semidirect
136. C2×C22⋊C4C2×D61semidirect
137. C2×C42C2×D61semidirect
156. C2×D4D244semidirect