Finite Group Databasebeta

← #21456295

Subgroups — #21456295

Order 7808.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519810C211yesmaximal, characteristic, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3C2×#14519799C211yesmaximal, characteristic, complemented
4C22×#11758190C211yesmaximal, characteristic, complemented
5#16840338C211yesmaximal, characteristic, complemented
6#16840331C211yesmaximal, characteristic, complemented
7#16840156C212yesmaximal, complemented
8#16840151C212yesmaximal, complemented
9#16840146C212yesmaximal, complemented
10#16840135C212yesmaximal, complemented
11C61×#405C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2211yescharacteristic
14C22×Dic122C2211yescharacteristic
15C22×D244C2211yescharacteristic
16#14519810—24no—
17#14519805—24no—
18#14519799—24no—
19C2×Dic244C2211yescharacteristic, complemented
20C2×Dic244C2212yescomplemented
21C2×#11758190—24no—
22C2×#11758190C2212yes—
23C2×#11758190C2212yes—
24C2×#11758190C2212yes—
25C2×#11758190C2211yescharacteristic, complemented
26C2×#11758190C2211yescharacteristic, complemented
27C2×#11758190C2212yescomplemented
28C2×D488C2212yes—
29C2×D488C2211yescharacteristic, complemented
30#14519777C2212yescomplemented
31#14519774C2212yes—
32#14519765C2212yes—
33#14519765C2212yescomplemented
34#14519761—22no—
35#14519757—22no—
36#14519752—22no—
37#14519747—22no—
38C2×M16×C61C2211yescharacteristic
39C22×C8×C61C2211yescharacteristic
40#117×C61C2211yescharacteristic
41#97×C61C2212yescomplemented
42C4×C8×C61C2212yescomplemented
43C23×D61—21no—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—21no—
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48#11758222—22no—
49#11758222—22no—
50#11758222—22no—
51#11758222—22no—
52C2×D244—22no—
53C2×D244—22no—
54C2×D244—21no—
55C2×D244—24no—
56C2×D244C2312yes—
57C2×D244C2311yescharacteristic
58C2×D244C2311yescharacteristic
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×Dic122—22no—
62C2×Dic122—22no—
63C2×Dic122—21no—
64C2×Dic122C2312yes—
65C2×Dic122C2311yescharacteristic
66C2×Dic122C2311yescharacteristic
67M16×C61D414yescomplemented
68C2×C8×C61D414yescomplemented
69C2×C8×C61C2311yescharacteristic
70C2×C8×C61C2312yes—
71C2×C8×C61C2311yescharacteristic
72C4⋊C4×C61D412yes—
73C22⋊C4×C61D412yes—
74C42×C61C2312yes—
75#11758198—24no—
76#11758198—24no—
77C4⋊Dic61—24no—
78Dic244—24no—
79Dic244—22no—
80D488—24no—
81D488—22no—
82#11758190—24no—
83#11758190—24no—
84#11758190—24no—
85#11758190—24no—
86#11758190—22no—
87#11758190—22no—
88C23×C61C2×D411yescharacteristic
89C22×D61—21no—
90C22×D61—22no—
91C22×D61—21no—
92C22×D61—42no—
93C22×D61—82no—
94C2×C4×C61C2×D414yes—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D412yes—
98C2×C4×C61C2411yescharacteristic
99C22⋊D61—42no—
100C22⋊D61—42no—
101C2×Dic61—21no—
102C2×Dic61—22no—
103C2×Dic61—21no—
104C2×Dic61—42no—
105D244—22no—
106D244—21no—
107D244—22no—
108D244—21no—
109D244—21no—
110D244—21no—
111D244—42no—
112D244—84no—
113C4×D61—42no—
114C4×D61—42no—
115Dic122—22no—
116Dic122—21no—
117Dic122—22no—
118Dic122—21no—
119Dic122—21no—
120Dic122—21no—
121Dic122—42no—
122C8×C61C2×D412yes—
123C8×C61C2×D412yes—
124C8×C61C2×D414yes—
125C22×C61—22no—
126C22×C61#12712yes—
127C22×C61C22×D411yescharacteristic
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—44no—
133C2×D61—42no—
134C2×D61—84no—
135C4×C61—24no—
136C4×C61#12712yes—
137C4×C61C22×D411yescharacteristic
138C4×C61C22×D411yescharacteristic
139Dic61—42no—
140Dic61—41no—
141Dic61—41no—
142#3154—611nomaximal, Sylow
143C2×C61—22no—
144C2×C61C2×#12711yescharacteristic
145C2×C61#57712yes—
146D61—81no—
147D61—81no—
148D61—82no—
149C2×#137—611no—
150C2×AGL(1,ℤ/8)—611no—
151C2×#135—611no—
152C22×SD16—611no—
153#536—611no—
154#535—611no—
155#497—612no—
156#496—612no—
157#495—612no—
158#492—612no—
159#405D6111yescharacteristic, complemented
160C61#315411yescharacteristic, complemented, Sylow
161C2×#41—611no—
162C2×#41—611no—
163C22×Q8—611no—
164C22×D4—611no—
165#137—1224no—
166AGL(1,ℤ/8)—1224no—
167#135—1224no—
168C2×Q16—611no—
169C2×Q16—612no—
170C2×SD16—612no—
171C2×SD16—612no—
172C2×SD16—611no—
173C2×SD16—611no—
174C2×SD16—612no—
175C2×SD16—612no—
176C2×SD16—1224no—
177C2×D8—611no—
178C2×D8—612no—
179C2×M16C2×D6111yescharacteristic
180C22×C8C2×D6111yescharacteristic
181C4⋊Q8—612no—
182#127—612no—
183#124—612no—
184#124—612no—
185#123—1222no—
186C22⋊Q8—1222no—
187#121—1222no—
188#120—1222no—
189#117C2×D6111yescharacteristic
190#97C2×D6112yescomplemented
191C4×C8C2×D6112yescomplemented
192C24—1221no—
193#41—1222no—
194#41—1222no—
195#41—1222no—
196#41—1222no—
197C2×Q8—611no—
198C2×Q8—612no—
199C2×Q8—611no—
200C2×Q8—1221no—
201C2×Q8—1222no—
202C2×Q8—1222no—
203C2×D4—611no—
204C2×D4—612no—
205C2×D4—611no—
206C2×D4—1221no—
207C2×D4—1221no—
208C2×D4—1222no—
209C2×D4—1222no—
210C2×D4—1224no—
211C2×D4—1221no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4C22×D6111yescharacteristic
216Q16—1222no—
217Q16—1224no—
218SD16—1224no—
219SD16—1224no—
220SD16—1222no—
221SD16—1222no—
222SD16—1224no—
223SD16—1224no—
224D8—1222no—
225D8—1224no—
226M16D24414yescomplemented
227C2×C8D24414yescomplemented
228C2×C8C22×D6111yescharacteristic
229C2×C8C22×D6112yes—
230C2×C8C22×D6111yescharacteristic
231C4⋊C4—1224no—
232C4⋊C4D24412yes—
233C22⋊C4—1224no—
234C22⋊C4—1224no—
235C22⋊C4D24412yes—
236C42C22×D6112yes—
237C23—1221no—
238C23—1222no—
239C23—1221no—
240C23—4882no—
241C23—2442no—
242C23C2×D24411yescharacteristic
243Q8—1222no—
244Q8—1221no—
245Q8—1222no—
246Q8—1221no—
247Q8—1221no—
248Q8—1221no—
249Q8—2442no—
250D4—1221no—
251D4—1222no—
252D4—1221no—
253D4—1221no—
254D4—1222no—
255D4—1221no—
256D4—4884no—
257D4—2442no—
258D4—2442no—
259D4—2442no—
260C2×C4—1221no—
261C2×C4—1222no—
262C2×C4—1221no—
263C2×C4—2442no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4C2×D24414yes—
267C2×C4C2×D24412yes—
268C2×C4C2×D24412yes—
269C2×C4C2×D24411yescharacteristic
270C2×C4C23×D6111yescharacteristic
271C8C2×D24412yes—
272C8C2×D24412yes—
273C8C2×D24414yes—
274C22—22no—
275C22—4884no—
276C22—2441no—
277C22—2441no—
278C22—2442no—
279C22—2442no—
280C22—2444no—
281C22—2442no—
282C22#1451977412yes—
283C22C22×D24411yescharacteristic
284C4—24no—
285C4—2441no—
286C4—2441no—
287C4—2442no—
288C4#1451977412yes—
289C4C22×D24411yescharacteristic
290C4C22×D24411yescharacteristic
291C2—22no—
292C2—4882no—
293C2—4881no—
294C2—4881no—
295C2C2×#1451977411yescharacteristic
296C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#405C2
socleC22×C61C22×D4
hypercenter#405D61
hypocenterC61#3154
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
2. C2×#14519805C2semidirect
3. C2×#14519799C2semidirect
4. C22×#11758190C2semidirect
5. #16840338C2semidirect
6. #16840331C2semidirect
7. #16840156C2semidirect
8. #16840151C2semidirect
9. #16840146C2semidirect
10. #16840135C2semidirect
11. C61×#405C2semidirect
19. C2×Dic244C22semidirect
20. C2×Dic244C22semidirect
25. C2×#11758190C22semidirect
26. C2×#11758190C22semidirect
27. C2×#11758190C22semidirect
29. C2×D488C22semidirect
30. #14519777C22semidirect
33. #14519765C22semidirect
41. #97×C61C22semidirect
42. C4×C8×C61C22semidirect
67. M16×C61D4semidirect
68. C2×C8×C61D4semidirect
159. #405D61semidirect
160. C61#3154semidirect
190. #97C2×D61semidirect
191. C4×C8C2×D61semidirect
226. M16D244semidirect
227. C2×C8D244semidirect