Finite Group Databasebeta

← #21457421

Subgroups — #21457421

Order 7808.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519805C212yesmaximal, complemented
2#16840417C211yesmaximal, characteristic, complemented
3D4×D244C211yesmaximal, characteristic, complemented
4#16840135C211yesmaximal, characteristic, complemented
5#16840008C212yesmaximal, complemented
6#16839968C211yesmaximal, characteristic, complemented
7#16839958C211yesmaximal, characteristic, complemented
8#16839915C212yesmaximal, complemented
9#16839909C212yesmaximal, complemented
10C4×D488C211yesmaximal, characteristic, complemented
11C61×#436C211yesmaximal, characteristic, complemented
12C2×#11758222C2212yescomplemented
13C22×D244C2212yes—
14C2×D4×D61—21no—
15#14519805—28no—
16C2×#11758190C2212yes—
17C2×#11758190C2212yescomplemented
18C2×#11758190C2212yescomplemented
19C2×D488C2211yescharacteristic
20C2×D488C2212yescomplemented
21#14519777C2211yescharacteristic, complemented
22#14519774C2211yescharacteristic
23#14519759—22no—
24#14519756C2212yescomplemented
25#14519752—21no—
26#14519751C2212yes—
27#14519748—21no—
28#14519747—22no—
29C4×D244C2211yescharacteristic
30C4×D244C2211yescharacteristic, complemented
31C4⋊C4×D61—21no—
32#14519711C2211yescharacteristic, complemented
33#14519702C2212yescomplemented
34#14519699C2211yescharacteristic
35#14519699C2212yescomplemented
36#14519699C2211yescharacteristic, complemented
37C2×M16×C61C2212yescomplemented
38C4×D4×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic, complemented
40C22⋊C8×C61C2212yescomplemented
41C4×C8×C61C2211yescharacteristic, complemented
42C23×D61—22no—
43C2×D4×C61D411yescharacteristic
44C22×C4×C61C2312yes—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47D4×D61—44no—
48#11758222—24no—
49#11758222—42no—
50C2×D244—24no—
51C2×D244—21no—
52C2×D244—22no—
53C2×D244—21no—
54C2×D244—42no—
55C2×D244C2312yes—
56C2×D244C2311yescharacteristic
57C2×D244C2311yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—22no—
60C2×C4×D61—21no—
61C2×Dic122C2312yes—
62M16×C61—24no—
63C2×C8×C61C2311yescharacteristic
64C2×C8×C61C2312yes—
65C2×C8×C61C2311yescharacteristic
66C4⋊C4×C61D411yescharacteristic
67C22⋊C4×C61D412yes—
68C42×C61C2311yescharacteristic
69C22⋊Dic61—22no—
70#11758198—21no—
71#11758198—21no—
72#11758198—22no—
73C4⋊Dic61—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2311yescharacteristic
76C4⋊Dic61C2311yescharacteristic
77#11758196—22no—
78D488—24no—
79D488D414yescomplemented
80#11758190—24no—
81#11758190—24no—
82#11758190—42no—
83C23×C61C2×D412yes—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—22no—
87C22×D61—44no—
88C22×D61—44no—
89C22×D61—82no—
90D4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61C2×D412yes—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—44no—
98C22⋊D61—44no—
99C2×Dic61—21no—
100C2×Dic61—22no—
101C2×Dic61—21no—
102D244—22no—
103D244—21no—
104D244—21no—
105D244—22no—
106D244—44no—
107D244—42no—
108D244—81no—
109D244C2×D412yes—
110D244C2×D412yescomplemented
111C4×D61—44no—
112C4×D61—42no—
113C4×D61—42no—
114Dic122—22no—
115Dic122—22no—
116C8×C61—22no—
117C8×C61—21no—
118C8×C61C2×D412yescomplemented
119C22×C61—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61C22×D411yescharacteristic
123C2×D61—22no—
124C2×D61—22no—
125C2×D61—41no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—88no—
133C4×C61—22no—
134C4×C61—21no—
135C4×C61AGL(1,ℤ/8)12yescomplemented
136C4×C61C22×D411yescharacteristic
137C4×C61H(5,𝔽2)11yescharacteristic
138Dic61—42no—
139Dic61—41no—
140Dic61—41no—
141#3272—611nomaximal, Sylow
142C2×C61—42no—
143C2×C61D4211yescharacteristic
144C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C61#57711yescharacteristic
146D61—42no—
147D61—42no—
148D61—82no—
149C2×AGL(1,ℤ/8)—612no—
150#547—611no—
151D42—611no—
152#492—611no—
153#468—612no—
154#461—611no—
155#459—611no—
156#450—612no—
157#449—612no—
158C4×D8—611no—
159#436D6111yescharacteristic, complemented
160C61#327211yescharacteristic, complemented, Sylow
161C2×#41—612no—
162C22×D4—612no—
163C22×D4—1221no—
164AGL(1,ℤ/8)—1228no—
165C2×SD16—612no—
166C2×SD16—612no—
167C2×SD16—612no—
168C2×D8—611no—
169C2×D8—612no—
170C2×M16C2×D6112yescomplemented
171C4⋊Q8—611no—
172#127—611no—
173#123—1222no—
174C22⋊Q8—612no—
175#121—612no—
176#121—1221no—
177#121—1221no—
178#120—1222no—
179C4×D4—611no—
180C4×D4—611no—
181C4×D4C2×D6111yescharacteristic
182C2×C4⋊C4—1221no—
183#107—611no—
184C4⋊C8C2×D6111yescharacteristic, complemented
185#103—612no—
186#102—611no—
187#102—611no—
188#102—612no—
189C22⋊C8C2×D6112yescomplemented
190C4×C8C2×D6111yescharacteristic, complemented
191C24—1222no—
192#41—1224no—
193#41—2442no—
194C2×Q8—612no—
195C2×D4—611no—
196C2×D4—611no—
197C2×D4—612no—
198C2×D4—1224no—
199C2×D4—1222no—
200C2×D4—1222no—
201C2×D4—1221no—
202C2×D4—1222no—
203C2×D4—1221no—
204C2×D4—2442no—
205C2×D4—2444no—
206C2×D4D24411yescharacteristic
207C22×C4—1221no—
208C22×C4—1222no—
209C22×C4—1221no—
210C22×C4C22×D6112yes—
211SD16—1224no—
212SD16—1224no—
213SD16—2442no—
214D8—614no—
215D8—1224no—
216M16—24no—
217C2×C8C22×D6111yescharacteristic
218C2×C8C22×D6112yes—
219C2×C8C22×D6111yescharacteristic
220C4⋊C4—611no—
221C4⋊C4—611no—
222C4⋊C4—1222no—
223C4⋊C4—1221no—
224C4⋊C4—1221no—
225C4⋊C4D24411yescharacteristic
226C22⋊C4—1222no—
227C22⋊C4—1221no—
228C22⋊C4—1221no—
229C22⋊C4—1222no—
230C22⋊C4D24412yes—
231C42C22×D6111yescharacteristic
232C23—1221no—
233C23—1221no—
234C23—1222no—
235C23—4882no—
236C23—2444no—
237C23—2444no—
238C23C2×D24412yes—
239Q8—1222no—
240Q8—1222no—
241D4—22no—
242D4—612no—
243D4—612no—
244D4—1222no—
245D4—1221no—
246D4—1221no—
247D4—1222no—
248D4—4881no—
249D4—2444no—
250D4—2444no—
251D4—2444no—
252D4—2442no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1222no—
258C2×C4—2444no—
259C2×C4—2442no—
260C2×C4—2442no—
261C2×C4C2×D24411yescharacteristic
262C2×C4C2×D24412yes—
263C2×C4C2×D24411yescharacteristic
264C2×C4C23×D6111yescharacteristic
265C8—22no—
266C8—21no—
267C8D4×D6112yescomplemented
268C22—22no—
269C22—22no—
270C22—22no—
271C22—1222no—
272C22—1222no—
273C22—4888no—
274C22—2442no—
275C22—2442no—
276C22—2442no—
277C22—2441no—
278C22—2441no—
279C22—2441no—
280C22—2441no—
281C22C22×D24411yescharacteristic
282C4—21no—
283C4—22no—
284C4—2441no—
285C4—2441no—
286C4—2442no—
287C4#1451980512yescomplemented
288C4C2×D4×D6111yescharacteristic
289C4#1451982311yescharacteristic
290C2—42no—
291C2—4882no—
292C2—2442no—
293C2—2442no—
294C2D4×D24411yescharacteristic
295C2C2×#1451980511yescharacteristic
296C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#436C2
socleC22×C61C22×D4
hypercenter#436D61
hypocenterC61#3272
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. #16840417C2semidirect
3. D4×D244C2semidirect
4. #16840135C2semidirect
5. #16840008C2semidirect
6. #16839968C2semidirect
7. #16839958C2semidirect
8. #16839915C2semidirect
9. #16839909C2semidirect
10. C4×D488C2semidirect
11. C61×#436C2semidirect
12. C2×#11758222C22semidirect
17. C2×#11758190C22semidirect
18. C2×#11758190C22semidirect
20. C2×D488C22semidirect
21. #14519777C22semidirect
24. #14519756C22semidirect
30. C4×D244C22semidirect
32. #14519711C22semidirect
33. #14519702C22semidirect
35. #14519699C22semidirect
36. #14519699C22semidirect
37. C2×M16×C61C22semidirect
39. C4⋊C8×C61C22semidirect
40. C22⋊C8×C61C22semidirect
41. C4×C8×C61C22semidirect
79. D488D4semidirect
110. D244C2×D4semidirect
118. C8×C61C2×D4semidirect
135. C4×C61AGL(1,ℤ/8)semidirect
159. #436D61semidirect
160. C61#3272semidirect
170. C2×M16C2×D61semidirect
184. C4⋊C8C2×D61semidirect
189. C22⋊C8C2×D61semidirect
190. C4×C8C2×D61semidirect
267. C8D4×D61semidirect
287. C4#14519805semidirect