Finite Group Databasebeta

← #21457441

Subgroups — #21457441

Order 7808.

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

normal subgroups only

This group has 556 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#16840433C211yesmaximal, characteristic, complemented
3D4×D244C211yesmaximal, characteristic, complemented
4#16840139C211yesmaximal, characteristic, complemented
5#16840015C212yesmaximal, complemented
6#16839963C211yesmaximal, characteristic, complemented
7#16839958C211yesmaximal, characteristic, complemented
8#16839909C212yesmaximal, complemented
9#16839898C212yesmaximal, complemented
10C4×#11758190C211yesmaximal, characteristic, complemented
11C61×#436C211yesmaximal, characteristic, complemented
12C2×#11758222C2212yescomplemented
13C22×D244C2212yes—
14C2×D4×D61—21no—
15#14519805—28no—
16C2×#11758190C2211yescharacteristic
17C2×#11758190C2212yescomplemented
18C2×D488C2212yes—
19C2×D488C2212yescomplemented
20C2×D488C2212yescomplemented
21#14519774C2211yescharacteristic
22#14519774C2211yescharacteristic, complemented
23#14519773—21no—
24#14519752—21no—
25#14519751C2212yes—
26#14519751C2212yescomplemented
27#14519750—22no—
28#14519747—22no—
29C4×Dic122C2211yescharacteristic, complemented
30C4×D244C2211yescharacteristic
31#14519739—21no—
32#14519709C2211yescharacteristic, complemented
33#14519702C2211yescharacteristic, complemented
34#14519699C2211yescharacteristic
35#14519699C2212yescomplemented
36#14519699C2212yescomplemented
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—
47C2×C22⋊D61—22no—
48D4×D61—44no—
49#11758222—24no—
50#11758222—42no—
51C2×D244—24no—
52C2×D244—21no—
53C2×D244—22no—
54C2×D244—21no—
55C2×D244—21no—
56C2×D244—21no—
57C2×D244—42no—
58C2×D244C2312yes—
59C2×D244C2312yes—
60C2×D244C2311yescharacteristic
61C2×C4×D61—21no—
62C2×C4×D61—22no—
63C2×Dic122C2311yescharacteristic
64M16×C61—24no—
65C2×C8×C61C2311yescharacteristic
66C2×C8×C61C2312yes—
67C2×C8×C61C2311yescharacteristic
68C4⋊C4×C61D411yescharacteristic
69C22⋊C4×C61D412yes—
70C42×C61C2311yescharacteristic
71#11758198—22no—
72#11758198—21no—
73#11758198—22no—
74C4⋊Dic61C2311yescharacteristic
75C4⋊Dic61C2311yescharacteristic
76#11758196—21no—
77C4×Dic61—21no—
78D488—24no—
79D488—24no—
80D488—42no—
81#11758190—24no—
82#11758190D414yescomplemented
83C23×C61C2×D412yes—
84C22×D61—21no—
85C22×D61—22no—
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×D411yescharacteristic
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—44no—
98C22⋊D61—44no—
99C22⋊D61—82no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103D244—22no—
104D244—22no—
105D244—21no—
106D244—22no—
107D244—22no—
108D244—44no—
109D244—42no—
110D244—42no—
111D244—81no—
112D244—81no—
113D244C2×D412yes—
114C4×D61—44no—
115C4×D61—42no—
116Dic122—21no—
117Dic122C2×D412yescomplemented
118C8×C61—22no—
119C8×C61—21no—
120C8×C61C2×D412yescomplemented
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61C22×D411yescharacteristic
125C2×D61—22no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—88no—
135C4×C61—22no—
136C4×C61—21no—
137C4×C61AGL(1,ℤ/8)12yescomplemented
138C4×C61C22×D411yescharacteristic
139C4×C61H(5,𝔽2)11yescharacteristic
140Dic61—22no—
141Dic61—41no—
142Dic61—41no—
143#3274—611nomaximal, Sylow
144C2×C61—42no—
145C2×C61D4211yescharacteristic
146C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C61#57611yescharacteristic
148D61—42no—
149D61—82no—
150D61—82no—
151C2×AGL(1,ℤ/8)—612no—
152#550—611no—
153D42—611no—
154#493—611no—
155#469—612no—
156#460—611no—
157#459—611no—
158#449—612no—
159#447—612no—
160C4×SD16—611no—
161#436D6111yescharacteristic, complemented
162C61#327411yescharacteristic, complemented, Sylow
163C2×#41—612no—
164C22×D4—612no—
165C22×D4—1221no—
166AGL(1,ℤ/8)—1228no—
167C2×SD16—611no—
168C2×SD16—612no—
169C2×D8—612no—
170C2×D8—612no—
171C2×D8—612no—
172C2×M16C2×D6112yescomplemented
173#127—611no—
174#127—611no—
175#127—1221no—
176#121—612no—
177#121—612no—
178#121—1221no—
179#121—1222no—
180#120—1222no—
181C4×Q8—611no—
182C4×D4—611no—
183C4×D4—1221no—
184C4×D4C2×D6111yescharacteristic
185#106—611no—
186C4⋊C8C2×D6111yescharacteristic, complemented
187#103—611no—
188#102—611no—
189#102—612no—
190#102—612no—
191C22⋊C8C2×D6112yescomplemented
192C4×C8C2×D6111yescharacteristic, complemented
193C24—1222no—
194#41—1224no—
195#41—2442no—
196C2×Q8—611no—
197C2×D4—611no—
198C2×D4—612no—
199C2×D4—612no—
200C2×D4—1224no—
201C2×D4—1222no—
202C2×D4—1222no—
203C2×D4—1222no—
204C2×D4—1221no—
205C2×D4—1221no—
206C2×D4—1221no—
207C2×D4—1222no—
208C2×D4—1221no—
209C2×D4—2442no—
210C2×D4—2444no—
211C2×D4D24411yescharacteristic
212C22×C4—1221no—
213C22×C4—1222no—
214C22×C4C22×D6112yes—
215SD16—614no—
216SD16—1224no—
217D8—1224no—
218D8—1224no—
219D8—2442no—
220M16—24no—
221C2×C8C22×D6111yescharacteristic
222C2×C8C22×D6112yes—
223C2×C8C22×D6111yescharacteristic
224C4⋊C4—611no—
225C4⋊C4—611no—
226C4⋊C4—1221no—
227C4⋊C4D24411yescharacteristic
228C22⋊C4—1221no—
229C22⋊C4—1222no—
230C22⋊C4—1222no—
231C22⋊C4D24412yes—
232C42—1221no—
233C42C22×D6111yescharacteristic
234C23—1221no—
235C23—1222no—
236C23—1222no—
237C23—4882no—
238C23—2444no—
239C23—2444no—
240C23C2×D24412yes—
241Q8—612no—
242Q8—1221no—
243D4—22no—
244D4—612no—
245D4—1222no—
246D4—1222no—
247D4—1221no—
248D4—1222no—
249D4—1222no—
250D4—4881no—
251D4—4881no—
252D4—4882no—
253D4—2444no—
254D4—2444no—
255D4—2444no—
256D4—2442no—
257D4—2442no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—2444no—
264C2×C4—2442no—
265C2×C4C2×D24411yescharacteristic
266C2×C4C2×D24412yes—
267C2×C4C2×D24411yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—22no—
270C8—21no—
271C8D4×D6112yescomplemented
272C22—22no—
273C22—22no—
274C22—22no—
275C22—1222no—
276C22—4888no—
277C22—2442no—
278C22—2442no—
279C22—2442no—
280C22—2442no—
281C22—2442no—
282C22—2442no—
283C22—2441no—
284C22—2441no—
285C22C22×D24411yescharacteristic
286C4—21no—
287C4—22no—
288C4—1222no—
289C4—2441no—
290C4—2441no—
291C4#1451980512yescomplemented
292C4C2×D4×D6111yescharacteristic
293C4#1451982311yescharacteristic
294C2—42no—
295C2—4882no—
296C2—4882no—
297C2—2442no—
298C2D4×D24411yescharacteristic
299C2C2×#1451980511yescharacteristic
300C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#436C2
socleC22×C61C22×D4
hypercenter#436D61
hypocenterC61#3274
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. #16840433C2semidirect
3. D4×D244C2semidirect
4. #16840139C2semidirect
5. #16840015C2semidirect
6. #16839963C2semidirect
7. #16839958C2semidirect
8. #16839909C2semidirect
9. #16839898C2semidirect
10. C4×#11758190C2semidirect
11. C61×#436C2semidirect
12. C2×#11758222C22semidirect
17. C2×#11758190C22semidirect
19. C2×D488C22semidirect
20. C2×D488C22semidirect
22. #14519774C22semidirect
26. #14519751C22semidirect
29. C4×Dic122C22semidirect
32. #14519709C22semidirect
33. #14519702C22semidirect
35. #14519699C22semidirect
36. #14519699C22semidirect
37. C2×M16×C61C22semidirect
39. C4⋊C8×C61C22semidirect
40. C22⋊C8×C61C22semidirect
41. C4×C8×C61C22semidirect
82. #11758190D4semidirect
117. Dic122C2×D4semidirect
120. C8×C61C2×D4semidirect
137. C4×C61AGL(1,ℤ/8)semidirect
161. #436D61semidirect
162. C61#3274semidirect
172. C2×M16C2×D61semidirect
186. C4⋊C8C2×D61semidirect
191. C22⋊C8C2×D61semidirect
192. C4×C8C2×D61semidirect
271. C8D4×D61semidirect
291. C4#14519805semidirect