Finite Group Databasebeta

← #21458062

Subgroups — #21458062

Order 7808.

460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#16840477C211yesmaximal, characteristic, complemented
2D4×D244C211yesmaximal, characteristic, complemented
3#16840109C211yesmaximal, characteristic, complemented
4#16840087C212yesmaximal, complemented
5#16840053C211yesmaximal, characteristic, complemented
6#16840015C212yesmaximal, complemented
7#16839958C211yesmaximal, characteristic, complemented
8#16839898C212yesmaximal, complemented
9C4×D488C211yesmaximal, characteristic, complemented
10#16839768C212yesmaximal, complemented
11C61×#436C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C2×D4×D61—21no—
14C2×D488C2211yescharacteristic
15C2×D488C2212yescomplemented
16#14519777C2211yescharacteristic, complemented
17#14519774C2211yescharacteristic
18#14519763—22no—
19#14519752—21no—
20#14519751C2212yes—
21#14519751C2212yescomplemented
22#14519748—21no—
23#14519747—22no—
24C4×D244C2211yescharacteristic
25C4×D244C2211yescharacteristic, complemented
26#14519736C2212yescomplemented
27#14519735—21no—
28#14519711C2211yescharacteristic, complemented
29#14519709C2212yescomplemented
30#14519699C2211yescharacteristic
31#14519699C2212yes—
32#14519699C2212yescomplemented
33#14519699C2211yescharacteristic, complemented
34#14519699C2212yescomplemented
35#14519699C2212yescomplemented
36C2×M16×C61C2212yescomplemented
37C4×D4×C61C2211yescharacteristic
38C4⋊C8×C61C2211yescharacteristic, complemented
39C22⋊C8×C61C2212yescomplemented
40C4×C8×C61C2211yescharacteristic, complemented
41C23×D61—22no—
42C2×D4×C61D411yescharacteristic
43C22×C4×C61C2312yes—
44C2×C22⋊D61—22no—
45C2×C22⋊D61—22no—
46D4×D61—44no—
47C2×D244—24no—
48C2×D244—21no—
49C2×D244—22no—
50C2×D244—21no—
51C2×D244—42no—
52C2×D244C2312yes—
53C2×D244C2311yescharacteristic
54C2×D244C2311yescharacteristic
55C2×C4×D61—21no—
56C2×C4×D61—21no—
57C2×Dic122—21no—
58M16×C61—42no—
59C2×C8×C61C2311yescharacteristic
60C2×C8×C61C2311yescharacteristic
61C2×C8×C61C2312yes—
62C4⋊C4×C61D411yescharacteristic
63C22⋊C4×C61D412yes—
64C42×C61C2311yescharacteristic
65C22⋊Dic61—22no—
66#11758198—22no—
67#11758198—21no—
68#11758198—21no—
69#11758198—22no—
70C4⋊Dic61—21no—
71C4⋊Dic61C2312yes—
72C4⋊Dic61C2311yescharacteristic
73C4⋊Dic61C2311yescharacteristic
74C4×Dic61—22no—
75D488—22no—
76D488—42no—
77C23×C61C2×D412yes—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—22no—
81C22×D61—44no—
82C22×D61—44no—
83C22×D61—82no—
84D4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61C2×D412yes—
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2411yescharacteristic
91C22⋊D61—44no—
92C22⋊D61—82no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61—21no—
96D244—21no—
97D244—22no—
98D244—21no—
99D244—21no—
100D244—22no—
101D244—44no—
102D244—42no—
103D244—81no—
104D244#4112yes—
105C4×D61—42no—
106C4×D61—42no—
107Dic122—81no—
108C8×C61—21no—
109C8×C61—22no—
110C8×C61—21no—
111C22×C61—22no—
112C22×C61—22no—
113C22×C61—22no—
114C22×C61C22×D411yescharacteristic
115C2×D61—22no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—42no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—41no—
124C2×D61—88no—
125C4×C61—22no—
126C4×C61—21no—
127C4×C61AGL(1,ℤ/8)12yes—
128C4×C61C2×#4111yescharacteristic
129C4×C61H(5,𝔽2)11yescharacteristic
130Dic61—41no—
131Dic61—41no—
132Dic61—42no—
133#3325—611nomaximal, Sylow
134C2×C61—42no—
135C2×C61#54611yescharacteristic
136C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C61#57611yescharacteristic
138D61—42no—
139D61—81no—
140D61—82no—
141#555—611no—
142D42—611no—
143#486—611no—
144#482—612no—
145#476—611no—
146#469—612no—
147#459—611no—
148#447—612no—
149C4×D8—611no—
150#436D6111yescharacteristic, complemented
151#418—612no—
152C61#332511yescharacteristic, complemented, Sylow
153C22×D4—612no—
154C22×D4—1221no—
155C2×D8—611no—
156C2×D8—612no—
157C2×M16C2×D6112yescomplemented
158C4⋊Q8—611no—
159#127—611no—
160#124—1222no—
161#121—612no—
162#121—612no—
163#121—1221no—
164#121—1221no—
165#120—1222no—
166C4×D4—611no—
167C4×D4—611no—
168C4×D4C2×D6111yescharacteristic
169#117—612no—
170#117—1221no—
171#107—611no—
172#106—612no—
173C4⋊C8C2×D6111yescharacteristic, complemented
174#102—611no—
175#102—612no—
176#102—612no—
177#102—612no—
178#102—611no—
179#102—612no—
180C22⋊C8C2×D6112yescomplemented
181C4×C8C2×D6111yescharacteristic, complemented
182C24—1222no—
183C2×Q8—1221no—
184C2×D4—611no—
185C2×D4—612no—
186C2×D4—611no—
187C2×D4—1224no—
188C2×D4—1222no—
189C2×D4—1222no—
190C2×D4—1221no—
191C2×D4—1222no—
192C2×D4—1221no—
193C2×D4—2442no—
194C2×D4—2444no—
195C2×D4D24411yescharacteristic
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4C22×D6112yes—
199D8—1222no—
200D8—2442no—
201M16—42no—
202C2×C8C22×D6111yescharacteristic
203C2×C8C22×D6111yescharacteristic
204C2×C8C22×D6112yes—
205C4⋊C4—612no—
206C4⋊C4—611no—
207C4⋊C4—611no—
208C4⋊C4—1221no—
209C4⋊C4D24411yescharacteristic
210C22⋊C4—1222no—
211C22⋊C4—1222no—
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C22⋊C4—1222no—
215C22⋊C4D24412yes—
216C42—1222no—
217C42C22×D6111yescharacteristic
218C23—1221no—
219C23—1221no—
220C23—1222no—
221C23—4882no—
222C23—2444no—
223C23—2444no—
224C23C2×D24412yes—
225Q8—4881no—
226D4—22no—
227D4—612no—
228D4—1221no—
229D4—1222no—
230D4—1221no—
231D4—1221no—
232D4—1222no—
233D4—4881no—
234D4—4882no—
235D4—2444no—
236D4—2444no—
237D4—2442no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—2442no—
244C2×C4—2442no—
245C2×C4C2×D24412yes—
246C2×C4C2×D24411yescharacteristic
247C2×C4C2×D24411yescharacteristic
248C2×C4C23×D6111yescharacteristic
249C8—21no—
250C8—21no—
251C8—22no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—1222no—
256C22—4888no—
257C22—2441no—
258C22—2442no—
259C22—2441no—
260C22—2442no—
261C22—2442no—
262C22—2441no—
263C22—2441no—
264C22—2441no—
265C22C22×D24411yescharacteristic
266C4—21no—
267C4—22no—
268C4—2441no—
269C4—2441no—
270C4—2442no—
271C4#1451980512yes—
272C4#41×D6111yescharacteristic
273C4#1451982211yescharacteristic
274C2—42no—
275C2—4882no—
276C2—4881no—
277C2—2442no—
278C2#1684040711yescharacteristic
279C2C2×#1451980511yescharacteristic
280C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#436C2
socleC22×C61C22×D4
hypercenter#436D61
hypocenterC61#3325
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. #16840477C2semidirect
2. D4×D244C2semidirect
3. #16840109C2semidirect
4. #16840087C2semidirect
5. #16840053C2semidirect
6. #16840015C2semidirect
7. #16839958C2semidirect
8. #16839898C2semidirect
9. C4×D488C2semidirect
10. #16839768C2semidirect
11. C61×#436C2semidirect
15. C2×D488C22semidirect
16. #14519777C22semidirect
21. #14519751C22semidirect
25. C4×D244C22semidirect
26. #14519736C22semidirect
28. #14519711C22semidirect
29. #14519709C22semidirect
32. #14519699C22semidirect
33. #14519699C22semidirect
34. #14519699C22semidirect
35. #14519699C22semidirect
36. C2×M16×C61C22semidirect
38. C4⋊C8×C61C22semidirect
39. C22⋊C8×C61C22semidirect
40. C4×C8×C61C22semidirect
150. #436D61semidirect
152. C61#3325semidirect
157. C2×M16C2×D61semidirect
173. C4⋊C8C2×D61semidirect
180. C22⋊C8C2×D61semidirect
181. C4×C8C2×D61semidirect