Finite Group Databasebeta

← #21458061

Subgroups — #21458061

Order 7808.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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
2#16840108C211yesmaximal, characteristic, complemented
3#16840083C212yesmaximal, complemented
4#16840052C211yesmaximal, characteristic, complemented
5#16840013C212yesmaximal, complemented
6#16839954C211yesmaximal, characteristic, complemented
7#16839896C212yesmaximal, complemented
8C4×#11758199C211yesmaximal, characteristic, complemented
9#16839840C211yesmaximal, characteristic, complemented
10#16839767C212yesmaximal, complemented
11D42×C61C211yesmaximal, characteristic, complemented
12C2×#11758199C2211yescharacteristic
13C2×#11758199C2212yescomplemented
14C2×#11758194C2212yescomplemented
15#14519777C2211yescharacteristic, complemented
16#14519763—22no—
17#14519751C2212yescomplemented
18#14519748—21no—
19C4×D244C2211yescharacteristic, complemented
20#14519736C2212yescomplemented
21#14519735—21no—
22#14519710C2211yescharacteristic, complemented
23#14519708C2212yescomplemented
24C4⋊#92418C2211yescharacteristic, complemented
25#14519698C2211yescharacteristic
26#14519698C2212yes—
27#14519698C2212yescomplemented
28#14519698C2212yescomplemented
29#14519698C2212yescomplemented
30#14519697C2211yescharacteristic, complemented
31C22⋊#92418C2212yescomplemented
32C4×#92418C2211yescharacteristic, complemented
33C22×D4×C61—21no—
34C22×D4×C61C2212yes—
35#127×C61C2211yescharacteristic
36#121×C61—21no—
37#121×C61C2212yes—
38#120×C61—22no—
39C4×D4×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic
41C24×C61—22no—
42C2×D4×C61—24no—
43C2×D4×C61—22no—
44C2×D4×C61—22no—
45C2×D4×C61—21no—
46C2×D4×C61—21no—
47C2×D4×C61—42no—
48C2×D4×C61—44no—
49C2×D4×C61D411yescharacteristic
50C2×D4×C61C2312yes—
51C2×D4×C61C2311yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61C2312yes—
54C2×C22⋊D61—22no—
55C2×D244C2311yescharacteristic
56C2×C4×D61—21no—
57C2×Dic122—21no—
58C4⋊C4×C61D411yescharacteristic
59C4⋊C4×C61C2311yescharacteristic
60C22⋊C4×C61—21no—
61C22⋊C4×C61—22no—
62C22⋊C4×C61D412yes—
63C42×C61C2311yescharacteristic
64C22⋊Dic61—22no—
65#11758199—22no—
66#11758199—42no—
67#11758198—22no—
68#11758198—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61C2312yes—
71C4⋊Dic61C2311yescharacteristic
72C4×Dic61—22no—
73#11758194—42no—
74C2×#92418C2311yescharacteristic
75C2×#92418C2311yescharacteristic
76C2×#92418C2312yes—
77C23×C61—21no—
78C23×C61—22no—
79C23×C61—44no—
80C23×C61—44no—
81C23×C61—82no—
82C23×C61C2×D412yes—
83C22×D61—21no—
84D4×C61—22no—
85D4×C61—22no—
86D4×C61—21no—
87D4×C61—22no—
88D4×C61—44no—
89D4×C61—44no—
90D4×C61—42no—
91D4×C61—81no—
92D4×C61#4112yes—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—42no—
97C2×C4×C61C2×D412yes—
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2411yescharacteristic
101C22⋊D61—82no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104D244—21no—
105D244—21no—
106C4×D61—42no—
107Dic122—81no—
108#92418—21no—
109#92418—21no—
110#92418—22no—
111C22×C61—22no—
112C22×C61—22no—
113C22×C61—22no—
114C22×C61—22no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—88no—
121C22×C61C22×D411yescharacteristic
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—41no—
125C4×C61—22no—
126C4×C61—21no—
127C4×C61—41no—
128C4×C61AGL(1,ℤ/8)12yes—
129C4×C61C2×#4111yescharacteristic
130C4×C61H(5,𝔽2)11yescharacteristic
131Dic61—41no—
132Dic61—42no—
133#3325—611nomaximal, Sylow
134C2×C61—42no—
135C2×C61—42no—
136C2×C61—82no—
137C2×C61#54611yescharacteristic
138C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C61#57611yescharacteristic
140D61—81no—
141#555—611no—
142D42D6111yescharacteristic, complemented
143#486—611no—
144#482—612no—
145#476—611no—
146#469—612no—
147#459—611no—
148#447—612no—
149C4×D8—611no—
150#436—611no—
151#418—612no—
152C61#332511yescharacteristic, complemented, Sylow
153C22×D4—21no—
154C22×D4C2×D6112yes—
155C2×D8—611no—
156C2×D8—612no—
157C2×M16—612no—
158C4⋊Q8—611no—
159#127C2×D6111yescharacteristic
160#124—1222no—
161#121—21no—
162#121—612no—
163#121—1221no—
164#121C2×D6112yes—
165#120—22no—
166C4×D4—611no—
167C4×D4C2×D6111yescharacteristic
168C4×D4C2×D6111yescharacteristic
169#117—612no—
170#117—1221no—
171#107—611no—
172#106—612no—
173C4⋊C8—611no—
174#102—611no—
175#102—612no—
176#102—612no—
177#102—612no—
178#102—612no—
179#102—611no—
180C22⋊C8—612no—
181C4×C8—611no—
182C24—22no—
183C2×Q8—1221no—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—42no—
190C2×D4—44no—
191C2×D4—611no—
192C2×D4—1222no—
193C2×D4C22⋊D6111yescharacteristic
194C2×D4C22×D6112yes—
195C2×D4C22×D6111yescharacteristic
196C22×C4—21no—
197C22×C4—1221no—
198C22×C4C22×D6112yes—
199D8—1222no—
200D8—2442no—
201M16—2442no—
202C2×C8—611no—
203C2×C8—611no—
204C2×C8—612no—
205C4⋊C4—612no—
206C4⋊C4—611no—
207C4⋊C4—1221no—
208C4⋊C4C22⋊D6111yescharacteristic
209C4⋊C4C22×D6111yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—22no—
212C22⋊C4—1222no—
213C22⋊C4—1222no—
214C22⋊C4—1221no—
215C22⋊C4C22⋊D6112yes—
216C42—1222no—
217C42C22×D6111yescharacteristic
218C23—21no—
219C23—22no—
220C23—44no—
221C23—44no—
222C23—82no—
223C23—1221no—
224C23C2×C22⋊D6112yes—
225Q8—4881no—
226D4—22no—
227D4—21no—
228D4—22no—
229D4—22no—
230D4—44no—
231D4—44no—
232D4—42no—
233D4—81no—
234D4—1221no—
235D4—1221no—
236D4—4882no—
237D4#1175822412yes—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—1221no—
243C2×C4—1222no—
244C2×C4—2442no—
245C2×C4C2×C22⋊D6112yes—
246C2×C4C2×C22⋊D6111yescharacteristic
247C2×C4C2×C22⋊D6111yescharacteristic
248C2×C4C23×D6111yescharacteristic
249C8—1221no—
250C8—1221no—
251C8—1222no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—41no—
257C22—41no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—88no—
262C22—2441no—
263C22—2441no—
264C22—2441no—
265C22C22×C22⋊D6111yescharacteristic
266C4—21no—
267C4—22no—
268C4—41no—
269C4—2441no—
270C4—2442no—
271C4#1451980312yes—
272C4C2×#1175822411yescharacteristic
273C4#1451982211yescharacteristic
274C2—42no—
275C2—42no—
276C2—82no—
277C2—4881no—
278C2#1684040611yescharacteristic
279C2C2×#1451980311yescharacteristic
280C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingD42×C61C2
socleC22×C61C22×D4
hypercenterD42D61
hypocenterC61#3325
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #16840477C2semidirect
2. #16840108C2semidirect
3. #16840083C2semidirect
4. #16840052C2semidirect
5. #16840013C2semidirect
6. #16839954C2semidirect
7. #16839896C2semidirect
8. C4×#11758199C2semidirect
9. #16839840C2semidirect
10. #16839767C2semidirect
11. D42×C61C2semidirect
13. C2×#11758199C22semidirect
14. C2×#11758194C22semidirect
15. #14519777C22semidirect
17. #14519751C22semidirect
19. C4×D244C22semidirect
20. #14519736C22semidirect
22. #14519710C22semidirect
23. #14519708C22semidirect
24. C4⋊#92418C22semidirect
27. #14519698C22semidirect
28. #14519698C22semidirect
29. #14519698C22semidirect
30. #14519697C22semidirect
31. C22⋊#92418C22semidirect
32. C4×#92418C22semidirect
142. D42D61semidirect
152. C61#3325semidirect