Finite Group Databasebeta

← #21457505

Subgroups — #21457505

Order 7808.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14519796C211yesmaximal, characteristic, complemented
2C2×D8×D61C211yesmaximal, characteristic, complemented
3#16840407C212yesmaximal, complemented
4#16840146C211yesmaximal, characteristic, complemented
5#16840004C211yesmaximal, characteristic, complemented
6#16839999C211yesmaximal, characteristic, complemented
7#16839977C212yesmaximal, complemented
8#16839914C212yesmaximal, complemented
9#16839908C212yesmaximal, complemented
10C8×D244C211yesmaximal, characteristic, complemented
11C4×D8×C61C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yescomplemented
13C2×D4×D61C2212yes—
14#14519796—24no—
15C2×Dic244C2211yescharacteristic, complemented
16C2×#11758190C2212yescomplemented
17C2×#11758200C2212yescomplemented
18C2×D488C2211yescharacteristic
19C2×#11758199C2212yes—
20D8×D61—24no—
21C2×C8×D61C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic, complemented
23#14519765C2212yescomplemented
24#14519761—22no—
25#14519757C2212yes—
26#14519752C2212yescomplemented
27#14519751—22no—
28#14519747—22no—
29C4×D244C2211yescharacteristic
30C2×#11758198—22no—
31C4⋊#92418C2211yescharacteristic, complemented
32#14519700C2212yescomplemented
33#14519697C2212yescomplemented
34#14519689C2211yescharacteristic
35#14519689C2211yescharacteristic, complemented
36C2×D8×C61C2211yescharacteristic
37C4×D4×C61C2212yescomplemented
38#107×C61C2211yescharacteristic, complemented
39#102×C61C2212yescomplemented
40C4×C8×C61C2211yescharacteristic, complemented
41C23×D61—22no—
42C2×D4×C61C2312yes—
43C22×C4×C61—22no—
44C2×C22⋊D61—22no—
45C2×C22⋊D61—22no—
46C22×Dic61—22no—
47#11758224—24no—
48#11758224—42no—
49D4×D61—24no—
50D4×D61—42no—
51C2×D244—22no—
52C2×D244D411yescharacteristic
53C2×D244C2312yes—
54C2×C4×D61C2311yescharacteristic
55C2×C4×D61C2311yescharacteristic
56C2×Dic122C2312yes—
57D8×C61D414yescomplemented
58C2×C8×C61C2311yescharacteristic
59C2×C8×C61C2311yescharacteristic
60C4⋊C4×C61C2312yes—
61C22⋊C4×C61—22no—
62C42×C61C2311yescharacteristic
63#11758200—24no—
64#11758199—24no—
65#11758198—22no—
66#11758198—22no—
67#11758198—22no—
68#11758198—22no—
69#11758198D411yescharacteristic
70#11758198D411yescharacteristic
71C4⋊Dic61—22no—
72C4⋊Dic61D411yescharacteristic
73C2×#92418C2311yescharacteristic
74C2×#92418C2311yescharacteristic
75Dic244—22no—
76D488—22no—
77#11758190—42no—
78C8×D61—22no—
79C8×D61—22no—
80C23×C61—22no—
81C22×D61—22no—
82C22×D61—44no—
83C22×D61—44no—
84C22×D61—82no—
85C22×D61C2×D411yescharacteristic
86C22×D61C2×D411yescharacteristic
87D4×C61—22no—
88D4×C61C2×D414yes—
89C2×C4×C61—22no—
90C2×C4×C61—82no—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2411yescharacteristic
94C22⋊D61—44no—
95C22⋊D61—44no—
96C2×Dic61—22no—
97C2×Dic61—44no—
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100D244—22no—
101D244—22no—
102D244—22no—
103D244—82no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—21no—
108Dic122—22no—
109Dic122—22no—
110C8×C61—21no—
111C8×C61C2×D412yes—
112#92418—21no—
113#92418—21no—
114C22×C61—24no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61C22×D411yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—88no—
127C2×D61#13512yescomplemented
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—42no—
131C4×C61C22×D411yescharacteristic
132C4×C61H(5,𝔽2)11yescharacteristic
133Dic61—21no—
134Dic61—21no—
135Dic61—42no—
136#3280—611nomaximal, Sylow
137C2×C61—44no—
138C2×C61D4211yescharacteristic
139C2×C61C2×#13511yescharacteristic
140C2×C61#57611yescharacteristic
141D61—22no—
142D61—41no—
143D61—82no—
144C2×#135—611no—
145C22×D8—611no—
146#546—612no—
147#495—611no—
148#467—611no—
149#466—611no—
150#463—612no—
151#450—612no—
152#449—612no—
153C4×D8D6111yescharacteristic, complemented
154C8×D4—611no—
155C61#328011yescharacteristic, complemented, Sylow
156C2×#41—612no—
157C22×D4—612no—
158#135—1224no—
159C2×Q16—611no—
160C2×SD16—612no—
161C2×SD16—612no—
162C2×D8—612no—
163C2×D8—611no—
164C2×D8—1224no—
165C2×D8C2×D6111yescharacteristic
166C22×C8—611no—
167C22×C8—611no—
168#124—612no—
169#123—1222no—
170C22⋊Q8—612no—
171#121—612no—
172#121—1222no—
173#120—1222no—
174C4×D4—611no—
175C4×D4C2×D6112yescomplemented
176C2×C22⋊C4—1222no—
177#107C2×D6111yescharacteristic, complemented
178C4⋊C8—611no—
179#103—612no—
180#102—612no—
181#102C2×D6112yescomplemented
182C22⋊C8—611no—
183C22⋊C8—611no—
184C4×C8C2×D6111yescharacteristic, complemented
185C24—1222no—
186#41—1224no—
187#41—2442no—
188C2×Q8—612no—
189C2×D4—611no—
190C2×D4—612no—
191C2×D4—1222no—
192C2×D4—1222no—
193C2×D4—1224no—
194C2×D4—1222no—
195C2×D4—2442no—
196C2×D4C22×D6112yes—
197C22×C4—22no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—1222no—
201Q16—1222no—
202SD16—1224no—
203SD16—2442no—
204D8—1224no—
205D8—1222no—
206D8D24414yescomplemented
207C2×C8—611no—
208C2×C8—611no—
209C2×C8—1222no—
210C2×C8—1222no—
211C2×C8C22×D6111yescharacteristic
212C2×C8C22×D6111yescharacteristic
213C4⋊C4—611no—
214C4⋊C4—1222no—
215C4⋊C4C22×D6112yes—
216C22⋊C4—22no—
217C22⋊C4—611no—
218C22⋊C4—611no—
219C22⋊C4—1222no—
220C22⋊C4—1222no—
221C22⋊C4—1222no—
222C22⋊C4—1222no—
223C42C22×D6111yescharacteristic
224C23—22no—
225C23—611no—
226C23—611no—
227C23—1222no—
228C23—4882no—
229C23—2444no—
230C23—2444no—
231Q8—1222no—
232Q8—1222no—
233D4—22no—
234D4—1222no—
235D4—1222no—
236D4—1222no—
237D4—4882no—
238D4—2444no—
239D4—2444no—
240D4C2×D24414yes—
241C2×C4—22no—
242C2×C4—82no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—2444no—
251C2×C4D4×D6111yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4C23×D6111yescharacteristic
254C8—21no—
255C8—1221no—
256C8—1221no—
257C8C2×D24412yes—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—612no—
262C22—1221no—
263C22—1221no—
264C22—1221no—
265C22—1221no—
266C22—1221no—
267C22—4888no—
268C22—2442no—
269C22—2442no—
270C22—2442no—
271C22C2×D4×D6111yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—1221no—
276C4—1221no—
277C4—2442no—
278C4C22×D24411yescharacteristic
279C4#1451982311yescharacteristic
280C2—44no—
281C2—1222no—
282C2—4882no—
283C2—2441no—
284C2D4×D24411yescharacteristic
285C2#135×D6111yescharacteristic
286C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×D8×C61C2
socleC22×C61C22×D4
hypercenterC4×D8D61
hypocenterC61#3280
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14519796C2semidirect
2. C2×D8×D61C2semidirect
3. #16840407C2semidirect
4. #16840146C2semidirect
5. #16840004C2semidirect
6. #16839999C2semidirect
7. #16839977C2semidirect
8. #16839914C2semidirect
9. #16839908C2semidirect
10. C8×D244C2semidirect
11. C4×D8×C61C2semidirect
12. C2×#11758224C22semidirect
15. C2×Dic244C22semidirect
16. C2×#11758190C22semidirect
17. C2×#11758200C22semidirect
22. C2×C8×D61C22semidirect
23. #14519765C22semidirect
26. #14519752C22semidirect
31. C4⋊#92418C22semidirect
32. #14519700C22semidirect
33. #14519697C22semidirect
35. #14519689C22semidirect
37. C4×D4×C61C22semidirect
38. #107×C61C22semidirect
39. #102×C61C22semidirect
40. C4×C8×C61C22semidirect
57. D8×C61D4semidirect
127. C2×D61#135semidirect
153. C4×D8D61semidirect
155. C61#3280semidirect
175. C4×D4C2×D61semidirect
177. #107C2×D61semidirect
181. #102C2×D61semidirect
184. C4×C8C2×D61semidirect
206. D8D244semidirect