Finite Group Databasebeta

← #21455920

Subgroups — #21455920

Order 7808.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840317C211yesmaximal, characteristic, complemented
2C4×D4×D61C211yesmaximal, characteristic
3#16840099C212yesmaximal, complemented
4#16840039C211yesmaximal, characteristic, complemented
5#16839968C211yesmaximal, characteristic, complemented
6#16839967C211yesmaximal, characteristic, complemented
7#16839914C212yesmaximal
8#16839861C212yesmaximal, complemented
9#16839859C212yesmaximal, complemented
10#16839818C211yesmaximal, characteristic, complemented
11C61×#474C211yesmaximal, characteristic, complemented
12C2×D4×D61C2211yescharacteristic
13C22×C4×D61—21no—
14C2×#11758190C2212yes—
15C2×#11758200C2212yes—
16#14519777C2211yescharacteristic, complemented
17#14519768—21no—
18#14519757C2212yes—
19#14519753—21no—
20Q8×Dic61—21no—
21#14519742C2212yescomplemented
22C4×D244C2211yescharacteristic
23D4×Dic61C2211yescharacteristic
24#14519739C2211yescharacteristic
25C4×C22⋊D61—21no—
26#14519737—21no—
27#14519735—21no—
28C4⋊C4×D61C2211yescharacteristic
29C22⋊C4×D61—21no—
30C42×D61C2211yescharacteristic
31#14519710C2212yescomplemented
32C4⋊#92418C2211yescharacteristic, complemented
33#14519702C2212yescomplemented
34#14519700C2212yescomplemented
35#14519697C2212yes—
36#14519689C2212yes—
37#14519687C2212yescomplemented
38C4⋊Q8×C61C2211yescharacteristic, complemented
39C4×D4×C61C2211yescharacteristic
40#107×C61C2212yescomplemented
41C4⋊C8×C61C2211yescharacteristic, complemented
42#102×C61C2212yes—
43C23×D61—21no—
44C2×Q8×C61—21no—
45C2×D4×C61C2311yescharacteristic
46C22×C4×C61—21no—
47C2×C22⋊D61—21no—
48C22×Dic61—21no—
49D4×D61—22no—
50D4×D61—22no—
51C2×D244C2311yescharacteristic
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—44no—
56C2×C4×D61D411yescharacteristic
57C2×C4×D61D411yescharacteristic
58C2×C4×D61C2311yescharacteristic
59C2×Dic122C2312yes—
60C2×C8×C61C2312yes—
61C4⋊C4×C61—21no—
62C4⋊C4×C61C2312yes—
63C4⋊C4×C61C2311yescharacteristic
64C22⋊C4×C61—21no—
65C42×C61C2311yescharacteristic
66C22⋊Dic61—21no—
67#11758200—24no—
68#11758198—22no—
69#11758198—21no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61—22no—
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76#11758196—22no—
77C4×Dic61—22no—
78C4×Dic61D411yescharacteristic
79C4×Dic61D411yescharacteristic
80C4×Dic61C2311yescharacteristic
81C2×#92418C2312yes—
82#11758190—24no—
83C23×C61—21no—
84C22×D61—24no—
85C22×D61—21no—
86C22×D61—42no—
87C22×D61—42no—
88C22×D61C2×D411yescharacteristic
89Q8×C61—42no—
90D4×C61—21no—
91D4×C61#4112yes—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—42no—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2411yescharacteristic
98C22⋊D61—24no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—42no—
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105D244—21no—
106D244#4112yes—
107C4×D61—22no—
108C4×D61—22no—
109C4×D61—21no—
110C4×D61—21no—
111C4×D61—42no—
112C4×D61—42no—
113C4×D61—42no—
114Dic122—22no—
115Dic122—22no—
116C8×C61—22no—
117#92418—22no—
118C22×C61—22no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61C22×D411yescharacteristic
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—22no—
125C2×D61—48no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61#13712yes—
129C4×C61—21no—
130C4×C61—41no—
131C4×C61—42no—
132C4×C61AGL(1,ℤ/8)12yes—
133C4×C61C2×#4111yescharacteristic
134C4×C61C2×#4111yescharacteristic
135Dic61—21no—
136Dic61—21no—
137Dic61—21no—
138Dic61—42no—
139Dic61—41no—
140#3110—611nomaximal, Sylow
141C2×C61—42no—
142C2×C61#52511yescharacteristic
143C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C61C2×#13711yescharacteristic
145D61—22no—
146D61—42no—
147#533—611no—
148C2×C4×D4—611no—
149#484—612no—
150#474—611no—
151#474D6111yescharacteristic, complemented
152#461—611no—
153#461—611no—
154#450—612no—
155#440—612no—
156#440—612no—
157#432—611no—
158C61#311011yescharacteristic, complemented, Sylow
159C22×D4—611no—
160C23×C4—1221no—
161C2×SD16—612no—
162C2×SD16—612no—
163C4⋊Q8—611no—
164C4⋊Q8C2×D6111yescharacteristic, complemented
165#125—1221no—
166C22⋊Q8—612no—
167C22⋊Q8—1221no—
168C4×Q8—612no—
169C4×Q8—1221no—
170C4×D4—611no—
171C4×D4—611no—
172C4×D4—611no—
173C4×D4—1221no—
174C4×D4—1221no—
175C4×D4C2×D6111yescharacteristic
176#117—1221no—
177C2×C4⋊C4—611no—
178C2×C22⋊C4—1221no—
179C2×C42—611no—
180#107—612no—
181#107C2×D6112yescomplemented
182C4⋊C8—611no—
183C4⋊C8C2×D6111yescharacteristic, complemented
184#103—612no—
185#103—612no—
186#102—612no—
187#102C2×D6112yes—
188C22⋊C8—612no—
189#97—612no—
190C24—1221no—
191C2×Q8—21no—
192C2×Q8—612no—
193C2×D4—611no—
194C2×D4—1221no—
195C2×D4—1222no—
196C2×D4—1222no—
197C2×D4C22×D6111yescharacteristic
198C22×C4—21no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4—2444no—
207SD16—1224no—
208SD16—1224no—
209C2×C8—612no—
210C2×C8C22×D6112yes—
211C4⋊C4—21no—
212C4⋊C4—611no—
213C4⋊C4—1221no—
214C4⋊C4—1222no—
215C4⋊C4—1222no—
216C4⋊C4—1221no—
217C4⋊C4—1221no—
218C4⋊C4C22×D6112yes—
219C4⋊C4C22×D6111yescharacteristic
220C22⋊C4—21no—
221C22⋊C4—1221no—
222C22⋊C4—1222no—
223C22⋊C4—1221no—
224C22⋊C4—1221no—
225C42—611no—
226C42—611no—
227C42—611no—
228C42—1222no—
229C42C22×D6111yescharacteristic
230C23—21no—
231C23—611no—
232C23—1224no—
233C23—1221no—
234C23—2442no—
235C23—2442no—
236Q8—42no—
237Q8—1222no—
238Q8—1222no—
239D4—21no—
240D4—612no—
241D4—1224no—
242D4—1221no—
243D4#1175822612yes—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—1222no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1221no—
256C2×C4—2442no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4—2442no—
260C2×C4D4×D6111yescharacteristic
261C2×C4D4×D6111yescharacteristic
262C2×C4C23×D6111yescharacteristic
263C8—22no—
264C8—1222no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—612no—
269C22—1221no—
270C22—1221no—
271C22—1222no—
272C22—2448no—
273C22—2441no—
274C22—2441no—
275C22C2×D4×D6111yescharacteristic
276C4—21no—
277C4—41no—
278C4—42no—
279C4—1221no—
280C4—1221no—
281C4—1221no—
282C4—2442no—
283C4—2441no—
284C4#1451980112yes—
285C4#41×D6111yescharacteristic
286C4C2×#1175822611yescharacteristic
287C2—42no—
288C2—1222no—
289C2—2442no—
290C2#1684027511yescharacteristic
291C2C2×#1451980111yescharacteristic
292C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#474C2
socleC22×C61C22×D4
hypercenter#474D61
hypocenterC61#3110
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840099C2semidirect
4. #16840039C2semidirect
5. #16839968C2semidirect
6. #16839967C2semidirect
8. #16839861C2semidirect
9. #16839859C2semidirect
10. #16839818C2semidirect
11. C61×#474C2semidirect
16. #14519777C22semidirect
21. #14519742C22semidirect
31. #14519710C22semidirect
32. C4⋊#92418C22semidirect
33. #14519702C22semidirect
34. #14519700C22semidirect
37. #14519687C22semidirect
38. C4⋊Q8×C61C22semidirect
40. #107×C61C22semidirect
41. C4⋊C8×C61C22semidirect
151. #474D61semidirect
158. C61#3110semidirect
164. C4⋊Q8C2×D61semidirect
181. #107C2×D61semidirect
183. C4⋊C8C2×D61semidirect