Finite Group Databasebeta

← #21456648

Subgroups — #21456648

Order 7808.

414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840272C211yesmaximal, characteristic
2C2×#14519757C211yesmaximal, characteristic, complemented
3#16840106C212yesmaximal, complemented
4#16840097C211yesmaximal, characteristic, complemented
5#16840021C212yesmaximal, complemented
6#16840007C212yesmaximal, complemented
7#16839925C212yesmaximal, complemented
8#16839920C211yesmaximal, characteristic, complemented
9#16839900C211yesmaximal, characteristic, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#481C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15C2×Dic244C2212yescomplemented
16C2×#11758200C2212yescomplemented
17C2×#11758189C2212yes—
18#14519759—21no—
19#14519757—21no—
20#14519757—21no—
21#14519757C2212yes—
22#14519757C2212yes—
23#14519757C2211yescharacteristic
24#14519756C2211yescharacteristic
25#14519748C2211yescharacteristic
26#14519745—21no—
27D4×Dic61—21no—
28#14519737—21no—
29#14519735C2211yescharacteristic
30C2×C4⋊Dic61—21no—
31C2×#11758198—21no—
32#14519710C2212yescomplemented
33#14519702C2212yescomplemented
34#14519700C2212yescomplemented
35#14519700C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519689C2212yes—
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#106×C61C2212yescomplemented
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C23×D61D411yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61C2311yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—21no—
49C2×C22⋊D61—21no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61D411yescharacteristic
53#11758224—42no—
54C2×C4×D61—42no—
55C2×C4×D61D411yescharacteristic
56C2×C4×D61D411yescharacteristic
57C2×C4×D61C2311yescharacteristic
58C2×C4×D61C2311yescharacteristic
59C2×Dic122—21no—
60C2×Dic122—42no—
61C2×Dic122C2312yes—
62C2×Dic122C2311yescharacteristic
63C2×C8×C61C2312yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61C2312yes—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C22⋊Dic61—21no—
69C22⋊Dic61—21no—
70#11758200—42no—
71#11758198—22no—
72#11758198—22no—
73#11758198—21no—
74#11758198—21no—
75C4⋊Dic61—22no—
76C4⋊Dic61—22no—
77C4⋊Dic61—21no—
78C4⋊Dic61C2311yescharacteristic
79#11758196—21no—
80C4×Dic61—21no—
81C2×#92418C2312yes—
82Dic244—42no—
83#11758189—42no—
84C23×C61—21no—
85C23×C61C2×D411yescharacteristic
86C22×D61—22no—
87C22×D61—41no—
88C22×D61—41no—
89C22×D61C2×D411yescharacteristic
90C22×D61C2×D411yescharacteristic
91D4×C61—22no—
92D4×C61—42no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—42no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2411yescharacteristic
99C22⋊D61—42no—
100C22⋊D61—42no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—41no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61C2×D411yescharacteristic
108C2×Dic61C2×D411yescharacteristic
109C4×D61—22no—
110C4×D61—22no—
111C4×D61—41no—
112C4×D61—41no—
113Dic122—22no—
114Dic122—22no—
115Dic122—22no—
116Dic122—42no—
117C8×C61—22no—
118#92418—22no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61#13712yes—
125C22×C61C22×D411yescharacteristic
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—21no—
131C2×D61—21no—
132C2×D61—44no—
133C4×C61—21no—
134C4×C61—41no—
135C4×C61—42no—
136C4×C61H(5,𝔽2)12yes—
137Dic61—21no—
138Dic61—21no—
139Dic61—42no—
140Dic61—41no—
141Dic61—41no—
142#3196—611nomaximal, Sylow
143C2×C61—22no—
144C2×C61—81no—
145C2×C61#53411yescharacteristic
146C2×C61C2×#13711yescharacteristic
147C2×C61#57511yescharacteristic
148D61—41no—
149D61—41no—
150#525—611no—
151C2×C22⋊Q8—611no—
152#485—612no—
153#484—611no—
154#481D6111yescharacteristic, complemented
155#470—612no—
156#468—612no—
157#452—612no—
158#451—611no—
159#448—611no—
160#407—611no—
161C61#319611yescharacteristic, complemented, Sylow
162C2×#41—611no—
163C22×Q8—611no—
164C23×C4—611no—
165C2×Q16—612no—
166C2×SD16—612no—
167C2×M16—612no—
168#123—1221no—
169C22⋊Q8—611no—
170C22⋊Q8—612no—
171C22⋊Q8—612no—
172C22⋊Q8—611no—
173C22⋊Q8—1221no—
174C22⋊Q8—1221no—
175#121—611no—
176#121C2×D6111yescharacteristic
177#120—1221no—
178C4×D4—1221no—
179C4×D4—1221no—
180#117—611no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4C2×D6111yescharacteristic
183C2×C22⋊C4—1221no—
184#107—612no—
185#106C2×D6112yescomplemented
186#103—612no—
187#103—612no—
188#103—612no—
189#102C2×D6112yescomplemented
190C22⋊C8—611no—
191C22⋊C8—612no—
192C22⋊C8C2×D6111yescharacteristic
193C24—611no—
194#41—2442no—
195C2×Q8—612no—
196C2×Q8—611no—
197C2×Q8—1221no—
198C2×Q8—2442no—
199C2×D4—21no—
200C2×D4—1221no—
201C2×D4—1221no—
202C2×D4C22×D6111yescharacteristic
203C22×C4—21no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—2442no—
212C22×C4C22×D6111yescharacteristic
213Q16—2442no—
214SD16—2442no—
215M16—2442no—
216C2×C8—612no—
217C2×C8C22×D6112yes—
218C4⋊C4—21no—
219C4⋊C4—611no—
220C4⋊C4—1222no—
221C4⋊C4—1222no—
222C4⋊C4—1221no—
223C4⋊C4—1221no—
224C4⋊C4C22×D6112yes—
225C4⋊C4C22×D6111yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—1222no—
228C22⋊C4—1222no—
229C22⋊C4—1221no—
230C22⋊C4—1221no—
231C22⋊C4—1221no—
232C22⋊C4—1221no—
233C42—1221no—
234C23—21no—
235C23—611no—
236C23—611no—
237C23—1222no—
238C23—2441no—
239C23—2441no—
240C23D4×D6111yescharacteristic
241Q8—1222no—
242Q8—1222no—
243Q8—1222no—
244Q8—2442no—
245D4—22no—
246D4—42no—
247D4—2442no—
248D4—2442no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—611no—
254C2×C4—611no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1222no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2442no—
264C2×C4—2442no—
265C2×C4D4×D6111yescharacteristic
266C2×C4C23×D6111yescharacteristic
267C8—22no—
268C8—1222no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—1221no—
275C22—1221no—
276C22—1221no—
277C22—1221no—
278C22—1221no—
279C22—1221no—
280C22—2444no—
281C22#1451980612yes—
282C22C2×D4×D6111yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—1221no—
287C4—1221no—
288C4—2441no—
289C4—2441no—
290C4—2442no—
291C4#1451982312yes—
292C2—22no—
293C2—81no—
294C2—2441no—
295C2—2441no—
296C2#1684032311yescharacteristic
297C2C2×#1451980611yescharacteristic
298C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#481C2
socleC22×C61C22×D4
hypercenter#481D61
hypocenterC61#3196
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#14519757C2semidirect
3. #16840106C2semidirect
4. #16840097C2semidirect
5. #16840021C2semidirect
6. #16840007C2semidirect
7. #16839925C2semidirect
8. #16839920C2semidirect
9. #16839900C2semidirect
10. #16839724C2semidirect
11. C61×#481C2semidirect
15. C2×Dic244C22semidirect
16. C2×#11758200C22semidirect
32. #14519710C22semidirect
33. #14519702C22semidirect
34. #14519700C22semidirect
35. #14519700C22semidirect
40. #106×C61C22semidirect
41. #102×C61C22semidirect
154. #481D61semidirect
161. C61#3196semidirect
185. #106C2×D61semidirect
189. #102C2×D61semidirect