Finite Group Databasebeta

← #21456632

Subgroups — #21456632

Order 7808.

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

normal subgroups only

This group has 466 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, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3#16840092C211yesmaximal, characteristic, complemented
4#16840089C212yesmaximal, complemented
5#16840014C212yesmaximal, complemented
6#16840009C212yesmaximal, complemented
7#16839915C211yesmaximal, characteristic, complemented
8#16839908C212yesmaximal, complemented
9#16839895C211yesmaximal, characteristic, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#480C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic, complemented
13C22×D244—21no—
14C22×D244C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16C2×#11758190C2212yescomplemented
17C2×#11758199C2212yescomplemented
18C2×#11758189C2212yescomplemented
19#14519759—21no—
20#14519757C2211yescharacteristic, complemented
21#14519756C2211yescharacteristic
22#14519752—21no—
23#14519752—21no—
24#14519752C2212yes—
25#14519752C2212yes—
26#14519748C2211yescharacteristic, complemented
27#14519745—21no—
28D4×Dic61—21no—
29#14519737—21no—
30#14519735C2211yescharacteristic, complemented
31C2×#11758198—21no—
32#14519708C2212yescomplemented
33#14519700C2212yescomplemented
34#14519699C2212yescomplemented
35#14519697C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519689C2212yescomplemented
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2212yescomplemented
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C23×D61—21no—
44C23×D61D411yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—21no—
50C2×C22⋊D61—21no—
51C22×Dic61—21no—
52C22×Dic61D411yescharacteristic
53#11758224—42no—
54C2×D244—22no—
55C2×D244—22no—
56C2×D244—21no—
57C2×D244—42no—
58C2×D244—44no—
59C2×D244C2312yes—
60C2×C4×D61—42no—
61C2×C4×D61D411yescharacteristic
62C2×C4×D61D411yescharacteristic
63C2×C4×D61C2311yescharacteristic
64C2×C4×D61C2311yescharacteristic
65C2×Dic122C2311yescharacteristic
66C2×C8×C61C2312yes—
67C4⋊C4×C61—21no—
68C4⋊C4×C61C2312yes—
69C4⋊C4×C61C2311yescharacteristic
70C22⋊C4×C61—21no—
71C22⋊Dic61—21no—
72C22⋊Dic61—21no—
73#11758199—42no—
74#11758198—21no—
75#11758198—21no—
76#11758198—22no—
77#11758198—22no—
78C4⋊Dic61—21no—
79C4⋊Dic61C2311yescharacteristic
80#11758196—21no—
81C4×Dic61—21no—
82C2×#92418C2312yes—
83#11758190—42no—
84#11758189—42no—
85C23×C61—21no—
86C23×C61C2×D411yescharacteristic
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—41no—
90C22×D61—41no—
91C22×D61—42no—
92C22×D61—42no—
93C22×D61—42no—
94C22×D61C2×D411yescharacteristic
95C22×D61C2×D411yescharacteristic
96D4×C61—22no—
97D4×C61—42no—
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61—42no—
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2411yescharacteristic
104C22⋊D61—42no—
105C22⋊D61—42no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—41no—
109C2×Dic61—42no—
110C2×Dic61C2×D411yescharacteristic
111C2×Dic61C2×D411yescharacteristic
112D244—22no—
113D244—22no—
114D244—42no—
115D244—44no—
116D244—44no—
117C4×D61—22no—
118C4×D61—22no—
119C4×D61—41no—
120C4×D61—41no—
121Dic122—22no—
122C8×C61—22no—
123#92418—22no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61AGL(1,ℤ/8)12yes—
130C22×C61C22×D411yescharacteristic
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—21no—
136C2×D61—21no—
137C2×D61—44no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—42no—
141C2×D61—84no—
142C4×C61—21no—
143C4×C61—42no—
144C4×C61—41no—
145C4×C61H(5,𝔽2)12yes—
146Dic61—21no—
147Dic61—21no—
148Dic61—41no—
149Dic61—41no—
150#3194—611nomaximal, Sylow
151C2×C61—22no—
152C2×C61—81no—
153C2×C61#53411yescharacteristic
154C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
155C2×C61#57511yescharacteristic
156D61—41no—
157D61—41no—
158D61—82no—
159#525—611no—
160C2×#121—611no—
161#483—611no—
162#482—612no—
163#480D6111yescharacteristic, complemented
164#469—612no—
165#468—612no—
166#450—611no—
167#449—612no—
168#447—611no—
169#407—611no—
170C61#319411yescharacteristic, complemented, Sylow
171C2×#41—611no—
172C22×D4—611no—
173C22×D4—1221no—
174C23×C4—611no—
175C2×SD16—612no—
176C2×D8—612no—
177C2×M16—612no—
178#123—1221no—
179C22⋊Q8—611no—
180C22⋊Q8—611no—
181#121—611no—
182#121—612no—
183#121—612no—
184#121—1221no—
185#121—1221no—
186#121C2×D6111yescharacteristic
187#120—1221no—
188C4×D4—1221no—
189C4×D4—1221no—
190#117—611no—
191C2×C4⋊C4C2×D6111yescharacteristic
192C2×C22⋊C4—1221no—
193#107C2×D6112yescomplemented
194#106—612no—
195#103—612no—
196#102—612no—
197#102—612no—
198#102C2×D6112yescomplemented
199C22⋊C8—611no—
200C22⋊C8—612no—
201C22⋊C8C2×D6111yescharacteristic
202C24—611no—
203C24—1221no—
204#41—2442no—
205C2×Q8—611no—
206C2×D4—21no—
207C2×D4—612no—
208C2×D4—1222no—
209C2×D4—1222no—
210C2×D4—1221no—
211C2×D4—1221no—
212C2×D4—1221no—
213C2×D4—2442no—
214C2×D4—2444no—
215C2×D4C22×D6111yescharacteristic
216C22×C4—21no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—1221no—
223C22×C4—2442no—
224C22×C4C22×D6111yescharacteristic
225SD16—2442no—
226D8—2442no—
227M16—2442no—
228C2×C8—612no—
229C2×C8C22×D6112yes—
230C4⋊C4—21no—
231C4⋊C4—611no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C4⋊C4C22×D6111yescharacteristic
235C4⋊C4C22×D6112yes—
236C22⋊C4—21no—
237C22⋊C4—1222no—
238C22⋊C4—1222no—
239C22⋊C4—1221no—
240C22⋊C4—1221no—
241C22⋊C4—1221no—
242C22⋊C4—1221no—
243C42—1221no—
244C23—21no—
245C23—611no—
246C23—611no—
247C23—1222no—
248C23—1222no—
249C23—2441no—
250C23—2441no—
251C23—2442no—
252C23—2442no—
253C23—2442no—
254C23D4×D6111yescharacteristic
255Q8—1222no—
256D4—22no—
257D4—42no—
258D4—1222no—
259D4—1222no—
260D4—2442no—
261D4—2444no—
262D4—2444no—
263D4—2442no—
264D4—2442no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—42no—
269C2×C4—611no—
270C2×C4—611no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2442no—
279C2×C4D4×D6111yescharacteristic
280C2×C4C23×D6111yescharacteristic
281C8—22no—
282C8—1222no—
283C22—21no—
284C22—21no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—1221no—
289C22—1221no—
290C22—1221no—
291C22—1221no—
292C22—1221no—
293C22—1221no—
294C22—4884no—
295C22—2444no—
296C22—2442no—
297C22—2442no—
298C22—2442no—
299C22#1451980112yes—
300C22C2×D4×D6111yescharacteristic
301C4—21no—
302C4—42no—
303C4—41no—
304C4—1221no—
305C4—1221no—
306C4—2441no—
307C4—2441no—
308C4#1451982312yes—
309C2—22no—
310C2—81no—
311C2—4882no—
312C2—2441no—
313C2—2441no—
314C2#1684032311yescharacteristic
315C2C2×#1451980111yescharacteristic
316C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3194
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #16840272C2semidirect
2. C2×#14519752C2semidirect
3. #16840092C2semidirect
4. #16840089C2semidirect
5. #16840014C2semidirect
6. #16840009C2semidirect
7. #16839915C2semidirect
8. #16839908C2semidirect
9. #16839895C2semidirect
10. #16839724C2semidirect
11. C61×#480C2semidirect
12. C2×#11758224C22semidirect
16. C2×#11758190C22semidirect
17. C2×#11758199C22semidirect
18. C2×#11758189C22semidirect
20. #14519757C22semidirect
26. #14519748C22semidirect
30. #14519735C22semidirect
32. #14519708C22semidirect
33. #14519700C22semidirect
34. #14519699C22semidirect
35. #14519697C22semidirect
37. #14519689C22semidirect
40. #107×C61C22semidirect
41. #102×C61C22semidirect
163. #480D61semidirect
170. C61#3194semidirect
193. #107C2×D61semidirect
198. #102C2×D61semidirect