Finite Group Databasebeta

← #21456838

Subgroups — #21456838

Order 7808.

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

normal subgroups only

This group has 490 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#127×D61C211yesmaximal, characteristic, complemented
2#16840297C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840149C211yesmaximal, characteristic, complemented
5#16840128C211yesmaximal, characteristic, complemented
6#16839961C212yesmaximal, complemented
7#16839956C212yesmaximal, complemented
8#16839914C212yesmaximal, complemented
9#16839897C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#490C211yesmaximal, characteristic, complemented
12C2×D4×D61—21no—
13C2×D4×D61—21no—
14C2×D4×D61C2212yes—
15C2×#11758190C2212yescomplemented
16C2×#11758200C2212yescomplemented
17C2×D488C2212yescomplemented
18C2×#11758199C2212yescomplemented
19#14519774C2211yescharacteristic
20#14519773—21no—
21#14519773—21no—
22#14519773C2212yes—
23#14519772—21no—
24#14519765C2211yescharacteristic, complemented
25#14519762—21no—
26#14519757C2211yescharacteristic
27#14519752C2211yescharacteristic
28#14519742C2211yescharacteristic, complemented
29#14519739—21no—
30#14519739C2211yescharacteristic, complemented
31#14519735—21no—
32C42×D61C2211yescharacteristic
33#14519706C2212yescomplemented
34#14519697C2212yescomplemented
35#14519697C2212yescomplemented
36#14519689C2212yes—
37#14519688C2211yescharacteristic, complemented
38#127×C61C2211yescharacteristic
39#125×C61C2211yescharacteristic, complemented
40#102×C61C2212yescomplemented
41#102×C61C2212yescomplemented
42#97×C61C2211yescharacteristic, complemented
43C23×D61—22no—
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61C2312yes—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—22no—
50D4×D61—42no—
51D4×D61—42no—
52D4×D61—44no—
53D4×D61—44no—
54C2×D244—21no—
55C2×D244—21no—
56C2×D244—21no—
57C2×D244C2312yes—
58C2×D244C2311yescharacteristic
59C2×C4×D61—21no—
60C2×C4×D61D411yescharacteristic
61C2×C4×D61D411yescharacteristic
62C2×C4×D61C2311yescharacteristic
63C2×Dic122C2311yescharacteristic
64C2×C8×C61C2312yes—
65C4⋊C4×C61—21no—
66C4⋊C4×C61—21no—
67C4⋊C4×C61C2311yescharacteristic
68C4⋊C4×C61C2311yescharacteristic
69C42×C61C2311yescharacteristic
70#11758200—42no—
71#11758199—42no—
72#11758198—21no—
73#11758198—21no—
74#11758198—21no—
75#11758198—21no—
76#11758198—21no—
77C4⋊Dic61—21no—
78#11758196—21no—
79C4×Dic61—21no—
80C4×Dic61D411yescharacteristic
81C4×Dic61D411yescharacteristic
82C4×Dic61C2311yescharacteristic
83C2×#92418C2312yes—
84D488—42no—
85#11758190—42no—
86C23×C61—22no—
87C22×D61—21no—
88C22×D61—22no—
89C22×D61—44no—
90C22×D61—44no—
91C22×D61—44no—
92C22×D61C2×D411yescharacteristic
93D4×C61—22no—
94D4×C61—22no—
95D4×C61—42no—
96D4×C61—42no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2411yescharacteristic
102C22⋊D61—44no—
103C22⋊D61—44no—
104C22⋊D61—44no—
105C2×Dic61—21no—
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108C2×Dic61C2×D411yescharacteristic
109D244—22no—
110D244—22no—
111D244—22no—
112D244—42no—
113D244—42no—
114D244—42no—
115C4×D61—22no—
116C4×D61—22no—
117C4×D61—22no—
118C4×D61—42no—
119Dic122—22no—
120C8×C61—22no—
121#92418—22no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61C22×D411yescharacteristic
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—42no—
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—41no—
134C2×D61—88no—
135C2×D61AGL(1,ℤ/8)12yes—
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—41no—
139C4×C61—41no—
140C4×C61H(5,𝔽2)12yes—
141Dic61—21no—
142Dic61—21no—
143Dic61—41no—
144Dic61AGL(1,ℤ/8)12yes—
145#3217—611nomaximal, Sylow
146C2×C61—82no—
147C2×C61#53511yescharacteristic
148C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
150D61—22no—
151D61—81no—
152D61—82no—
153C2×#127—611no—
154#529—611no—
155#496—611no—
156#496—611no—
157#490—611no—
158#490D6111yescharacteristic, complemented
159#460—612no—
160#459—612no—
161#450—612no—
162#447—612no—
163#432—611no—
164C61#321711yescharacteristic, complemented, Sylow
165C22×D4—612no—
166C22×D4—1221no—
167C22×D4—1221no—
168C2×SD16—612no—
169C2×SD16—612no—
170C2×D8—612no—
171C2×D8—612no—
172#127—612no—
173#127—611no—
174#127—1221no—
175#127—1221no—
176#127C2×D6111yescharacteristic
177#126—1221no—
178#125C2×D6111yescharacteristic, complemented
179#124—611no—
180#123—1221no—
181C22⋊Q8—611no—
182#121—611no—
183C4×Q8—611no—
184C4×D4—611no—
185C4×D4—1221no—
186#117—1221no—
187C2×C42—611no—
188C4⋊C8—612no—
189#102—612no—
190#102—612no—
191#102C2×D6112yescomplemented
192#102C2×D6112yescomplemented
193C22⋊C8—612no—
194#97—611no—
195#97C2×D6111yescharacteristic, complemented
196C24—1222no—
197C2×Q8—611no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—612no—
201C2×D4—611no—
202C2×D4—1221no—
203C2×D4—1222no—
204C2×D4—1222no—
205C2×D4—1222no—
206C2×D4—1221no—
207C2×D4—1221no—
208C2×D4—2442no—
209C2×D4—2442no—
210C2×D4—2444no—
211C2×D4—2444no—
212C2×D4C22×D6112yes—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1221no—
217SD16—2442no—
218SD16—2442no—
219D8—2442no—
220D8—2442no—
221C2×C8—612no—
222C2×C8C22×D6112yes—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4C22×D6111yescharacteristic
228C4⋊C4C22×D6111yescharacteristic
229C22⋊C4—1221no—
230C22⋊C4—1221no—
231C22⋊C4—1221no—
232C22⋊C4—1221no—
233C22⋊C4—1221no—
234C42—611no—
235C42—611no—
236C42—611no—
237C42—1221no—
238C42C22×D6111yescharacteristic
239C23—22no—
240C23—611no—
241C23—1221no—
242C23—1222no—
243C23—2444no—
244C23—2444no—
245C23—2444no—
246Q8—1222no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—42no—
251D4—1222no—
252D4—1222no—
253D4—1222no—
254D4—2442no—
255D4—2442no—
256D4—2442no—
257D4—2444no—
258D4—2444no—
259D4—2444no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—2442no—
270C2×C4D4×D6111yescharacteristic
271C2×C4D4×D6111yescharacteristic
272C2×C4C23×D6111yescharacteristic
273C8—22no—
274C8—1222no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—612no—
279C22—1221no—
280C22—1221no—
281C22—4888no—
282C22—2441no—
283C22—2442no—
284C22—2442no—
285C22—2441no—
286C22—2442no—
287C22—2441no—
288C22C2×D4×D6111yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—612no—
294C4—1221no—
295C4—1221no—
296C4—2441no—
297C4#1451982312yes—
298C2—82no—
299C2—1222no—
300C2—4882no—
301C2—4881no—
302C2#1684033011yescharacteristic
303C2AGL(1,ℤ/8)×D6111yescharacteristic
304C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#490C2
socleC22×C61C22×D4
hypercenter#490D61
hypocenterC61#3217
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #127×D61C2semidirect
2. #16840297C2semidirect
3. #16840151C2semidirect
4. #16840149C2semidirect
5. #16840128C2semidirect
6. #16839961C2semidirect
7. #16839956C2semidirect
8. #16839914C2semidirect
9. #16839897C2semidirect
10. #16839817C2semidirect
11. C61×#490C2semidirect
15. C2×#11758190C22semidirect
16. C2×#11758200C22semidirect
17. C2×D488C22semidirect
18. C2×#11758199C22semidirect
24. #14519765C22semidirect
28. #14519742C22semidirect
30. #14519739C22semidirect
33. #14519706C22semidirect
34. #14519697C22semidirect
35. #14519697C22semidirect
37. #14519688C22semidirect
39. #125×C61C22semidirect
40. #102×C61C22semidirect
41. #102×C61C22semidirect
42. #97×C61C22semidirect
158. #490D61semidirect
164. C61#3217semidirect
178. #125C2×D61semidirect
191. #102C2×D61semidirect
192. #102C2×D61semidirect
195. #97C2×D61semidirect