Finite Group Databasebeta

← #21457604

Subgroups — #21457604

Order 7808.

454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840575C211yesmaximal, characteristic, complemented
2#16840568C212yesmaximal, complemented
3#16840563C211yesmaximal, characteristic, complemented
4#16840034C211yesmaximal, characteristic, complemented
5#16840029C211yesmaximal, characteristic, complemented
6#16840022C212yesmaximal, complemented
7#16839939C212yesmaximal, complemented
8#16839934C212yesmaximal, complemented
9#16839880C211yesmaximal, characteristic, complemented
10#16839880C211yesmaximal, characteristic, complemented
11C61×#495C211yesmaximal, characteristic, complemented
12#14519825C2212yescomplemented
13#14519822C2212yes—
14#14519809—22no—
15#14519808C2212yes—
16#14519808C2212yescomplemented
17#14519806—22no—
18#14519804—22no—
19#14519803C2212yes—
20#14519803C2212yescomplemented
21#14519801—22no—
22#14519800—21no—
23#14519799C2211yescharacteristic
24#14519799C2211yescharacteristic
25#14519798—22no—
26#14519796—21no—
27Q16×D61—21no—
28SD16×D61—22no—
29D8×D61—21no—
30#14519783C2211yescharacteristic
31#14519783C2212yescomplemented
32#14519783C2211yescharacteristic, complemented
33#14519713C2211yescharacteristic, complemented
34#14519713C2211yescharacteristic, complemented
35#14519705C2211yescharacteristic
36#14519705C2212yescomplemented
37#14519705C2211yescharacteristic, complemented
38#14519696C2212yescomplemented
39#14519694C2212yescomplemented
40C2×Q16×C61C2211yescharacteristic, complemented
41C2×SD16×C61C2212yescomplemented
42C2×D8×C61C2211yescharacteristic
43#124×C61C2212yescomplemented
44C4×C8×C61C2211yescharacteristic, complemented
45C2×Q8×C61C2312yes—
46C2×D4×C61C2312yes—
47C2×C22⋊D61—42no—
48#11758226—22no—
49#11758226—22no—
50Q8×D61—22no—
51Q8×D61—22no—
52#11758224—22no—
53#11758224—22no—
54D4×D61—22no—
55D4×D61—22no—
56#11758222—42no—
57#11758222C2311yescharacteristic
58#11758222C2312yes—
59#11758222C2311yescharacteristic
60Q16×C61—21no—
61Q16×C61—21no—
62SD16×C61—22no—
63SD16×C61—22no—
64D8×C61—21no—
65D8×C61—21no—
66C2×C8×C61C2311yescharacteristic
67C2×C8×C61C2311yescharacteristic
68C22⋊C4×C61—42no—
69C42×C61C2311yescharacteristic
70#11758202—22no—
71#11758202—22no—
72#11758201—22no—
73#11758201—22no—
74#11758200—22no—
75#11758200—22no—
76#11758199—22no—
77#11758199—22no—
78#11758194C2312yes—
79#11758194C2311yescharacteristic
80#11758194C2311yescharacteristic
81Dic244D411yescharacteristic
82Dic244D411yescharacteristic
83D488D411yescharacteristic
84D488D411yescharacteristic
85#11758190D412yes—
86#11758190D411yescharacteristic
87#11758190D411yescharacteristic
88#11758189—21no—
89#11758189—21no—
90#11758189—22no—
91C8×D61—21no—
92C8×D61—22no—
93C8×D61—21no—
94C23×C61—22no—
95C22×D61—42no—
96Q8×C61—22no—
97Q8×C61—22no—
98D4×C61—22no—
99D4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61C2411yescharacteristic
103C22⋊D61—21no—
104C22⋊D61—22no—
105C22⋊D61—21no—
106C22⋊D61—42no—
107C22⋊D61—42no—
108C2×Dic61—42no—
109D244—42no—
110D244C2×D411yescharacteristic
111D244C2×D412yes—
112D244C2×D411yescharacteristic
113C4×D61—21no—
114C4×D61—22no—
115C4×D61—21no—
116C4×D61—42no—
117C4×D61—42no—
118Dic122—42no—
119Dic122C2×D411yescharacteristic
120Dic122C2×D412yes—
121Dic122C2×D411yescharacteristic
122C8×C61C2×D411yescharacteristic
123C8×C61C2×D411yescharacteristic
124C8×C61C2×D411yescharacteristic
125C8×C61C2×D411yescharacteristic
126#92418—21no—
127#92418—22no—
128#92418—21no—
129C22×C61—42no—
130C22×C61—82no—
131C22×C61H(5,𝔽2)11yescharacteristic
132C2×D61—21no—
133C2×D61—22no—
134C2×D61—21no—
135C2×D61—162no—
136C4×C61—41no—
137C4×C61—42no—
138C4×C61C22×D411yescharacteristic
139C4×C61C22×D411yescharacteristic
140Dic61—21no—
141Dic61—22no—
142Dic61—21no—
143#3290—611nomaximal, Sylow
144C2×C61—21no—
145C2×C61—82no—
146C2×C61D4211yescharacteristic
147D61—41no—
148D61—42no—
149D61—41no—
150#578—611no—
151#577—612no—
152#576—611no—
153#495D6111yescharacteristic, complemented
154#473—611no—
155#472—611no—
156#471—612no—
157#455—612no—
158#454—612no—
159#443—611no—
160#443—611no—
161C61#329011yescharacteristic, complemented, Sylow
1622−1+4—612no—
163H(5,𝔽2)—612no—
164#137—612no—
165#137—612no—
166#137—1222no—
167#137—1222no—
168AGL(1,ℤ/8)—612no—
169AGL(1,ℤ/8)—612no—
170AGL(1,ℤ/8)—1222no—
171AGL(1,ℤ/8)—1222no—
172#135—611no—
173#135—611no—
174#135—1221no—
175#135—1221no—
176#135—1222no—
177C2×Q16—1221no—
178C2×Q16C2×D6111yescharacteristic, complemented
179C2×SD16—1222no—
180C2×SD16C2×D6112yescomplemented
181C2×D8—1221no—
182C2×D8C2×D6111yescharacteristic
183#131—611no—
184#131—612no—
185#131—611no—
186#124C2×D6112yescomplemented
187#108—611no—
188#108—611no—
189#104—611no—
190#104—611no—
191#104—612no—
192#101—612no—
193#100—612no—
194C4×C8C2×D6111yescharacteristic, complemented
195#41—611no—
196#41—612no—
197#41—611no—
198#41—1222no—
199#41—1222no—
200#41—1222no—
201#41—1222no—
202#41—2442no—
203C2×Q8—1222no—
204C2×Q8—1222no—
205C2×Q8C22×D6112yes—
206C2×D4—1222no—
207C2×D4—1222no—
208C2×D4—2442no—
209C2×D4C22×D6112yes—
210Q16—21no—
211Q16—21no—
212Q16—611no—
213Q16—611no—
214Q16—1222no—
215Q16—1222no—
216SD16—22no—
217SD16—22no—
218SD16—611no—
219SD16—611no—
220SD16—612no—
221SD16—1222no—
222SD16—1222no—
223SD16—1222no—
224SD16—1222no—
225D8—21no—
226D8—21no—
227D8—611no—
228D8—611no—
229D8—1222no—
230D8—1222no—
231M16—611no—
232M16—612no—
233M16—611no—
234M16—1221no—
235M16—1222no—
236M16—1221no—
237C2×C8—1221no—
238C2×C8—1222no—
239C2×C8—1221no—
240C2×C8C22×D6111yescharacteristic
241C2×C8C22×D6111yescharacteristic
242C22⋊C4—42no—
243C42C22×D6111yescharacteristic
244C23—22no—
245C23—2442no—
246Q8—22no—
247Q8—22no—
248Q8—611no—
249Q8—612no—
250Q8—611no—
251Q8—2442no—
252D4—22no—
253D4—22no—
254D4—611no—
255D4—612no—
256D4—611no—
257D4—1221no—
258D4—1222no—
259D4—1221no—
260D4—2442no—
261D4—2442no—
262D4—2442no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—1221no—
266C2×C4—1222no—
267C2×C4—1221no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4C23×D6111yescharacteristic
272C8—1221no—
273C8—1222no—
274C8—1221no—
275C8D4×D6111yescharacteristic
276C8D4×D6111yescharacteristic
277C8D4×D6111yescharacteristic
278C8D4×D6111yescharacteristic
279C22—42no—
280C22—82no—
281C22—1221no—
282C22—1222no—
283C22—1221no—
284C22—9762no—
285C22#1451982211yescharacteristic
286C4—41no—
287C4—42no—
288C4—1221no—
289C4—1222no—
290C4—1221no—
291C4C2×D4×D6111yescharacteristic
292C4C2×D4×D6111yescharacteristic
293C2—21no—
294C2—82no—
295C2—2441no—
296C2—2442no—
297C2—2441no—
298C2#1684039711yescharacteristic
subgroupG/H
centerC2#16840397
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#495C2
socleC2×C61D42
hypercenter#495D61
hypocenterC61#3290
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #16840575C2semidirect
2. #16840568C2semidirect
3. #16840563C2semidirect
4. #16840034C2semidirect
5. #16840029C2semidirect
6. #16840022C2semidirect
7. #16839939C2semidirect
8. #16839934C2semidirect
9. #16839880C2semidirect
10. #16839880C2semidirect
11. C61×#495C2semidirect
12. #14519825C22semidirect
16. #14519808C22semidirect
20. #14519803C22semidirect
31. #14519783C22semidirect
32. #14519783C22semidirect
33. #14519713C22semidirect
34. #14519713C22semidirect
36. #14519705C22semidirect
37. #14519705C22semidirect
38. #14519696C22semidirect
39. #14519694C22semidirect
40. C2×Q16×C61C22semidirect
41. C2×SD16×C61C22semidirect
43. #124×C61C22semidirect
44. C4×C8×C61C22semidirect
153. #495D61semidirect
161. C61#3290semidirect
178. C2×Q16C2×D61semidirect
180. C2×SD16C2×D61semidirect
186. #124C2×D61semidirect
194. C4×C8C2×D61semidirect