Finite Group Databasebeta

← #21457607

Subgroups — #21457607

Order 7808.

454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840576C211yesmaximal, characteristic, complemented
2#16840574C212yesmaximal, complemented
3#16840564C211yesmaximal, characteristic, complemented
4#16840146C211yesmaximal, characteristic, complemented
5#16840038C211yesmaximal, characteristic, complemented
6#16840033C211yesmaximal, characteristic, complemented
7#16840025C212yesmaximal, complemented
8#16839941C212yesmaximal, complemented
9#16839936C212yesmaximal, complemented
10#16839880C211yesmaximal, characteristic, complemented
11C61×#443C211yesmaximal, characteristic, complemented
12#14519824C2212yescomplemented
13#14519823C2212yes—
14#14519810—22no—
15#14519810C2212yes—
16#14519807C2212yescomplemented
17#14519806—22no—
18#14519805—22no—
19#14519805C2212yescomplemented
20#14519804—22no—
21#14519802C2212yes—
22#14519800—21no—
23#14519799—22no—
24#14519799C2211yescharacteristic
25#14519796—21no—
26C2×Dic244C2211yescharacteristic, complemented
27Q16×D61—21no—
28C2×#11758190—22no—
29C2×#11758190C2212yescomplemented
30C2×D488C2211yescharacteristic
31D8×D61—21no—
32#14519783C2211yescharacteristic
33#14519783C2211yescharacteristic, complemented
34#14519765C2212yescomplemented
35#14519713C2211yescharacteristic, complemented
36#14519705C2211yescharacteristic
37#14519705C2211yescharacteristic, complemented
38#14519695C2212yescomplemented
39#14519693C2212yescomplemented
40#135×C61C2211yescharacteristic
41#131×C61C2212yescomplemented
42#108×C61C2211yescharacteristic, complemented
43#104×C61C2212yescomplemented
44C4×C8×C61C2211yescharacteristic, complemented
45#41×C61C2312yes—
46#11758226—22no—
47Q8×D61—22no—
48#11758224—22no—
49#11758224—42no—
50D4×D61—22no—
51D4×D61—42no—
52#11758222—22no—
53#11758222—22no—
54#11758222C2311yescharacteristic
55#11758222C2311yescharacteristic
56C2×D244—22no—
57C2×D244C2312yes—
58C2×Dic122—22no—
59C2×Dic122C2312yes—
60Q16×C61D411yescharacteristic
61SD16×C61D412yes—
62D8×C61D411yescharacteristic
63M16×C61—22no—
64M16×C61C2312yes—
65C2×C8×C61—22no—
66C2×C8×C61C2311yescharacteristic
67C2×C8×C61C2311yescharacteristic
68C42×C61C2311yescharacteristic
69#11758202—22no—
70#11758201—22no—
71#11758200—22no—
72#11758199—22no—
73#11758198—42no—
74#11758194C2311yescharacteristic
75#11758194C2311yescharacteristic
76Dic244—22no—
77Dic244—21no—
78Dic244—21no—
79Dic244D411yescharacteristic
80D488—22no—
81D488—21no—
82D488—21no—
83D488D411yescharacteristic
84#11758190—22no—
85#11758190—22no—
86#11758190—22no—
87#11758190—22no—
88#11758190D411yescharacteristic
89#11758190D411yescharacteristic
90#11758189—21no—
91#11758189—21no—
92C8×D61—21no—
93C8×D61—21no—
94C22×D61—22no—
95C22×D61—42no—
96Q8×C61C2×D412yes—
97D4×C61—22no—
98D4×C61C2×D412yes—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61C2411yescharacteristic
102C22⋊D61—21no—
103C22⋊D61—21no—
104C22⋊D61—42no—
105C22⋊D61—42no—
106C2×Dic61—22no—
107C2×Dic61—42no—
108D244—22no—
109D244—22no—
110D244—42no—
111D244C2×D411yescharacteristic
112D244C2×D411yescharacteristic
113C4×D61—21no—
114C4×D61—21no—
115C4×D61—42no—
116C4×D61—42no—
117Dic122—22no—
118Dic122—22no—
119Dic122—42no—
120Dic122C2×D411yescharacteristic
121Dic122C2×D411yescharacteristic
122C8×C61—22no—
123C8×C61C2×D411yescharacteristic
124C8×C61C2×D411yescharacteristic
125C8×C61C2×D411yescharacteristic
126C8×C61C2×D411yescharacteristic
127#92418—21no—
128#92418—21no—
129C22×C61—22no—
130C22×C61H(5,𝔽2)11yescharacteristic
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—42no—
134C2×D61—82no—
135C2×D61—162no—
136C4×C61—22no—
137C4×C61—41no—
138C4×C61C22×D411yescharacteristic
139C4×C61C22×D411yescharacteristic
140Dic61—21no—
141Dic61—21no—
142Dic61—42no—
143#3290—611nomaximal, Sylow
144C2×C61—21no—
145C2×C61—42no—
146C2×C61D4211yescharacteristic
147D61—41no—
148D61—41no—
149D61—82no—
150#578—611no—
151#577—612no—
152#576—611no—
153#495—611no—
154#473—611no—
155#472—611no—
156#471—612no—
157#455—612no—
158#454—612no—
159#443—611no—
160#443D6111yescharacteristic, complemented
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—1222no—
174#135—1221no—
175#135—1221no—
176#135C2×D6111yescharacteristic
177C2×Q16—611no—
178C2×Q16—1221no—
179C2×SD16—612no—
180C2×SD16—1222no—
181C2×D8—611no—
182C2×D8—1221no—
183#131—611no—
184#131—611no—
185#131C2×D6112yescomplemented
186#124—612no—
187#108—611no—
188#108C2×D6111yescharacteristic, complemented
189#104—611no—
190#104—611no—
191#104C2×D6112yescomplemented
192#101—612no—
193#100—612no—
194C4×C8C2×D6111yescharacteristic, complemented
195#41—611no—
196#41—611no—
197#41—1222no—
198#41—1222no—
199#41—1222no—
200#41—1222no—
201#41—2442no—
202#41C22×D6112yes—
203C2×Q8—612no—
204C2×Q8—1222no—
205C2×Q8—1222no—
206C2×D4—612no—
207C2×D4—1222no—
208C2×D4—1222no—
209C2×D4—2442no—
210Q16—611no—
211Q16—1222no—
212Q16—1222no—
213Q16—1221no—
214Q16—1221no—
215Q16D24411yescharacteristic
216SD16—611no—
217SD16—611no—
218SD16—1222no—
219SD16—1222no—
220SD16—1222no—
221SD16—1222no—
222SD16—1222no—
223SD16—1222no—
224SD16D24412yes—
225D8—611no—
226D8—1222no—
227D8—1222no—
228D8—1221no—
229D8—1221no—
230D8D24411yescharacteristic
231M16—22no—
232M16—611no—
233M16—611no—
234M16—1221no—
235M16—1221no—
236M16C22×D6112yes—
237C2×C8—22no—
238C2×C8—1221no—
239C2×C8—1221no—
240C2×C8C22×D6111yescharacteristic
241C2×C8C22×D6111yescharacteristic
242C22⋊C4—2442no—
243C42C22×D6111yescharacteristic
244C23—1222no—
245C23—2442no—
246Q8—611no—
247Q8—611no—
248Q8—1222no—
249Q8—1222no—
250Q8—2442no—
251Q8C2×D24412yes—
252D4—22no—
253D4—611no—
254D4—611no—
255D4—1221no—
256D4—1221no—
257D4—1222no—
258D4—1222no—
259D4—2442no—
260D4—2442no—
261D4—2442no—
262D4C2×D24412yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4C23×D6111yescharacteristic
272C8—22no—
273C8—1221no—
274C8—1221no—
275C8C2×D24411yescharacteristic
276C8C2×D24411yescharacteristic
277C8D4×D6111yescharacteristic
278C8D4×D6111yescharacteristic
279C22—22no—
280C22—1221no—
281C22—1221no—
282C22—9762no—
283C22—4882no—
284C22—2442no—
285C22#1451982311yescharacteristic
286C4—22no—
287C4—41no—
288C4—1221no—
289C4—1221no—
290C4—2442no—
291C4C2×D4×D6111yescharacteristic
292C4C22×D24411yescharacteristic
293C2—21no—
294C2—42no—
295C2—4882no—
296C2—2441no—
297C2—2441no—
298C2D4×D24411yescharacteristic
subgroupG/H
centerC2D4×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#443C2
socleC2×C61D42
hypercenter#443D61
hypocenterC61#3290
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #16840576C2semidirect
2. #16840574C2semidirect
3. #16840564C2semidirect
4. #16840146C2semidirect
5. #16840038C2semidirect
6. #16840033C2semidirect
7. #16840025C2semidirect
8. #16839941C2semidirect
9. #16839936C2semidirect
10. #16839880C2semidirect
11. C61×#443C2semidirect
12. #14519824C22semidirect
16. #14519807C22semidirect
19. #14519805C22semidirect
26. C2×Dic244C22semidirect
29. C2×#11758190C22semidirect
33. #14519783C22semidirect
34. #14519765C22semidirect
35. #14519713C22semidirect
37. #14519705C22semidirect
38. #14519695C22semidirect
39. #14519693C22semidirect
41. #131×C61C22semidirect
42. #108×C61C22semidirect
43. #104×C61C22semidirect
44. C4×C8×C61C22semidirect
160. #443D61semidirect
161. C61#3290semidirect
185. #131C2×D61semidirect
188. #108C2×D61semidirect
191. #104C2×D61semidirect
194. C4×C8C2×D61semidirect