Finite Group Databasebeta

← #21457601

Subgroups — #21457601

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#16840573C212yesmaximal, complemented
3#16840145C211yesmaximal, characteristic, complemented
4#16840037C211yesmaximal, characteristic, complemented
5#16840029C211yesmaximal, characteristic, complemented
6#16840023C212yesmaximal, complemented
7#16839940C212yesmaximal, complemented
8#16839933C212yesmaximal, complemented
9#16839879C211yesmaximal, characteristic, complemented
10#16839877C211yesmaximal, characteristic, complemented
11C61×#576C211yesmaximal, characteristic, complemented
12#14519824C2212yescomplemented
13#14519807—22no—
14#14519807C2212yes—
15#14519807C2212yescomplemented
16#14519806—22no—
17#14519803—22no—
18#14519803C2212yescomplemented
19#14519797—22no—
20#14519797C2211yescharacteristic
21#14519796—21no—
22C2×Dic244C2211yescharacteristic, complemented
23Q16×D61—21no—
24C2×#11758200—22no—
25C2×#11758200C2212yescomplemented
26#14519784C2212yescomplemented
27#14519783C2211yescharacteristic, complemented
28#14519764C2212yescomplemented
29#14519713C2211yescharacteristic, complemented
30#14519712C2211yescharacteristic, complemented
31#14519704C2211yescharacteristic
32#14519704C2212yescomplemented
33#14519703C2211yescharacteristic, complemented
34#14519695C2212yescomplemented
35#14519694C2212yescomplemented
36C8×Dic61C2211yescharacteristic, complemented
37H(5,𝔽2)×C61C2212yes—
38AGL(1,ℤ/8)×C61—22no—
39AGL(1,ℤ/8)×C61C2212yes—
40#135×C61—21no—
41#135×C61C2211yescharacteristic
42C2×D8×C61—21no—
43C2×D8×C61C2211yescharacteristic
44#131×C61C2211yescharacteristic
45#41×C61—22no—
46#41×C61—22no—
47#41×C61C2312yes—
48#41×C61C2311yescharacteristic
49C2×D4×C61—22no—
50C2×D4×C61—22no—
51C2×D4×C61—42no—
52C2×D4×C61C2312yes—
53Q8×D61—22no—
54#11758224—22no—
55#11758224—42no—
56#11758222—22no—
57#11758222C2311yescharacteristic
58C2×Dic122—22no—
59C2×Dic122C2312yes—
60Q16×C61D411yescharacteristic
61SD16×C61—22no—
62SD16×C61D412yes—
63D8×C61—22no—
64D8×C61—21no—
65D8×C61—21no—
66D8×C61D411yescharacteristic
67M16×C61—21no—
68M16×C61C2311yescharacteristic
69C2×C8×C61—21no—
70C2×C8×C61C2311yescharacteristic
71C22⋊Dic61—42no—
72#11758202—22no—
73#11758202—22no—
74#11758202D411yescharacteristic
75#11758201D411yescharacteristic
76#11758200—22no—
77#11758200—22no—
78#11758200—22no—
79#11758200—22no—
80#11758200—22no—
81#11758200D411yescharacteristic
82#11758199—22no—
83#11758199D411yescharacteristic
84C4×Dic61C2311yescharacteristic
85#11758194—22no—
86#11758194C2311yescharacteristic
87#11758194C2312yes—
88C2×#92418—22no—
89C2×#92418C2311yescharacteristic
90Dic244—21no—
91Dic244—21no—
92#11758189—21no—
93C8×D61—21no—
94C23×C61—22no—
95C23×C61—42no—
96Q8×C61C2×D411yescharacteristic
97Q8×C61C2×D412yes—
98D4×C61—22no—
99D4×C61—21no—
100D4×C61—22no—
101D4×C61—22no—
102D4×C61—42no—
103D4×C61—42no—
104D4×C61C2×D411yescharacteristic
105D4×C61C2×D412yes—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61—42no—
109C2×C4×C61C2411yescharacteristic
110C22⋊D61—21no—
111C22⋊D61—42no—
112C2×Dic61—21no—
113C2×Dic61—22no—
114C2×Dic61—42no—
115D244C2×D411yescharacteristic
116C4×D61—21no—
117C4×D61—42no—
118Dic122—22no—
119Dic122—22no—
120Dic122—42no—
121Dic122C2×D411yescharacteristic
122C8×C61—21no—
123C8×C61C2×D411yescharacteristic
124C8×C61C2×D411yescharacteristic
125#92418—21no—
126#92418—22no—
127#92418C2×D411yescharacteristic
128#92418C2×D411yescharacteristic
129C22×C61—22no—
130C22×C61—21no—
131C22×C61—42no—
132C22×C61—82no—
133C22×C61—162no—
134C22×C61H(5,𝔽2)11yescharacteristic
135C2×D61—21no—
136C4×C61—22no—
137C4×C61—21no—
138C4×C61C22×D411yescharacteristic
139C4×C61C22×D411yescharacteristic
140Dic61—21no—
141Dic61—41no—
142Dic61—42no—
143#3290—611nomaximal, Sylow
144C2×C61—21no—
145C2×C61—42no—
146C2×C61—41no—
147C2×C61—82no—
148C2×C61D4211yescharacteristic
149D61—41no—
150#578—611no—
151#577—612no—
152#576D6111yescharacteristic, complemented
153#495—611no—
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)C2×D6112yes—
164#137—612no—
165#137—612no—
166#137—1222no—
167#137—1222no—
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—612no—
170AGL(1,ℤ/8)—1222no—
171AGL(1,ℤ/8)C2×D6112yes—
172#135—21no—
173#135—611no—
174#135—1222no—
175#135—1221no—
176#135C2×D6111yescharacteristic
177C2×Q16—611no—
178C2×Q16—1221no—
179C2×SD16—612no—
180C2×SD16—1222no—
181C2×D8—21no—
182C2×D8C2×D6111yescharacteristic
183#131—612no—
184#131—611no—
185#131C2×D6111yescharacteristic
186#124—612no—
187#108—611no—
188#108—611no—
189#104—611no—
190#104—612no—
191#104—611no—
192#101—612no—
193#100—612no—
194C4×C8—611no—
195#41—22no—
196#41—22no—
197#41—611no—
198#41—1222no—
199#41—1222no—
200#41—2442no—
201#41C22×D6111yescharacteristic
202#41C22×D6112yes—
203C2×Q8—612no—
204C2×Q8—1222no—
205C2×Q8—1222no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4C22×D6112yes—
210Q16—611no—
211Q16—1222no—
212Q16—1222no—
213Q16—1221no—
214Q16—1221no—
215Q16C22⋊D6111yescharacteristic
216SD16—22no—
217SD16—611no—
218SD16—611no—
219SD16—1222no—
220SD16—1222no—
221SD16—1222no—
222SD16—1222no—
223SD16—1222no—
224SD16C22⋊D6112yes—
225D8—22no—
226D8—21no—
227D8—21no—
228D8—611no—
229D8—1222no—
230D8C22⋊D6111yescharacteristic
231M16—21no—
232M16—611no—
233M16—612no—
234M16—1222no—
235M16—1221no—
236M16C22×D6111yescharacteristic
237C2×C8—21no—
238C2×C8—611no—
239C2×C8—1222no—
240C2×C8—1221no—
241C2×C8C22×D6111yescharacteristic
242C22⋊C4—2442no—
243C42—611no—
244C23—22no—
245C23—42no—
246Q8—611no—
247Q8—1222no—
248Q8—1222no—
249Q8—2442no—
250Q8D4×D6111yescharacteristic
251Q8C2×C22⋊D6112yes—
252D4—21no—
253D4—22no—
254D4—22no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—611no—
259D4—1221no—
260D4—2442no—
261D4D4×D6111yescharacteristic
262D4C2×C22⋊D6112yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1222no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4C23×D6111yescharacteristic
272C8—21no—
273C8—611no—
274C8—611no—
275C8—1222no—
276C8—1221no—
277C8C2×C22⋊D6111yescharacteristic
278C8C2×C22⋊D6111yescharacteristic
279C22—22no—
280C22—21no—
281C22—42no—
282C22—82no—
283C22—162no—
284C22—1221no—
285C22#1451982211yescharacteristic
286C4—21no—
287C4—22no—
288C4—1221no—
289C4—2441no—
290C4—2442no—
291C4C2×D4×D6111yescharacteristic
292C4C22×C22⋊D6111yescharacteristic
293C2—21no—
294C2—41no—
295C2—42no—
296C2—82no—
297C2—2441no—
298C2D4×C22⋊D6111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#576C2
socleC2×C61D42
hypercenter#576D61
hypocenterC61#3290
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #16840576C2semidirect
2. #16840573C2semidirect
3. #16840145C2semidirect
4. #16840037C2semidirect
5. #16840029C2semidirect
6. #16840023C2semidirect
7. #16839940C2semidirect
8. #16839933C2semidirect
9. #16839879C2semidirect
10. #16839877C2semidirect
11. C61×#576C2semidirect
12. #14519824C22semidirect
15. #14519807C22semidirect
18. #14519803C22semidirect
22. C2×Dic244C22semidirect
25. C2×#11758200C22semidirect
26. #14519784C22semidirect
27. #14519783C22semidirect
28. #14519764C22semidirect
29. #14519713C22semidirect
30. #14519712C22semidirect
32. #14519704C22semidirect
33. #14519703C22semidirect
34. #14519695C22semidirect
35. #14519694C22semidirect
36. C8×Dic61C22semidirect
152. #576D61semidirect
161. C61#3290semidirect