Finite Group Databasebeta

← #20255173

Subgroups — #20255173

Order 6016.

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#15689936C211yesmaximal, characteristic, complemented
2#15689929C212yesmaximal, complemented
3#15689924C211yesmaximal, characteristic, complemented
4#15689395C211yesmaximal, characteristic, complemented
5#15689390C211yesmaximal, characteristic, complemented
6#15689383C212yesmaximal, complemented
7#15689300C212yesmaximal, complemented
8#15689295C212yesmaximal, complemented
9#15689241C211yesmaximal, characteristic, complemented
10#15689241C211yesmaximal, characteristic, complemented
11C47×#495C211yesmaximal, characteristic, complemented
12#13094072C2212yescomplemented
13#13094069C2212yes—
14#13094056—22no—
15#13094055C2212yes—
16#13094055C2212yescomplemented
17#13094053—22no—
18#13094051—22no—
19#13094050C2212yes—
20#13094050C2212yescomplemented
21#13094048—22no—
22#13094047—21no—
23#13094046C2211yescharacteristic
24#13094046C2211yescharacteristic
25#13094045—22no—
26#13094043—21no—
27Q16×D47—21no—
28SD16×D47—22no—
29D8×D47—21no—
30#13094030C2211yescharacteristic
31#13094030C2212yescomplemented
32#13094030C2211yescharacteristic, complemented
33#13093960C2211yescharacteristic, complemented
34#13093960C2211yescharacteristic, complemented
35#13093952C2211yescharacteristic
36#13093952C2211yescharacteristic, complemented
37#13093952C2212yescomplemented
38#13093943C2212yescomplemented
39#13093941C2212yescomplemented
40C2×Q16×C47C2211yescharacteristic, complemented
41C2×SD16×C47C2212yescomplemented
42C2×D8×C47C2211yescharacteristic
43#124×C47C2212yescomplemented
44C4×C8×C47C2211yescharacteristic, complemented
45C2×Q8×C47C2312yes—
46C2×D4×C47C2312yes—
47C2×C22⋊D47—42no—
48#10625354—22no—
49#10625354—22no—
50Q8×D47—22no—
51Q8×D47—22no—
52#10625352—22no—
53#10625352—22no—
54D4×D47—22no—
55D4×D47—22no—
56#10625350—42no—
57#10625350C2311yescharacteristic
58#10625350C2312yes—
59#10625350C2311yescharacteristic
60Q16×C47—21no—
61Q16×C47—21no—
62SD16×C47—22no—
63SD16×C47—22no—
64D8×C47—21no—
65D8×C47—21no—
66C2×C8×C47C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C22⋊C4×C47—42no—
69C42×C47C2311yescharacteristic
70#10625337—22no—
71#10625337—22no—
72#10625336—22no—
73#10625336—22no—
74#10625335—22no—
75#10625335—22no—
76#10625334—22no—
77#10625334—22no—
78#10625329C2311yescharacteristic
79#10625329C2312yes—
80#10625329C2311yescharacteristic
81Dic188D411yescharacteristic
82Dic188D411yescharacteristic
83D376D411yescharacteristic
84D376D411yescharacteristic
85#10625325D411yescharacteristic
86#10625325D411yescharacteristic
87#10625325D412yes—
88#10625324—21no—
89#10625324—22no—
90#10625324—21no—
91C8×D47—21no—
92C8×D47—22no—
93C8×D47—21no—
94C23×C47—22no—
95C22×D47—42no—
96Q8×C47—22no—
97Q8×C47—22no—
98D4×C47—22no—
99D4×C47—22no—
100C2×C4×C47—21no—
101C2×C4×C47—22no—
102C2×C4×C47C2411yescharacteristic
103C22⋊D47—21no—
104C22⋊D47—22no—
105C22⋊D47—21no—
106C22⋊D47—42no—
107C22⋊D47—42no—
108C2×Dic47—42no—
109D188—42no—
110D188C2×D411yescharacteristic
111D188C2×D412yes—
112D188C2×D411yescharacteristic
113C4×D47—21no—
114C4×D47—22no—
115C4×D47—21no—
116C4×D47—42no—
117C4×D47—42no—
118Dic94—42no—
119Dic94C2×D411yescharacteristic
120Dic94C2×D412yes—
121Dic94C2×D411yescharacteristic
122C8×C47C2×D411yescharacteristic
123C8×C47C2×D411yescharacteristic
124C8×C47C2×D411yescharacteristic
125C8×C47C2×D411yescharacteristic
126C47⋊C8—21no—
127C47⋊C8—22no—
128C47⋊C8—21no—
129C22×C47—42no—
130C22×C47—82no—
131C22×C47H(5,𝔽2)11yescharacteristic
132C2×D47—21no—
133C2×D47—22no—
134C2×D47—21no—
135C2×D47—162no—
136C4×C47—41no—
137C4×C47—42no—
138C4×C47C22×D411yescharacteristic
139C4×C47C22×D411yescharacteristic
140Dic47—21no—
141Dic47—22no—
142Dic47—21no—
143#3290—471nomaximal, Sylow
144C2×C47—21no—
145C2×C47—82no—
146C2×C47D4211yescharacteristic
147D47—41no—
148D47—42no—
149D47—41no—
150#578—471no—
151#577—472no—
152#576—471no—
153#495D4711yescharacteristic, complemented
154#473—471no—
155#472—471no—
156#471—472no—
157#455—472no—
158#454—472no—
159#443—471no—
160#443—471no—
161C47#329011yescharacteristic, complemented, Sylow
1622−1+4—472no—
163H(5,𝔽2)—472no—
164#137—472no—
165#137—472no—
166#137—942no—
167#137—942no—
168AGL(1,ℤ/8)—472no—
169AGL(1,ℤ/8)—472no—
170AGL(1,ℤ/8)—942no—
171AGL(1,ℤ/8)—942no—
172#135—471no—
173#135—471no—
174#135—941no—
175#135—941no—
176#135—942no—
177C2×Q16—941no—
178C2×Q16C2×D4711yescharacteristic, complemented
179C2×SD16—942no—
180C2×SD16C2×D4712yescomplemented
181C2×D8—941no—
182C2×D8C2×D4711yescharacteristic
183#131—471no—
184#131—472no—
185#131—471no—
186#124C2×D4712yescomplemented
187#108—471no—
188#108—471no—
189#104—471no—
190#104—471no—
191#104—472no—
192#101—472no—
193#100—472no—
194C4×C8C2×D4711yescharacteristic, complemented
195#41—471no—
196#41—472no—
197#41—471no—
198#41—942no—
199#41—942no—
200#41—942no—
201#41—942no—
202#41—1882no—
203C2×Q8—942no—
204C2×Q8—942no—
205C2×Q8C22×D4712yes—
206C2×D4—942no—
207C2×D4—942no—
208C2×D4—1882no—
209C2×D4C22×D4712yes—
210Q16—21no—
211Q16—21no—
212Q16—471no—
213Q16—471no—
214Q16—942no—
215Q16—942no—
216SD16—22no—
217SD16—22no—
218SD16—471no—
219SD16—471no—
220SD16—472no—
221SD16—942no—
222SD16—942no—
223SD16—942no—
224SD16—942no—
225D8—21no—
226D8—21no—
227D8—471no—
228D8—471no—
229D8—942no—
230D8—942no—
231M16—471no—
232M16—472no—
233M16—471no—
234M16—941no—
235M16—942no—
236M16—941no—
237C2×C8—941no—
238C2×C8—942no—
239C2×C8—941no—
240C2×C8C22×D4711yescharacteristic
241C2×C8C22×D4711yescharacteristic
242C22⋊C4—42no—
243C42C22×D4711yescharacteristic
244C23—22no—
245C23—1882no—
246Q8—22no—
247Q8—22no—
248Q8—471no—
249Q8—472no—
250Q8—471no—
251Q8—1882no—
252D4—22no—
253D4—22no—
254D4—471no—
255D4—472no—
256D4—471no—
257D4—941no—
258D4—942no—
259D4—941no—
260D4—1882no—
261D4—1882no—
262D4—1882no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—941no—
266C2×C4—942no—
267C2×C4—941no—
268C2×C4—1882no—
269C2×C4—1882no—
270C2×C4—1882no—
271C2×C4C23×D4711yescharacteristic
272C8—941no—
273C8—942no—
274C8—941no—
275C8D4×D4711yescharacteristic
276C8D4×D4711yescharacteristic
277C8D4×D4711yescharacteristic
278C8D4×D4711yescharacteristic
279C22—42no—
280C22—82no—
281C22—941no—
282C22—942no—
283C22—941no—
284C22—7522no—
285C22#1309406911yescharacteristic
286C4—41no—
287C4—42no—
288C4—941no—
289C4—942no—
290C4—941no—
291C4C2×D4×D4711yescharacteristic
292C4C2×D4×D4711yescharacteristic
293C2—21no—
294C2—82no—
295C2—1881no—
296C2—1882no—
297C2—1881no—
298C2#1568975811yescharacteristic
subgroupG/H
centerC2#15689758
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#495C2
socleC2×C47D42
hypercenter#495D47
hypocenterC47#3290
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #15689936C2semidirect
2. #15689929C2semidirect
3. #15689924C2semidirect
4. #15689395C2semidirect
5. #15689390C2semidirect
6. #15689383C2semidirect
7. #15689300C2semidirect
8. #15689295C2semidirect
9. #15689241C2semidirect
10. #15689241C2semidirect
11. C47×#495C2semidirect
12. #13094072C22semidirect
16. #13094055C22semidirect
20. #13094050C22semidirect
31. #13094030C22semidirect
32. #13094030C22semidirect
33. #13093960C22semidirect
34. #13093960C22semidirect
36. #13093952C22semidirect
37. #13093952C22semidirect
38. #13093943C22semidirect
39. #13093941C22semidirect
40. C2×Q16×C47C22semidirect
41. C2×SD16×C47C22semidirect
43. #124×C47C22semidirect
44. C4×C8×C47C22semidirect
153. #495D47semidirect
161. C47#3290semidirect
178. C2×Q16C2×D47semidirect
180. C2×SD16C2×D47semidirect
186. #124C2×D47semidirect
194. C4×C8C2×D47semidirect