Finite Group Databasebeta

← #20255170

Subgroups — #20255170

Order 6016.

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#15689937C211yesmaximal, characteristic, complemented
2#15689934C212yesmaximal, complemented
3#15689506C211yesmaximal, characteristic, complemented
4#15689398C211yesmaximal, characteristic, complemented
5#15689390C211yesmaximal, characteristic, complemented
6#15689384C212yesmaximal, complemented
7#15689301C212yesmaximal, complemented
8#15689294C212yesmaximal, complemented
9#15689240C211yesmaximal, characteristic, complemented
10#15689238C211yesmaximal, characteristic, complemented
11C47×#576C211yesmaximal, characteristic, complemented
12#13094071C2212yescomplemented
13#13094054—22no—
14#13094054C2212yes—
15#13094054C2212yescomplemented
16#13094053—22no—
17#13094050—22no—
18#13094050C2212yescomplemented
19#13094044—22no—
20#13094044C2211yescharacteristic
21#13094043—21no—
22C2×Dic188C2211yescharacteristic, complemented
23Q16×D47—21no—
24C2×#10625335—22no—
25C2×#10625335C2212yescomplemented
26#13094031C2212yescomplemented
27#13094030C2211yescharacteristic, complemented
28#13094011C2212yescomplemented
29#13093960C2211yescharacteristic, complemented
30#13093959C2211yescharacteristic, complemented
31#13093951C2211yescharacteristic
32#13093951C2212yescomplemented
33#13093950C2211yescharacteristic, complemented
34#13093942C2212yescomplemented
35#13093941C2212yescomplemented
36C8×Dic47C2211yescharacteristic, complemented
37H(5,𝔽2)×C47C2212yes—
38AGL(1,ℤ/8)×C47—22no—
39AGL(1,ℤ/8)×C47C2212yes—
40#135×C47—21no—
41#135×C47C2211yescharacteristic
42C2×D8×C47—21no—
43C2×D8×C47C2211yescharacteristic
44#131×C47C2211yescharacteristic
45#41×C47—22no—
46#41×C47—22no—
47#41×C47C2311yescharacteristic
48#41×C47C2312yes—
49C2×D4×C47—22no—
50C2×D4×C47—22no—
51C2×D4×C47—42no—
52C2×D4×C47C2312yes—
53Q8×D47—22no—
54#10625352—22no—
55#10625352—42no—
56#10625350—22no—
57#10625350C2311yescharacteristic
58C2×Dic94—22no—
59C2×Dic94C2312yes—
60Q16×C47D411yescharacteristic
61SD16×C47—22no—
62SD16×C47D412yes—
63D8×C47—22no—
64D8×C47—21no—
65D8×C47—21no—
66D8×C47D411yescharacteristic
67M16×C47—21no—
68M16×C47C2311yescharacteristic
69C2×C8×C47—21no—
70C2×C8×C47C2311yescharacteristic
71C22⋊Dic47—42no—
72#10625337—22no—
73#10625337—22no—
74#10625337D411yescharacteristic
75#10625336D411yescharacteristic
76#10625335—22no—
77#10625335—22no—
78#10625335—22no—
79#10625335—22no—
80#10625335—22no—
81#10625335D411yescharacteristic
82#10625334—22no—
83#10625334D411yescharacteristic
84C4×Dic47C2311yescharacteristic
85#10625329—22no—
86#10625329C2311yescharacteristic
87#10625329C2312yes—
88C2×C47⋊C8—22no—
89C2×C47⋊C8C2311yescharacteristic
90Dic188—21no—
91Dic188—21no—
92#10625324—21no—
93C8×D47—21no—
94C23×C47—22no—
95C23×C47—42no—
96Q8×C47C2×D411yescharacteristic
97Q8×C47C2×D412yes—
98D4×C47—22no—
99D4×C47—21no—
100D4×C47—22no—
101D4×C47—22no—
102D4×C47—42no—
103D4×C47—42no—
104D4×C47C2×D411yescharacteristic
105D4×C47C2×D412yes—
106C2×C4×C47—22no—
107C2×C4×C47—21no—
108C2×C4×C47—42no—
109C2×C4×C47C2411yescharacteristic
110C22⋊D47—21no—
111C22⋊D47—42no—
112C2×Dic47—21no—
113C2×Dic47—22no—
114C2×Dic47—42no—
115D188C2×D411yescharacteristic
116C4×D47—21no—
117C4×D47—42no—
118Dic94—22no—
119Dic94—22no—
120Dic94—42no—
121Dic94C2×D411yescharacteristic
122C8×C47—21no—
123C8×C47C2×D411yescharacteristic
124C8×C47C2×D411yescharacteristic
125C47⋊C8—21no—
126C47⋊C8—22no—
127C47⋊C8C2×D411yescharacteristic
128C47⋊C8C2×D411yescharacteristic
129C22×C47—22no—
130C22×C47—21no—
131C22×C47—42no—
132C22×C47—82no—
133C22×C47—162no—
134C22×C47H(5,𝔽2)11yescharacteristic
135C2×D47—21no—
136C4×C47—22no—
137C4×C47—21no—
138C4×C47C22×D411yescharacteristic
139C4×C47C22×D411yescharacteristic
140Dic47—21no—
141Dic47—41no—
142Dic47—42no—
143#3290—471nomaximal, Sylow
144C2×C47—21no—
145C2×C47—42no—
146C2×C47—41no—
147C2×C47—82no—
148C2×C47D4211yescharacteristic
149D47—41no—
150#578—471no—
151#577—472no—
152#576D4711yescharacteristic, complemented
153#495—471no—
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)C2×D4712yes—
164#137—472no—
165#137—472no—
166#137—942no—
167#137—942no—
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—472no—
170AGL(1,ℤ/8)—942no—
171AGL(1,ℤ/8)C2×D4712yes—
172#135—21no—
173#135—471no—
174#135—942no—
175#135—941no—
176#135C2×D4711yescharacteristic
177C2×Q16—471no—
178C2×Q16—941no—
179C2×SD16—472no—
180C2×SD16—942no—
181C2×D8—21no—
182C2×D8C2×D4711yescharacteristic
183#131—472no—
184#131—471no—
185#131C2×D4711yescharacteristic
186#124—472no—
187#108—471no—
188#108—471no—
189#104—471no—
190#104—472no—
191#104—471no—
192#101—472no—
193#100—472no—
194C4×C8—471no—
195#41—22no—
196#41—22no—
197#41—471no—
198#41—942no—
199#41—942no—
200#41—1882no—
201#41C22×D4711yescharacteristic
202#41C22×D4712yes—
203C2×Q8—472no—
204C2×Q8—942no—
205C2×Q8—942no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4C22×D4712yes—
210Q16—471no—
211Q16—942no—
212Q16—942no—
213Q16—941no—
214Q16—941no—
215Q16C22⋊D4711yescharacteristic
216SD16—22no—
217SD16—471no—
218SD16—471no—
219SD16—942no—
220SD16—942no—
221SD16—942no—
222SD16—942no—
223SD16—942no—
224SD16C22⋊D4712yes—
225D8—22no—
226D8—21no—
227D8—21no—
228D8—471no—
229D8—942no—
230D8C22⋊D4711yescharacteristic
231M16—21no—
232M16—471no—
233M16—472no—
234M16—942no—
235M16—941no—
236M16C22×D4711yescharacteristic
237C2×C8—21no—
238C2×C8—471no—
239C2×C8—942no—
240C2×C8—941no—
241C2×C8C22×D4711yescharacteristic
242C22⋊C4—1882no—
243C42—471no—
244C23—22no—
245C23—42no—
246Q8—471no—
247Q8—942no—
248Q8—942no—
249Q8—1882no—
250Q8D4×D4711yescharacteristic
251Q8C2×C22⋊D4712yes—
252D4—21no—
253D4—22no—
254D4—22no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—471no—
259D4—941no—
260D4—1882no—
261D4D4×D4711yescharacteristic
262D4C2×C22⋊D4712yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—942no—
269C2×C4—1882no—
270C2×C4—1882no—
271C2×C4C23×D4711yescharacteristic
272C8—21no—
273C8—471no—
274C8—471no—
275C8—942no—
276C8—941no—
277C8C2×C22⋊D4711yescharacteristic
278C8C2×C22⋊D4711yescharacteristic
279C22—22no—
280C22—21no—
281C22—42no—
282C22—82no—
283C22—162no—
284C22—941no—
285C22#1309406911yescharacteristic
286C4—21no—
287C4—22no—
288C4—941no—
289C4—1881no—
290C4—1882no—
291C4C2×D4×D4711yescharacteristic
292C4C22×C22⋊D4711yescharacteristic
293C2—21no—
294C2—41no—
295C2—42no—
296C2—82no—
297C2—1881no—
298C2D4×C22⋊D4711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#576C2
socleC2×C47D42
hypercenter#576D47
hypocenterC47#3290
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #15689937C2semidirect
2. #15689934C2semidirect
3. #15689506C2semidirect
4. #15689398C2semidirect
5. #15689390C2semidirect
6. #15689384C2semidirect
7. #15689301C2semidirect
8. #15689294C2semidirect
9. #15689240C2semidirect
10. #15689238C2semidirect
11. C47×#576C2semidirect
12. #13094071C22semidirect
15. #13094054C22semidirect
18. #13094050C22semidirect
22. C2×Dic188C22semidirect
25. C2×#10625335C22semidirect
26. #13094031C22semidirect
27. #13094030C22semidirect
28. #13094011C22semidirect
29. #13093960C22semidirect
30. #13093959C22semidirect
32. #13093951C22semidirect
33. #13093950C22semidirect
34. #13093942C22semidirect
35. #13093941C22semidirect
36. C8×Dic47C22semidirect
152. #576D47semidirect
161. C47#3290semidirect