Finite Group Databasebeta

← #20255185

Subgroups — #20255185

Order 6016.

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

normal subgroups only

This group has 476 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#15689926C212yesmaximal, complemented
2#15689925C211yesmaximal, characteristic, complemented
3#15689498C211yesmaximal, characteristic, complemented
4#15689393C211yesmaximal, characteristic, complemented
5#15689391C212yesmaximal, complemented
6#15689390C211yesmaximal, characteristic, complemented
7#15689291C212yesmaximal, complemented
8#15689289C212yesmaximal, complemented
9#15689240C211yesmaximal, characteristic, complemented
10#15689238C211yesmaximal, characteristic, complemented
11C47×#576C211yesmaximal, characteristic, complemented
12#13094070C2212yescomplemented
13#13094051—22no—
14#13094050—22no—
15#13094050C2212yescomplemented
16#13094049—22no—
17#13094049C2212yescomplemented
18#13094049C2212yescomplemented
19#13094047—21no—
20#13094044—22no—
21#13094044C2211yescharacteristic
22C2×D376C2211yescharacteristic, complemented
23C2×#10625334—22no—
24C2×#10625334C2212yescomplemented
25D8×D47—21no—
26#13094031C2212yescomplemented
27#13094030C2211yescharacteristic, complemented
28#13094020C2212yescomplemented
29#13093960C2211yescharacteristic, complemented
30#13093959C2211yescharacteristic, complemented
31#13093951C2211yescharacteristic, complemented
32#13093951C2212yescomplemented
33#13093950C2211yescharacteristic, complemented
34#13093941C2212yescomplemented
35#13093940C2212yescomplemented
36C8×Dic47C2211yescharacteristic, complemented
37H(5,𝔽2)×C47C2212yescomplemented
38AGL(1,ℤ/8)×C47—22no—
39AGL(1,ℤ/8)×C47C2212yescomplemented
40#135×C47—21no—
41#135×C47C2211yescharacteristic
42C2×D8×C47—21no—
43C2×D8×C47C2211yescharacteristic, complemented
44#131×C47C2211yescharacteristic, complemented
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—
53C2×C22⋊D47—42no—
54#10625354—22no—
55D4×D47—22no—
56D4×D47—42no—
57#10625350—22no—
58#10625350C2311yescharacteristic
59C2×D188—22no—
60C2×D188C2312yes—
61Q16×C47D411yescharacteristic, complemented
62SD16×C47—22no—
63SD16×C47D412yescomplemented
64D8×C47—22no—
65D8×C47—21no—
66D8×C47—21no—
67D8×C47D411yescharacteristic, complemented
68M16×C47—21no—
69M16×C47C2311yescharacteristic
70C2×C8×C47—21no—
71C2×C8×C47C2311yescharacteristic
72#10625337D411yescharacteristic, complemented
73#10625336—22no—
74#10625336—22no—
75#10625336D411yescharacteristic, complemented
76#10625335—22no—
77#10625335D411yescharacteristic, complemented
78#10625334—22no—
79#10625334—22no—
80#10625334—22no—
81#10625334—22no—
82#10625334—22no—
83#10625334D411yescharacteristic, complemented
84C4×Dic47C2311yescharacteristic
85#10625329—22no—
86#10625329C2312yes—
87#10625329C2311yescharacteristic
88C2×C47⋊C8—22no—
89C2×C47⋊C8C2311yescharacteristic
90D376—21no—
91D376—21no—
92#10625324—21no—
93C8×D47—21no—
94C23×C47—22no—
95C23×C47—42no—
96C22×D47—22no—
97C22×D47—42no—
98Q8×C47C2×D411yescharacteristic
99Q8×C47C2×D412yes—
100D4×C47—22no—
101D4×C47—21no—
102D4×C47—22no—
103D4×C47—22no—
104D4×C47—42no—
105D4×C47—42no—
106D4×C47C2×D411yescharacteristic
107D4×C47C2×D412yes—
108C2×C4×C47—22no—
109C2×C4×C47—21no—
110C2×C4×C47—42no—
111C2×C4×C47C2411yescharacteristic
112C22⋊D47—21no—
113C22⋊D47—42no—
114C22⋊D47—84no—
115C2×Dic47—21no—
116D188—22no—
117D188—22no—
118D188—42no—
119D188C2×D411yescharacteristic
120C4×D47—21no—
121C4×D47—42no—
122Dic94C2×D411yescharacteristic
123C8×C47—21no—
124C8×C47C2×D411yescharacteristic
125C8×C47C2×D411yescharacteristic
126C47⋊C8—21no—
127C47⋊C8—22no—
128C47⋊C8C2×D411yescharacteristic
129C47⋊C8C2×D411yescharacteristic
130C22×C47—22no—
131C22×C47—21no—
132C22×C47—42no—
133C22×C47—82no—
134C22×C47—162no—
135C22×C47H(5,𝔽2)11yescharacteristic
136C2×D47—21no—
137C2×D47—42no—
138C2×D47—82no—
139C2×D47—162no—
140C4×C47—22no—
141C4×C47—21no—
142C4×C47C22×D411yescharacteristic
143C4×C47C22×D411yescharacteristic
144Dic47—22no—
145Dic47—21no—
146#3292—471nomaximal, Sylow
147C2×C47—21no—
148C2×C47—42no—
149C2×C47—41no—
150C2×C47—82no—
151C2×C47D4211yescharacteristic
152D47—41no—
153D47—82no—
154#576—472no—
155#576—471no—
156#576D4711yescharacteristic, complemented
157#493—471no—
158#472—472no—
159#472—471no—
160#472—471no—
161#453—472no—
162#453—472no—
163#443—471no—
164#443—471no—
165C47#329211yescharacteristic, complemented, Sylow
166H(5,𝔽2)—472no—
167H(5,𝔽2)C2×D4712yescomplemented
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—472no—
170AGL(1,ℤ/8)—472no—
171AGL(1,ℤ/8)—472no—
172AGL(1,ℤ/8)—942no—
173AGL(1,ℤ/8)—942no—
174AGL(1,ℤ/8)—942no—
175AGL(1,ℤ/8)C2×D4712yescomplemented
176#135—21no—
177#135—471no—
178#135—942no—
179#135—941no—
180#135C2×D4711yescharacteristic
181C2×D8—21no—
182C2×D8—472no—
183C2×D8—471no—
184C2×D8—942no—
185C2×D8—941no—
186C2×D8C2×D4711yescharacteristic, complemented
187#131—472no—
188#131—471no—
189#131C2×D4711yescharacteristic, complemented
190#127—472no—
191#108—471no—
192#108—471no—
193#104—471no—
194#104—472no—
195#104—471no—
196#100—472no—
197#100—472no—
198C4×C8—471no—
199#41—22no—
200#41—22no—
201#41—471no—
202#41—942no—
203#41—942no—
204#41C22×D4711yescharacteristic
205#41C22×D4712yes—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4—472no—
210C2×D4—942no—
211C2×D4—942no—
212C2×D4—1882no—
213C2×D4—1882no—
214C2×D4C22×D4712yes—
215Q16—471no—
216Q16C22⋊D4711yescharacteristic, complemented
217SD16—22no—
218SD16—471no—
219SD16—471no—
220SD16—942no—
221SD16—942no—
222SD16—942no—
223SD16C22⋊D4712yescomplemented
224D8—22no—
225D8—21no—
226D8—21no—
227D8—471no—
228D8—942no—
229D8—942no—
230D8—942no—
231D8—942no—
232D8—942no—
233D8—941no—
234D8—941no—
235D8C22⋊D4711yescharacteristic, complemented
236M16—21no—
237M16—472no—
238M16—471no—
239M16—942no—
240M16—941no—
241M16C22×D4711yescharacteristic
242C2×C8—21no—
243C2×C8—471no—
244C2×C8—942no—
245C2×C8—941no—
246C2×C8C22×D4711yescharacteristic
247C42—471no—
248C23—22no—
249C23—42no—
250C23—942no—
251C23—1882no—
252Q8—471no—
253Q8D4×D4711yescharacteristic
254Q8C2×C22⋊D4712yes—
255D4—21no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—471no—
262D4—941no—
263D4—942no—
264D4—942no—
265D4—3764no—
266D4—1882no—
267D4—1882no—
268D4D4×D4711yescharacteristic
269D4C2×C22⋊D4712yes—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—941no—
274C2×C4—941no—
275C2×C4—1882no—
276C2×C4C23×D4711yescharacteristic
277C8—21no—
278C8—471no—
279C8—471no—
280C8—942no—
281C8—941no—
282C8C2×C22⋊D4711yescharacteristic
283C8C2×C22⋊D4711yescharacteristic
284C22—21no—
285C22—22no—
286C22—42no—
287C22—82no—
288C22—162no—
289C22—941no—
290C22—3762no—
291C22—1882no—
292C22—7522no—
293C22#1309406911yescharacteristic
294C4—21no—
295C4—22no—
296C4—942no—
297C4—941no—
298C4C2×D4×D4711yescharacteristic
299C4C22×C22⋊D4711yescharacteristic
300C2—21no—
301C2—41no—
302C2—42no—
303C2—82no—
304C2—3762no—
305C2—1881no—
306C2D4×C22⋊D4711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#576C2
socleC2×C47D42
hypercenter#576D47
hypocenterC47#3292
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. #15689926C2semidirect
2. #15689925C2semidirect
3. #15689498C2semidirect
4. #15689393C2semidirect
5. #15689391C2semidirect
6. #15689390C2semidirect
7. #15689291C2semidirect
8. #15689289C2semidirect
9. #15689240C2semidirect
10. #15689238C2semidirect
11. C47×#576C2semidirect
12. #13094070C22semidirect
15. #13094050C22semidirect
17. #13094049C22semidirect
18. #13094049C22semidirect
22. C2×D376C22semidirect
24. C2×#10625334C22semidirect
26. #13094031C22semidirect
27. #13094030C22semidirect
28. #13094020C22semidirect
29. #13093960C22semidirect
30. #13093959C22semidirect
31. #13093951C22semidirect
32. #13093951C22semidirect
33. #13093950C22semidirect
34. #13093941C22semidirect
35. #13093940C22semidirect
36. C8×Dic47C22semidirect
37. H(5,𝔽2)×C47C22semidirect
39. AGL(1,ℤ/8)×C47C22semidirect
43. C2×D8×C47C22semidirect
44. #131×C47C22semidirect
61. Q16×C47D4semidirect
63. SD16×C47D4semidirect
67. D8×C47D4semidirect
72. #10625337D4semidirect
75. #10625336D4semidirect
77. #10625335D4semidirect
83. #10625334D4semidirect
156. #576D47semidirect
165. C47#3292semidirect
167. H(5,𝔽2)C2×D47semidirect
175. AGL(1,ℤ/8)C2×D47semidirect
186. C2×D8C2×D47semidirect
189. #131C2×D47semidirect
216. Q16C22⋊D47semidirect
223. SD16C22⋊D47semidirect
235. D8C22⋊D47semidirect