Finite Group Databasebeta

← #20255186

Subgroups — #20255186

Order 6016.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 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#15689928C211yesmaximal, characteristic, complemented
2#15689927C212yesmaximal, complemented
3#15689924C211yesmaximal, characteristic, complemented
4#15689498C211yesmaximal, characteristic, complemented
5#15689394C211yesmaximal, characteristic, complemented
6#15689392C212yesmaximal, complemented
7#15689293C212yesmaximal, complemented
8#15689289C212yesmaximal, complemented
9#15689239C211yesmaximal, characteristic, complemented
10#15689238C211yesmaximal, characteristic, complemented
11C47×#472C211yesmaximal, characteristic, complemented
12#13094070C2212yescomplemented
13#13094069C2212yescomplemented
14#13094052—22no—
15#13094052C2212yescomplemented
16#13094052C2212yescomplemented
17#13094051—22no—
18#13094050C2212yescomplemented
19#13094048—22no—
20#13094048—22no—
21#13094046—21no—
22#13094046C2211yescharacteristic
23#13094045—22no—
24#13094044C2211yescharacteristic
25#13094043—21no—
26C2×D376—21no—
27C2×D376C2211yescharacteristic, complemented
28C2×#10625334C2212yescomplemented
29D8×D47—22no—
30D8×D47—21no—
31#13094032C2212yescomplemented
32#13094030C2211yescharacteristic, complemented
33#13094020C2212yescomplemented
34#13093959C2211yescharacteristic, complemented
35#13093951C2211yescharacteristic, complemented
36#13093950C2211yescharacteristic, complemented
37#13093950C2212yescomplemented
38#13093940C2212yescomplemented
39C8×Dic47C2211yescharacteristic, complemented
40AGL(1,ℤ/8)×C47C2212yescomplemented
41C2×D8×C47C2211yescharacteristic, complemented
42#131×C47C2211yescharacteristic, complemented
43#108×C47C2211yescharacteristic, complemented
44#100×C47C2212yescomplemented
45#41×C47C2311yescharacteristic
46C2×D4×C47C2312yes—
47C2×C22⋊D47—42no—
48C2×C22⋊D47—42no—
49#10625354—22no—
50#10625352—22no—
51#10625352—22no—
52D4×D47—22no—
53D4×D47—22no—
54D4×D47—22no—
55D4×D47—42no—
56#10625350—22no—
57#10625350C2311yescharacteristic
58#10625350C2312yes—
59C2×D188—22no—
60C2×D188C2312yes—
61SD16×C47—22no—
62D8×C47—22no—
63D8×C47—21no—
64D8×C47—21no—
65M16×C47—21no—
66M16×C47C2312yes—
67M16×C47C2311yescharacteristic
68C2×C8×C47—21no—
69C2×C8×C47C2311yescharacteristic
70#10625337D411yescharacteristic, complemented
71#10625336D411yescharacteristic, complemented
72#10625335—22no—
73#10625335D411yescharacteristic, complemented
74#10625334—22no—
75#10625334—22no—
76#10625334—22no—
77#10625334D411yescharacteristic, complemented
78C4×Dic47C2311yescharacteristic
79#10625329C2311yescharacteristic
80C2×C47⋊C8C2311yescharacteristic
81Dic188D411yescharacteristic, complemented
82D376—22no—
83D376—22no—
84D376—21no—
85D376—21no—
86D376D411yescharacteristic, complemented
87#10625325—22no—
88#10625325—22no—
89#10625325D412yescomplemented
90#10625324—21no—
91#10625324—22no—
92C8×D47—21no—
93C8×D47—22no—
94C23×C47—22no—
95C22×D47—22no—
96C22×D47—42no—
97C22×D47—42no—
98Q8×C47C2×D411yescharacteristic
99D4×C47—21no—
100D4×C47—22no—
101D4×C47—22no—
102D4×C47C2×D411yescharacteristic
103C2×C4×C47—21no—
104C2×C4×C47C2411yescharacteristic
105C22⋊D47—22no—
106C22⋊D47—21no—
107C22⋊D47—42no—
108C22⋊D47—42no—
109C22⋊D47—42no—
110C22⋊D47—84no—
111C2×Dic47—21no—
112C2×Dic47—42no—
113D188—22no—
114D188—22no—
115D188—42no—
116D188C2×D412yes—
117D188C2×D411yescharacteristic
118C4×D47—21no—
119C4×D47—22no—
120C4×D47—42no—
121Dic94C2×D411yescharacteristic
122Dic94C2×D412yes—
123C8×C47—22no—
124C8×C47—21no—
125C8×C47C2×D411yescharacteristic
126C8×C47C2×D411yescharacteristic
127C47⋊C8—21no—
128C47⋊C8C2×D411yescharacteristic
129C47⋊C8C2×D411yescharacteristic
130C22×C47—21no—
131C22×C47—42no—
132C22×C47—82no—
133C22×C47H(5,𝔽2)11yescharacteristic
134C2×D47—22no—
135C2×D47—21no—
136C2×D47—42no—
137C2×D47—82no—
138C2×D47—162no—
139C2×D47—162no—
140C4×C47—21no—
141C4×C47C22×D411yescharacteristic
142C4×C47C22×D411yescharacteristic
143Dic47—22no—
144Dic47—22no—
145Dic47—21no—
146#3292—471nomaximal, Sylow
147C2×C47—21no—
148C2×C47—41no—
149C2×C47—82no—
150C2×C47D4211yescharacteristic
151D47—42no—
152D47—41no—
153D47—82no—
154#576—472no—
155#576—471no—
156#576—471no—
157#493—471no—
158#472—471no—
159#472—472no—
160#472D4711yescharacteristic, complemented
161#453—472no—
162#453—472no—
163#443—471no—
164#443—471no—
165C47#329211yescharacteristic, complemented, Sylow
166H(5,𝔽2)—472no—
167H(5,𝔽2)—472no—
168AGL(1,ℤ/8)—472no—
169AGL(1,ℤ/8)—472no—
170AGL(1,ℤ/8)—472no—
171AGL(1,ℤ/8)—942no—
172AGL(1,ℤ/8)—942no—
173AGL(1,ℤ/8)—942no—
174AGL(1,ℤ/8)—942no—
175AGL(1,ℤ/8)C2×D4712yescomplemented
176#135—471no—
177#135—471no—
178#135—941no—
179#135—941no—
180#135—942no—
181C2×D8—472no—
182C2×D8—471no—
183C2×D8—941no—
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#108C2×D4711yescharacteristic, complemented
193#104—471no—
194#104—472no—
195#104—471no—
196#100—472no—
197#100C2×D4712yescomplemented
198C4×C8—471no—
199#41—471no—
200#41—472no—
201#41—942no—
202#41—942no—
203#41—942no—
204#41—942no—
205#41C22×D4711yescharacteristic
206C2×D4—472no—
207C2×D4—942no—
208C2×D4—942no—
209C2×D4—942no—
210C2×D4—942no—
211C2×D4—1882no—
212C2×D4—1882no—
213C2×D4—1882no—
214C2×D4C22×D4712yes—
215Q16—471no—
216Q16—471no—
217SD16—22no—
218SD16—471no—
219SD16—471no—
220SD16—472no—
221SD16—942no—
222SD16—942no—
223SD16—942no—
224D8—22no—
225D8—21no—
226D8—21no—
227D8—471no—
228D8—471no—
229D8—942no—
230D8—942no—
231D8—942no—
232D8—942no—
233D8—942no—
234D8—941no—
235D8—941no—
236M16—21no—
237M16—471no—
238M16—942no—
239M16—941no—
240M16C22×D4712yes—
241M16C22×D4711yescharacteristic
242C2×C8—21no—
243C2×C8—471no—
244C2×C8—942no—
245C2×C8—941no—
246C2×C8C22×D4711yescharacteristic
247C42—471no—
248C23—22no—
249C23—942no—
250C23—1882no—
251C23—1882no—
252Q8—471no—
253Q8—472no—
254Q8D4×D4711yescharacteristic
255D4—21no—
256D4—22no—
257D4—22no—
258D4—471no—
259D4—472no—
260D4—942no—
261D4—941no—
262D4—942no—
263D4—942no—
264D4—3764no—
265D4—1882no—
266D4—1882no—
267D4—1882no—
268D4—1882no—
269D4D4×D4711yescharacteristic
270C2×C4—21no—
271C2×C4—941no—
272C2×C4—942no—
273C2×C4—941no—
274C2×C4—1882no—
275C2×C4—1882no—
276C2×C4C23×D4711yescharacteristic
277C8—21no—
278C8—22no—
279C8—471no—
280C8—471no—
281C8—941no—
282C8D4×D4711yescharacteristic
283C8D4×D4711yescharacteristic
284C22—21no—
285C22—42no—
286C22—82no—
287C22—942no—
288C22—941no—
289C22—3762no—
290C22—1882no—
291C22—7522no—
292C22—7522no—
293C22#1309407011yescharacteristic
294C4—21no—
295C4—942no—
296C4—942no—
297C4—941no—
298C4C2×D4×D4711yescharacteristic
299C4C2×D4×D4711yescharacteristic
300C2—21no—
301C2—41no—
302C2—82no—
303C2—3762no—
304C2—1882no—
305C2—1881no—
306C2#1568975711yescharacteristic
subgroupG/H
centerC2#15689757
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#472C2
socleC2×C47D42
hypercenter#472D47
hypocenterC47#3292
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #15689928C2semidirect
2. #15689927C2semidirect
3. #15689924C2semidirect
4. #15689498C2semidirect
5. #15689394C2semidirect
6. #15689392C2semidirect
7. #15689293C2semidirect
8. #15689289C2semidirect
9. #15689239C2semidirect
10. #15689238C2semidirect
11. C47×#472C2semidirect
12. #13094070C22semidirect
13. #13094069C22semidirect
15. #13094052C22semidirect
16. #13094052C22semidirect
18. #13094050C22semidirect
27. C2×D376C22semidirect
28. C2×#10625334C22semidirect
31. #13094032C22semidirect
32. #13094030C22semidirect
33. #13094020C22semidirect
34. #13093959C22semidirect
35. #13093951C22semidirect
36. #13093950C22semidirect
37. #13093950C22semidirect
38. #13093940C22semidirect
39. C8×Dic47C22semidirect
40. AGL(1,ℤ/8)×C47C22semidirect
41. C2×D8×C47C22semidirect
42. #131×C47C22semidirect
43. #108×C47C22semidirect
44. #100×C47C22semidirect
70. #10625337D4semidirect
71. #10625336D4semidirect
73. #10625335D4semidirect
77. #10625334D4semidirect
81. Dic188D4semidirect
86. D376D4semidirect
89. #10625325D4semidirect
160. #472D47semidirect
165. C47#3292semidirect
175. AGL(1,ℤ/8)C2×D47semidirect
186. C2×D8C2×D47semidirect
189. #131C2×D47semidirect
192. #108C2×D47semidirect
197. #100C2×D47semidirect