Finite Group Databasebeta

← #20255177

Subgroups — #20255177

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#15689932C212yesmaximal, complemented
3#15689928C211yesmaximal, characteristic, complemented
4#15689508C211yesmaximal, characteristic, complemented
5#15689394C211yesmaximal, characteristic, complemented
6#15689389C212yesmaximal, complemented
7#15689299C212yesmaximal, complemented
8#15689298C212yesmaximal, complemented
9#15689239C211yesmaximal, characteristic, complemented
10#15689238C211yesmaximal, characteristic, complemented
11C47×#473C211yesmaximal, characteristic, complemented
12#13094072C2212yescomplemented
13#13094070C2212yes—
14#13094056—22no—
15#13094056—22no—
16#13094055C2212yescomplemented
17#13094052—22no—
18#13094052C2212yes—
19#13094052C2212yescomplemented
20#13094051—22no—
21#13094047—22no—
22#13094047—21no—
23#13094046—21no—
24#13094046C2211yescharacteristic
25#13094044C2211yescharacteristic
26Q16×D47—21no—
27C2×#10625336C2212yescomplemented
28SD16×D47—22no—
29C2×D376—21no—
30C2×D376C2211yescharacteristic
31#13094032C2212yescomplemented
32#13094030C2211yescharacteristic, complemented
33#13094013C2212yescomplemented
34#13093959C2211yescharacteristic, complemented
35#13093951C2211yescharacteristic
36#13093950C2211yescharacteristic, complemented
37#13093950C2212yescomplemented
38#13093940C2212yescomplemented
39C8×Dic47C2211yescharacteristic, complemented
40#137×C47C2212yes—
41C2×Q16×C47C2211yescharacteristic, complemented
42#131×C47C2211yescharacteristic
43#108×C47C2211yescharacteristic, complemented
44#101×C47C2212yescomplemented
45#41×C47C2311yescharacteristic
46C2×Q8×C47C2312yes—
47#10625354—22no—
48#10625354—22no—
49#10625354—22no—
50Q8×D47—22no—
51Q8×D47—22no—
52D4×D47—22no—
53D4×D47—42no—
54#10625350—22no—
55#10625350—42no—
56#10625350C2311yescharacteristic
57#10625350C2312yes—
58C2×D188—22no—
59C2×D188C2312yes—
60Q16×C47—22no—
61Q16×C47—21no—
62Q16×C47—21no—
63SD16×C47—22no—
64M16×C47—21no—
65M16×C47C2312yes—
66M16×C47C2311yescharacteristic
67C2×C8×C47—21no—
68C2×C8×C47C2311yescharacteristic
69#10625337—22no—
70#10625337D411yescharacteristic
71#10625336—22no—
72#10625336—22no—
73#10625336—22no—
74#10625336D411yescharacteristic
75#10625335D411yescharacteristic
76#10625334D411yescharacteristic
77(C2×D47)⋊C4—42no—
78C4×Dic47C2311yescharacteristic
79#10625329C2311yescharacteristic
80C2×C47⋊C8C2311yescharacteristic
81Dic188D411yescharacteristic
82D376—22no—
83D376—22no—
84D376—21no—
85D376—21no—
86D376D411yescharacteristic
87#10625325—22no—
88#10625325—22no—
89#10625325D412yes—
90#10625324—21no—
91#10625324—22no—
92C8×D47—21no—
93C8×D47—22no—
94C22×D47—22no—
95C22×D47—42no—
96Q8×C47—22no—
97Q8×C47—22no—
98Q8×C47C2×D411yescharacteristic
99D4×C47—21no—
100D4×C47C2×D411yescharacteristic
101C2×C4×C47—21no—
102C2×C4×C47—22no—
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—21no—
105C22⋊D47—22no—
106C22⋊D47—42no—
107C2×Dic47—21no—
108D188—22no—
109D188—22no—
110D188—42no—
111D188—42no—
112D188C2×D412yes—
113D188C2×D411yescharacteristic
114C4×D47—22no—
115C4×D47—21no—
116C4×D47—42no—
117C4×D47—42no—
118C4×D47—42no—
119Dic94—42no—
120Dic94C2×D411yescharacteristic
121Dic94C2×D412yes—
122C8×C47—22no—
123C8×C47—21no—
124C8×C47C2×D411yescharacteristic
125C8×C47C2×D411yescharacteristic
126C47⋊C8—21no—
127C47⋊C8C2×D411yescharacteristic
128C47⋊C8C2×D411yescharacteristic
129C22×C47—21no—
130C22×C47H(5,𝔽2)11yescharacteristic
131C2×D47—21no—
132C2×D47—22no—
133C2×D47—42no—
134C2×D47—82no—
135C2×D47—162no—
136C4×C47—21no—
137C4×C47—42no—
138C4×C47C22×D411yescharacteristic
139C4×C47C22×D411yescharacteristic
140Dic47—21no—
141Dic47—22no—
142Dic47—41no—
143#3290—471nomaximal, Sylow
144C2×C47—21no—
145C2×C47—41no—
146C2×C47D4211yescharacteristic
147D47—41no—
148D47—42no—
149D47—82no—
150#578—471no—
151#577—472no—
152#576—471no—
153#495—471no—
154#473D4711yescharacteristic, complemented
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—942no—
166#137—942no—
167#137C2×D4712yes—
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—472no—
180C2×SD16—942no—
181C2×D8—471no—
182C2×D8—941no—
183#131—472no—
184#131—471no—
185#131C2×D4711yescharacteristic
186#124—472no—
187#108—471no—
188#108C2×D4711yescharacteristic, complemented
189#104—471no—
190#104—471no—
191#104—472no—
192#101C2×D4712yescomplemented
193#100—472no—
194C4×C8—471no—
195#41—471no—
196#41—472no—
197#41—942no—
198#41—942no—
199#41—942no—
200#41—942no—
201#41—1882no—
202#41C22×D4711yescharacteristic
203C2×Q8—942no—
204C2×Q8—942no—
205C2×Q8C22×D4712yes—
206C2×D4—472no—
207C2×D4—942no—
208C2×D4—942no—
209C2×D4—1882no—
210Q16—22no—
211Q16—21no—
212Q16—21no—
213Q16—471no—
214Q16—471no—
215Q16—942no—
216SD16—22no—
217SD16—471no—
218SD16—471no—
219SD16—472no—
220SD16—942no—
221SD16—942no—
222SD16—942no—
223SD16—942no—
224SD16—942no—
225D8—471no—
226D8—471no—
227D8—942no—
228D8—942no—
229D8—941no—
230D8—941no—
231M16—21no—
232M16—471no—
233M16—942no—
234M16—941no—
235M16C22×D4712yes—
236M16C22×D4711yescharacteristic
237C2×C8—21no—
238C2×C8—471no—
239C2×C8—942no—
240C2×C8—941no—
241C2×C8C22×D4711yescharacteristic
242C22⋊C4—1882no—
243C42—471no—
244C23—942no—
245C23—1882no—
246Q8—22no—
247Q8—22no—
248Q8—471no—
249Q8—472no—
250Q8—1882no—
251Q8D4×D4711yescharacteristic
252D4—21no—
253D4—471no—
254D4—472no—
255D4—942no—
256D4—941no—
257D4—942no—
258D4—942no—
259D4—1882no—
260D4—1882no—
261D4—1882no—
262D4D4×D4711yescharacteristic
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—942no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—1882no—
269C2×C4—1882no—
270C2×C4—1882no—
271C2×C4C23×D4711yescharacteristic
272C8—21no—
273C8—22no—
274C8—471no—
275C8—471no—
276C8—941no—
277C8D4×D4711yescharacteristic
278C8D4×D4711yescharacteristic
279C22—21no—
280C22—941no—
281C22—942no—
282C22—3762no—
283C22—1882no—
284C22—7522no—
285C22#1309407011yescharacteristic
286C4—21no—
287C4—42no—
288C4—942no—
289C4—941no—
290C4—1881no—
291C4C2×D4×D4711yescharacteristic
292C4C2×D4×D4711yescharacteristic
293C2—21no—
294C2—41no—
295C2—3762no—
296C2—1882no—
297C2—1881no—
298C2#1568975711yescharacteristic
subgroupG/H
centerC2#15689757
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#473C2
socleC2×C47D42
hypercenter#473D47
hypocenterC47#3290
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #15689936C2semidirect
2. #15689932C2semidirect
3. #15689928C2semidirect
4. #15689508C2semidirect
5. #15689394C2semidirect
6. #15689389C2semidirect
7. #15689299C2semidirect
8. #15689298C2semidirect
9. #15689239C2semidirect
10. #15689238C2semidirect
11. C47×#473C2semidirect
12. #13094072C22semidirect
16. #13094055C22semidirect
19. #13094052C22semidirect
27. C2×#10625336C22semidirect
31. #13094032C22semidirect
32. #13094030C22semidirect
33. #13094013C22semidirect
34. #13093959C22semidirect
36. #13093950C22semidirect
37. #13093950C22semidirect
38. #13093940C22semidirect
39. C8×Dic47C22semidirect
41. C2×Q16×C47C22semidirect
43. #108×C47C22semidirect
44. #101×C47C22semidirect
154. #473D47semidirect
161. C47#3290semidirect
178. C2×Q16C2×D47semidirect
188. #108C2×D47semidirect
192. #101C2×D47semidirect