Finite Group Databasebeta

← #20253864

Subgroups — #20253864

Order 6016.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#13094057C211yesmaximal, characteristic, complemented
2C2×#13094052C211yesmaximal, characteristic, complemented
3C2×#13094046C211yesmaximal, characteristic, complemented
4C22×#10625325C211yesmaximal, characteristic, complemented
5#15689699C211yesmaximal, characteristic, complemented
6#15689692C211yesmaximal, characteristic, complemented
7#15689517C212yesmaximal, complemented
8#15689512C212yesmaximal, complemented
9#15689507C212yesmaximal, complemented
10#15689496C212yesmaximal, complemented
11C47×#405C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C2×#10625350C2211yescharacteristic
14C22×Dic94C2211yescharacteristic
15C22×D188C2211yescharacteristic
16#13094057—24no—
17#13094052—24no—
18#13094046—24no—
19C2×Dic188C2212yescomplemented
20C2×Dic188C2211yescharacteristic, complemented
21C2×#10625325—24no—
22C2×#10625325C2212yes—
23C2×#10625325C2212yes—
24C2×#10625325C2212yes—
25C2×#10625325C2211yescharacteristic, complemented
26C2×#10625325C2212yescomplemented
27C2×#10625325C2211yescharacteristic, complemented
28C2×D376C2212yes—
29C2×D376C2211yescharacteristic, complemented
30#13094024C2212yescomplemented
31#13094021C2212yes—
32#13094012C2212yes—
33#13094012C2212yescomplemented
34#13094008—22no—
35#13094004—22no—
36#13093999—22no—
37#13093994—22no—
38C2×M16×C47C2211yescharacteristic
39C22×C8×C47C2211yescharacteristic
40#117×C47C2211yescharacteristic
41#97×C47C2212yescomplemented
42C4×C8×C47C2212yescomplemented
43C23×D47—21no—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—21no—
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48#10625350—22no—
49#10625350—22no—
50#10625350—22no—
51#10625350—22no—
52C2×D188—22no—
53C2×D188—22no—
54C2×D188—21no—
55C2×D188—24no—
56C2×D188C2312yes—
57C2×D188C2311yescharacteristic
58C2×D188C2311yescharacteristic
59C2×C4×D47—21no—
60C2×C4×D47—21no—
61C2×Dic94—22no—
62C2×Dic94—22no—
63C2×Dic94—21no—
64C2×Dic94C2311yescharacteristic
65C2×Dic94C2312yes—
66C2×Dic94C2311yescharacteristic
67M16×C47D414yescomplemented
68C2×C8×C47D414yescomplemented
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2312yes—
72C4⋊C4×C47D412yes—
73C22⋊C4×C47D412yes—
74C42×C47C2312yes—
75(C2×D47)⋊C4—24no—
76(C2×D47)⋊C4—24no—
77C4⋊Dic47—24no—
78Dic188—22no—
79Dic188—24no—
80D376—24no—
81D376—22no—
82#10625325—24no—
83#10625325—24no—
84#10625325—24no—
85#10625325—22no—
86#10625325—22no—
87#10625325—24no—
88C23×C47C2×D411yescharacteristic
89C22×D47—21no—
90C22×D47—22no—
91C22×D47—21no—
92C22×D47—42no—
93C22×D47—82no—
94C2×C4×C47C2×D414yes—
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D412yes—
98C2×C4×C47C2411yescharacteristic
99C22⋊D47—42no—
100C22⋊D47—42no—
101C2×Dic47—21no—
102C2×Dic47—22no—
103C2×Dic47—21no—
104C2×Dic47—42no—
105D188—22no—
106D188—21no—
107D188—22no—
108D188—21no—
109D188—21no—
110D188—21no—
111D188—42no—
112D188—84no—
113C4×D47—42no—
114C4×D47—42no—
115Dic94—22no—
116Dic94—21no—
117Dic94—22no—
118Dic94—21no—
119Dic94—21no—
120Dic94—21no—
121Dic94—42no—
122C8×C47C2×D412yes—
123C8×C47C2×D412yes—
124C8×C47C2×D414yes—
125C22×C47—22no—
126C22×C47#12712yes—
127C22×C47C22×D411yescharacteristic
128C2×D47—41no—
129C2×D47—41no—
130C2×D47—42no—
131C2×D47—42no—
132C2×D47—44no—
133C2×D47—42no—
134C2×D47—84no—
135C4×C47—24no—
136C4×C47#12712yes—
137C4×C47C22×D411yescharacteristic
138C4×C47C22×D411yescharacteristic
139Dic47—42no—
140Dic47—41no—
141Dic47—41no—
142#3154—471nomaximal, Sylow
143C2×C47—22no—
144C2×C47C2×#12711yescharacteristic
145C2×C47#57712yes—
146D47—81no—
147D47—81no—
148D47—82no—
149C2×#137—471no—
150C2×AGL(1,ℤ/8)—471no—
151C2×#135—471no—
152C22×SD16—471no—
153#536—471no—
154#535—471no—
155#497—472no—
156#496—472no—
157#495—472no—
158#492—472no—
159#405D4711yescharacteristic, complemented
160C47#315411yescharacteristic, complemented, Sylow
161C2×#41—471no—
162C2×#41—471no—
163C22×Q8—471no—
164C22×D4—471no—
165#137—944no—
166AGL(1,ℤ/8)—944no—
167#135—944no—
168C2×Q16—471no—
169C2×Q16—472no—
170C2×SD16—472no—
171C2×SD16—472no—
172C2×SD16—471no—
173C2×SD16—471no—
174C2×SD16—472no—
175C2×SD16—472no—
176C2×SD16—944no—
177C2×D8—471no—
178C2×D8—472no—
179C2×M16C2×D4711yescharacteristic
180C22×C8C2×D4711yescharacteristic
181C4⋊Q8—472no—
182#127—472no—
183#124—472no—
184#124—472no—
185#123—942no—
186C22⋊Q8—942no—
187#121—942no—
188#120—942no—
189#117C2×D4711yescharacteristic
190#97C2×D4712yescomplemented
191C4×C8C2×D4712yescomplemented
192C24—941no—
193#41—942no—
194#41—942no—
195#41—942no—
196#41—942no—
197C2×Q8—471no—
198C2×Q8—472no—
199C2×Q8—471no—
200C2×Q8—941no—
201C2×Q8—942no—
202C2×Q8—942no—
203C2×D4—471no—
204C2×D4—472no—
205C2×D4—471no—
206C2×D4—941no—
207C2×D4—941no—
208C2×D4—942no—
209C2×D4—942no—
210C2×D4—944no—
211C2×D4—941no—
212C22×C4—941no—
213C22×C4—941no—
214C22×C4—941no—
215C22×C4C22×D4711yescharacteristic
216Q16—942no—
217Q16—944no—
218SD16—944no—
219SD16—944no—
220SD16—942no—
221SD16—942no—
222SD16—944no—
223SD16—944no—
224D8—942no—
225D8—944no—
226M16D18814yescomplemented
227C2×C8D18814yescomplemented
228C2×C8C22×D4711yescharacteristic
229C2×C8C22×D4712yes—
230C2×C8C22×D4711yescharacteristic
231C4⋊C4—944no—
232C4⋊C4D18812yes—
233C22⋊C4—944no—
234C22⋊C4—944no—
235C22⋊C4D18812yes—
236C42C22×D4712yes—
237C23—941no—
238C23—942no—
239C23—941no—
240C23—3762no—
241C23—1882no—
242C23C2×D18811yescharacteristic
243Q8—942no—
244Q8—941no—
245Q8—942no—
246Q8—941no—
247Q8—941no—
248Q8—941no—
249Q8—1882no—
250D4—941no—
251D4—942no—
252D4—941no—
253D4—941no—
254D4—942no—
255D4—941no—
256D4—3764no—
257D4—1882no—
258D4—1882no—
259D4—1882no—
260C2×C4—941no—
261C2×C4—942no—
262C2×C4—941no—
263C2×C4—1882no—
264C2×C4—1882no—
265C2×C4—1882no—
266C2×C4C2×D18814yes—
267C2×C4C2×D18811yescharacteristic
268C2×C4C2×D18812yes—
269C2×C4C2×D18812yes—
270C2×C4C23×D4711yescharacteristic
271C8C2×D18812yes—
272C8C2×D18812yes—
273C8C2×D18814yes—
274C22—22no—
275C22—3764no—
276C22—1881no—
277C22—1881no—
278C22—1882no—
279C22—1882no—
280C22—1884no—
281C22—1882no—
282C22#1309402112yes—
283C22C22×D18811yescharacteristic
284C4—24no—
285C4—1881no—
286C4—1881no—
287C4—1882no—
288C4#1309402112yes—
289C4C22×D18811yescharacteristic
290C4C22×D18811yescharacteristic
291C2—22no—
292C2—3762no—
293C2—3761no—
294C2—3761no—
295C2C2×#1309402111yescharacteristic
296C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#405C2
socleC22×C47C22×D4
hypercenter#405D47
hypocenterC47#3154
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. C2×#13094057C2semidirect
2. C2×#13094052C2semidirect
3. C2×#13094046C2semidirect
4. C22×#10625325C2semidirect
5. #15689699C2semidirect
6. #15689692C2semidirect
7. #15689517C2semidirect
8. #15689512C2semidirect
9. #15689507C2semidirect
10. #15689496C2semidirect
11. C47×#405C2semidirect
19. C2×Dic188C22semidirect
20. C2×Dic188C22semidirect
25. C2×#10625325C22semidirect
26. C2×#10625325C22semidirect
27. C2×#10625325C22semidirect
29. C2×D376C22semidirect
30. #13094024C22semidirect
33. #13094012C22semidirect
41. #97×C47C22semidirect
42. C4×C8×C47C22semidirect
67. M16×C47D4semidirect
68. C2×C8×C47D4semidirect
159. #405D47semidirect
160. C47#3154semidirect
190. #97C2×D47semidirect
191. C4×C8C2×D47semidirect
226. M16D188semidirect
227. C2×C8D188semidirect