Finite Group Databasebeta

← #20253866

Subgroups — #20253866

Order 6016.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094055C211yesmaximal, characteristic, complemented
2C2×#13094049C211yesmaximal, characteristic, complemented
3C2×#13094044C211yesmaximal, characteristic, complemented
4C22×#10625336C211yesmaximal, characteristic, complemented
5#15689692C211yesmaximal, characteristic, complemented
6#15689515C212yesmaximal, complemented
7#15689513C212yesmaximal, complemented
8#15689505C212yesmaximal, complemented
9#15689497C212yesmaximal, complemented
10#15689079C211yesmaximal, characteristic, complemented
11C47×#536C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×D188C2211yescharacteristic
14#13094055—24no—
15#13094049—24no—
16#13094044—24no—
17C2×#10625337C2212yescomplemented
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625335C2211yescharacteristic, complemented
20C2×#10625336—24no—
21C2×#10625336C2212yes—
22C2×#10625336C2212yes—
23C2×#10625336C2212yes—
24C2×#10625336C2211yescharacteristic, complemented
25C2×#10625336C2212yescomplemented
26C2×#10625334C2212yes—
27C2×#10625334C2211yescharacteristic, complemented
28C2×#10625329C2211yescharacteristic
29C22×C47⋊C8C2211yescharacteristic
30#13094021C2212yes—
31#13094012C2212yes—
32#13093999—22no—
33#13093994—22no—
34#13093935C2212yescomplemented
35C4×C47⋊C8C2212yescomplemented
36C2×#41×C47C2211yescharacteristic
37C22×Q8×C47C2211yescharacteristic
38C4⋊Q8×C47C2212yescomplemented
39#124×C47C2212yescomplemented
40#123×C47—22no—
41C22⋊Q8×C47—22no—
42#117×C47C2211yescharacteristic
43C23×D47—21no—
44#41×C47—22no—
45#41×C47—22no—
46C2×Q8×C47—21no—
47C2×Q8×C47—22no—
48C2×Q8×C47—22no—
49C2×Q8×C47C2312yes—
50C2×Q8×C47C2311yescharacteristic
51C2×D4×C47—21no—
52C2×D4×C47C2311yescharacteristic
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47C2311yescharacteristic
56C2×C22⋊D47—21no—
57#10625350—22no—
58#10625350—22no—
59C2×D188—22no—
60C2×D188—22no—
61C2×D188—21no—
62C2×D188—24no—
63C2×D188C2312yes—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×Dic94C2311yescharacteristic
67C4⋊C4×C47—24no—
68C4⋊C4×C47D412yes—
69C22⋊C4×C47—24no—
70C22⋊C4×C47D412yes—
71C42×C47C2312yes—
72#10625337—22no—
73#10625337—24no—
74#10625336—24no—
75#10625336—24no—
76#10625336—24no—
77#10625336—22no—
78#10625336—24no—
79#10625335—22no—
80#10625334—24no—
81#10625334—22no—
82(C2×D47)⋊C4—24no—
83#10625329D414yescomplemented
84C2×C47⋊C8D414yescomplemented
85C2×C47⋊C8C2311yescharacteristic
86C2×C47⋊C8C2312yes—
87C2×C47⋊C8C2311yescharacteristic
88C23×C47—21no—
89C23×C47C2×D411yescharacteristic
90C22×D47—22no—
91C22×D47—21no—
92C22×D47—42no—
93C22×D47—82no—
94Q8×C47—22no—
95Q8×C47—21no—
96Q8×C47—22no—
97Q8×C47—21no—
98Q8×C47—42no—
99D4×C47—21no—
100D4×C47—21no—
101D4×C47—42no—
102C2×C4×C47—22no—
103C2×C4×C47—21no—
104C2×C4×C47—42no—
105C2×C4×C47—42no—
106C2×C4×C47C2×D412yes—
107C2×C4×C47C2×D412yes—
108C2×C4×C47C2×D414yes—
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2411yescharacteristic
111C22⋊D47—42no—
112C2×Dic47—21no—
113D188—22no—
114D188—21no—
115D188—22no—
116D188—21no—
117D188—42no—
118D188—84no—
119C4×D47—42no—
120Dic94—21no—
121Dic94—21no—
122C47⋊C8C2×D412yes—
123C47⋊C8C2×D412yes—
124C47⋊C8C2×D414yes—
125C22×C47—22no—
126C22×C47—41no—
127C22×C47—42no—
128C22×C47#12712yes—
129C22×C47C22×D411yescharacteristic
130C2×D47—41no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—44no—
134C2×D47—84no—
135C4×C47—24no—
136C4×C47—41no—
137C4×C47—42no—
138C4×C47#12712yes—
139C4×C47C22×D411yescharacteristic
140C4×C47C22×D411yescharacteristic
141Dic47—41no—
142#3154—471nomaximal, Sylow
143C2×C47—22no—
144C2×C47—81no—
145C2×C47C2×#12711yescharacteristic
146C2×C47#57712yes—
147D47—81no—
148D47—82no—
149C2×#137—471no—
150C2×AGL(1,ℤ/8)—471no—
151C2×#135—471no—
152C22×SD16—471no—
153#536D4711yescharacteristic, complemented
154#535—471no—
155#497—472no—
156#496—472no—
157#495—472no—
158#492—472no—
159#405—471no—
160C47#315411yescharacteristic, complemented, Sylow
161C2×#41—471no—
162C2×#41C2×D4711yescharacteristic
163C22×Q8C2×D4711yescharacteristic
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—472no—
174C2×SD16—472no—
175C2×SD16—471no—
176C2×SD16—944no—
177C2×D8—471no—
178C2×D8—472no—
179C2×M16—471no—
180C22×C8—471no—
181C4⋊Q8C2×D4712yescomplemented
182#127—472no—
183#124—472no—
184#124C2×D4712yescomplemented
185#123—22no—
186C22⋊Q8—22no—
187#121—942no—
188#120—942no—
189#117C2×D4711yescharacteristic
190#97—472no—
191C4×C8—472no—
192C24—941no—
193#41—22no—
194#41—22no—
195#41—942no—
196#41—942no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—471no—
201C2×Q8C22×D4712yes—
202C2×Q8C22×D4711yescharacteristic
203C2×D4—21no—
204C2×D4—472no—
205C2×D4—471no—
206C2×D4—941no—
207C2×D4—942no—
208C2×D4—942no—
209C2×D4—944no—
210C2×D4—941no—
211C2×D4C22×D4711yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—941no—
215C22×C4C22×D4711yescharacteristic
216Q16—942no—
217Q16—944no—
218SD16—942no—
219SD16—944no—
220SD16—944no—
221SD16—942no—
222SD16—944no—
223SD16—944no—
224D8—942no—
225D8—944no—
226M16—474no—
227C2×C8—474no—
228C2×C8—471no—
229C2×C8—472no—
230C2×C8—471no—
231C4⋊C4—24no—
232C4⋊C4C22⋊D4712yes—
233C22⋊C4—24no—
234C22⋊C4—944no—
235C22⋊C4C22⋊D4712yes—
236C42C22×D4712yes—
237C23—21no—
238C23—942no—
239C23—941no—
240C23—3762no—
241C23—1882no—
242C23C2×C22⋊D4711yescharacteristic
243Q8—22no—
244Q8—21no—
245Q8—22no—
246Q8—21no—
247Q8—42no—
248Q8—941no—
249Q8—941no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—942no—
254D4—941no—
255D4—942no—
256D4—941no—
257D4—3764no—
258D4—1882no—
259D4—1882no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—941no—
265C2×C4—1882no—
266C2×C4D4×D4712yes—
267C2×C4D4×D4712yes—
268C2×C4C2×C22⋊D4714yes—
269C2×C4C2×C22⋊D4711yescharacteristic
270C2×C4C23×D4711yescharacteristic
271C8—472no—
272C8—472no—
273C8—474no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—3764no—
278C22—1881no—
279C22—1882no—
280C22—1882no—
281C22—1884no—
282C22#1309402012yes—
283C22C22×C22⋊D4711yescharacteristic
284C4—24no—
285C4—41no—
286C4—42no—
287C4—1881no—
288C4#1309402012yes—
289C4C2×D4×D4711yescharacteristic
290C4C2×D4×D4711yescharacteristic
291C2—22no—
292C2—81no—
293C2—3762no—
294C2—3761no—
295C2C2×#1309402011yescharacteristic
296C2#1568993112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#536C2
socleC22×C47C22×D4
hypercenter#536D47
hypocenterC47#3154
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
2. C2×#13094049C2semidirect
3. C2×#13094044C2semidirect
4. C22×#10625336C2semidirect
5. #15689692C2semidirect
6. #15689515C2semidirect
7. #15689513C2semidirect
8. #15689505C2semidirect
9. #15689497C2semidirect
10. #15689079C2semidirect
11. C47×#536C2semidirect
17. C2×#10625337C22semidirect
18. C2×#10625337C22semidirect
19. C2×#10625335C22semidirect
24. C2×#10625336C22semidirect
25. C2×#10625336C22semidirect
27. C2×#10625334C22semidirect
34. #13093935C22semidirect
35. C4×C47⋊C8C22semidirect
38. C4⋊Q8×C47C22semidirect
39. #124×C47C22semidirect
83. #10625329D4semidirect
84. C2×C47⋊C8D4semidirect
153. #536D47semidirect
160. C47#3154semidirect
181. C4⋊Q8C2×D47semidirect
184. #124C2×D47semidirect