Finite Group Databasebeta

← #20252741

Subgroups — #20252741

Order 6016.

724 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 145 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#15689959C211yesmaximal, characteristic, complemented
2#15689923C212yesmaximal, complemented
3#15689669C211yesmaximal, characteristic, complemented
4#15689308C212yesmaximal, complemented
5#15689303C212yesmaximal, complemented
6#15689298C212yesmaximal, complemented
7#15689293C212yesmaximal, complemented
8C2×#13093950C212yesmaximal, complemented
9C47×#413C211yesmaximal, characteristic, complemented
10#13094072C2212yes—
11#13094071—22no—
12#13094070—22no—
13#13094069—22no—
14#13094069C2212yes—
15C2×#10625350—22no—
16C2×#10625350C2212yes—
17C2×#10625350C2211yescharacteristic, complemented
18#41×D47—24no—
19#13094057—22no—
20#13094057C2214yescomplemented
21#13094052—22no—
22#13094052C2214yescomplemented
23#13094046—24no—
24#13094022C2211yescharacteristic, complemented
25#13094020C2211yescharacteristic, complemented
26#13094013C2211yescharacteristic, complemented
27#13094011C2211yescharacteristic, complemented
28#13093996—22no—
29C4×C22⋊D47—22no—
30C2×C4×Dic47C2211yescharacteristic, complemented
31#13093950C2214yescomplemented
32#13093950C2214yescomplemented
33C2×#41×C47C2211yescharacteristic
34C2×M16×C47C2212yescomplemented
35#101×C47C2212yescomplemented
36#100×C47C2212yescomplemented
37#41×C47—22no—
38#41×C47—22no—
39C2×Q8×C47C2311yescharacteristic
40C2×D4×C47D412yes—
41C2×D4×C47C2311yescharacteristic
42C22×C4×C47D412yes—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—24no—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—21no—
48C22×Dic47—21no—
49#10625354—24no—
50Q8×D47—24no—
51#10625352—28no—
52#10625352—24no—
53D4×D47—28no—
54D4×D47—24no—
55#10625350—24no—
56#10625350—24no—
57#10625350—22no—
58#10625350—24no—
59#10625350—22no—
60#10625350—22no—
61#10625350—22no—
62#10625350D414yescomplemented
63#10625350C2314yes—
64C2×D188—22no—
65C2×D188D412yescomplemented
66C2×D188C2311yescharacteristic
67C2×C4×D47—24no—
68C2×C4×D47—22no—
69C2×C4×D47—21no—
70C2×Dic94—22no—
71C2×Dic94D412yescomplemented
72C2×Dic94C2311yescharacteristic
73M16×C47—22no—
74M16×C47C2314yes—
75C2×C8×C47—22no—
76C22⋊Dic47—22no—
77(C2×D47)⋊C4—22no—
78Dic47⋊C4—22no—
79C4×Dic47—21no—
80C4×Dic47C2311yescharacteristic
81C4×Dic47C2311yescharacteristic
82Dic188—24no—
83D376—24no—
84#10625325—24no—
85#10625325—24no—
86C23×C47C2×D412yes—
87C23×C47C2×D411yescharacteristic
88C22×D47—24no—
89C22×D47—22no—
90C22×D47—21no—
91Q8×C47—22no—
92D4×C47—24no—
93D4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2×D412yes—
99C2×C4×C47C2×D412yes—
100C2×C4×C47C2411yescharacteristic
101C22⋊D47—28no—
102C22⋊D47—24no—
103C22⋊D47—24no—
104C22⋊D47—44no—
105C22⋊D47—42no—
106C2×Dic47—24no—
107C2×Dic47—22no—
108C2×Dic47—21no—
109C2×Dic47—21no—
110C2×Dic47—21no—
111C2×Dic47—42no—
112D188—24no—
113D188—22no—
114D188—22no—
115D188C2×D414yes—
116C4×D47—28no—
117C4×D47—24no—
118C4×D47—24no—
119C4×D47—41no—
120C4×D47—41no—
121Dic94—24no—
122Dic94—22no—
123Dic94—22no—
124Dic94C2×D414yes—
125C8×C47—24no—
126C22×C47—22no—
127C22×C47—41no—
128C22×C47—42no—
129C22×C47#12012yes—
130C22×C47C22×D411yescharacteristic
131C2×D47—24no—
132C2×D47—42no—
133C2×D47—41no—
134C2×D47—82no—
135C2×D47—84no—
136C4×C47—22no—
137C4×C47#12011yescharacteristic
138C4×C47#12011yescharacteristic
139C4×C47C22×D412yes—
140Dic47—22no—
141Dic47—24no—
142Dic47—41no—
143Dic47—41no—
144#3018—471nomaximal, Sylow
145C2×C47—21no—
146C2×C47—22no—
147C2×C47—42no—
148C2×C47C2×#12011yescharacteristic
149D47—44no—
150D47—81no—
151#585—471no—
152#575—472no—
153#532—471no—
154#456—472no—
155#455—472no—
156#454—472no—
157#453—472no—
158C2×#104—472no—
159#413D4711yescharacteristic, complemented
160C47#301811yescharacteristic, complemented, Sylow
1612−1+4—472no—
1622−1+4—942no—
163H(5,𝔽2)—472no—
164H(5,𝔽2)—942no—
165H(5,𝔽2)—942no—
166C2×#41—472no—
167C2×#41—471no—
168C2×#41—944no—
169C2×#41—942no—
170C2×#41C2×D4711yescharacteristic
171#137—474no—
172#137—942no—
173AGL(1,ℤ/8)—474no—
174AGL(1,ℤ/8)—942no—
175#135—944no—
176C2×M16C2×D4712yescomplemented
177C4⋊Q8—471no—
178#127—471no—
179#124—471no—
180#124—471no—
181#121—942no—
182C4×D4—942no—
183C2×C42—471no—
184#104—474no—
185#104—474no—
186#101C2×D4712yescomplemented
187#100C2×D4712yescomplemented
188#41—22no—
189#41—22no—
190#41—474no—
191#41—474no—
192#41—944no—
193#41—944no—
194#41—944no—
195#41—948no—
196#41—944no—
197#41—942no—
198#41—944no—
199#41—942no—
200#41—942no—
201#41—942no—
202C2×Q8—472no—
203C2×Q8—471no—
204C2×Q8—942no—
205C2×Q8—944no—
206C2×Q8C22×D4711yescharacteristic
207C2×D4—472no—
208C2×D4—471no—
209C2×D4—942no—
210C2×D4—944no—
211C2×D4—948no—
212C2×D4—942no—
213C2×D4—944no—
214C2×D4—942no—
215C2×D4—941no—
216C2×D4D18812yes—
217C2×D4C22×D4711yescharacteristic
218C22×C4—944no—
219C22×C4—942no—
220C22×C4—941no—
221C22×C4—941no—
222C22×C4D18812yes—
223C22×C4C22×D4711yescharacteristic
224Q16—944no—
225SD16—944no—
226SD16—944no—
227D8—944no—
228M16—22no—
229M16C22×D4714yes—
230C2×C8—22no—
231C4⋊C4—942no—
232C22⋊C4—942no—
233C22⋊C4—942no—
234C42—471no—
235C42—471no—
236C42—941no—
237C23—944no—
238C23—942no—
239C23—941no—
240C23C2×D18812yes—
241C23C2×D18811yescharacteristic
242Q8—22no—
243Q8—474no—
244Q8—944no—
245Q8—942no—
246Q8—942no—
247D4—24no—
248D4—22no—
249D4—474no—
250D4—944no—
251D4—948no—
252D4—944no—
253D4—944no—
254D4—942no—
255D4—942no—
256D4—1884no—
257D4—1882no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—948no—
261C2×C4—944no—
262C2×C4—942no—
263C2×C4—941no—
264C2×C4—944no—
265C2×C4—944no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—1882no—
269C2×C4—1881no—
270C2×C4—1881no—
271C2×C4C2×D18812yes—
272C2×C4C2×D18811yescharacteristic
273C2×C4D4×D4712yes—
274C2×C4D4×D4712yes—
275C2×C4C23×D4711yescharacteristic
276C8—24no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—944no—
281C22—3762no—
282C22—3764no—
283C22—1882no—
284C22—1881no—
285C22#1309399412yes—
286C22C22×D18811yescharacteristic
287C4—22no—
288C4—942no—
289C4—944no—
290C4—1881no—
291C4—1881no—
292C4#1309399411yescharacteristic
293C4#1309399411yescharacteristic
294C4C2×D4×D4712yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—3761no—
299C2—1884no—
300C2C2×#1309399411yescharacteristic
subgroupG/H
centerC4#13093994
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#413C2
socleC2×C47C2×#120
hypercenter#413D47
hypocenterC47#3018
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #15689959C2semidirect
2. #15689923C2semidirect
3. #15689669C2semidirect
4. #15689308C2semidirect
5. #15689303C2semidirect
6. #15689298C2semidirect
7. #15689293C2semidirect
8. C2×#13093950C2semidirect
9. C47×#413C2semidirect
17. C2×#10625350C22semidirect
20. #13094057C22semidirect
22. #13094052C22semidirect
24. #13094022C22semidirect
25. #13094020C22semidirect
26. #13094013C22semidirect
27. #13094011C22semidirect
30. C2×C4×Dic47C22semidirect
31. #13093950C22semidirect
32. #13093950C22semidirect
34. C2×M16×C47C22semidirect
35. #101×C47C22semidirect
36. #100×C47C22semidirect
62. #10625350D4semidirect
65. C2×D188D4semidirect
71. C2×Dic94D4semidirect
159. #413D47semidirect
160. C47#3018semidirect
176. C2×M16C2×D47semidirect
186. #101C2×D47semidirect
187. #100C2×D47semidirect