Finite Group Databasebeta

← #20252762

Subgroups — #20252762

Order 6016.

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

normal subgroups only

This group has 736 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
2C2×#13094052C212yesmaximal, complemented
3#15689687C211yesmaximal, characteristic, complemented
4#15689298C214yesmaximal, complemented
5#15689293C214yesmaximal, complemented
6#15689139C212yesmaximal, complemented
7C47×#413C211yesmaximal, characteristic, complemented
8#13094072C2212yescomplemented
9#13094071—22no—
10#13094070—22no—
11#13094069—22no—
12#13094069C2212yescomplemented
13C2×#10625350—22no—
14C2×#10625350C2212yes—
15#41×D47—24no—
16C22×D188C2211yescharacteristic, complemented
17#13094052—24no—
18#13094052C2218yescomplemented
19C2×#10625325—22no—
20C2×D376—22no—
21#13094020C2212yescomplemented
22#13094013C2212yescomplemented
23#13093998—22no—
24#13093992—22no—
25#13093983C2211yescharacteristic, complemented
26#13093950C2218yescomplemented
27C2×#41×C47C2211yescharacteristic
28C2×M16×C47C2212yescomplemented
29#101×C47C2212yescomplemented
30#100×C47C2212yescomplemented
31C23×D47—21no—
32#41×C47—22no—
33#41×C47—22no—
34C2×Q8×C47C2311yescharacteristic
35C2×D4×C47D412yes—
36C2×D4×C47C2311yescharacteristic
37C22×C4×C47D412yes—
38C22×C4×C47C2311yescharacteristic
39C2×C22⋊D47—24no—
40C2×C22⋊D47—22no—
41C2×C22⋊D47—24no—
42#10625354—24no—
43Q8×D47—24no—
44#10625352—28no—
45#10625352—24no—
46D4×D47—28no—
47D4×D47—24no—
48#10625350—24no—
49#10625350—24no—
50#10625350—22no—
51#10625350—24no—
52#10625350—22no—
53#10625350D414yescomplemented
54#10625350C2314yes—
55C2×D188—22no—
56C2×D188—22no—
57C2×D188—22no—
58C2×D188—21no—
59C2×D188D412yescomplemented
60C2×D188C2312yes—
61C2×C4×D47—24no—
62C2×C4×D47—22no—
63C2×Dic94—22no—
64C2×Dic94D412yescomplemented
65M16×C47—22no—
66M16×C47C2314yes—
67C2×C8×C47—22no—
68C22⋊Dic47—21no—
69(C2×D47)⋊C4—24no—
70C4⋊Dic47—21no—
71C4×Dic47C2312yes—
72D376—28no—
73#10625325—28no—
74C23×C47C2×D412yes—
75C23×C47C2×D411yescharacteristic
76C22×D47—24no—
77C22×D47—22no—
78C22×D47—22no—
79C22×D47—42no—
80C22×D47—82no—
81Q8×C47—22no—
82D4×C47—24no—
83D4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47C2×D412yes—
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D412yes—
89C2×C4×C47C2×D412yes—
90C2×C4×C47C2411yescharacteristic
91C22⋊D47—28no—
92C22⋊D47—24no—
93C22⋊D47—24no—
94C22⋊D47—84no—
95C2×Dic47—24no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98D188—24no—
99D188—22no—
100D188—24no—
101D188—41no—
102D188—41no—
103D188C2×D414yes—
104C4×D47—28no—
105C4×D47—24no—
106C4×D47—24no—
107Dic94—24no—
108Dic94—22no—
109Dic94C2×D414yes—
110C8×C47—24no—
111C22×C47—22no—
112C22×C47—41no—
113C22×C47—42no—
114C22×C47#12012yes—
115C22×C47C22×D411yescharacteristic
116C2×D47—24no—
117C2×D47—44no—
118C2×D47—42no—
119C2×D47—82no—
120C2×D47—84no—
121C2×D47—84no—
122C4×C47—22no—
123C4×C47#12011yescharacteristic
124C4×C47#12011yescharacteristic
125C4×C47C22×D412yes—
126Dic47—24no—
127Dic47—42no—
128#3021—471nomaximal, Sylow
129C2×C47—21no—
130C2×C47—22no—
131C2×C47—42no—
132C2×C47C2×#12011yescharacteristic
133D47—44no—
134D47—82no—
135#585—471no—
136C2×AGL(1,ℤ/8)—472no—
137#535—471no—
138#454—474no—
139#453—474no—
140#421—472no—
141#413D4711yescharacteristic, complemented
142C47#302111yescharacteristic, complemented, Sylow
1432−1+4—472no—
1442−1+4—942no—
145H(5,𝔽2)—472no—
146H(5,𝔽2)—942no—
147H(5,𝔽2)—942no—
148C2×#41—472no—
149C2×#41—944no—
150C2×#41—942no—
151C2×#41C2×D4711yescharacteristic
152C22×D4—471no—
153AGL(1,ℤ/8)—478no—
154AGL(1,ℤ/8)—944no—
155C2×SD16—942no—
156C2×D8—942no—
157C2×M16C2×D4712yescomplemented
158#127—472no—
159#124—472no—
160#121—942no—
161#120—942no—
162#117—471no—
163#104—478no—
164#101C2×D4712yescomplemented
165#100C2×D4712yescomplemented
166C24—941no—
167#41—22no—
168#41—22no—
169#41—474no—
170#41—474no—
171#41—944no—
172#41—944no—
173#41—944no—
174#41—948no—
175#41—944no—
176#41—942no—
177#41—944no—
178#41—942no—
179C2×Q8—472no—
180C2×Q8—942no—
181C2×Q8—944no—
182C2×Q8C22×D4711yescharacteristic
183C2×D4—472no—
184C2×D4—472no—
185C2×D4—942no—
186C2×D4—944no—
187C2×D4—948no—
188C2×D4—942no—
189C2×D4—944no—
190C2×D4—944no—
191C2×D4—941no—
192C2×D4—942no—
193C2×D4—942no—
194C2×D4D18812yes—
195C2×D4C22×D4711yescharacteristic
196C22×C4—944no—
197C22×C4—942no—
198C22×C4D18812yes—
199C22×C4C22×D4711yescharacteristic
200SD16—948no—
201D8—948no—
202M16—22no—
203M16C22×D4714yes—
204C2×C8—22no—
205C4⋊C4—941no—
206C22⋊C4—941no—
207C22⋊C4—944no—
208C42—472no—
209C23—944no—
210C23—942no—
211C23—942no—
212C23—3762no—
213C23—1882no—
214C23C2×D18812yes—
215C23C2×D18811yescharacteristic
216Q8—22no—
217Q8—474no—
218Q8—944no—
219Q8—942no—
220D4—24no—
221D4—22no—
222D4—474no—
223D4—944no—
224D4—948no—
225D4—944no—
226D4—944no—
227D4—942no—
228D4—944no—
229D4—3764no—
230D4—1881no—
231D4—1881no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—948no—
235C2×C4—944no—
236C2×C4—942no—
237C2×C4—944no—
238C2×C4—944no—
239C2×C4—942no—
240C2×C4C2×D18812yes—
241C2×C4C2×D18811yescharacteristic
242C2×C4D4×D4712yes—
243C2×C4D4×D4712yes—
244C2×C4C23×D4711yescharacteristic
245C8—24no—
246C22—22no—
247C22—41no—
248C22—42no—
249C22—944no—
250C22—3764no—
251C22—3762no—
252C22—3764no—
253C22—1884no—
254C22—1882no—
255C22#1309399412yes—
256C22C22×D18811yescharacteristic
257C4—22no—
258C4—944no—
259C4—1882no—
260C4#1309399411yescharacteristic
261C4#1309399411yescharacteristic
262C4C2×D4×D4712yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—3762no—
267C2—1884no—
268C2C2×#1309399411yescharacteristic
subgroupG/H
centerC2C2×#13093994
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#413C2
socleC2×C47C2×#120
hypercenter#413D47
hypocenterC47#3021
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #15689959C2semidirect
2. C2×#13094052C2semidirect
3. #15689687C2semidirect
4. #15689298C2semidirect
5. #15689293C2semidirect
6. #15689139C2semidirect
7. C47×#413C2semidirect
8. #13094072C22semidirect
12. #13094069C22semidirect
16. C22×D188C22semidirect
18. #13094052C22semidirect
21. #13094020C22semidirect
22. #13094013C22semidirect
25. #13093983C22semidirect
26. #13093950C22semidirect
28. C2×M16×C47C22semidirect
29. #101×C47C22semidirect
30. #100×C47C22semidirect
53. #10625350D4semidirect
59. C2×D188D4semidirect
64. C2×Dic94D4semidirect
141. #413D47semidirect
142. C47#3021semidirect
157. C2×M16C2×D47semidirect
164. #101C2×D47semidirect
165. #100C2×D47semidirect