Finite Group Databasebeta

← #20252789

Subgroups — #20252789

Order 6016.

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

normal subgroups only

This group has 772 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#15689690C212yesmaximal, complemented
3#15689309C218yesmaximal, complemented
4#15689097C211yesmaximal, characteristic, complemented
5#15689096C212yesmaximal, complemented
6C47×#535C211yesmaximal, characteristic, complemented
7#13094072—21no—
8#13094071—22no—
9#13094070—22no—
10#13094069—21no—
11#13094069C2214yes—
12C2×#10625350—22no—
13C2×#10625350C2212yes—
14#41×D47—24no—
15#13094020—22no—
16#13094011—22no—
17#13093995—24no—
18#13093993C2218yescomplemented
19#13093983C2212yescomplemented
20#13093939C2214yescomplemented
21#13093938C2218yescomplemented
22C2×#41×C47C2211yescharacteristic
23C22×D4×C47C2211yescharacteristic, complemented
24#127×C47—21no—
25#124×C47—21no—
26#121×C47—22no—
27#120×C47C2214yescomplemented
28#117×C47C2211yescharacteristic, complemented
29C24×C47C2312yes—
30#41×C47—22no—
31#41×C47—22no—
32C2×Q8×C47D411yescharacteristic, complemented
33C2×D4×C47—24no—
34C2×D4×C47—21no—
35C2×D4×C47—21no—
36C2×D4×C47—22no—
37C2×D4×C47—22no—
38C2×D4×C47D411yescharacteristic, complemented
39C2×D4×C47C2312yes—
40C22×C4×C47D412yescomplemented
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—24no—
43C2×C22⋊D47—28no—
44C2×C22⋊D47C2314yes—
45#10625354—24no—
46Q8×D47—24no—
47#10625352—24no—
48#10625352—28no—
49D4×D47—24no—
50D4×D47—28no—
51#10625350—24no—
52#10625350—24no—
53#10625350—22no—
54#10625350—22no—
55#10625350—24no—
56#10625350—22no—
57#10625350—22no—
58C2×D188—22no—
59C2×D188D412yescomplemented
60C2×C4×D47—24no—
61C2×C4×D47D414yescomplemented
62C2×Dic94—22no—
63C2×Dic94D412yescomplemented
64C4⋊C4×C47—21no—
65C22⋊C4×C47—24no—
66C22⋊C4×C47C2312yes—
67C42×C47—21no—
68C22⋊Dic47—28no—
69C22⋊Dic47C2314yes—
70C4⋊Dic47—22no—
71C4×Dic47—22no—
72C23×C47—24no—
73C23×C47—22no—
74C23×C47—82no—
75C23×C47C2×D412yes—
76C23×C47C2411yescharacteristic
77C22×D47—24no—
78C22×D47C2×D414yes—
79Q8×C47—22no—
80D4×C47—24no—
81D4×C47—22no—
82D4×C47—41no—
83D4×C47—42no—
84D4×C47—41no—
85D4×C47—84no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47C2×D412yes—
90C2×C4×C47C2×D412yes—
91C2×C4×C47C2×D412yes—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C22⋊D47—28no—
95C22⋊D47—24no—
96C22⋊D47—24no—
97C22⋊D47—88no—
98C2×Dic47—24no—
99C2×Dic47—24no—
100C2×Dic47C2×D414yes—
101D188—24no—
102D188—22no—
103D188—22no—
104C4×D47—28no—
105C4×D47—24no—
106C4×D47—24no—
107Dic94—24no—
108Dic94—22no—
109Dic94—22no—
110C22×C47—22no—
111C22×C47—41no—
112C22×C47—42no—
113C22×C47—48no—
114C22×C47—44no—
115C22×C47—42no—
116C22×C47C22×D412yes—
117C22×C47C22×D411yescharacteristic
118C2×D47—24no—
119C2×D47—44no—
120C2×D47—84no—
121C4×C47—22no—
122C4×C47—42no—
123C4×C47#12011yescharacteristic
124C4×C47#12012yes—
125C4×C47#12011yescharacteristic
126Dic47—24no—
127Dic47—44no—
128#3027—471nomaximal, Sylow
129C2×C47—22no—
130C2×C47—21no—
131C2×C47—42no—
132C2×C47—82no—
133C2×C47C2×#12011yescharacteristic
134D47—44no—
135#585—471no—
136#535—472no—
137#535D4711yescharacteristic, complemented
138B(4,𝔽2)—478no—
139#410—471no—
140#410—472no—
141C47#302711yescharacteristic, complemented, Sylow
1422−1+4—942no—
1432−1+4—941no—
144H(5,𝔽2)—474no—
145H(5,𝔽2)—942no—
146H(5,𝔽2)—941no—
147C2×#41—472no—
148C2×#41—944no—
149C2×#41—942no—
150C2×#41C2×D4711yescharacteristic
151C22×D4C2×D4711yescharacteristic, complemented
152#127—21no—
153#127—942no—
154#124—21no—
155#124—942no—
156#121—22no—
157#121—944no—
158#120—478no—
159#120C2×D4714yescomplemented
160#117—472no—
161#117C2×D4711yescharacteristic, complemented
162#99—474no—
163#99—478no—
164C24C22×D4712yes—
165#41—22no—
166#41—22no—
167#41—944no—
168#41—944no—
169#41—948no—
170#41—944no—
171#41—944no—
172#41—942no—
173#41—942no—
174#41—942no—
175#41—942no—
176#41—944no—
177C2×Q8—472no—
178C2×Q8—942no—
179C2×Q8—944no—
180C2×Q8C22⋊D4711yescharacteristic, complemented
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—474no—
187C2×D4—472no—
188C2×D4—942no—
189C2×D4—948no—
190C2×D4—944no—
191C2×D4—944no—
192C2×D4—948no—
193C2×D4C22⋊D4711yescharacteristic, complemented
194C2×D4C22×D4712yes—
195C22×C4—474no—
196C22×C4—944no—
197C22×C4C22⋊D4712yescomplemented
198C22×C4C22×D4711yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—942no—
201C22⋊C4—24no—
202C22⋊C4—474no—
203C22⋊C4—948no—
204C22⋊C4C22×D4712yes—
205C42—21no—
206C42—942no—
207C23—24no—
208C23—22no—
209C23—82no—
210C23—474no—
211C23—944no—
212C23C2×C22⋊D4712yes—
213C23C23×D4711yescharacteristic
214Q8—22no—
215Q8—944no—
216Q8—942no—
217Q8—942no—
218D4—24no—
219D4—22no—
220D4—41no—
221D4—41no—
222D4—42no—
223D4—84no—
224D4—944no—
225D4—948no—
226D4—944no—
227D4—944no—
228D4—942no—
229D4—942no—
230D4—3768no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—474no—
235C2×C4—948no—
236C2×C4—944no—
237C2×C4—944no—
238C2×C4—944no—
239C2×C4—944no—
240C2×C4D4×D4712yes—
241C2×C4D4×D4712yes—
242C2×C4C2×C22⋊D4712yes—
243C2×C4C2×C22⋊D4711yescharacteristic
244C2×C4C2×C22⋊D4711yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—44no—
249C22—48no—
250C22—42no—
251C22—944no—
252C22—3764no—
253C22—1884no—
254C22C2×D4×D4712yes—
255C22C22×C22⋊D4711yescharacteristic
256C4—22no—
257C4—42no—
258C4—944no—
259C4—1884no—
260C4#1309399211yescharacteristic
261C4#1309399211yescharacteristic
262C4#1309399212yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—1884no—
268C2C2×#1309399211yescharacteristic
subgroupG/H
centerC2C2×#13093992
commutatorC23×C47C24
FrattiniC23C23×D47
FittingC47×#535C2
socleC2×C47C2×#120
hypercenter#535D47
hypocenterC47#3027
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #15689959C2semidirect
2. #15689690C2semidirect
3. #15689309C2semidirect
4. #15689097C2semidirect
5. #15689096C2semidirect
6. C47×#535C2semidirect
18. #13093993C22semidirect
19. #13093983C22semidirect
20. #13093939C22semidirect
21. #13093938C22semidirect
23. C22×D4×C47C22semidirect
27. #120×C47C22semidirect
28. #117×C47C22semidirect
32. C2×Q8×C47D4semidirect
38. C2×D4×C47D4semidirect
40. C22×C4×C47D4semidirect
59. C2×D188D4semidirect
61. C2×C4×D47D4semidirect
63. C2×Dic94D4semidirect
137. #535D47semidirect
141. C47#3027semidirect
151. C22×D4C2×D47semidirect
159. #120C2×D47semidirect
161. #117C2×D47semidirect
180. C2×Q8C22⋊D47semidirect
193. C2×D4C22⋊D47semidirect
197. C22×C4C22⋊D47semidirect