Finite Group Databasebeta

← #20252759

Subgroups — #20252759

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×#13094050C212yesmaximal, complemented
3#15689295C214yesmaximal, complemented
4#15689290C214yesmaximal, complemented
5#15689141C212yesmaximal, complemented
6#15689107C211yesmaximal, characteristic, complemented
7C47×#535C211yesmaximal, characteristic, complemented
8#13094072C2212yescomplemented
9#13094071—22no—
10#13094070—22no—
11#13094069—22no—
12#13094069C2212yescomplemented
13C2×#10625350—22no—
14C2×#10625350C2212yes—
15#41×D47—24no—
16#13094050—24no—
17#13094050C2218yescomplemented
18C2×#10625335—22no—
19C2×#10625334—22no—
20C2×#10625329C2212yescomplemented
21#13093952C2218yescomplemented
22#13093943C2212yescomplemented
23#13093941C2212yescomplemented
24C2×#41×C47C2211yescharacteristic
25C22×D4×C47C2211yescharacteristic, complemented
26#127×C47C2212yescomplemented
27#124×C47C2212yescomplemented
28#121×C47—22no—
29#120×C47—22no—
30#117×C47C2211yescharacteristic, complemented
31C24×C47—21no—
32#41×C47—22no—
33#41×C47—22no—
34C2×Q8×C47C2311yescharacteristic
35C2×D4×C47—24no—
36C2×D4×C47—22no—
37C2×D4×C47—22no—
38C2×D4×C47—21no—
39C2×D4×C47D412yes—
40C2×D4×C47C2312yes—
41C2×D4×C47C2311yescharacteristic
42C22×C4×C47D412yes—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—24no—
45C2×C22⋊D47—22no—
46#10625354—24no—
47Q8×D47—24no—
48#10625352—28no—
49#10625352—24no—
50D4×D47—28no—
51D4×D47—24no—
52#10625350—24no—
53#10625350—24no—
54#10625350—22no—
55#10625350—24no—
56#10625350—22no—
57#10625350D414yescomplemented
58#10625350C2314yes—
59C2×D188—22no—
60C2×D188D412yescomplemented
61C2×C4×D47—24no—
62C2×C4×D47—22no—
63C2×Dic94—22no—
64C2×Dic94D412yescomplemented
65C4⋊C4×C47—21no—
66C22⋊C4×C47—21no—
67C22⋊C4×C47—24no—
68C42×C47C2312yes—
69#10625335—28no—
70#10625334—28no—
71#10625329—22no—
72#10625329C2314yes—
73C2×C47⋊C8—22no—
74C23×C47—22no—
75C23×C47—42no—
76C23×C47—82no—
77C23×C47C2×D412yes—
78C23×C47C2×D411yescharacteristic
79C22×D47—24no—
80C22×D47—22no—
81Q8×C47—22no—
82D4×C47—24no—
83D4×C47—22no—
84D4×C47—24no—
85D4×C47—41no—
86D4×C47—41no—
87D4×C47—84no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47C2×D412yes—
92C2×C4×C47C2×D412yes—
93C2×C4×C47C2×D412yes—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2411yescharacteristic
96C22⋊D47—28no—
97C22⋊D47—24no—
98C22⋊D47—24no—
99C2×Dic47—24no—
100C2×Dic47—22no—
101D188—24no—
102D188—22no—
103D188C2×D414yes—
104C4×D47—28no—
105C4×D47—24no—
106C4×D47—24no—
107Dic94—24no—
108Dic94—22no—
109Dic94C2×D414yes—
110C47⋊C8—24no—
111C22×C47—22no—
112C22×C47—41no—
113C22×C47—42no—
114C22×C47—44no—
115C22×C47—42no—
116C22×C47—84no—
117C22×C47#12012yes—
118C22×C47C22×D411yescharacteristic
119C2×D47—24no—
120C2×D47—82no—
121C2×D47—84no—
122C4×C47—22no—
123C4×C47—42no—
124C4×C47#12011yescharacteristic
125C4×C47#12011yescharacteristic
126C4×C47C22×D412yes—
127Dic47—24no—
128#3021—471nomaximal, Sylow
129C2×C47—21no—
130C2×C47—22no—
131C2×C47—42no—
132C2×C47—82no—
133C2×C47C2×#12011yescharacteristic
134D47—44no—
135#585—471no—
136C2×AGL(1,ℤ/8)—472no—
137#535D4711yescharacteristic, complemented
138#454—474no—
139#453—474no—
140#421—472no—
141#413—471no—
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×D4C2×D4711yescharacteristic, complemented
153AGL(1,ℤ/8)—478no—
154AGL(1,ℤ/8)—944no—
155C2×SD16—942no—
156C2×D8—942no—
157C2×M16—472no—
158#127C2×D4712yescomplemented
159#124C2×D4712yescomplemented
160#121—22no—
161#120—22no—
162#117C2×D4711yescharacteristic, complemented
163#104—478no—
164#101—472no—
165#100—472no—
166C24—21no—
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—942no—
178#41—944no—
179C2×Q8—472no—
180C2×Q8—942no—
181C2×Q8—944no—
182C2×Q8C22×D4711yescharacteristic
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—21no—
187C2×D4—472no—
188C2×D4—942no—
189C2×D4—944no—
190C2×D4—948no—
191C2×D4—942no—
192C2×D4—944no—
193C2×D4C22⋊D4712yes—
194C2×D4C22×D4712yes—
195C2×D4C22×D4711yescharacteristic
196C22×C4—944no—
197C22×C4—942no—
198C22×C4C22⋊D4712yes—
199C22×C4C22×D4711yescharacteristic
200SD16—948no—
201D8—948no—
202M16—474no—
203M16—942no—
204C2×C8—942no—
205C4⋊C4—21no—
206C22⋊C4—21no—
207C22⋊C4—24no—
208C42C22×D4712yes—
209C23—22no—
210C23—42no—
211C23—82no—
212C23—944no—
213C23—942no—
214C23C2×C22⋊D4712yes—
215C23C2×C22⋊D4711yescharacteristic
216Q8—22no—
217Q8—474no—
218Q8—944no—
219Q8—942no—
220D4—24no—
221D4—22no—
222D4—24no—
223D4—41no—
224D4—41no—
225D4—84no—
226D4—474no—
227D4—944no—
228D4—948no—
229D4—944no—
230D4—944no—
231D4—942no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—948no—
236C2×C4—944no—
237C2×C4—942no—
238C2×C4—944no—
239C2×C4—944no—
240C2×C4D4×D4712yes—
241C2×C4D4×D4712yes—
242C2×C4C2×C22⋊D4712yes—
243C2×C4C2×C22⋊D4711yescharacteristic
244C2×C4C23×D4711yescharacteristic
245C8—944no—
246C22—22no—
247C22—41no—
248C22—42no—
249C22—44no—
250C22—42no—
251C22—84no—
252C22—944no—
253C22—3762no—
254C22—3764no—
255C22#1309399212yes—
256C22C22×C22⋊D4711yescharacteristic
257C4—22no—
258C4—42no—
259C4—944no—
260C4#1309399211yescharacteristic
261C4#1309399211yescharacteristic
262C4C2×D4×D4712yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—1884no—
268C2C2×#1309399211yescharacteristic
subgroupG/H
centerC2C2×#13093992
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#535C2
socleC2×C47C2×#120
hypercenter#535D47
hypocenterC47#3021
LCSG ▷ C2×C4×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. C2×#13094050C2semidirect
3. #15689295C2semidirect
4. #15689290C2semidirect
5. #15689141C2semidirect
6. #15689107C2semidirect
7. C47×#535C2semidirect
8. #13094072C22semidirect
12. #13094069C22semidirect
17. #13094050C22semidirect
20. C2×#10625329C22semidirect
21. #13093952C22semidirect
22. #13093943C22semidirect
23. #13093941C22semidirect
25. C22×D4×C47C22semidirect
26. #127×C47C22semidirect
27. #124×C47C22semidirect
30. #117×C47C22semidirect
57. #10625350D4semidirect
60. C2×D188D4semidirect
64. C2×Dic94D4semidirect
137. #535D47semidirect
142. C47#3021semidirect
152. C22×D4C2×D47semidirect
158. #127C2×D47semidirect
159. #124C2×D47semidirect
162. #117C2×D47semidirect