Finite Group Databasebeta

← #20252767

Subgroups — #20252767

Order 6016.

704 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 161 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×#13094054C212yesmaximal, complemented
2#15689694C211yesmaximal, characteristic, complemented
3#15689306C214yesmaximal, complemented
4#15689301C214yesmaximal, complemented
5#15689140C212yesmaximal, complemented
6#15689107C211yesmaximal, characteristic, complemented
7C47×#585C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic, complemented
9#13094054—24no—
10#13094054C2218yescomplemented
11C2×#10625337—22no—
12C2×#10625335—22no—
13C2×#10625329C2212yescomplemented
14#13094022C2212yescomplemented
15#13094011C2212yescomplemented
16#13094005—22no—
17#13094003—22no—
18#13093983C2211yescharacteristic, complemented
19#13093951C2218yescomplemented
20#13093943C2212yescomplemented
21#13093941C2212yescomplemented
222−1+4×C47—22no—
232−1+4×C47C2212yes—
24H(5,𝔽2)×C47—22no—
25H(5,𝔽2)×C47—22no—
26H(5,𝔽2)×C47C2212yes—
27C2×#41×C47—24no—
28C2×#41×C47—22no—
29C2×#41×C47C2212yes—
30C2×#41×C47C2211yescharacteristic
31#41×C47—24no—
32#41×C47—28no—
33#41×C47—24no—
34#41×C47—24no—
35#41×C47—24no—
36#41×C47—22no—
37#41×C47—22no—
38#41×C47—24no—
39#41×C47—22no—
40#41×C47—22no—
41#41×C47D414yes—
42#41×C47C2314yes—
43C2×Q8×C47—22no—
44C2×Q8×C47—24no—
45C2×Q8×C47D412yes—
46C2×Q8×C47C2311yescharacteristic
47C2×D4×C47—28no—
48C2×D4×C47—22no—
49C2×D4×C47—24no—
50C2×D4×C47—22no—
51C2×D4×C47—24no—
52C2×D4×C47D412yes—
53C2×D4×C47D412yes—
54C2×D4×C47C2311yescharacteristic
55C22×C4×C47—24no—
56C22×C4×C47—22no—
57C22×C4×C47D412yes—
58C22×C4×C47C2311yescharacteristic
59C22×Dic47—21no—
60C2×Dic94—22no—
61C2×Dic94—22no—
62C2×Dic94—21no—
63C2×Dic94C2312yes—
64C22⋊Dic47—21no—
65C22⋊Dic47—24no—
66#10625337—28no—
67#10625335—28no—
68C4⋊Dic47—21no—
69Dic47⋊C4—24no—
70C4×Dic47C2312yes—
71#10625329—22no—
72#10625329C2314yes—
73C2×C47⋊C8—22no—
74C23×C47—24no—
75C23×C47—22no—
76C23×C47C2×D412yes—
77C23×C47C2×D411yescharacteristic
78Q8×C47—24no—
79Q8×C47—22no—
80Q8×C47—22no—
81Q8×C47C2×D414yes—
82D4×C47—28no—
83D4×C47—24no—
84D4×C47—24no—
85D4×C47—24no—
86D4×C47—24no—
87D4×C47—22no—
88D4×C47—22no—
89D4×C47C2×D414yes—
90C2×C4×C47—24no—
91C2×C4×C47—28no—
92C2×C4×C47—22no—
93C2×C4×C47—24no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—24no—
97C2×C4×C47C2×D412yes—
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D412yes—
100C2×C4×C47C2×D412yes—
101C2×C4×C47C2411yescharacteristic
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—42no—
105Dic94—24no—
106Dic94—41no—
107Dic94—41no—
108C47⋊C8—24no—
109C22×C47—22no—
110C22×C47—24no—
111C22×C47—41no—
112C22×C47—42no—
113C22×C47—82no—
114C22×C47—84no—
115C22×C47#12012yes—
116C22×C47C22×D411yescharacteristic
117C4×C47—24no—
118C4×C47—22no—
119C4×C47#12011yescharacteristic
120C4×C47#12011yescharacteristic
121C4×C47C22×D412yes—
122Dic47—42no—
123Dic47—42no—
124#3022—471nomaximal, Sylow
125C2×C47—21no—
126C2×C47—22no—
127C2×C47—42no—
128C2×C47—44no—
129C2×C47C2×#12011yescharacteristic
130#585D4711yescharacteristic
131C2×#137—472no—
132#536—471no—
133#456—474no—
134#455—474no—
135#421—472no—
136#413—471no—
137C47#302211yescharacteristic, complemented, Sylow
1382−1+4—22no—
1392−1+4C2×D4712yes—
140H(5,𝔽2)—22no—
141H(5,𝔽2)—22no—
142H(5,𝔽2)C2×D4712yes—
143C2×#41—24no—
144C2×#41—22no—
145C2×#41C2×D4712yes—
146C2×#41C2×D4711yescharacteristic
147C22×Q8—471no—
148#137—478no—
149#137—944no—
150C2×Q16—942no—
151C2×SD16—942no—
152C2×M16—472no—
153C4⋊Q8—472no—
154#124—472no—
155#123—942no—
156C22⋊Q8—942no—
157#117—471no—
158#104—478no—
159#101—472no—
160#100—472no—
161#41—24no—
162#41—28no—
163#41—24no—
164#41—24no—
165#41—24no—
166#41—22no—
167#41—22no—
168#41—24no—
169#41—22no—
170#41—22no—
171#41C22⋊D4714yes—
172#41C22×D4714yes—
173C2×Q8—22no—
174C2×Q8—24no—
175C2×Q8—472no—
176C2×Q8—941no—
177C2×Q8—942no—
178C2×Q8—942no—
179C2×Q8C22⋊D4712yes—
180C2×Q8C22×D4711yescharacteristic
181C2×D4—28no—
182C2×D4—22no—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—24no—
186C2×D4C22⋊D4712yes—
187C2×D4C22⋊D4712yes—
188C2×D4C22×D4711yescharacteristic
189C22×C4—24no—
190C22×C4—22no—
191C22×C4—941no—
192C22×C4C22⋊D4712yes—
193C22×C4C22×D4711yescharacteristic
194Q16—948no—
195SD16—948no—
196M16—474no—
197M16—942no—
198C2×C8—942no—
199C4⋊C4—944no—
200C4⋊C4—941no—
201C22⋊C4—941no—
202C22⋊C4—944no—
203C42—472no—
204C23—24no—
205C23—22no—
206C23C2×C22⋊D4712yes—
207C23C2×C22⋊D4711yescharacteristic
208Q8—24no—
209Q8—22no—
210Q8—22no—
211Q8—944no—
212Q8—1881no—
213Q8—1881no—
214Q8C2×C22⋊D4714yes—
215D4—28no—
216D4—24no—
217D4—24no—
218D4—24no—
219D4—24no—
220D4—22no—
221D4—22no—
222D4C2×C22⋊D4714yes—
223C2×C4—24no—
224C2×C4—28no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—1882no—
233C2×C4C2×C22⋊D4712yes—
234C2×C4C2×C22⋊D4711yescharacteristic
235C2×C4C2×C22⋊D4712yes—
236C2×C4C2×C22⋊D4712yes—
237C2×C4C23×D4711yescharacteristic
238C8—944no—
239C22—22no—
240C22—24no—
241C22—41no—
242C22—42no—
243C22—82no—
244C22—84no—
245C22#1309399312yes—
246C22C22×C22⋊D4711yescharacteristic
247C4—24no—
248C4—22no—
249C4—1882no—
250C4—1882no—
251C4#1309399311yescharacteristic
252C4#1309399311yescharacteristic
253C4C22×C22⋊D4712yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—44no—
258C2C2×#1309399311yescharacteristic
subgroupG/H
centerC2C2×#13093993
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#585C2
socleC2×C47C2×#120
hypercenter#585D47
hypocenterC47#3022
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C2×#13094054C2semidirect
2. #15689694C2semidirect
3. #15689306C2semidirect
4. #15689301C2semidirect
5. #15689140C2semidirect
6. #15689107C2semidirect
8. C22×Dic94C22semidirect
10. #13094054C22semidirect
13. C2×#10625329C22semidirect
14. #13094022C22semidirect
15. #13094011C22semidirect
18. #13093983C22semidirect
19. #13093951C22semidirect
20. #13093943C22semidirect
21. #13093941C22semidirect
137. C47#3022semidirect