Finite Group Databasebeta

← #20252745

Subgroups — #20252745

Order 6016.

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

normal subgroups only

This group has 762 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
1#15689921C212yesmaximal, complemented
2#15689690C211yesmaximal, characteristic, complemented
3#15689301C214yesmaximal, complemented
4#15689291C214yesmaximal, complemented
5#15689140C212yesmaximal, complemented
6C2×#13093941C211yesmaximal, characteristic, complemented
7C2×H(5,𝔽2)×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic, complemented
9#13094055—22no—
10#13094054C2214yescomplemented
11#13094050—22no—
12#13094049C2214yescomplemented
13#13094044—24no—
14C2×#10625329C2212yescomplemented
15#13094020C2212yescomplemented
16#13094011C2212yescomplemented
17#13093995—22no—
18#13093993—22no—
19#13093983C2211yescharacteristic, complemented
20#13093951C2218yescomplemented
21#13093941C2214yescomplemented
22H(5,𝔽2)×C47—24no—
23H(5,𝔽2)×C47—22no—
24H(5,𝔽2)×C47C2214yes—
25C2×#41×C47—22no—
26C2×#41×C47C2212yes—
27C22×D4×C47—22no—
28C22×D4×C47—22no—
29C22×D4×C47C2211yescharacteristic
30C24×C47—22no—
31C24×C47D412yes—
32#41×C47—28no—
33#41×C47—28no—
34#41×C47—22no—
35#41×C47—22no—
36#41×C47D414yescomplemented
37#41×C47C2314yes—
38C2×Q8×C47D412yescomplemented
39C2×D4×C47—24no—
40C2×D4×C47—28no—
41C2×D4×C47—28no—
42C2×D4×C47—22no—
43C2×D4×C47—28no—
44C2×D4×C47—28no—
45C2×D4×C47—22no—
46C2×D4×C47—22no—
47C2×D4×C47D412yes—
48C2×D4×C47D412yescomplemented
49C2×D4×C47C2312yes—
50C22×C4×C47—22no—
51C22×C4×C47—22no—
52C22×C4×C47C2311yescharacteristic
53C2×C22⋊D47—21no—
54C2×C22⋊D47—24no—
55#10625350—22no—
56#10625350—22no—
57C2×D188C2311yescharacteristic, complemented
58C2×C4×D47—21no—
59C2×Dic94C2311yescharacteristic, complemented
60C22⋊Dic47—21no—
61C22⋊Dic47—24no—
62#10625337—24no—
63#10625336—24no—
64#10625335—24no—
65#10625334—24no—
66C4⋊Dic47—21no—
67C4×Dic47C2312yescomplemented
68#10625329—22no—
69#10625329C2314yescomplemented
70C2×C47⋊C8—22no—
71C23×C47—28no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—82no—
76C23×C47—84no—
77C23×C47C2×D414yes—
78C23×C47C2×D411yescharacteristic
79C22×D47—21no—
80Q8×C47—22no—
81Q8×C47C2×D414yes—
82D4×C47—216no—
83D4×C47—24no—
84D4×C47—24no—
85D4×C47—24no—
86D4×C47—22no—
87D4×C47—24no—
88D4×C47C2×D414yes—
89C2×C4×C47—28no—
90C2×C4×C47—22no—
91C2×C4×C47—24no—
92C2×C4×C47—24no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D412yes—
95C2×C4×C47C2×D412yes—
96C2×C4×C47C2411yescharacteristic
97C22⋊D47—41no—
98C22⋊D47—41no—
99C22⋊D47—84no—
100C2×Dic47—22no—
101C2×Dic47—21no—
102D188—22no—
103C4×D47—42no—
104Dic94—22no—
105C47⋊C8—24no—
106C22×C47—24no—
107C22×C47—24no—
108C22×C47—41no—
109C22×C47—44no—
110C22×C47—44no—
111C22×C47—44no—
112C22×C47—82no—
113C22×C47—88no—
114C22×C47#12011yescharacteristic
115C22×C47#12011yescharacteristic
116C22×C47C22×D411yescharacteristic
117C2×D47—42no—
118C2×D47—41no—
119C4×C47—24no—
120C4×C47#12012yes—
121C4×C47C22×D412yes—
122Dic47—42no—
123Dic47—41no—
124#3019—471nomaximal, Sylow
125C2×C47—21no—
126C2×C47—21no—
127C2×C47—21no—
128C2×C47—44no—
129C2×C47—44no—
130C2×C47C2×#12011yescharacteristic
131D47—81no—
132C2×H(5,𝔽2)D4711yescharacteristic, complemented
133#575—472no—
134#535—471no—
135#455—474no—
136#453—474no—
137#421—472no—
138C2×#100—471no—
139C47#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—24no—
141H(5,𝔽2)—22no—
142H(5,𝔽2)C2×D4714yes—
143C2×#41—22no—
144C2×#41—471no—
145C2×#41C2×D4712yes—
146C22×D4—22no—
147C22×D4—22no—
148C22×D4C2×D4711yescharacteristic
149#137—474no—
150#137—942no—
151AGL(1,ℤ/8)—474no—
152AGL(1,ℤ/8)—942no—
153#135—944no—
154C2×M16—472no—
155#127—472no—
156#124—472no—
157#121—942no—
158#120—942no—
159#117—471no—
160#104—478no—
161#100—474no—
162C24—22no—
163C24C22⋊D4712yes—
164#41—28no—
165#41—28no—
166#41—22no—
167#41—22no—
168#41—942no—
169#41—942no—
170#41C22⋊D4714yescomplemented
171#41C22×D4714yes—
172C2×Q8—471no—
173C2×Q8C22⋊D4712yescomplemented
174C2×D4—24no—
175C2×D4—28no—
176C2×D4—28no—
177C2×D4—22no—
178C2×D4—28no—
179C2×D4—28no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—471no—
183C2×D4—944no—
184C2×D4—941no—
185C2×D4C22⋊D4712yes—
186C2×D4C22⋊D4712yescomplemented
187C2×D4C22×D4712yes—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—941no—
191C22×C4C22×D4711yescharacteristic
192Q16—944no—
193SD16—944no—
194SD16—944no—
195D8—944no—
196M16—474no—
197M16—942no—
198C2×C8—942no—
199C4⋊C4—941no—
200C22⋊C4—941no—
201C22⋊C4—944no—
202C42—472no—
203C23—28no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—82no—
208C23—84no—
209C23—941no—
210C23C2×C22⋊D4714yes—
211C23C2×C22⋊D4711yescharacteristic
212Q8—22no—
213Q8—942no—
214Q8C2×C22⋊D4714yes—
215D4—216no—
216D4—24no—
217D4—24no—
218D4—24no—
219D4—22no—
220D4—24no—
221D4—942no—
222D4—3764no—
223D4—1881no—
224D4—1881no—
225D4C2×C22⋊D4714yes—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—942no—
231C2×C4—941no—
232C2×C4—1882no—
233C2×C4C2×C22⋊D4711yescharacteristic
234C2×C4C2×C22⋊D4712yes—
235C2×C4C2×C22⋊D4712yes—
236C2×C4C23×D4711yescharacteristic
237C8—944no—
238C22—24no—
239C22—24no—
240C22—41no—
241C22—44no—
242C22—44no—
243C22—44no—
244C22—82no—
245C22—88no—
246C22—1882no—
247C22—1881no—
248C22#1309399311yescharacteristic
249C22#1309399311yescharacteristic
250C22C22×C22⋊D4711yescharacteristic
251C4—24no—
252C4—1882no—
253C4—1881no—
254C4#1309399312yes—
255C4C22×C22⋊D4712yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—44no—
261C2—3761no—
262C2C2×#1309399311yescharacteristic
subgroupG/H
centerC2C2×#13093993
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×H(5,𝔽2)×C47C2
socleC2×C47C2×#120
hypercenterC2×H(5,𝔽2)D47
hypocenterC47#3019
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #15689921C2semidirect
2. #15689690C2semidirect
3. #15689301C2semidirect
4. #15689291C2semidirect
5. #15689140C2semidirect
6. C2×#13093941C2semidirect
7. C2×H(5,𝔽2)×C47C2semidirect
8. C2×#10625350C22semidirect
10. #13094054C22semidirect
12. #13094049C22semidirect
14. C2×#10625329C22semidirect
15. #13094020C22semidirect
16. #13094011C22semidirect
19. #13093983C22semidirect
20. #13093951C22semidirect
21. #13093941C22semidirect
36. #41×C47D4semidirect
38. C2×Q8×C47D4semidirect
48. C2×D4×C47D4semidirect
57. C2×D188C23semidirect
59. C2×Dic94C23semidirect
67. C4×Dic47C23semidirect
69. #10625329C23semidirect
132. C2×H(5,𝔽2)D47semidirect
139. C47#3019semidirect
170. #41C22⋊D47semidirect
173. C2×Q8C22⋊D47semidirect
186. C2×D4C22⋊D47semidirect