Finite Group Databasebeta

← #20252744

Subgroups — #20252744

Order 6016.

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

normal subgroups only

This group has 762 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
1C2×#13094069C211yesmaximal, characteristic, complemented
2#15689921C212yesmaximal, complemented
3#15689300C214yesmaximal, complemented
4#15689290C214yesmaximal, complemented
5#15689141C212yesmaximal, complemented
6C2×#13093941C211yesmaximal, characteristic, complemented
7C47×#535C211yesmaximal, characteristic, complemented
8#13094069—22no—
9#13094069—24no—
10#13094069C2214yes—
11C2×#10625350C2212yes—
12C2×#10625352—22no—
13C22×C22⋊D47—22no—
14C2×D4×D47—22no—
15#13094055C2214yescomplemented
16#13094054—22no—
17#13094050C2214yescomplemented
18#13094049—22no—
19#13094044—24no—
20C2×#10625329C2212yescomplemented
21#13093952C2218yescomplemented
22#13093941C2214yescomplemented
23C2×#41×C47C2211yescharacteristic, complemented
24C22×D4×C47C2211yescharacteristic
25#127×C47C2212yescomplemented
26#124×C47C2212yescomplemented
27#121×C47—22no—
28#120×C47—22no—
29#117×C47C2211yescharacteristic, complemented
30C24×C47D412yes—
31C23×D47—22no—
32#41×C47—22no—
33#41×C47—22no—
34C2×Q8×C47C2311yescharacteristic, complemented
35C2×D4×C47—21no—
36C2×D4×C47—24no—
37C2×D4×C47—22no—
38C2×D4×C47—22no—
39C2×D4×C47D412yes—
40C2×D4×C47C2312yes—
41C2×D4×C47C2311yescharacteristic, complemented
42C22×C4×C47—21no—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—24no—
45C2×C22⋊D47—28no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—28no—
48C22×Dic47—22no—
49#10625352—28no—
50#10625352—28no—
51D4×D47—28no—
52D4×D47—28no—
53#10625350—22no—
54#10625350—22no—
55#10625350D414yescomplemented
56#10625350C2314yes—
57C2×D188D412yescomplemented
58C2×C4×D47—22no—
59C2×Dic94D412yescomplemented
60C4⋊C4×C47—21no—
61C22⋊C4×C47—21no—
62C22⋊C4×C47—24no—
63C42×C47C2312yescomplemented
64#10625337—24no—
65#10625336—24no—
66#10625335—24no—
67#10625334—24no—
68#10625329—22no—
69#10625329C2314yescomplemented
70C2×C47⋊C8—22no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—21no—
74C23×C47—82no—
75C23×C47C2×D414yes—
76C23×C47C2×D411yescharacteristic
77C22×D47—22no—
78C22×D47—28no—
79C22×D47—84no—
80Q8×C47—22no—
81D4×C47—24no—
82D4×C47—24no—
83D4×C47—22no—
84D4×C47—41no—
85D4×C47—41no—
86D4×C47—84no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—42no—
90C2×C4×C47C2×D412yes—
91C2×C4×C47C2×D412yes—
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2411yescharacteristic
94C22⋊D47—216no—
95C22⋊D47—24no—
96C22⋊D47—24no—
97C2×Dic47—28no—
98C2×Dic47—22no—
99D188—22no—
100D188C2×D414yes—
101C4×D47—24no—
102C4×D47—24no—
103Dic94—22no—
104Dic94C2×D414yes—
105C47⋊C8—24no—
106C22×C47—24no—
107C22×C47—41no—
108C22×C47—44no—
109C22×C47—44no—
110C22×C47—42no—
111C22×C47—41no—
112C22×C47—82no—
113C22×C47#12011yescharacteristic
114C22×C47#12011yescharacteristic
115C22×C47C22×D411yescharacteristic
116C2×D47—24no—
117C2×D47—44no—
118C2×D47—88no—
119C4×C47—42no—
120C4×C47—41no—
121C4×C47#12012yes—
122C4×C47C22×D412yes—
123Dic47—24no—
124#3019—471nomaximal, Sylow
125C2×C47—21no—
126C2×C47—21no—
127C2×C47—21no—
128C2×C47—44no—
129C2×C47—81no—
130C2×C47C2×#12011yescharacteristic
131D47—44no—
132C2×H(5,𝔽2)—471no—
133#575—472no—
134#535D4711yescharacteristic, complemented
135#455—474no—
136#453—474no—
137#421—472no—
138C2×#100—471no—
139C47#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—474no—
141H(5,𝔽2)—944no—
142H(5,𝔽2)—942no—
143C2×#41—472no—
144C2×#41—942no—
145C2×#41C2×D4711yescharacteristic, complemented
146C22×D4—942no—
147C22×D4—942no—
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#127C2×D4712yescomplemented
156#124C2×D4712yescomplemented
157#121—22no—
158#120—22no—
159#117C2×D4711yescharacteristic, complemented
160#104—478no—
161#100—474no—
162C24—942no—
163C24C22⋊D4712yes—
164#41—22no—
165#41—22no—
166#41—474no—
167#41—474no—
168#41—948no—
169#41—948no—
170#41—942no—
171#41—942no—
172C2×Q8—472no—
173C2×Q8C22×D4711yescharacteristic, complemented
174C2×D4—21no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—472no—
179C2×D4—948no—
180C2×D4—948no—
181C2×D4—944no—
182C2×D4—948no—
183C2×D4—942no—
184C2×D4—948no—
185C2×D4C22⋊D4712yes—
186C2×D4C22×D4712yes—
187C2×D4C22×D4711yescharacteristic, complemented
188C22×C4—21no—
189C22×C4—942no—
190C22×C4—942no—
191C22×C4C22×D4711yescharacteristic
192Q16—944no—
193SD16—944no—
194SD16—944no—
195D8—944no—
196M16—474no—
197M16—942no—
198C2×C8—942no—
199C4⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—24no—
202C42C22×D4712yescomplemented
203C23—22no—
204C23—22no—
205C23—21no—
206C23—82no—
207C23—948no—
208C23—942no—
209C23—3764no—
210C23C2×C22⋊D4714yes—
211C23C2×C22⋊D4711yescharacteristic
212Q8—22no—
213Q8—474no—
214Q8—942no—
215D4—24no—
216D4—24no—
217D4—22no—
218D4—41no—
219D4—41no—
220D4—84no—
221D4—474no—
222D4—9416no—
223D4—944no—
224D4—944no—
225D4—942no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—948no—
230C2×C4—942no—
231C2×C4—944no—
232C2×C4—944no—
233C2×C4D4×D4712yes—
234C2×C4D4×D4712yes—
235C2×C4C2×C22⋊D4711yescharacteristic
236C2×C4C23×D4711yescharacteristic
237C8—944no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—41no—
244C22—82no—
245C22—944no—
246C22—3768no—
247C22—1884no—
248C22#1309399211yescharacteristic
249C22#1309399211yescharacteristic
250C22C22×C22⋊D4711yescharacteristic
251C4—42no—
252C4—41no—
253C4—944no—
254C4#1309399212yes—
255C4C2×D4×D4712yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—81no—
261C2—1884no—
262C2C2×#1309399211yescharacteristic
subgroupG/H
centerC2C2×#13093992
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#535C2
socleC2×C47C2×#120
hypercenter#535D47
hypocenterC47#3019
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. C2×#13094069C2semidirect
2. #15689921C2semidirect
3. #15689300C2semidirect
4. #15689290C2semidirect
5. #15689141C2semidirect
6. C2×#13093941C2semidirect
7. C47×#535C2semidirect
15. #13094055C22semidirect
17. #13094050C22semidirect
20. C2×#10625329C22semidirect
21. #13093952C22semidirect
22. #13093941C22semidirect
23. C2×#41×C47C22semidirect
25. #127×C47C22semidirect
26. #124×C47C22semidirect
29. #117×C47C22semidirect
34. C2×Q8×C47C23semidirect
41. C2×D4×C47C23semidirect
55. #10625350D4semidirect
57. C2×D188D4semidirect
59. C2×Dic94D4semidirect
63. C42×C47C23semidirect
69. #10625329C23semidirect
134. #535D47semidirect
139. C47#3019semidirect
145. C2×#41C2×D47semidirect
155. #127C2×D47semidirect
156. #124C2×D47semidirect
159. #117C2×D47semidirect
173. C2×Q8C22×D47semidirect
187. C2×D4C22×D47semidirect
202. C42C22×D47semidirect