Finite Group Databasebeta

← #20252760

Subgroups — #20252760

Order 6016.

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

normal subgroups only

This group has 736 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×#13094049C212yesmaximal, complemented
2#15689687C211yesmaximal, characteristic, complemented
3#15689296C214yesmaximal, complemented
4#15689291C214yesmaximal, complemented
5#15689140C212yesmaximal, complemented
6#15689107C211yesmaximal, characteristic, complemented
7C47×#585C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic, complemented
9#13094049—24no—
10#13094049C2218yescomplemented
11C2×#10625336—22no—
12C2×#10625334—22no—
13C2×#10625329C2212yescomplemented
14#13094020C2212yescomplemented
15#13094013C2212yescomplemented
16#13093998—22no—
17#13093992—22no—
18#13093983C2211yescharacteristic, complemented
19#13093951C2218yescomplemented
20#13093943C2212yescomplemented
21#13093941C2212yescomplemented
222−1+4×C47—22no—
232−1+4×C47C2212yescomplemented
24H(5,𝔽2)×C47—22no—
25H(5,𝔽2)×C47—22no—
26H(5,𝔽2)×C47C2212yescomplemented
27C2×#41×C47—24no—
28C2×#41×C47—22no—
29C2×#41×C47C2212yes—
30C2×#41×C47C2211yescharacteristic
31C23×D47—21no—
32#41×C47—24no—
33#41×C47—28no—
34#41×C47—24no—
35#41×C47—24no—
36#41×C47—24no—
37#41×C47—22no—
38#41×C47—22no—
39#41×C47—24no—
40#41×C47—22no—
41#41×C47—22no—
42#41×C47D414yescomplemented
43#41×C47C2314yes—
44C2×Q8×C47—22no—
45C2×Q8×C47—24no—
46C2×Q8×C47D412yescomplemented
47C2×Q8×C47C2311yescharacteristic
48C2×D4×C47—28no—
49C2×D4×C47—22no—
50C2×D4×C47—24no—
51C2×D4×C47—22no—
52C2×D4×C47—24no—
53C2×D4×C47D412yes—
54C2×D4×C47D412yescomplemented
55C2×D4×C47C2311yescharacteristic
56C22×C4×C47—24no—
57C22×C4×C47—22no—
58C22×C4×C47D412yes—
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—24no—
61C2×D188—22no—
62C2×D188—22no—
63C2×D188—21no—
64C2×D188C2312yes—
65C22⋊Dic47—21no—
66#10625336—28no—
67#10625334—28no—
68(C2×D47)⋊C4—24no—
69C4⋊Dic47—21no—
70C4×Dic47C2312yes—
71#10625329—22no—
72#10625329C2314yes—
73C2×C47⋊C8—22no—
74C23×C47—24no—
75C23×C47—22no—
76C23×C47C2×D412yes—
77C23×C47C2×D411yescharacteristic
78C22×D47—22no—
79C22×D47—42no—
80C22×D47—82no—
81Q8×C47—24no—
82Q8×C47—22no—
83Q8×C47—22no—
84Q8×C47C2×D414yes—
85D4×C47—28no—
86D4×C47—24no—
87D4×C47—24no—
88D4×C47—24no—
89D4×C47—24no—
90D4×C47—22no—
91D4×C47—22no—
92D4×C47C2×D414yes—
93C2×C4×C47—24no—
94C2×C4×C47—28no—
95C2×C4×C47—22no—
96C2×C4×C47—24no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—24no—
100C2×C4×C47C2×D412yes—
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D412yes—
103C2×C4×C47C2×D412yes—
104C2×C4×C47C2411yescharacteristic
105C22⋊D47—84no—
106C2×Dic47—22no—
107D188—24no—
108D188—41no—
109D188—41no—
110C47⋊C8—24no—
111C22×C47—22no—
112C22×C47—24no—
113C22×C47—41no—
114C22×C47—42no—
115C22×C47—82no—
116C22×C47—84no—
117C22×C47#12012yes—
118C22×C47C22×D411yescharacteristic
119C2×D47—44no—
120C2×D47—42no—
121C2×D47—84no—
122C4×C47—24no—
123C4×C47—22no—
124C4×C47#12011yescharacteristic
125C4×C47#12011yescharacteristic
126C4×C47C22×D412yes—
127Dic47—42no—
128#3021—471nomaximal, Sylow
129C2×C47—21no—
130C2×C47—22no—
131C2×C47—42no—
132C2×C47—44no—
133C2×C47C2×#12011yescharacteristic
134D47—82no—
135#585D4711yescharacteristic, complemented
136C2×AGL(1,ℤ/8)—472no—
137#535—471no—
138#454—474no—
139#453—474no—
140#421—472no—
141#413—471no—
142C47#302111yescharacteristic, complemented, Sylow
1432−1+4—22no—
1442−1+4C2×D4712yescomplemented
145H(5,𝔽2)—22no—
146H(5,𝔽2)—22no—
147H(5,𝔽2)C2×D4712yescomplemented
148C2×#41—24no—
149C2×#41—22no—
150C2×#41C2×D4712yes—
151C2×#41C2×D4711yescharacteristic
152C22×D4—471no—
153AGL(1,ℤ/8)—478no—
154AGL(1,ℤ/8)—944no—
155C2×SD16—942no—
156C2×D8—942no—
157C2×M16—472no—
158#127—472no—
159#124—472no—
160#121—942no—
161#120—942no—
162#117—471no—
163#104—478no—
164#101—472no—
165#100—472no—
166C24—941no—
167#41—24no—
168#41—28no—
169#41—24no—
170#41—24no—
171#41—24no—
172#41—22no—
173#41—22no—
174#41—24no—
175#41—22no—
176#41—22no—
177#41C22⋊D4714yescomplemented
178#41C22×D4714yes—
179C2×Q8—22no—
180C2×Q8—24no—
181C2×Q8C22⋊D4712yescomplemented
182C2×Q8C22×D4711yescharacteristic
183C2×D4—28no—
184C2×D4—22no—
185C2×D4—24no—
186C2×D4—22no—
187C2×D4—24no—
188C2×D4—472no—
189C2×D4—944no—
190C2×D4—942no—
191C2×D4—942no—
192C2×D4—941no—
193C2×D4C22⋊D4712yes—
194C2×D4C22⋊D4712yescomplemented
195C2×D4C22×D4711yescharacteristic
196C22×C4—24no—
197C22×C4—22no—
198C22×C4C22⋊D4712yes—
199C22×C4C22×D4711yescharacteristic
200SD16—948no—
201D8—948no—
202M16—474no—
203M16—942no—
204C2×C8—942no—
205C4⋊C4—941no—
206C22⋊C4—941no—
207C22⋊C4—944no—
208C42—472no—
209C23—24no—
210C23—22no—
211C23—942no—
212C23—3762no—
213C23—1882no—
214C23C2×C22⋊D4712yes—
215C23C2×C22⋊D4711yescharacteristic
216Q8—24no—
217Q8—22no—
218Q8—22no—
219Q8C2×C22⋊D4714yes—
220D4—28no—
221D4—24no—
222D4—24no—
223D4—24no—
224D4—24no—
225D4—22no—
226D4—22no—
227D4—944no—
228D4—3764no—
229D4—1881no—
230D4—1881no—
231D4C2×C22⋊D4714yes—
232C2×C4—24no—
233C2×C4—28no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—942no—
240C2×C4C2×C22⋊D4712yes—
241C2×C4C2×C22⋊D4711yescharacteristic
242C2×C4C2×C22⋊D4712yes—
243C2×C4C2×C22⋊D4712yes—
244C2×C4C23×D4711yescharacteristic
245C8—944no—
246C22—22no—
247C22—24no—
248C22—41no—
249C22—42no—
250C22—82no—
251C22—84no—
252C22—3764no—
253C22—1884no—
254C22—1882no—
255C22#1309399312yes—
256C22C22×C22⋊D4711yescharacteristic
257C4—24no—
258C4—22no—
259C4—1882no—
260C4#1309399311yescharacteristic
261C4#1309399311yescharacteristic
262C4C22×C22⋊D4712yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—44no—
267C2—3762no—
268C2C2×#1309399311yescharacteristic
subgroupG/H
centerC2C2×#13093993
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#585C2
socleC2×C47C2×#120
hypercenter#585D47
hypocenterC47#3021
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×#13094049C2semidirect
2. #15689687C2semidirect
3. #15689296C2semidirect
4. #15689291C2semidirect
5. #15689140C2semidirect
6. #15689107C2semidirect
7. C47×#585C2semidirect
8. C22×D188C22semidirect
10. #13094049C22semidirect
13. C2×#10625329C22semidirect
14. #13094020C22semidirect
15. #13094013C22semidirect
18. #13093983C22semidirect
19. #13093951C22semidirect
20. #13093943C22semidirect
21. #13093941C22semidirect
23. 2−1+4×C47C22semidirect
26. H(5,𝔽2)×C47C22semidirect
42. #41×C47D4semidirect
46. C2×Q8×C47D4semidirect
54. C2×D4×C47D4semidirect
135. #585D47semidirect
142. C47#3021semidirect
144. 2−1+4C2×D47semidirect
147. H(5,𝔽2)C2×D47semidirect
177. #41C22⋊D47semidirect
181. C2×Q8C22⋊D47semidirect
194. C2×D4C22⋊D47semidirect