Finite Group Databasebeta

← #20255156

Subgroups — #20255156

Order 6016.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689931C212yesmaximal, complemented
2#15689927C212yesmaximal, complemented
3#15689513C211yesmaximal, characteristic, complemented
4#15689391C212yesmaximal, complemented
5#15689389C212yesmaximal, complemented
6#15689300C211yesmaximal, characteristic, complemented
7#15689292C212yesmaximal, complemented
8#15689242C212yesmaximal, complemented
9C47×#454C211yesmaximal, characteristic, complemented
10#13094070C2212yescomplemented
11#13094069C2211yescharacteristic
12#13094055—22no—
13#13094055C2212yescomplemented
14#13094052C2212yes—
15#13094051—22no—
16#13094049—22no—
17#13094049C2212yescomplemented
18#13094048—22no—
19#13094045—22no—
20#13094044—22no—
21#13094044C2212yes—
22C2×#10625336—22no—
23C2×#10625336C2212yescomplemented
24C2×#10625334C2212yescomplemented
25D8×D47—22no—
26#13094032C2212yescomplemented
27#13094031C2212yescomplemented
28#13094021C2211yescharacteristic, complemented
29#13093959C2212yescomplemented
30#13093952C2212yescomplemented
31#13093941C2211yescharacteristic, complemented
32#13093940C2212yescomplemented
33#13093935C2211yescharacteristic, complemented
342−1+4×C47C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C47C2212yescomplemented
36#124×C47C2211yescharacteristic, complemented
37#104×C47C2212yescomplemented
38#101×C47C2211yescharacteristic, complemented
39#41×C47—22no—
40#41×C47—41no—
41#41×C47C2312yes—
42C2×Q8×C47—22no—
43C2×Q8×C47C2311yescharacteristic
44C2×D4×C47C2311yescharacteristic
45C2×C22⋊D47—41no—
46#10625354—22no—
47#10625352—22no—
48D4×D47—22no—
49D4×D47—22no—
50D4×D47—42no—
51#10625350—22no—
52#10625350C2312yes—
53C2×D188—22no—
54C2×D188—41no—
55C2×D188C2312yes—
56SD16×C47—22no—
57D8×C47—22no—
58M16×C47C2312yes—
59C22⋊C4×C47—41no—
60C42×C47C2311yescharacteristic
61#10625337—22no—
62#10625337D412yescomplemented
63#10625336—22no—
64#10625336—22no—
65#10625336—22no—
66#10625336—22no—
67#10625336D412yescomplemented
68#10625335D412yescomplemented
69#10625334—22no—
70#10625334—22no—
71#10625334—22no—
72#10625334D412yescomplemented
73#10625329—22no—
74#10625329C2312yes—
75C2×C47⋊C8—22no—
76C2×C47⋊C8C2312yes—
77D376—22no—
78#10625325—22no—
79#10625324—22no—
80C8×D47—22no—
81C23×C47—21no—
82C22×D47—22no—
83C22×D47—41no—
84C22×D47—42no—
85Q8×C47—22no—
86Q8×C47—41no—
87Q8×C47C2×D412yes—
88D4×C47—22no—
89D4×C47—22no—
90D4×C47—41no—
91D4×C47C2×D412yes—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—42no—
96C2×C4×C47C2411yescharacteristic
97C22⋊D47—22no—
98C22⋊D47—42no—
99C22⋊D47—42no—
100C2×Dic47—41no—
101D188—22no—
102D188—22no—
103D188—42no—
104D188—82no—
105D188C2×D412yes—
106C4×D47—22no—
107C4×D47—42no—
108Dic94C2×D412yes—
109C8×C47—22no—
110C47⋊C8—22no—
111C47⋊C8C2×D412yes—
112C47⋊C8C2×D412yes—
113C22×C47—22no—
114C22×C47—41no—
115C22×C47—81no—
116C22×C47H(5,𝔽2)11yescharacteristic
117C2×D47—22no—
118C2×D47—42no—
119C2×D47—82no—
120C2×D47—161no—
121C2×D47—162no—
122C4×C47—22no—
123C4×C47—41no—
124C4×C47—41no—
125C4×C47C22×D412yes—
126Dic47—22no—
127#3288—471nomaximal, Sylow
128C2×C47—21no—
129C2×C47—42no—
130C2×C47—81no—
131C2×C47D4211yescharacteristic
132D47—42no—
133D47—82no—
134#577—472no—
135#576—472no—
136#496—471no—
137#472—472no—
138#471—472no—
139#455—471no—
140#454D4711yescharacteristic, complemented
141#453—472no—
142#444—472no—
143C47#328811yescharacteristic, complemented, Sylow
1442−1+4C2×D4711yescharacteristic, complemented
145H(5,𝔽2)—472no—
146H(5,𝔽2)—471no—
147#137—472no—
148#137—942no—
149AGL(1,ℤ/8)—472no—
150AGL(1,ℤ/8)—472no—
151AGL(1,ℤ/8)—942no—
152AGL(1,ℤ/8)—942no—
153AGL(1,ℤ/8)—942no—
154AGL(1,ℤ/8)C2×D4712yescomplemented
155#135—472no—
156#135—942no—
157#135—942no—
158C2×SD16—472no—
159C2×SD16—942no—
160C2×D8—472no—
161C2×D8—942no—
162#131—472no—
163#131—472no—
164#127—471no—
165#124C2×D4711yescharacteristic, complemented
166#108—472no—
167#104—472no—
168#104C2×D4712yescomplemented
169#101C2×D4711yescharacteristic, complemented
170#100—471no—
171#100—472no—
172#97—471no—
173#41—22no—
174#41—41no—
175#41—472no—
176#41—942no—
177#41—942no—
178#41—942no—
179#41C22×D4712yes—
180C2×Q8—22no—
181C2×Q8C22×D4711yescharacteristic
182C2×D4—472no—
183C2×D4—942no—
184C2×D4—942no—
185C2×D4—942no—
186C2×D4—1881no—
187C2×D4—1882no—
188C2×D4—1881no—
189C2×D4C22×D4711yescharacteristic
190Q16—472no—
191Q16—942no—
192SD16—22no—
193SD16—472no—
194SD16—472no—
195SD16—942no—
196SD16—942no—
197SD16—942no—
198SD16—942no—
199SD16—942no—
200D8—22no—
201D8—472no—
202D8—942no—
203D8—942no—
204D8—942no—
205D8—942no—
206M16—472no—
207M16—942no—
208M16—942no—
209M16C22×D4712yes—
210C2×C8—472no—
211C2×C8—942no—
212C2×C8—942no—
213C22⋊C4—41no—
214C42C22×D4711yescharacteristic
215C23—21no—
216C23—942no—
217C23—1882no—
218C23—1881no—
219Q8—22no—
220Q8—41no—
221Q8—472no—
222Q8D4×D4712yes—
223D4—22no—
224D4—22no—
225D4—41no—
226D4—472no—
227D4—942no—
228D4—942no—
229D4—942no—
230D4—3762no—
231D4—1882no—
232D4—1882no—
233D4—1882no—
234D4D4×D4712yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—942no—
240C2×C4—1882no—
241C2×C4—1881no—
242C2×C4C23×D4711yescharacteristic
243C8—22no—
244C8—472no—
245C8—472no—
246C8—942no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—942no—
251C22—3762no—
252C22—1882no—
253C22—7522no—
254C22—7521no—
255C22#1309406911yescharacteristic
256C4—22no—
257C4—41no—
258C4—41no—
259C4—942no—
260C4C2×D4×D4712yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—3762no—
265C2—1882no—
266C2#1568975511yescharacteristic
subgroupG/H
centerC2#15689755
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#454C2
socleC2×C47D42
hypercenter#454D47
hypocenterC47#3288
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #15689931C2semidirect
2. #15689927C2semidirect
3. #15689513C2semidirect
4. #15689391C2semidirect
5. #15689389C2semidirect
6. #15689300C2semidirect
7. #15689292C2semidirect
8. #15689242C2semidirect
9. C47×#454C2semidirect
10. #13094070C22semidirect
13. #13094055C22semidirect
17. #13094049C22semidirect
23. C2×#10625336C22semidirect
24. C2×#10625334C22semidirect
26. #13094032C22semidirect
27. #13094031C22semidirect
28. #13094021C22semidirect
29. #13093959C22semidirect
30. #13093952C22semidirect
31. #13093941C22semidirect
32. #13093940C22semidirect
33. #13093935C22semidirect
34. 2−1+4×C47C22semidirect
35. AGL(1,ℤ/8)×C47C22semidirect
36. #124×C47C22semidirect
37. #104×C47C22semidirect
38. #101×C47C22semidirect
62. #10625337D4semidirect
67. #10625336D4semidirect
68. #10625335D4semidirect
72. #10625334D4semidirect
140. #454D47semidirect
143. C47#3288semidirect
144. 2−1+4C2×D47semidirect
154. AGL(1,ℤ/8)C2×D47semidirect
165. #124C2×D47semidirect
168. #104C2×D47semidirect
169. #101C2×D47semidirect