Finite Group Databasebeta

← #20255154

Subgroups — #20255154

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#15689929C212yesmaximal, complemented
2#15689924C212yesmaximal, complemented
3#15689390C212yesmaximal, complemented
4#15689383C212yesmaximal, complemented
5#15689300C211yesmaximal, characteristic, complemented
6#15689295C211yesmaximal, characteristic, complemented
7#15689290C212yesmaximal, complemented
8#15689246C212yesmaximal, complemented
9C47×#496C211yesmaximal, characteristic, complemented
10#13094072C2211yescharacteristic, complemented
11#13094069C2211yescharacteristic
12#13094069C2212yescomplemented
13#13094055C2212yescomplemented
14#13094053—22no—
15#13094051—22no—
16#13094050C2212yes—
17#13094050C2212yescomplemented
18#13094050C2212yescomplemented
19#13094048—22no—
20#13094048—22no—
21#13094046C2212yes—
22#13094045—22no—
23#13094043—22no—
24SD16×D47—22no—
25D8×D47—22no—
26#13094030C2212yescomplemented
27#13094030C2212yescomplemented
28#13093960C2212yescomplemented
29#13093952C2212yescomplemented
30#13093952C2212yescomplemented
31#13093943C2211yescharacteristic, complemented
32#13093941C2212yescomplemented
33#13093941C2211yescharacteristic, complemented
34C2×SD16×C47C2212yescomplemented
35C2×D8×C47C2212yescomplemented
36#127×C47C2211yescharacteristic, complemented
37#124×C47C2211yescharacteristic, complemented
38#97×C47C2211yescharacteristic, complemented
39C2×Q8×C47C2311yescharacteristic
40C2×D4×C47—41no—
41C2×D4×C47C2311yescharacteristic
42C2×D4×C47C2312yes—
43C2×C22⋊D47—41no—
44C2×C22⋊D47—42no—
45#10625354—22no—
46Q8×D47—22no—
47#10625352—22no—
48#10625352—22no—
49#10625352—22no—
50D4×D47—22no—
51D4×D47—22no—
52D4×D47—22no—
53#10625350—41no—
54#10625350C2312yes—
55#10625350C2312yes—
56SD16×C47—22no—
57SD16×C47—22no—
58D8×C47—22no—
59D8×C47—22no—
60C2×C8×C47C2312yes—
61C22⋊C4×C47—41no—
62C42×C47C2311yescharacteristic
63#10625337—22no—
64#10625336—22no—
65#10625335—22no—
66#10625335—22no—
67#10625335—22no—
68#10625334—22no—
69#10625334—22no—
70#10625334—22no—
71#10625329C2312yes—
72#10625329C2312yes—
73Dic188D412yescomplemented
74D376D412yescomplemented
75#10625325D412yescomplemented
76#10625325D412yescomplemented
77#10625324—22no—
78#10625324—22no—
79C8×D47—22no—
80C8×D47—22no—
81C23×C47—21no—
82C23×C47—22no—
83C22×D47—42no—
84C22×D47—41no—
85Q8×C47—22no—
86D4×C47—22no—
87D4×C47—22no—
88D4×C47—22no—
89D4×C47—82no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47C2411yescharacteristic
93C22⋊D47—22no—
94C22⋊D47—22no—
95C22⋊D47—42no—
96C22⋊D47—42no—
97C22⋊D47—42no—
98C2×Dic47—42no—
99C2×Dic47—41no—
100D188—41no—
101D188C2×D412yes—
102D188C2×D412yes—
103C4×D47—22no—
104C4×D47—22no—
105C4×D47—42no—
106Dic94—41no—
107Dic94C2×D412yes—
108Dic94C2×D412yes—
109C8×C47C2×D412yes—
110C8×C47C2×D412yes—
111C47⋊C8—22no—
112C47⋊C8—22no—
113C22×C47—41no—
114C22×C47—42no—
115C22×C47—82no—
116C22×C47—81no—
117C22×C47H(5,𝔽2)11yescharacteristic
118C2×D47—22no—
119C2×D47—22no—
120C2×D47—162no—
121C2×D47—161no—
122C4×C47—41no—
123C4×C47—41no—
124C4×C47C22×D412yes—
125Dic47—22no—
126Dic47—22no—
127#3288—471nomaximal, Sylow
128C2×C47—21no—
129C2×C47—82no—
130C2×C47—81no—
131C2×C47D4211yescharacteristic
132D47—42no—
133D47—42no—
134#577—472no—
135#576—472no—
136#496D4711yescharacteristic, complemented
137#472—472no—
138#471—472no—
139#455—471no—
140#454—471no—
141#453—472no—
142#444—472no—
143C47#328811yescharacteristic, complemented, Sylow
1442−1+4—471no—
145H(5,𝔽2)—471no—
146H(5,𝔽2)—472no—
147#137—472no—
148#137—942no—
149AGL(1,ℤ/8)—472no—
150AGL(1,ℤ/8)—472no—
151AGL(1,ℤ/8)—472no—
152AGL(1,ℤ/8)—942no—
153AGL(1,ℤ/8)—942no—
154AGL(1,ℤ/8)—942no—
155#135—472no—
156#135—942no—
157#135—942no—
158C2×SD16—942no—
159C2×SD16C2×D4712yescomplemented
160C2×D8—942no—
161C2×D8C2×D4712yescomplemented
162#131—472no—
163#131—472no—
164#127C2×D4711yescharacteristic, complemented
165#124C2×D4711yescharacteristic, complemented
166#108—472no—
167#104—472no—
168#104—472no—
169#101—471no—
170#100—472no—
171#100—471no—
172#97C2×D4711yescharacteristic, complemented
173#41—472no—
174#41—472no—
175#41—942no—
176#41—942no—
177#41—942no—
178#41—942no—
179#41—1881no—
180C2×Q8—942no—
181C2×Q8C22×D4711yescharacteristic
182C2×D4—41no—
183C2×D4—942no—
184C2×D4—942no—
185C2×D4—942no—
186C2×D4—1881no—
187C2×D4—1882no—
188C2×D4C22×D4711yescharacteristic
189C2×D4C22×D4712yes—
190Q16—472no—
191Q16—942no—
192SD16—22no—
193SD16—22no—
194SD16—472no—
195SD16—472no—
196SD16—942no—
197SD16—942no—
198SD16—942no—
199SD16—942no—
200D8—22no—
201D8—22no—
202D8—472no—
203D8—942no—
204D8—942no—
205D8—942no—
206M16—472no—
207M16—472no—
208M16—942no—
209M16—942no—
210C2×C8—942no—
211C2×C8—942no—
212C2×C8C22×D4712yes—
213C22⋊C4—41no—
214C42C22×D4711yescharacteristic
215C23—21no—
216C23—22no—
217C23—1882no—
218C23—1881no—
219Q8—22no—
220Q8—472no—
221Q8—472no—
222Q8—1881no—
223D4—22no—
224D4—22no—
225D4—22no—
226D4—82no—
227D4—472no—
228D4—472no—
229D4—942no—
230D4—942no—
231D4—1881no—
232D4—1882no—
233D4—1882no—
234D4—1882no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—1882no—
240C2×C4—1881no—
241C2×C4—1882no—
242C2×C4C23×D4711yescharacteristic
243C8—942no—
244C8—942no—
245C8D4×D4712yes—
246C8D4×D4712yes—
247C22—41no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—942no—
252C22—942no—
253C22—7521no—
254C22—7522no—
255C22#1309406911yescharacteristic
256C4—41no—
257C4—41no—
258C4—942no—
259C4—942no—
260C4C2×D4×D4712yes—
261C2—21no—
262C2—82no—
263C2—81no—
264C2—1882no—
265C2—1882no—
266C2#1568975811yescharacteristic
subgroupG/H
centerC2#15689758
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#496C2
socleC2×C47D42
hypercenter#496D47
hypocenterC47#3288
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #15689929C2semidirect
2. #15689924C2semidirect
3. #15689390C2semidirect
4. #15689383C2semidirect
5. #15689300C2semidirect
6. #15689295C2semidirect
7. #15689290C2semidirect
8. #15689246C2semidirect
9. C47×#496C2semidirect
10. #13094072C22semidirect
12. #13094069C22semidirect
13. #13094055C22semidirect
17. #13094050C22semidirect
18. #13094050C22semidirect
26. #13094030C22semidirect
27. #13094030C22semidirect
28. #13093960C22semidirect
29. #13093952C22semidirect
30. #13093952C22semidirect
31. #13093943C22semidirect
32. #13093941C22semidirect
33. #13093941C22semidirect
34. C2×SD16×C47C22semidirect
35. C2×D8×C47C22semidirect
36. #127×C47C22semidirect
37. #124×C47C22semidirect
38. #97×C47C22semidirect
73. Dic188D4semidirect
74. D376D4semidirect
75. #10625325D4semidirect
76. #10625325D4semidirect
136. #496D47semidirect
143. C47#3288semidirect
159. C2×SD16C2×D47semidirect
161. C2×D8C2×D47semidirect
164. #127C2×D47semidirect
165. #124C2×D47semidirect
172. #97C2×D47semidirect