Finite Group Databasebeta

← #20252629

Subgroups — #20252629

Order 6016.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#10625354C211yesmaximal, characteristic, complemented
2C2×#13094049C211yesmaximal, characteristic, complemented
3#15689630C211yesmaximal, characteristic, complemented
4#15689284C214yesmaximal, complemented
5#15689267C214yesmaximal, complemented
6#15689132C211yesmaximal, characteristic, complemented
7#15689129C211yesmaximal, characteristic, complemented
8#15689086C211yesmaximal, characteristic, complemented
9C2×#137×C47C211yesmaximal, characteristic, complemented
10C2×#10625354—24no—
11C2×#10625354—24no—
12C2×#10625354—22no—
13C2×#10625354C2214yes—
14C22×D188—21no—
15C22×D188C2211yescharacteristic
16C22×C4×D47—21no—
17C22×C4×D47C2211yescharacteristic
18#13094049—24no—
19C2×#10625336C2212yescomplemented
20C2×#10625334C2212yescomplemented
21C2×#10625329C2211yescharacteristic
22#13094005—21no—
23#13094000C2212yescomplemented
24#13093995C2212yescomplemented
25#13093992—21no—
26C4×C22⋊D47—22no—
27#13093983C2211yescharacteristic
28#13093948C2214yescomplemented
29#13093946C2214yescomplemented
30(C2×D47)⋊C8C2214yescomplemented
31C2×#41×C47C2211yescharacteristic
32C22×Q8×C47C2211yescharacteristic
33#137×C47—24no—
34C2×Q16×C47C2212yescomplemented
35C2×SD16×C47C2212yescomplemented
36C2×M16×C47C2211yescharacteristic
37C23×D47—21no—
38C23×D47D411yescharacteristic
39#41×C47—22no—
40#41×C47—22no—
41C2×Q8×C47—22no—
42C2×Q8×C47—21no—
43C2×Q8×C47D414yescomplemented
44C2×Q8×C47C2311yescharacteristic
45C2×Q8×C47C2312yes—
46C2×D4×C47—21no—
47C2×D4×C47C2311yescharacteristic
48C22×C4×C47—21no—
49C22×C4×C47—21no—
50C22×C4×C47C2311yescharacteristic
51C2×C22⋊D47—22no—
52C22×Dic47D411yescharacteristic
53#10625354—216no—
54#10625354—28no—
55#10625354—28no—
56C2×D188—28no—
57C2×D188—24no—
58C2×D188—21no—
59C2×D188—22no—
60C2×D188D414yescomplemented
61C2×D188C2312yes—
62C2×C4×D47—28no—
63C2×C4×D47—22no—
64C2×C4×D47—22no—
65C2×C4×D47—24no—
66C2×C4×D47D412yes—
67C2×C4×D47C2312yes—
68Q16×C47—24no—
69SD16×C47—24no—
70M16×C47—22no—
71C2×C8×C47C2312yes—
72C22⋊Dic47—21no—
73C22⋊Dic47—22no—
74#10625336—24no—
75#10625334—24no—
76(C2×D47)⋊C4—22no—
77C4⋊Dic47C2312yes—
78Dic47⋊C4—22no—
79C4×Dic47—21no—
80#10625329—22no—
81C2×C47⋊C8C2312yes—
82C23×C47—21no—
83C23×C47C2×D411yescharacteristic
84C22×D47—22no—
85C22×D47—24no—
86C22×D47—22no—
87C22×D47—42no—
88C22×D47—44no—
89C22×D47C2×D412yes—
90Q8×C47—24no—
91Q8×C47—22no—
92Q8×C47—21no—
93Q8×C47—21no—
94Q8×C47C2×D414yes—
95D4×C47—21no—
96D4×C47—21no—
97D4×C47—42no—
98C2×C4×C47—24no—
99C2×C4×C47—22no—
100C2×C4×C47—21no—
101C2×C4×C47—42no—
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2×D412yes—
104C2×C4×C47C2×D412yes—
105C2×C4×C47C2411yescharacteristic
106C22⋊D47—44no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47C2×D412yes—
110D188—216no—
111D188—24no—
112D188—22no—
113D188C2×D414yes—
114C4×D47—216no—
115C4×D47—24no—
116C4×D47—22no—
117C4×D47—22no—
118C8×C47—22no—
119C47⋊C8—22no—
120C22×C47—22no—
121C22×C47—41no—
122C22×C47—42no—
123C22×C47#12012yes—
124C22×C47C22×D411yescharacteristic
125C2×D47—22no—
126C2×D47—24no—
127C2×D47—22no—
128C2×D47—22no—
129C2×D47—44no—
130C2×D47—48no—
131C2×D47—44no—
132C4×C47—24no—
133C4×C47—41no—
134C4×C47#12012yes—
135C4×C47C22×D411yescharacteristic
136C4×C47C22×D411yescharacteristic
137Dic47—22no—
138Dic47—42no—
139#3005—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47—81no—
142C2×C47C2×#12011yescharacteristic
143C2×C47#57512yes—
144D47—42no—
145D47—44no—
146C22×#41—471no—
147C2×#137D4711yescharacteristic, complemented
148C2×AGL(1,ℤ/8)—471no—
149#525—471no—
150#452—474no—
151#449—474no—
152#419—471no—
153#418—471no—
154#407—471no—
155C47#300511yescharacteristic, complemented, Sylow
156C2×#41—474no—
157C2×#41—942no—
158C2×#41—944no—
159C2×#41—944no—
160C2×#41C2×D4711yescharacteristic
161C22×Q8C2×D4711yescharacteristic
162C22×D4—471no—
163C22×D4—941no—
164C23×C4—471no—
165C23×C4—941no—
166#137—24no—
167AGL(1,ℤ/8)—944no—
168C2×Q16C2×D4712yescomplemented
169C2×SD16—472no—
170C2×SD16C2×D4712yescomplemented
171C2×D8—472no—
172C2×M16—471no—
173C2×M16C2×D4711yescharacteristic
174#123—941no—
175C22⋊Q8—472no—
176#121—472no—
177#120—941no—
178C4×D4—942no—
179#117—471no—
180#103—474no—
181#102—474no—
182C22⋊C8—474no—
183C24—471no—
184C24—941no—
185#41—22no—
186#41—22no—
187#41—948no—
188#41—9416no—
189#41—948no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8C22⋊D4714yescomplemented
193C2×Q8C22×D4711yescharacteristic
194C2×Q8C22×D4712yes—
195C2×D4—21no—
196C2×D4—474no—
197C2×D4—472no—
198C2×D4—944no—
199C2×D4—948no—
200C2×D4—942no—
201C2×D4—941no—
202C2×D4—942no—
203C2×D4C22×D4711yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—471no—
207C22×C4—472no—
208C22×C4—472no—
209C22×C4—944no—
210C22×C4—948no—
211C22×C4—942no—
212C22×C4—942no—
213C22×C4C22×D4711yescharacteristic
214Q16—24no—
215SD16—24no—
216SD16—944no—
217D8—944no—
218M16—22no—
219M16—942no—
220C2×C8—472no—
221C2×C8C22×D4712yes—
222C4⋊C4—472no—
223C4⋊C4—942no—
224C22⋊C4—942no—
225C22⋊C4—942no—
226C22⋊C4—941no—
227C42—941no—
228C23—21no—
229C23—472no—
230C23—944no—
231C23—942no—
232C23—942no—
233C23—1882no—
234C23—1884no—
235C23D4×D4711yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—21no—
239Q8—21no—
240Q8C2×C22⋊D4714yes—
241D4—21no—
242D4—21no—
243D4—42no—
244D4—474no—
245D4—9416no—
246D4—944no—
247D4—942no—
248D4—1884no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—472no—
254C2×C4—9416no—
255C2×C4—942no—
256C2×C4—944no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—942no—
260C2×C4D4×D4711yescharacteristic
261C2×C4D4×D4712yes—
262C2×C4C2×C22⋊D4712yes—
263C2×C4C23×D4711yescharacteristic
264C8—22no—
265C8—942no—
266C22—22no—
267C22—41no—
268C22—42no—
269C22—944no—
270C22—942no—
271C22—942no—
272C22—942no—
273C22—1884no—
274C22—1888no—
275C22—1884no—
276C22#1309399212yes—
277C22C2×D4×D4711yescharacteristic
278C4—24no—
279C4—41no—
280C4—942no—
281C4—1882no—
282C4#1309399212yes—
283C4C2×D4×D4711yescharacteristic
284C4C22×C22⋊D4711yescharacteristic
285C2—22no—
286C2—81no—
287C2—1882no—
288C2—1884no—
289C2C2×#1309399211yescharacteristic
290C2#1568992212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#137×C47C2
socleC22×C47C22×D4
hypercenterC2×#137D47
hypocenterC47#3005
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#10625354C2semidirect
2. C2×#13094049C2semidirect
3. #15689630C2semidirect
4. #15689284C2semidirect
5. #15689267C2semidirect
6. #15689132C2semidirect
7. #15689129C2semidirect
8. #15689086C2semidirect
9. C2×#137×C47C2semidirect
19. C2×#10625336C22semidirect
20. C2×#10625334C22semidirect
23. #13094000C22semidirect
24. #13093995C22semidirect
28. #13093948C22semidirect
29. #13093946C22semidirect
30. (C2×D47)⋊C8C22semidirect
34. C2×Q16×C47C22semidirect
35. C2×SD16×C47C22semidirect
43. C2×Q8×C47D4semidirect
60. C2×D188D4semidirect
147. C2×#137D47semidirect
155. C47#3005semidirect
168. C2×Q16C2×D47semidirect
170. C2×SD16C2×D47semidirect
192. C2×Q8C22⋊D47semidirect