Finite Group Databasebeta

← #20252632

Subgroups — #20252632

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×#10625352C211yesmaximal, characteristic, complemented
2C2×#13094057C211yesmaximal, characteristic, complemented
3C2×#13094050C211yesmaximal, characteristic, complemented
4#15689635C211yesmaximal, characteristic, complemented
5#15689286C214yesmaximal, complemented
6#15689269C214yesmaximal, complemented
7#15689131C211yesmaximal, characteristic, complemented
8#15689086C211yesmaximal, characteristic, complemented
9C47×#418C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C2×#10625352—24no—
12C2×#10625352—22no—
13C2×#10625352—24no—
14C2×#10625352C2214yes—
15C22×Dic94C2211yescharacteristic
16C22×C22⋊D47—21no—
17C23×Dic47—21no—
18C22×C4×D47C2211yescharacteristic
19#13094057—24no—
20#13094050—24no—
21C2×Dic188C2212yescomplemented
22C2×#10625325C2212yescomplemented
23C2×#10625335C2212yescomplemented
24C2×#10625334C2212yescomplemented
25C2×#10625329C2211yescharacteristic
26#13094008—21no—
27#13094004C2212yescomplemented
28#13093999C2212yescomplemented
29#13093994—21no—
30C4×D188—22no—
31#13093947C2214yescomplemented
32(C2×D47)⋊C8C2214yescomplemented
33C22×D4×C47C2211yescharacteristic
34C2×M16×C47C2211yescharacteristic
35#117×C47C2211yescharacteristic
36#102×C47C2214yescomplemented
37C24×C47—21no—
38C23×D47D411yescharacteristic
39C2×D4×C47—21no—
40C2×D4×C47—22no—
41C2×D4×C47D414yescomplemented
42C2×D4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—28no—
45C2×C22⋊D47—24no—
46C2×C22⋊D47—21no—
47C22×Dic47—28no—
48C22×Dic47—21no—
49C22×Dic47—24no—
50C22×Dic47D411yescharacteristic
51#10625352—216no—
52#10625352—28no—
53#10625352—28no—
54#10625350—22no—
55#10625350—22no—
56C2×D188—22no—
57C2×D188C2311yescharacteristic
58C2×C4×D47—22no—
59C2×C4×D47—22no—
60C2×C4×D47—21no—
61C2×C4×D47D412yes—
62C2×C4×D47C2312yes—
63C2×Dic94—21no—
64C2×Dic94—22no—
65C2×Dic94D414yescomplemented
66C2×Dic94C2311yescharacteristic
67C2×Dic94C2312yes—
68M16×C47—22no—
69C2×C8×C47C2312yes—
70C4⋊C4×C47C2312yes—
71C22⋊C4×C47—21no—
72C42×C47—21no—
73#10625335—24no—
74#10625334—24no—
75(C2×D47)⋊C4—22no—
76(C2×D47)⋊C4—22no—
77C4⋊Dic47—22no—
78#10625329—22no—
79C2×C47⋊C8C2312yes—
80Dic188—24no—
81#10625325—24no—
82C23×C47—24no—
83C23×C47—22no—
84C23×C47—44no—
85C23×C47C2×D411yescharacteristic
86C22×D47—22no—
87C22×D47—21no—
88C22×D47—42no—
89C22×D47C2×D412yes—
90D4×C47—24no—
91D4×C47—22no—
92D4×C47C2×D414yes—
93C2×C4×C47—22no—
94C2×C4×C47C2×D412yes—
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2411yescharacteristic
98C22⋊D47—216no—
99C22⋊D47—42no—
100C2×Dic47—216no—
101C2×Dic47—24no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—21no—
105C2×Dic47C2×D412yes—
106D188—21no—
107D188—21no—
108D188—44no—
109C4×D47—24no—
110C4×D47—22no—
111C4×D47—22no—
112C4×D47—42no—
113Dic94—24no—
114Dic94—22no—
115Dic94—21no—
116Dic94—21no—
117Dic94C2×D414yes—
118C8×C47—22no—
119C47⋊C8—22no—
120C22×C47—22no—
121C22×C47—24no—
122C22×C47—48no—
123C22×C47—44no—
124C22×C47#12012yes—
125C22×C47C22×D411yescharacteristic
126C2×D47—22no—
127C2×D47—22no—
128C2×D47—22no—
129C2×D47—44no—
130C2×D47—41no—
131C2×D47—42no—
132C4×C47—42no—
133C4×C47#12012yes—
134C4×C47C22×D411yescharacteristic
135C4×C47C22×D411yescharacteristic
136Dic47—24no—
137Dic47—22no—
138Dic47—41no—
139#3005—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47—44no—
142C2×C47C2×#12011yescharacteristic
143C2×C47#57512yes—
144D47—42no—
145D47—81no—
146C22×#41—471no—
147C2×#137—471no—
148C2×AGL(1,ℤ/8)—471no—
149#525—471no—
150#452—474no—
151#449—474no—
152#419—471no—
153#418D4711yescharacteristic, complemented
154#407—471no—
155C47#300511yescharacteristic, complemented, Sylow
156C2×#41—474no—
157C2×#41—471no—
158C2×#41—942no—
159C2×#41—944no—
160C2×#41—944no—
161C22×Q8—471no—
162C22×D4—941no—
163C22×D4C2×D4711yescharacteristic
164C23×C4—471no—
165C23×C4—941no—
166#137—944no—
167AGL(1,ℤ/8)—944no—
168C2×Q16—472no—
169C2×SD16—472no—
170C2×SD16—472no—
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#117C2×D4711yescharacteristic
180#103—474no—
181#102C2×D4714yescomplemented
182C22⋊C8—474no—
183C24—21no—
184C24—471no—
185#41—948no—
186#41—9416no—
187#41—948no—
188#41—942no—
189#41—942no—
190C2×Q8—474no—
191C2×Q8—472no—
192C2×Q8—471no—
193C2×Q8—942no—
194C2×Q8—941no—
195C2×D4—21no—
196C2×D4—22no—
197C2×D4—471no—
198C2×D4—942no—
199C2×D4—944no—
200C2×D4—948no—
201C2×D4—941no—
202C2×D4D18814yescomplemented
203C2×D4C22×D4712yes—
204C22×C4—471no—
205C22×C4—472no—
206C22×C4—472no—
207C22×C4—944no—
208C22×C4—948no—
209C22×C4—941no—
210C22×C4—942no—
211C22×C4—942no—
212C22×C4—941no—
213C22×C4C22×D4711yescharacteristic
214Q16—944no—
215SD16—944no—
216SD16—944no—
217D8—944no—
218M16—22no—
219M16—942no—
220C2×C8—472no—
221C2×C8C22×D4712yes—
222C4⋊C4—942no—
223C4⋊C4C22×D4712yes—
224C22⋊C4—21no—
225C22⋊C4—942no—
226C22⋊C4—942no—
227C42—21no—
228C23—24no—
229C23—22no—
230C23—44no—
231C23—472no—
232C23—942no—
233C23—941no—
234C23—1882no—
235C23D4×D4711yescharacteristic
236Q8—474no—
237Q8—944no—
238Q8—942no—
239Q8—941no—
240Q8—941no—
241D4—24no—
242D4—22no—
243D4—9416no—
244D4—941no—
245D4—941no—
246D4—1884no—
247D4—1882no—
248D4C2×D18814yes—
249C2×C4—22no—
250C2×C4—472no—
251C2×C4—9416no—
252C2×C4—942no—
253C2×C4—944no—
254C2×C4—942no—
255C2×C4—944no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—941no—
259C2×C4—1882no—
260C2×C4C2×D18812yes—
261C2×C4D4×D4711yescharacteristic
262C2×C4D4×D4712yes—
263C2×C4C23×D4711yescharacteristic
264C8—22no—
265C8—942no—
266C22—22no—
267C22—24no—
268C22—48no—
269C22—44no—
270C22—942no—
271C22—942no—
272C22—942no—
273C22—1884no—
274C22—1881no—
275C22—1882no—
276C22#1309399412yes—
277C22C2×D4×D4711yescharacteristic
278C4—42no—
279C4—942no—
280C4—944no—
281C4—1881no—
282C4#1309399412yes—
283C4C2×D4×D4711yescharacteristic
284C4C22×D18811yescharacteristic
285C2—22no—
286C2—44no—
287C2—3761no—
288C2—1882no—
289C2C2×#1309399411yescharacteristic
290C2#1568991912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#418C2
socleC22×C47C22×D4
hypercenter#418D47
hypocenterC47#3005
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C22×#10625352C2semidirect
2. C2×#13094057C2semidirect
3. C2×#13094050C2semidirect
4. #15689635C2semidirect
5. #15689286C2semidirect
6. #15689269C2semidirect
7. #15689131C2semidirect
8. #15689086C2semidirect
9. C47×#418C2semidirect
21. C2×Dic188C22semidirect
22. C2×#10625325C22semidirect
23. C2×#10625335C22semidirect
24. C2×#10625334C22semidirect
27. #13094004C22semidirect
28. #13093999C22semidirect
31. #13093947C22semidirect
32. (C2×D47)⋊C8C22semidirect
36. #102×C47C22semidirect
41. C2×D4×C47D4semidirect
65. C2×Dic94D4semidirect
153. #418D47semidirect
155. C47#3005semidirect
181. #102C2×D47semidirect
202. C2×D4D188semidirect