Finite Group Databasebeta

← #20253001

Subgroups — #20253001

Order 6016.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D47C211yesmaximal, characteristic, complemented
2#15689630C211yesmaximal, characteristic, complemented
3C2×#13093995C211yesmaximal, characteristic, complemented
4#15689373C212yesmaximal, complemented
5#15689366C212yesmaximal, complemented
6#15689356C212yesmaximal, complemented
7#15689349C212yesmaximal, complemented
8#15689165C211yesmaximal, characteristic, complemented
9#15689128C211yesmaximal, characteristic, complemented
10#15689124C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47—21no—
13C22×C4×D47C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15C2×#10625324C2212yescomplemented
16M16×D47—24no—
17C2×C8×D47C2212yescomplemented
18#13094005—21no—
19#13094000C2211yescharacteristic, complemented
20#13094000C2211yescharacteristic, complemented
21#13093995—21no—
22#13093995—21no—
23#13093995C2212yes—
24#13093995C2212yes—
25#13093995C2211yescharacteristic, complemented
26#13093995C2211yescharacteristic, complemented
27#13093992—21no—
28C4×C22⋊D47—21no—
29C4×C22⋊D47—21no—
30#13093983C2211yescharacteristic
31C2×C4⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47—21no—
33#13093958C2212yescomplemented
34#13093956C2212yescomplemented
35#13093948C2212yescomplemented
36#13093945C2212yescomplemented
37#13093945C2212yescomplemented
38#13093945C2212yescomplemented
39C2×#41×C47C2211yescharacteristic
40C22×D4×C47C2211yescharacteristic
41AGL(1,ℤ/8)×C47—24no—
42C2×SD16×C47C2212yescomplemented
43C2×D8×C47C2212yescomplemented
44C2×M16×C47C2211yescharacteristic
45C24×C47—21no—
46C23×D47D411yescharacteristic
47#41×C47—22no—
48#41×C47—22no—
49C2×Q8×C47C2311yescharacteristic
50C2×D4×C47—21no—
51C2×D4×C47—22no—
52C2×D4×C47—21no—
53C2×D4×C47—22no—
54C2×D4×C47C2311yescharacteristic
55C2×D4×C47C2312yes—
56C22×C4×C47—21no—
57C22×C4×C47C2311yescharacteristic
58C2×C22⋊D47—21no—
59C2×C22⋊D47—21no—
60C2×C22⋊D47—22no—
61C2×C22⋊D47—22no—
62C2×C22⋊D47—44no—
63C22×Dic47—21no—
64C22×Dic47D411yescharacteristic
65C2×C4×D47—22no—
66C2×C4×D47—22no—
67C2×C4×D47D411yescharacteristic
68C2×C4×D47D411yescharacteristic
69C2×C4×D47C2311yescharacteristic
70C2×C4×D47C2311yescharacteristic
71SD16×C47—24no—
72D8×C47—24no—
73M16×C47D414yescomplemented
74C2×C8×C47C2312yes—
75C22⋊Dic47—21no—
76C22⋊Dic47—22no—
77C22⋊Dic47—22no—
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47C2311yescharacteristic
84C4⋊Dic47C2311yescharacteristic
85C4⋊Dic47C2312yes—
86Dic47⋊C4—21no—
87Dic47⋊C4—21no—
88C4×Dic47—21no—
89#10625329—22no—
90C2×C47⋊C8C2312yes—
91#10625324—24no—
92C8×D47—24no—
93C23×C47—21no—
94C23×C47—22no—
95C23×C47—42no—
96C23×C47—42no—
97C23×C47—42no—
98C23×C47C2×D411yescharacteristic
99C22×D47—22no—
100C22×D47—22no—
101C22×D47—41no—
102C22×D47C2×D411yescharacteristic
103C22×D47C2×D411yescharacteristic
104Q8×C47—21no—
105Q8×C47—21no—
106D4×C47—21no—
107D4×C47—22no—
108D4×C47—22no—
109D4×C47—21no—
110D4×C47—42no—
111D4×C47—42no—
112C2×C4×C47—21no—
113C2×C4×C47—42no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D412yes—
116C2×C4×C47#4112yes—
117C2×C4×C47C2411yescharacteristic
118C22⋊D47—42no—
119C22⋊D47—44no—
120C22⋊D47—42no—
121C22⋊D47—44no—
122C2×Dic47—22no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—22no—
126C2×Dic47—42no—
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C4×D47—22no—
130C4×D47—22no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—21no—
135C8×C47C2×D414yescomplemented
136C47⋊C8—22no—
137C22×C47—21no—
138C22×C47—21no—
139C22×C47—41no—
140C22×C47—42no—
141C22×C47—42no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—42no—
145C22×C47—84no—
146C22×C47#12112yes—
147C22×C47C22×D411yescharacteristic
148C2×D47—21no—
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—44no—
154C2×D47AGL(1,ℤ/8)12yescomplemented
155C4×C47—41no—
156C4×C47#12112yes—
157C4×C47C22×D411yescharacteristic
158C4×C47C2×#4111yescharacteristic
159Dic47—21no—
160Dic47—21no—
161Dic47—42no—
162Dic47—41no—
163Dic47—41no—
164#3055—471nomaximal, Sylow
165C2×C47—22no—
166C2×C47—81no—
167C2×C47—82no—
168C2×C47C2×#12111yescharacteristic
169C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C47#57511yescharacteristic
171D47—22no—
172D47—41no—
173C2×AGL(1,ℤ/8)D4711yescharacteristic, complemented
174C22×M16—471no—
175#525—471no—
176C2×#121—471no—
177#469—472no—
178#468—472no—
179#466—472no—
180#465—472no—
181#428—471no—
182#418—471no—
183#417—471no—
184C47#305511yescharacteristic, complemented, Sylow
185C2×#41C2×D4711yescharacteristic
186C22×D4—941no—
187C22×D4C2×D4711yescharacteristic
188C23×C4—471no—
189AGL(1,ℤ/8)—24no—
190C2×SD16C2×D4712yescomplemented
191C2×D8C2×D4712yescomplemented
192C2×M16—471no—
193C2×M16—472no—
194C2×M16—944no—
195C2×M16C2×D4711yescharacteristic
196C22×C8—472no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—471no—
200#121—472no—
201#121—472no—
202#121—471no—
203#121—471no—
204#121—941no—
205#121—941no—
206#120—941no—
207C4×D4—941no—
208C4×D4—941no—
209#117—471no—
210C2×C4⋊C4—471no—
211C2×C22⋊C4—941no—
212#107—472no—
213#106—472no—
214#103—472no—
215#102—472no—
216#102—472no—
217#102—472no—
218C24—21no—
219C24—471no—
220#41—22no—
221#41—22no—
222C2×Q8C22×D4711yescharacteristic
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—941no—
228C2×D4—941no—
229C2×D4—942no—
230C2×D4—942no—
231C2×D4—1884no—
232C2×D4C22×D4711yescharacteristic
233C2×D4C22×D4712yes—
234C22×C4—21no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—942no—
241C22×C4—942no—
242C22×C4—941no—
243C22×C4C22×D4711yescharacteristic
244SD16—24no—
245D8—24no—
246M16—942no—
247M16—944no—
248M16C22⋊D4714yescomplemented
249C2×C8—472no—
250C2×C8—944no—
251C2×C8C22×D4712yes—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—472no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—942no—
261C22⋊C4—942no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C42—941no—
266C23—21no—
267C23—22no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—471no—
272C23—471no—
273C23—942no—
274C23—942no—
275C23—1881no—
276C23D4×D4711yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—21no—
280D4—22no—
281D4—22no—
282D4—21no—
283D4—42no—
284D4—42no—
285D4—1882no—
286D4—1884no—
287D4—1882no—
288D4—1884no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—942no—
294C2×C4—942no—
295C2×C4—942no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—942no—
303C2×C4—1882no—
304C2×C4D4×D4711yescharacteristic
305C2×C4#1062535212yes—
306C2×C4C2×C22⋊D4712yes—
307C2×C4C23×D4711yescharacteristic
308C8—942no—
309C8C2×C22⋊D4714yescomplemented
310C22—21no—
311C22—21no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—42no—
318C22—84no—
319C22—472no—
320C22—941no—
321C22—941no—
322C22—941no—
323C22—941no—
324C22—941no—
325C22—1884no—
326C22#1309399512yes—
327C22C2×D4×D4711yescharacteristic
328C4—41no—
329C4—941no—
330C4—941no—
331C4—1882no—
332C4—1881no—
333C4—1881no—
334C4#1309399512yes—
335C4C22×C22⋊D4711yescharacteristic
336C4C2×#1062535211yescharacteristic
337C2—22no—
338C2—82no—
339C2—81no—
340C2—942no—
341C2—1881no—
342C2C2×#1309399511yescharacteristic
343C2AGL(1,ℤ/8)×D4711yescharacteristic
344C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC22×C47C22×D4
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47#3055
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×M16×D47C2semidirect
2. #15689630C2semidirect
3. C2×#13093995C2semidirect
4. #15689373C2semidirect
5. #15689366C2semidirect
6. #15689356C2semidirect
7. #15689349C2semidirect
8. #15689165C2semidirect
9. #15689128C2semidirect
10. #15689124C2semidirect
11. C2×AGL(1,ℤ/8)×C47C2semidirect
15. C2×#10625324C22semidirect
17. C2×C8×D47C22semidirect
19. #13094000C22semidirect
20. #13094000C22semidirect
25. #13093995C22semidirect
26. #13093995C22semidirect
33. #13093958C22semidirect
34. #13093956C22semidirect
35. #13093948C22semidirect
36. #13093945C22semidirect
37. #13093945C22semidirect
38. #13093945C22semidirect
42. C2×SD16×C47C22semidirect
43. C2×D8×C47C22semidirect
73. M16×C47D4semidirect
135. C8×C47C2×D4semidirect
154. C2×D47AGL(1,ℤ/8)semidirect
173. C2×AGL(1,ℤ/8)D47semidirect
184. C47#3055semidirect
190. C2×SD16C2×D47semidirect
191. C2×D8C2×D47semidirect
248. M16C22⋊D47semidirect
309. C8C2×C22⋊D47semidirect