Finite Group Databasebeta

← #20252612

Subgroups — #20252612

Order 6016.

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

normal subgroups only

This group has 994 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
1C22×D4×D47C211yesmaximal, characteristic, complemented
2C2×#13094048C212yesmaximal, complemented
3#15689633C211yesmaximal, characteristic, complemented
4#15689276C211yesmaximal, characteristic, complemented
5#15689275C212yesmaximal, complemented
6#15689274C211yesmaximal, characteristic, complemented
7#15689256C211yesmaximal, characteristic, complemented
8#15689255C212yesmaximal, complemented
9#15689126C212yesmaximal, complemented
10#15689085C211yesmaximal, characteristic, complemented
11C47×#447C211yesmaximal, characteristic, complemented
12C24×D47—21no—
13C2×#10625352C2211yescharacteristic, complemented
14C22×D188C2211yescharacteristic
15C22×C22⋊D47—21no—
16C2×D4×D47—28no—
17C2×D4×D47—21no—
18C2×D4×D47—21no—
19C2×D4×D47C2212yes—
20C2×D4×D47C2212yes—
21C22×C4×D47C2211yescharacteristic
22#13094048—28no—
23C2×#10625325C2212yescomplemented
24C2×#10625335C2212yescomplemented
25C2×#10625334C2212yescomplemented
26C2×#10625324C2212yescomplemented
27#13094006—21no—
28#13094004C2211yescharacteristic, complemented
29#13094003C2211yescharacteristic, complemented
30#13093995C2211yescharacteristic, complemented
31#13093992—21no—
32D4×Dic47—21no—
33(C22⋊D47)⋊C4—21no—
34#13093982C2211yescharacteristic, complemented
35#13093946C2212yescomplemented
36#13093945C2212yescomplemented
37#13093944C2212yescomplemented
38C22⋊(C47⋊C8)C2211yescharacteristic, complemented
39(C2×D47)⋊C8C2212yescomplemented
40C22×D4×C47C2211yescharacteristic
41C2×D8×C47C2212yescomplemented
42#121×C47C2211yescharacteristic, complemented
43#102×C47C2212yescomplemented
44C22⋊C8×C47C2211yescharacteristic, complemented
45C24×C47—21no—
46C23×D47—28no—
47C23×D47—21no—
48C23×D47—22no—
49C23×D47—22no—
50C23×D47—44no—
51C23×D47—44no—
52C23×D47D411yescharacteristic
53C2×D4×C47—24no—
54C2×D4×C47—21no—
55C2×D4×C47—21no—
56C2×D4×C47C2312yes—
57C2×D4×C47C2311yescharacteristic, complemented
58C22×C4×C47C2311yescharacteristic
59C2×C22⋊D47—28no—
60C2×C22⋊D47—21no—
61C2×C22⋊D47—21no—
62C2×C22⋊D47—22no—
63C2×C22⋊D47—22no—
64C22×Dic47—21no—
65C22×Dic47D411yescharacteristic
66#10625352—24no—
67D4×D47—28no—
68D4×D47—28no—
69D4×D47—24no—
70D4×D47—24no—
71D4×D47—24no—
72D4×D47D418yescomplemented
73C2×D188—21no—
74C2×D188—24no—
75C2×D188C2312yes—
76C2×C4×D47—24no—
77C2×C4×D47D411yescharacteristic
78C2×C4×D47D411yescharacteristic
79C2×C4×D47C2311yescharacteristic
80C2×C4×D47C2311yescharacteristic
81C2×Dic94C2311yescharacteristic, complemented
82D8×C47—24no—
83C2×C8×C47C2312yescomplemented
84C4⋊C4×C47C2311yescharacteristic, complemented
85C22⋊C4×C47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88#10625335—24no—
89#10625334—24no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic, complemented
94Dic47⋊C4—21no—
95C4×Dic47—21no—
96C2×C47⋊C8C2312yescomplemented
97#10625325—24no—
98#10625324—24no—
99C23×C47—24no—
100C23×C47—22no—
101C23×C47—21no—
102C23×C47—42no—
103C23×C47—42no—
104C23×C47C2×D411yescharacteristic
105C22×D47—22no—
106C22×D47—22no—
107C22×D47—22no—
108C22×D47—24no—
109C22×D47—28no—
110C22×D47—22no—
111C22×D47—28no—
112C22×D47—432no—
113C22×D47—44no—
114C22×D47—44no—
115C22×D47—44no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—44no—
119C22×D47C2×D411yescharacteristic
120C22×D47C2×D411yescharacteristic
121D4×C47—24no—
122D4×C47—22no—
123D4×C47—22no—
124D4×C47—42no—
125D4×C47C2×D414yes—
126C2×C4×C47—22no—
127C2×C4×C47—21no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—28no—
131C22⋊D47—28no—
132C22⋊D47—42no—
133C22⋊D47—42no—
134C2×Dic47—22no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—42no—
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140D188—24no—
141D188—22no—
142D188C2×D414yes—
143C4×D47—22no—
144C4×D47—22no—
145C4×D47—22no—
146C4×D47C2×D414yes—
147Dic94—22no—
148C8×C47—22no—
149C47⋊C8—22no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—24no—
153C22×C47—48no—
154C22×C47—42no—
155C22×C47—42no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47AGL(1,ℤ/8)12yescomplemented
160C22×C47C22×D411yescharacteristic
161C2×D47—28no—
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—21no—
165C2×D47—21no—
166C2×D47—24no—
167C2×D47—416no—
168C2×D47—416no—
169C2×D47—48no—
170C2×D47—42no—
171C2×D47—42no—
172C2×D47#12012yes—
173C2×D47AGL(1,ℤ/8)12yescomplemented
174C4×C47—21no—
175C4×C47—41no—
176C4×C47C22×D412yes—
177Dic47—21no—
178Dic47—41no—
179Dic47—41no—
180Dic47#12012yes—
181#3003—471nomaximal, Sylow
182C2×C47—22no—
183C2×C47—44no—
184C2×C47—81no—
185C2×C47C2×#12011yescharacteristic
186C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
188D47—22no—
189D47—22no—
190D47—44no—
191C23×D4—471no—
192C2×AGL(1,ℤ/8)—472no—
193#525—471no—
194#450—471no—
195#450—472no—
196#450—471no—
197#447—472no—
198#447—471no—
199#447D4711yescharacteristic, complemented
200#418—472no—
201#407—471no—
202C47#300311yescharacteristic, complemented, Sylow
203C25—941no—
204C2×#41—471no—
205C22×D4—472no—
206C22×D4—472no—
207C22×D4—471no—
208C22×D4—941no—
209C22×D4—941no—
210C22×D4—941no—
211C22×D4—948no—
212C22×D4C2×D4711yescharacteristic
213C23×C4—471no—
214AGL(1,ℤ/8)—948no—
215C2×SD16—472no—
216C2×SD16—472no—
217C2×D8—472no—
218C2×D8C2×D4712yescomplemented
219C2×M16—472no—
220#123—941no—
221C22⋊Q8—471no—
222C22⋊Q8—471no—
223#121—471no—
224#121C2×D4711yescharacteristic, complemented
225#120—941no—
226C4×D4—941no—
227C4×D4—941no—
228#117—471no—
229#102—472no—
230#102—472no—
231#102—472no—
232#102C2×D4712yescomplemented
233C22⋊C8—471no—
234C22⋊C8—472no—
235C22⋊C8C2×D4711yescharacteristic, complemented
236C24—21no—
237C24—471no—
238C24—942no—
239C24—942no—
240C24—948no—
241C24—941no—
242C24—1884no—
243C24—1884no—
244#41—944no—
245C2×Q8—471no—
246C2×D4—24no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—478no—
250C2×D4—472no—
251C2×D4—944no—
252C2×D4—944no—
253C2×D4—942no—
254C2×D4—942no—
255C2×D4—944no—
256C2×D4—948no—
257C2×D4—948no—
258C2×D4—948no—
259C2×D4—944no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4C22×D4712yes—
264C2×D4C22×D4711yescharacteristic, complemented
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—944no—
271C22×C4—941no—
272C22×C4C22×D4711yescharacteristic
273SD16—944no—
274SD16—944no—
275D8—24no—
276D8—944no—
277M16—944no—
278C2×C8—472no—
279C2×C8C22×D4712yescomplemented
280C4⋊C4—471no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4C22×D4711yescharacteristic, complemented
284C22⋊C4—21no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C42—941no—
290C23—24no—
291C23—22no—
292C23—21no—
293C23—42no—
294C23—42no—
295C23—471no—
296C23—471no—
297C23—942no—
298C23—942no—
299C23—948no—
300C23—944no—
301C23—948no—
302C23—942no—
303C23—942no—
304C23—1882no—
305C23—1884no—
306C23—18832no—
307C23—1884no—
308C23—1884no—
309C23—1884no—
310C23—1882no—
311C23D4×D4711yescharacteristic
312Q8—942no—
313D4—24no—
314D4—22no—
315D4—22no—
316D4—42no—
317D4—474no—
318D4—944no—
319D4—948no—
320D4—948no—
321D4—942no—
322D4—1882no—
323D4—1882no—
324D4D4×D4714yes—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—471no—
328C2×C4—474no—
329C2×C4—471no—
330C2×C4—942no—
331C2×C4—942no—
332C2×C4—942no—
333C2×C4—942no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—1882no—
337C2×C4D4×D4711yescharacteristic
338C2×C4C23×D4711yescharacteristic
339C8—22no—
340C8—942no—
341C22—21no—
342C22—21no—
343C22—24no—
344C22—48no—
345C22—42no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—472no—
351C22—472no—
352C22—948no—
353C22—941no—
354C22—941no—
355C22—941no—
356C22—941no—
357C22—944no—
358C22—1888no—
359C22—18816no—
360C22—18816no—
361C22—1882no—
362C22—1882no—
363C22#1309404812yescomplemented
364C22C2×D4×D4711yescharacteristic
365C4—21no—
366C4—41no—
367C4—472no—
368C4—941no—
369C4—1881no—
370C4—1881no—
371C4C2×D4×D4712yes—
372C2—22no—
373C2—44no—
374C2—81no—
375C2—942no—
376C2—942no—
377C2—1884no—
378C2#120×D4711yescharacteristic
379C2AGL(1,ℤ/8)×D4711yescharacteristic
380C2C2×#1309404811yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3003
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×D4×D47C2semidirect
2. C2×#13094048C2semidirect
3. #15689633C2semidirect
4. #15689276C2semidirect
5. #15689275C2semidirect
6. #15689274C2semidirect
7. #15689256C2semidirect
8. #15689255C2semidirect
9. #15689126C2semidirect
10. #15689085C2semidirect
11. C47×#447C2semidirect
13. C2×#10625352C22semidirect
23. C2×#10625325C22semidirect
24. C2×#10625335C22semidirect
25. C2×#10625334C22semidirect
26. C2×#10625324C22semidirect
28. #13094004C22semidirect
29. #13094003C22semidirect
30. #13093995C22semidirect
34. #13093982C22semidirect
35. #13093946C22semidirect
36. #13093945C22semidirect
37. #13093944C22semidirect
38. C22⋊(C47⋊C8)C22semidirect
39. (C2×D47)⋊C8C22semidirect
41. C2×D8×C47C22semidirect
42. #121×C47C22semidirect
43. #102×C47C22semidirect
44. C22⋊C8×C47C22semidirect
57. C2×D4×C47C23semidirect
72. D4×D47D4semidirect
81. C2×Dic94C23semidirect
83. C2×C8×C47C23semidirect
84. C4⋊C4×C47C23semidirect
93. C4⋊Dic47C23semidirect
96. C2×C47⋊C8C23semidirect
159. C22×C47AGL(1,ℤ/8)semidirect
173. C2×D47AGL(1,ℤ/8)semidirect
199. #447D47semidirect
202. C47#3003semidirect
218. C2×D8C2×D47semidirect
224. #121C2×D47semidirect
232. #102C2×D47semidirect
235. C22⋊C8C2×D47semidirect
264. C2×D4C22×D47semidirect
279. C2×C8C22×D47semidirect
283. C4⋊C4C22×D47semidirect
363. C22#13094048semidirect