Finite Group Databasebeta

← #20252616

Subgroups — #20252616

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×#13094051C212yesmaximal, complemented
3#15689636C211yesmaximal, characteristic, complemented
4#15689273C211yesmaximal, characteristic, complemented
5#15689272C212yesmaximal, complemented
6#15689259C211yesmaximal, characteristic, complemented
7#15689258C212yesmaximal, complemented
8#15689257C211yesmaximal, characteristic, complemented
9#15689126C212yesmaximal, complemented
10#15689085C211yesmaximal, characteristic, complemented
11C47×#450C211yesmaximal, characteristic, complemented
12C24×D47—21no—
13C2×#10625354C2211yescharacteristic, 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#13094051—28no—
23C2×#10625336C2212yescomplemented
24C2×D376C2212yescomplemented
25C2×#10625334C2212yescomplemented
26C2×#10625324C2212yescomplemented
27#13094009—21no—
28#13094000C2211yescharacteristic, complemented
29#13093999C2211yescharacteristic, complemented
30#13093998C2211yescharacteristic, complemented
31#13093994—21no—
32#13093986—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×SD16×C47C2212yescomplemented
42C22⋊Q8×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×Q8×C47C2311yescharacteristic, complemented
54C2×D4×C47—24no—
55C2×D4×C47—21no—
56C2×D4×C47C2312yes—
57C22×C4×C47C2311yescharacteristic
58C2×C22⋊D47—28no—
59C2×C22⋊D47—21no—
60C2×C22⋊D47—22no—
61C2×C22⋊D47—22no—
62C22×Dic47D411yescharacteristic
63#10625354—24no—
64D4×D47—28no—
65D4×D47—28no—
66D4×D47—24no—
67D4×D47—24no—
68D4×D47—24no—
69D4×D47D418yescomplemented
70C2×D188—21no—
71C2×D188—24no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188C2312yes—
75C2×D188C2311yescharacteristic, complemented
76C2×C4×D47—24no—
77C2×C4×D47—21no—
78C2×C4×D47D411yescharacteristic
79C2×C4×D47D411yescharacteristic
80C2×C4×D47C2311yescharacteristic
81C2×C4×D47C2311yescharacteristic
82SD16×C47—24no—
83C2×C8×C47C2312yescomplemented
84C4⋊C4×C47—21no—
85C4⋊C4×C47C2311yescharacteristic, complemented
86C22⋊C4×C47—21no—
87#10625336—24no—
88#10625334—24no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47C2311yescharacteristic, complemented
94Dic47⋊C4—21no—
95C4×Dic47—21no—
96C2×C47⋊C8C2312yescomplemented
97D376—24no—
98#10625324—24no—
99C23×C47—24no—
100C23×C47—22no—
101C23×C47—42no—
102C23×C47—42no—
103C23×C47C2×D411yescharacteristic
104C22×D47—22no—
105C22×D47—22no—
106C22×D47—22no—
107C22×D47—24no—
108C22×D47—28no—
109C22×D47—22no—
110C22×D47—28no—
111C22×D47—21no—
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
121Q8×C47—22no—
122D4×C47—24no—
123D4×C47—22no—
124D4×C47C2×D414yes—
125C2×C4×C47—22no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—28no—
131C22⋊D47—28no—
132C22⋊D47—42no—
133C2×Dic47—22no—
134C2×Dic47—21no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—24no—
138D188—22no—
139D188—22no—
140D188—42no—
141D188—42no—
142D188C2×D414yes—
143C4×D47—22no—
144C4×D47—22no—
145C4×D47—22no—
146C4×D47—42no—
147C4×D47C2×D414yes—
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×C47AGL(1,ℤ/8)12yescomplemented
157C22×C47C22×D411yescharacteristic
158C2×D47—28no—
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—24no—
164C2×D47—416no—
165C2×D47—416no—
166C2×D47—48no—
167C2×D47—42no—
168C2×D47—42no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47#12012yes—
173C2×D47AGL(1,ℤ/8)12yescomplemented
174C4×C47—21no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47C22×D412yes—
178Dic47—21no—
179Dic47—41no—
180Dic47#12012yes—
181#3003—471nomaximal, Sylow
182C2×C47—22no—
183C2×C47—44no—
184C2×C47C2×#12011yescharacteristic
185C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
187D47—22no—
188D47—22no—
189D47—44no—
190D47—81no—
191C23×D4—471no—
192C2×AGL(1,ℤ/8)—472no—
193#525—471no—
194#450—472no—
195#450—471no—
196#450D4711yescharacteristic, complemented
197#447—471no—
198#447—472no—
199#447—471no—
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×SD16C2×D4712yescomplemented
217C2×D8—472no—
218C2×D8—472no—
219C2×M16—472no—
220#123—941no—
221C22⋊Q8—471no—
222C22⋊Q8C2×D4711yescharacteristic, complemented
223#121—471no—
224#121—471no—
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×Q8C22×D4711yescharacteristic, complemented
246C2×D4—24no—
247C2×D4—21no—
248C2×D4—478no—
249C2×D4—472no—
250C2×D4—471no—
251C2×D4—944no—
252C2×D4—941no—
253C2×D4—941no—
254C2×D4—944no—
255C2×D4—942no—
256C2×D4—942no—
257C2×D4—944no—
258C2×D4—948no—
259C2×D4—948no—
260C2×D4—948no—
261C2×D4—944no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4C22×D4712yes—
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—24no—
274SD16—944no—
275D8—944no—
276D8—944no—
277M16—944no—
278C2×C8—472no—
279C2×C8C22×D4712yescomplemented
280C4⋊C4—21no—
281C4⋊C4—471no—
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—42no—
293C23—42no—
294C23—471no—
295C23—471no—
296C23—942no—
297C23—942no—
298C23—948no—
299C23—944no—
300C23—948no—
301C23—942no—
302C23—942no—
303C23—941no—
304C23—1882no—
305C23—1884no—
306C23—18832no—
307C23—1884no—
308C23—1884no—
309C23—1884no—
310C23—1882no—
311C23D4×D4711yescharacteristic
312Q8—22no—
313D4—24no—
314D4—22no—
315D4—474no—
316D4—944no—
317D4—948no—
318D4—948no—
319D4—942no—
320D4—942no—
321D4—1882no—
322D4—1882no—
323D4—1882no—
324D4D4×D4714yes—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—471no—
329C2×C4—474no—
330C2×C4—471no—
331C2×C4—942no—
332C2×C4—942no—
333C2×C4—942no—
334C2×C4—942no—
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—472no—
348C22—472no—
349C22—948no—
350C22—941no—
351C22—941no—
352C22—941no—
353C22—941no—
354C22—944no—
355C22—1888no—
356C22—18816no—
357C22—18816no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22—1882no—
362C22—1882no—
363C22#1309405112yescomplemented
364C22C2×D4×D4711yescharacteristic
365C4—21no—
366C4—41no—
367C4—41no—
368C4—472no—
369C4—941no—
370C4—1881no—
371C4C2×D4×D4712yes—
372C2—22no—
373C2—44no—
374C2—942no—
375C2—942no—
376C2—3761no—
377C2—1884no—
378C2#120×D4711yescharacteristic
379C2AGL(1,ℤ/8)×D4711yescharacteristic
380C2C2×#1309405111yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3003
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C22×D4×D47C2semidirect
2. C2×#13094051C2semidirect
3. #15689636C2semidirect
4. #15689273C2semidirect
5. #15689272C2semidirect
6. #15689259C2semidirect
7. #15689258C2semidirect
8. #15689257C2semidirect
9. #15689126C2semidirect
10. #15689085C2semidirect
11. C47×#450C2semidirect
13. C2×#10625354C22semidirect
23. C2×#10625336C22semidirect
24. C2×D376C22semidirect
25. C2×#10625334C22semidirect
26. C2×#10625324C22semidirect
28. #13094000C22semidirect
29. #13093999C22semidirect
30. #13093998C22semidirect
34. #13093982C22semidirect
35. #13093946C22semidirect
36. #13093945C22semidirect
37. #13093944C22semidirect
38. C22⋊(C47⋊C8)C22semidirect
39. (C2×D47)⋊C8C22semidirect
41. C2×SD16×C47C22semidirect
42. C22⋊Q8×C47C22semidirect
43. #102×C47C22semidirect
44. C22⋊C8×C47C22semidirect
53. C2×Q8×C47C23semidirect
69. D4×D47D4semidirect
75. C2×D188C23semidirect
83. C2×C8×C47C23semidirect
85. C4⋊C4×C47C23semidirect
93. C4⋊Dic47C23semidirect
96. C2×C47⋊C8C23semidirect
156. C22×C47AGL(1,ℤ/8)semidirect
173. C2×D47AGL(1,ℤ/8)semidirect
196. #450D47semidirect
202. C47#3003semidirect
216. C2×SD16C2×D47semidirect
222. C22⋊Q8C2×D47semidirect
232. #102C2×D47semidirect
235. C22⋊C8C2×D47semidirect
245. C2×Q8C22×D47semidirect
279. C2×C8C22×D47semidirect
283. C4⋊C4C22×D47semidirect
363. C22#13094051semidirect