Finite Group Databasebeta

← #447×D47 #20252561

Subgroups — #447×D47 #20252561

Order 6016.

1048 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 155 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×D8×D47C212yesmaximal, complemented
3#121×D47C211yesmaximal, characteristic, complemented
4#15689259C211yesmaximal, characteristic, complemented
5#15689258C212yesmaximal, complemented
6#15689257C211yesmaximal, characteristic, complemented
7#15689256C211yesmaximal, characteristic, complemented
8#15689255C212yesmaximal, complemented
9#102×D47C212yesmaximal, complemented
10C22⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#447C211yesmaximal, characteristic, complemented
12C24×D47—21no—
13C22×D188C2211yescharacteristic, complemented
14C22×C22⋊D47—21no—
15C2×D4×D47—28no—
16C2×D4×D47—21no—
17C2×D4×D47—21no—
18C2×D4×D47—21no—
19C2×D4×D47C2212yes—
20C2×D4×D47C2212yescomplemented
21C2×D4×D47C2211yescharacteristic, complemented
22C22×C4×D47C2211yescharacteristic
23C2×D376C2212yescomplemented
24C2×#10625334C2212yescomplemented
25C2×#10625334C2212yescomplemented
26D8×D47—28no—
27C2×C8×D47C2212yescomplemented
28#13093999C2211yescharacteristic, complemented
29#13093998C2211yescharacteristic, complemented
30#13093997—21no—
31#13093996—21no—
32#13093995C2211yescharacteristic, complemented
33C4⋊C4×D47C2211yescharacteristic, complemented
34C22⋊C4×D47—21no—
35#13093946C2212yescomplemented
36#13093945C2212yescomplemented
37#13093944C2212yescomplemented
38C22⋊(C47⋊C8)C2211yescharacteristic, complemented
39(C2×D47)⋊C8C2212yescomplemented
40C22×D4×C47C2211yescharacteristic, complemented
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—21no—
51C23×D47—44no—
52C23×D47—44no—
53C23×D47D411yescharacteristic
54C2×D4×C47—24no—
55C2×D4×C47—21no—
56C2×D4×C47—21no—
57C2×D4×C47C2312yes—
58C2×D4×C47C2311yescharacteristic, complemented
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—28no—
61C2×C22⋊D47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—22no—
64C2×C22⋊D47—22no—
65C2×C22⋊D47—21no—
66C22×Dic47D411yescharacteristic
67D4×D47—28no—
68D4×D47—28no—
69D4×D47—24no—
70D4×D47—24no—
71D4×D47—24no—
72D4×D47—24no—
73D4×D47—44no—
74D4×D47D418yescomplemented
75C2×D188—21no—
76C2×D188—24no—
77C2×D188—21no—
78C2×D188C2312yes—
79C2×D188C2311yescharacteristic, complemented
80C2×C4×D47—24no—
81C2×C4×D47—21no—
82C2×C4×D47D411yescharacteristic
83C2×C4×D47D411yescharacteristic
84C2×C4×D47C2311yescharacteristic
85C2×C4×D47C2311yescharacteristic
86D8×C47—24no—
87C2×C8×C47C2312yescomplemented
88C4⋊C4×C47C2311yescharacteristic, complemented
89C22⋊C4×C47—21no—
90C22⋊Dic47—21no—
91#10625334—24no—
92#10625334—24no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47C2311yescharacteristic, complemented
96Dic47⋊C4—21no—
97C2×C47⋊C8C2312yescomplemented
98D376—24no—
99C8×D47—24no—
100C23×C47—24no—
101C23×C47—22no—
102C23×C47—21no—
103C23×C47—42no—
104C23×C47—42no—
105C23×C47C2×D411yescharacteristic
106C22×D47—22no—
107C22×D47—22no—
108C22×D47—24no—
109C22×D47—28no—
110C22×D47—22no—
111C22×D47—28no—
112C22×D47—21no—
113C22×D47—44no—
114C22×D47—432no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—44no—
118C22×D47—44no—
119C22×D47—44no—
120C22×D47—42no—
121C22×D47—42no—
122C22×D47—42no—
123C22×D47D814yescomplemented
124C22×D47C2×D411yescharacteristic
125C22×D47C2×D411yescharacteristic
126D4×C47—24no—
127D4×C47—22no—
128D4×C47—22no—
129D4×C47—42no—
130D4×C47C2×D414yescomplemented
131C2×C4×C47—22no—
132C2×C4×C47—21no—
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—28no—
136C22⋊D47—28no—
137C22⋊D47—42no—
138C22⋊D47—42no—
139C22⋊D47—42no—
140C2×Dic47—22no—
141C2×Dic47—21no—
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144D188—24no—
145D188—22no—
146D188—22no—
147D188—42no—
148D188C2×D414yescomplemented
149C4×D47—22no—
150C4×D47—22no—
151C4×D47—22no—
152C4×D47—42no—
153C4×D47C2×D414yes—
154C8×C47—22no—
155C47⋊C8—22no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—24no—
159C22×C47—48no—
160C22×C47—42no—
161C22×C47—42no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47C2×D812yescomplemented
166C22×C47C22×D411yescharacteristic
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—28no—
170C2×D47—24no—
171C2×D47—416no—
172C2×D47—48no—
173C2×D47—42no—
174C2×D47—42no—
175C2×D47—416no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—84no—
180C2×D47#12012yes—
181C2×D47C2×D812yes—
182C2×D47C2×D812yescomplemented
183C2×D47AGL(1,ℤ/8)12yes—
184C4×C47—21no—
185C4×C47—41no—
186C4×C47C22×D412yes—
187Dic47—21no—
188Dic47—41no—
189Dic47#12012yes—
190C2×#447—471nomaximal, Sylow
191C2×C47—22no—
192C2×C47—44no—
193C2×C47—81no—
194C2×C47C2×#12011yescharacteristic
195C2×C47C22×D811yescharacteristic
196C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
197D47—22no—
198D47—44no—
199D47—81no—
200D47#44714yesdirect product factor
201C23×D4—471no—
202C22×D8—472no—
203C2×#121—471no—
204#447—471no—
205#447—472no—
206#447—471no—
207#447—472no—
208#447—471no—
209#447D4711yescharacteristic, direct product factor
210C2×#102—472no—
211C2×C22⋊C8—471no—
212C47C2×#44711yescharacteristic, complemented, Sylow
213C25—941no—
214C22×D4—472no—
215C22×D4—472no—
216C22×D4—471no—
217C22×D4—471no—
218C22×D4—941no—
219C22×D4—941no—
220C22×D4—941no—
221C22×D4—948no—
222C22×D4—941no—
223C22×D4C2×D4711yescharacteristic, complemented
224C23×C4—471no—
225C2×D8—472no—
226C2×D8—472no—
227C2×D8—472no—
228C2×D8—948no—
229C2×D8C2×D4712yescomplemented
230C22×C8—472no—
231#121—471no—
232#121—471no—
233#121—471no—
234#121—941no—
235#121—941no—
236#121C2×D4711yescharacteristic, complemented
237C2×C4⋊C4—471no—
238C2×C22⋊C4—941no—
239#102—472no—
240#102—472no—
241#102—472no—
242#102C2×D4712yescomplemented
243C22⋊C8—471no—
244C22⋊C8—472no—
245C22⋊C8C2×D4711yescharacteristic, complemented
246C24—21no—
247C24—471no—
248C24—942no—
249C24—942no—
250C24—941no—
251C24—948no—
252C24—941no—
253C24—1884no—
254C24—1884no—
255C2×D4—24no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—478no—
259C2×D4—472no—
260C2×D4—471no—
261C2×D4—944no—
262C2×D4—941no—
263C2×D4—944no—
264C2×D4—944no—
265C2×D4—942no—
266C2×D4—942no—
267C2×D4—941no—
268C2×D4—944no—
269C2×D4—948no—
270C2×D4—948no—
271C2×D4—948no—
272C2×D4—944no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—1884no—
277C2×D4C22×D4712yes—
278C2×D4C22×D4711yescharacteristic, complemented
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—471no—
282C22×C4—471no—
283C22×C4—471no—
284C22×C4—944no—
285C22×C4—941no—
286C22×C4C22×D4711yescharacteristic
287D8—24no—
288D8—944no—
289D8—944no—
290D8—944no—
291C2×C8—472no—
292C2×C8—944no—
293C2×C8C22×D4712yescomplemented
294C4⋊C4—471no—
295C4⋊C4—941no—
296C4⋊C4C22×D4711yescharacteristic, complemented
297C22⋊C4—21no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C23—24no—
302C23—22no—
303C23—21no—
304C23—42no—
305C23—42no—
306C23—471no—
307C23—474no—
308C23—471no—
309C23—942no—
310C23—942no—
311C23—948no—
312C23—944no—
313C23—948no—
314C23—942no—
315C23—941no—
316C23—1882no—
317C23—1882no—
318C23—1882no—
319C23—1882no—
320C23—1884no—
321C23—1884no—
322C23—1884no—
323C23—18832no—
324C23—1884no—
325C23—1882no—
326C23D4×D4711yescharacteristic
327D4—24no—
328D4—22no—
329D4—22no—
330D4—42no—
331D4—474no—
332D4—944no—
333D4—948no—
334D4—948no—
335D4—942no—
336D4—942no—
337D4—1882no—
338D4—1882no—
339D4—1882no—
340D4—1882no—
341D4D4×D4714yescomplemented
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—471no—
345C2×C4—474no—
346C2×C4—471no—
347C2×C4—942no—
348C2×C4—942no—
349C2×C4—942no—
350C2×C4—942no—
351C2×C4—941no—
352C2×C4—1882no—
353C2×C4D4×D4711yescharacteristic
354C2×C4C23×D4711yescharacteristic
355C8—22no—
356C8—942no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—48no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—472no—
367C22—472no—
368C22—472no—
369C22—472no—
370C22—948no—
371C22—941no—
372C22—941no—
373C22—944no—
374C22—3764no—
375C22—1888no—
376C22—18816no—
377C22—18816no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1882no—
382C22—1882no—
383C22D8×D4712yescomplemented
384C22C2×D4×D4711yescharacteristic
385C4—21no—
386C4—41no—
387C4—472no—
388C4—941no—
389C4—1881no—
390C4C2×D4×D4712yes—
391C2—22no—
392C2—44no—
393C2—81no—
394C2—474no—
395C2—942no—
396C2—3761no—
397C2—1884no—
398C2#120×D4711yescharacteristic
399C2C2×D8×D4711yescharacteristic
400C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47C2×#447
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×D8×D47C2semidirect
3. #121×D47C2semidirect
4. #15689259C2semidirect
5. #15689258C2semidirect
6. #15689257C2semidirect
7. #15689256C2semidirect
8. #15689255C2semidirect
9. #102×D47C2semidirect
10. C22⋊C8×D47C2semidirect
11. C47×#447C2semidirect
13. C22×D188C22semidirect
20. C2×D4×D47C22semidirect
21. C2×D4×D47C22semidirect
23. C2×D376C22semidirect
24. C2×#10625334C22semidirect
25. C2×#10625334C22semidirect
27. C2×C8×D47C22semidirect
28. #13093999C22semidirect
29. #13093998C22semidirect
32. #13093995C22semidirect
33. C4⋊C4×D47C22semidirect
35. #13093946C22semidirect
36. #13093945C22semidirect
37. #13093944C22semidirect
38. C22⋊(C47⋊C8)C22semidirect
39. (C2×D47)⋊C8C22semidirect
40. C22×D4×C47C22semidirect
41. C2×D8×C47C22semidirect
42. #121×C47C22semidirect
43. #102×C47C22semidirect
44. C22⋊C8×C47C22semidirect
58. C2×D4×C47C23semidirect
74. D4×D47D4semidirect
79. C2×D188C23semidirect
87. C2×C8×C47C23semidirect
88. C4⋊C4×C47C23semidirect
95. C4⋊Dic47C23semidirect
97. C2×C47⋊C8C23semidirect
123. C22×D47D8semidirect
130. D4×C47C2×D4semidirect
148. D188C2×D4semidirect
165. C22×C47C2×D8semidirect
182. C2×D47C2×D8semidirect
200. D47#447direct (N × H)
209. #447D47direct (N × H)
212. C47C2×#447semidirect
223. C22×D4C2×D47semidirect
229. C2×D8C2×D47semidirect
236. #121C2×D47semidirect
242. #102C2×D47semidirect
245. C22⋊C8C2×D47semidirect
278. C2×D4C22×D47semidirect
293. C2×C8C22×D47semidirect
296. C4⋊C4C22×D47semidirect
341. D4D4×D47semidirect
383. C22D8×D47semidirect