Finite Group Databasebeta

← #450×D47 #20252567

Subgroups — #450×D47 #20252567

Order 6016.

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

normal subgroups only

This group has 996 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
2C2×SD16×D47C212yesmaximal, complemented
3C22⋊Q8×D47C211yesmaximal, characteristic, complemented
4#15689276C211yesmaximal, characteristic, complemented
5#15689275C212yesmaximal, complemented
6#15689274C211yesmaximal, characteristic, complemented
7#15689273C211yesmaximal, characteristic, complemented
8#15689272C212yesmaximal, complemented
9#102×D47C212yesmaximal, complemented
10C22⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#450C211yesmaximal, characteristic, complemented
12C24×D47—21no—
13C2×Q8×D47C2211yescharacteristic, 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
22C2×#10625325C2212yescomplemented
23C2×#10625335C2212yescomplemented
24C2×#10625336C2212yescomplemented
25SD16×D47—28no—
26C2×C8×D47C2212yescomplemented
27#13094004C2211yescharacteristic, complemented
28#13094003C2211yescharacteristic, complemented
29#13094002—21no—
30#13094001—21no—
31#13094000C2211yescharacteristic, complemented
32C4⋊C4×D47—21no—
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
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—22no—
60C2×C22⋊D47—22no—
61C22×Dic47D411yescharacteristic
62Q8×D47—24no—
63D4×D47—28no—
64D4×D47—28no—
65D4×D47—24no—
66D4×D47—24no—
67D4×D47—24no—
68D4×D47D418yes—
69C2×D188—21no—
70C2×D188—24no—
71C2×D188C2312yes—
72C2×C4×D47—24no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47D411yescharacteristic
76C2×C4×D47D411yescharacteristic
77C2×C4×D47C2311yescharacteristic
78C2×C4×D47C2311yescharacteristic
79C2×Dic94—21no—
80C2×Dic94C2311yescharacteristic, complemented
81SD16×C47—24no—
82C2×C8×C47C2312yescomplemented
83C4⋊C4×C47—21no—
84C4⋊C4×C47C2311yescharacteristic, complemented
85C22⋊C4×C47—21no—
86C22⋊Dic47—21no—
87#10625336—24no—
88#10625335—24no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic, complemented
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96C2×C47⋊C8C2312yescomplemented
97#10625325—24no—
98C8×D47—24no—
99C23×C47—24no—
100C23×C47—22no—
101C23×C47—42no—
102C23×C47—42no—
103C23×C47C2×D411yescharacteristic
104C22×D47—22no—
105C22×D47—22no—
106C22×D47—24no—
107C22×D47—28no—
108C22×D47—22no—
109C22×D47—28no—
110C22×D47—44no—
111C22×D47—432no—
112C22×D47—42no—
113C22×D47—42no—
114C22×D47—44no—
115C22×D47—44no—
116C22×D47—44no—
117C22×D47SD1614yescomplemented
118C22×D47C2×D411yescharacteristic
119C22×D47C2×D411yescharacteristic
120Q8×C47—22no—
121D4×C47—24no—
122D4×C47—22no—
123D4×C47C2×D414yes—
124C2×C4×C47—22no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—28no—
130C22⋊D47—28no—
131C2×Dic47—22no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136D188—24no—
137D188—22no—
138D188C2×D414yes—
139C4×D47—22no—
140C4×D47—22no—
141C4×D47—22no—
142C4×D47—42no—
143C4×D47—42no—
144C4×D47C2×D414yes—
145Dic94—22no—
146Dic94—42no—
147C8×C47—22no—
148C47⋊C8—22no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—24no—
152C22×C47—48no—
153C22×C47—42no—
154C22×C47—42no—
155C22×C47C2×SD1612yescomplemented
156C22×C47C22×D411yescharacteristic
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—28no—
160C2×D47—24no—
161C2×D47—416no—
162C2×D47—48no—
163C2×D47—42no—
164C2×D47—42no—
165C2×D47—416no—
166C2×D47#12012yes—
167C2×D47C2×SD1612yes—
168C2×D47C2×SD1612yescomplemented
169C2×D47AGL(1,ℤ/8)12yes—
170C4×C47—21no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47C22×D412yes—
174Dic47—21no—
175Dic47—41no—
176Dic47—41no—
177Dic47#12012yes—
178C2×#450—471nomaximal, Sylow
179C2×C47—22no—
180C2×C47—44no—
181C2×C47C2×#12011yescharacteristic
182C2×C47C22×SD1611yescharacteristic
183C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
184D47—22no—
185D47—44no—
186D47#45014yesdirect product factor
187C23×D4—471no—
188C22×SD16—472no—
189C2×C22⋊Q8—471no—
190#450—471no—
191#450—472no—
192#450—471no—
193#450—472no—
194#450—471no—
195#450D4711yescharacteristic, direct product factor
196C2×#102—472no—
197C2×C22⋊C8—471no—
198C47C2×#45011yescharacteristic, complemented, Sylow
199C25—941no—
200C22×Q8—471no—
201C22×D4—472no—
202C22×D4—472no—
203C22×D4—471no—
204C22×D4—941no—
205C22×D4—941no—
206C22×D4—941no—
207C22×D4—948no—
208C22×D4C2×D4711yescharacteristic
209C23×C4—471no—
210C2×SD16—472no—
211C2×SD16—472no—
212C2×SD16—472no—
213C2×SD16—948no—
214C2×SD16C2×D4712yescomplemented
215C22×C8—472no—
216C22⋊Q8—471no—
217C22⋊Q8—471no—
218C22⋊Q8—471no—
219C22⋊Q8—941no—
220C22⋊Q8—941no—
221C22⋊Q8C2×D4711yescharacteristic, complemented
222C2×C4⋊C4—471no—
223C2×C4⋊C4—941no—
224C2×C22⋊C4—941no—
225#102—472no—
226#102—472no—
227#102—472no—
228#102C2×D4712yescomplemented
229C22⋊C8—471no—
230C22⋊C8—472no—
231C22⋊C8C2×D4711yescharacteristic, complemented
232C24—21no—
233C24—471no—
234C24—942no—
235C24—942no—
236C24—948no—
237C24—941no—
238C24—1884no—
239C24—1884no—
240C2×Q8—471no—
241C2×Q8—941no—
242C2×Q8—944no—
243C2×Q8C22×D4711yescharacteristic, complemented
244C2×D4—24no—
245C2×D4—21no—
246C2×D4—478no—
247C2×D4—472no—
248C2×D4—944no—
249C2×D4—944no—
250C2×D4—942no—
251C2×D4—942no—
252C2×D4—944no—
253C2×D4—948no—
254C2×D4—948no—
255C2×D4—948no—
256C2×D4—944no—
257C2×D4—941no—
258C2×D4C22×D4712yes—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—471no—
264C22×C4—944no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4C22×D4711yescharacteristic
268SD16—24no—
269SD16—944no—
270SD16—944no—
271SD16—944no—
272C2×C8—472no—
273C2×C8—944no—
274C2×C8C22×D4712yescomplemented
275C4⋊C4—21no—
276C4⋊C4—471no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4C22×D4711yescharacteristic, complemented
282C22⋊C4—21no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C23—24no—
287C23—22no—
288C23—42no—
289C23—42no—
290C23—471no—
291C23—474no—
292C23—471no—
293C23—942no—
294C23—942no—
295C23—948no—
296C23—944no—
297C23—948no—
298C23—942no—
299C23—1882no—
300C23—1884no—
301C23—1884no—
302C23—1884no—
303C23—18832no—
304C23—1884no—
305C23—1882no—
306C23D4×D4711yescharacteristic
307Q8—22no—
308Q8—942no—
309Q8—1882no—
310D4—24no—
311D4—22no—
312D4—474no—
313D4—944no—
314D4—948no—
315D4—948no—
316D4—942no—
317D4D4×D4714yes—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—471no—
322C2×C4—474no—
323C2×C4—471no—
324C2×C4—942no—
325C2×C4—942no—
326C2×C4—942no—
327C2×C4—942no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—1882no—
331C2×C4—1882no—
332C2×C4D4×D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—22no—
335C8—942no—
336C22—21no—
337C22—21no—
338C22—24no—
339C22—48no—
340C22—42no—
341C22—42no—
342C22—472no—
343C22—472no—
344C22—472no—
345C22—472no—
346C22—948no—
347C22—941no—
348C22—941no—
349C22—944no—
350C22—1888no—
351C22—18816no—
352C22—18816no—
353C22—1882no—
354C22—1882no—
355C22SD16×D4712yescomplemented
356C22C2×D4×D4711yescharacteristic
357C4—21no—
358C4—41no—
359C4—41no—
360C4—472no—
361C4—941no—
362C4—1881no—
363C4—1881no—
364C4C2×D4×D4712yes—
365C2—22no—
366C2—44no—
367C2—474no—
368C2—942no—
369C2—1884no—
370C2#120×D4711yescharacteristic
371C2C2×SD16×D4711yescharacteristic
372C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47C2×#450
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
2. C2×SD16×D47C2semidirect
3. C22⋊Q8×D47C2semidirect
4. #15689276C2semidirect
5. #15689275C2semidirect
6. #15689274C2semidirect
7. #15689273C2semidirect
8. #15689272C2semidirect
9. #102×D47C2semidirect
10. C22⋊C8×D47C2semidirect
11. C47×#450C2semidirect
13. C2×Q8×D47C22semidirect
22. C2×#10625325C22semidirect
23. C2×#10625335C22semidirect
24. C2×#10625336C22semidirect
26. C2×C8×D47C22semidirect
27. #13094004C22semidirect
28. #13094003C22semidirect
31. #13094000C22semidirect
33. C4⋊C4×D47C22semidirect
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
80. C2×Dic94C23semidirect
82. C2×C8×C47C23semidirect
84. C4⋊C4×C47C23semidirect
92. C4⋊Dic47C23semidirect
96. C2×C47⋊C8C23semidirect
117. C22×D47SD16semidirect
155. C22×C47C2×SD16semidirect
168. C2×D47C2×SD16semidirect
186. D47#450direct (N × H)
195. #450D47direct (N × H)
198. C47C2×#450semidirect
214. C2×SD16C2×D47semidirect
221. C22⋊Q8C2×D47semidirect
228. #102C2×D47semidirect
231. C22⋊C8C2×D47semidirect
243. C2×Q8C22×D47semidirect
274. C2×C8C22×D47semidirect
281. C4⋊C4C22×D47semidirect
355. C22SD16×D47semidirect