Finite Group Databasebeta

← #463×D47 #20252808

Subgroups — #463×D47 #20252808

Order 6016.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D47C211yesmaximal, characteristic, complemented
2C2×D8×D47C211yesmaximal, characteristic
3#124×D47C211yesmaximal, characteristic, complemented
4C4×D4×D47C211yesmaximal, characteristic, complemented
5#15689341C211yesmaximal, characteristic, complemented
6#15689340C211yesmaximal, characteristic, complemented
7#15689339C211yesmaximal, characteristic, complemented
8#15689338C211yesmaximal, characteristic, complemented
9#15689337C211yesmaximal, characteristic, complemented
10#15689336C211yesmaximal, characteristic, complemented
11#15689335C211yesmaximal, characteristic, complemented
12C4⋊C8×D47C211yesmaximal, characteristic, complemented
13#103×D47C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19C22×C4×D47—21no—
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic, complemented
22C2×#10625336C2211yescharacteristic, complemented
23SD16×D47—24no—
24C2×D376C2211yescharacteristic
25C2×#10625334C2211yescharacteristic
26C2×#10625334C2211yescharacteristic
27D8×D47—24no—
28C2×C8×D47C2211yescharacteristic
29C2×C8×D47C2211yescharacteristic
30#13094013C2211yescharacteristic, complemented
31#13094012C2211yescharacteristic, complemented
32#13094011C2211yescharacteristic, complemented
33#13094010—21no—
34#13094010—21no—
35C4×D188C2211yescharacteristic, complemented
36D4×Dic47C2211yescharacteristic, complemented
37#13093986C2211yescharacteristic, complemented
38C4×C22⋊D47—21no—
39(C22⋊D47)⋊C4—21no—
40C4⋊C4×D47C2211yescharacteristic
41C22⋊C4×D47—21no—
42C22⋊C4×D47—21no—
43C22⋊C4×D47—21no—
44C42×D47C2211yescharacteristic
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46Dic47⋊C8C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093948C2211yescharacteristic, complemented
50#13093947C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic, complemented
52#13093945C2211yescharacteristic, complemented
53#13093944C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic, complemented
58C4⋊C8×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C22×Dic47—21no—
70Q8×D47—22no—
71Q8×D47—22no—
72D4×D47—22no—
73D4×D47—22no—
74D4×D47—22no—
75D4×D47D414yes—
76C2×D188C2311yescharacteristic
77C2×D188C2311yescharacteristic
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—44no—
83C2×C4×D47D411yescharacteristic
84C2×C4×D47D411yescharacteristic
85C2×C4×D47C2311yescharacteristic
86C2×Dic94—21no—
87C2×Dic94C2311yescharacteristic
88SD16×C47—22no—
89D8×C47—22no—
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C42×C47C2311yescharacteristic
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47—21no—
100#10625336—22no—
101#10625335—22no—
102#10625334—22no—
103#10625334—22no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110C4⋊Dic47C2311yescharacteristic
111Dic47⋊C4—21no—
112C4×Dic47D411yescharacteristic
113C4×Dic47D411yescharacteristic
114C4×Dic47C2311yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116C2×C47⋊C8C2311yescharacteristic
117D376—22no—
118#10625325—22no—
119C8×D47—22no—
120C8×D47—22no—
121C23×C47—21no—
122C23×C47—21no—
123C22×D47—21no—
124C22×D47—24no—
125C22×D47—21no—
126C22×D47—42no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47C2×D411yescharacteristic
132Q8×C47—21no—
133Q8×C47—21no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—21no—
137D4×C47C2×D412yes—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—42no—
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2411yescharacteristic
144C22⋊D47—24no—
145C22⋊D47—42no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—42no—
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151C2×Dic47C2×D411yescharacteristic
152D188—21no—
153D188—21no—
154D188—21no—
155D188C2×D412yes—
156C4×D47—22no—
157C4×D47—22no—
158C4×D47—42no—
159C4×D47—42no—
160C4×D47—42no—
161C4×D47—42no—
162C4×D47C2×D412yes—
163C4×D47#4112yes—
164Dic94—21no—
165Dic94—21no—
166Dic94—42no—
167C8×C47—21no—
168C8×C47—21no—
169C47⋊C8—21no—
170C47⋊C8—21no—
171C22×C47—22no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47C22×D411yescharacteristic
178C2×D47—22no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—48no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—84no—
186C2×D47#12112yes—
187C2×D47#13512yes—
188C2×D47AGL(1,ℤ/8)12yes—
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47C22×D411yescharacteristic
194C4×C47C2×#4111yescharacteristic
195Dic47—21no—
196Dic47—21no—
197Dic47—41no—
198Dic47—41no—
199Dic47#12112yes—
200C2×#463—471nomaximal, Sylow
201C2×C47—42no—
202C2×C47—81no—
203C2×C47C2×#12111yescharacteristic
204C2×C47C2×#13511yescharacteristic
205C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
206D47—42no—
207D47—81no—
208D47#46314yesdirect product factor
209C22×SD16—471no—
210C22×D8—471no—
211C2×#124—471no—
212C2×C4×D4—471no—
213#463—471no—
214#463—471no—
215#463—471no—
216#463—471no—
217#463—471no—
218#463—471no—
219#463—471no—
220#463D4711yescharacteristic, direct product factor
221C2×C4⋊C8—471no—
222C2×#103—471no—
223C2×#102—471no—
224C47C2×#46311yescharacteristic, complemented, Sylow
225C22×Q8—471no—
226C22×D4—471no—
227C22×D4—471no—
228C23×C4—941no—
229C2×SD16—471no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×SD16—944no—
233C2×SD16C2×D4711yescharacteristic, complemented
234C2×D8—471no—
235C2×D8—471no—
236C2×D8—471no—
237C2×D8—944no—
238C2×D8C2×D4711yescharacteristic
239C22×C8—471no—
240C22×C8—471no—
241#124—471no—
242#124—471no—
243#124—471no—
244#124—941no—
245#124—941no—
246#124C2×D4711yescharacteristic, complemented
247C4×D4—471no—
248C4×D4—471no—
249C4×D4—471no—
250C4×D4—941no—
251C4×D4—941no—
252C4×D4C2×D4711yescharacteristic, complemented
253C2×C4⋊C4—471no—
254C2×C22⋊C4—941no—
255C2×C22⋊C4—941no—
256C2×C22⋊C4—941no—
257C2×C42—471no—
258C4⋊C8—471no—
259C4⋊C8—471no—
260C4⋊C8—471no—
261C4⋊C8C2×D4711yescharacteristic, complemented
262#103—471no—
263#103—471no—
264#103—471no—
265#103C2×D4711yescharacteristic, complemented
266#102—471no—
267#102—471no—
268#102—471no—
269#102C2×D4711yescharacteristic, complemented
270C24—941no—
271C24—941no—
272C2×Q8—471no—
273C2×Q8—941no—
274C2×Q8—942no—
275C2×Q8—942no—
276C2×Q8C22×D4711yescharacteristic
277C2×D4—474no—
278C2×D4—471no—
279C2×D4—471no—
280C2×D4—942no—
281C2×D4—942no—
282C2×D4—942no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4C22×D4711yescharacteristic
286C2×D4C22×D4711yescharacteristic
287C22×C4—21no—
288C22×C4—471no—
289C22×C4—471no—
290C22×C4—471no—
291C22×C4—941no—
292C22×C4—941no—
293C22×C4—941no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4—1884no—
297SD16—22no—
298SD16—942no—
299SD16—942no—
300SD16—942no—
301D8—22no—
302D8—942no—
303D8—942no—
304D8—942no—
305C2×C8—471no—
306C2×C8—471no—
307C2×C8—942no—
308C2×C8—942no—
309C2×C8C22×D4711yescharacteristic
310C2×C8C22×D4711yescharacteristic
311C4⋊C4—471no—
312C4⋊C4—941no—
313C4⋊C4C22×D4711yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C42—471no—
327C42—471no—
328C42—471no—
329C42C22×D4711yescharacteristic
330C23—21no—
331C23—21no—
332C23—471no—
333C23—944no—
334C23—941no—
335C23—941no—
336C23—1882no—
337C23—1882no—
338C23—1882no—
339C23—1882no—
340C23—1882no—
341Q8—21no—
342Q8—21no—
343Q8—941no—
344Q8—941no—
345Q8—1882no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—472no—
350D4—944no—
351D4—941no—
352D4—941no—
353D4—941no—
354D4—1882no—
355D4D4×D4712yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—471no—
360C2×C4—472no—
361C2×C4—472no—
362C2×C4—471no—
363C2×C4—471no—
364C2×C4—942no—
365C2×C4—942no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—1882no—
369C2×C4—1882no—
370C2×C4—1882no—
371C2×C4—1882no—
372C2×C4—1882no—
373C2×C4D4×D4711yescharacteristic
374C2×C4D4×D4711yescharacteristic
375C2×C4C23×D4711yescharacteristic
376C8—21no—
377C8—21no—
378C8—941no—
379C8—941no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—472no—
387C22—472no—
388C22—472no—
389C22—942no—
390C22—3764no—
391C22—1888no—
392C22—1881no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22C2×D4×D4711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—472no—
403C4—941no—
404C4—941no—
405C4—1881no—
406C4—1881no—
407C4C2×D4×D4711yescharacteristic
408C4#41×D4711yescharacteristic
409C2—42no—
410C2—81no—
411C2—474no—
412C2—3761no—
413C2—1882no—
414C2#121×D4711yescharacteristic
415C2#135×D4711yescharacteristic
416C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47C2×#463
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D47C2semidirect
3. #124×D47C2semidirect
4. C4×D4×D47C2semidirect
5. #15689341C2semidirect
6. #15689340C2semidirect
7. #15689339C2semidirect
8. #15689338C2semidirect
9. #15689337C2semidirect
10. #15689336C2semidirect
11. #15689335C2semidirect
12. C4⋊C8×D47C2semidirect
13. #103×D47C2semidirect
14. #102×D47C2semidirect
15. C47×#463C2semidirect
20. C2×#10625325C22semidirect
21. C2×#10625335C22semidirect
22. C2×#10625336C22semidirect
30. #13094013C22semidirect
31. #13094012C22semidirect
32. #13094011C22semidirect
35. C4×D188C22semidirect
36. D4×Dic47C22semidirect
37. #13093986C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. Dic47⋊C8C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093948C22semidirect
50. #13093947C22semidirect
51. #13093946C22semidirect
52. #13093945C22semidirect
53. #13093944C22semidirect
54. C2×SD16×C47C22semidirect
56. #124×C47C22semidirect
57. C4×D4×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #103×C47C22semidirect
60. #102×C47C22semidirect
208. D47#463direct (N × H)
220. #463D47direct (N × H)
224. C47C2×#463semidirect
233. C2×SD16C2×D47semidirect
246. #124C2×D47semidirect
252. C4×D4C2×D47semidirect
261. C4⋊C8C2×D47semidirect
265. #103C2×D47semidirect
269. #102C2×D47semidirect