Finite Group Databasebeta

← #468×D47 #20252972

Subgroups — #468×D47 #20252972

Order 6016.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D47C211yesmaximal, characteristic, complemented
2C2×M16×D47C211yesmaximal, characteristic, complemented
3C22⋊Q8×D47C211yesmaximal, characteristic, complemented
4#121×D47C211yesmaximal, characteristic
5#15689372C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689370C211yesmaximal, characteristic, complemented
8#15689369C211yesmaximal, characteristic, complemented
9#15689368C211yesmaximal, characteristic, complemented
10#15689367C211yesmaximal, characteristic, complemented
11#15689366C211yesmaximal, characteristic, complemented
12#107×D47C211yesmaximal, characteristic, complemented
13#103×D47C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×D4×D47—21no—
18C2×D4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic, complemented
22C2×#10625336C2211yescharacteristic, complemented
23SD16×D47—24no—
24C2×#10625329C2211yescharacteristic, complemented
25C2×#10625324C2211yescharacteristic, complemented
26C2×#10625324C2211yescharacteristic, complemented
27M16×D47—24no—
28C2×C8×D47C2211yescharacteristic
29C2×C8×D47C2211yescharacteristic
30#13094004C2211yescharacteristic, complemented
31#13094003C2211yescharacteristic, complemented
32#13094002—21no—
33#13094001—21no—
34#13094000C2211yescharacteristic, complemented
35#13093999C2211yescharacteristic
36#13093998C2211yescharacteristic
37#13093997—21no—
38#13093996—21no—
39#13093995C2211yescharacteristic
40C4⋊C4×D47—21no—
41C4⋊C4×D47C2211yescharacteristic
42C4⋊C4×D47C2211yescharacteristic
43C22⋊C4×D47—21no—
44C22⋊C4×D47—21no—
45#13093958C2211yescharacteristic, complemented
46#13093957C2211yescharacteristic, complemented
47#13093957C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093948C2211yescharacteristic, complemented
50#13093947C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic, complemented
52#13093945C2211yescharacteristic, complemented
53#13093944C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×M16×C47C2211yescharacteristic, complemented
56C22⋊Q8×C47C2211yescharacteristic, complemented
57#121×C47C2211yescharacteristic
58#107×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47D411yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C22×Dic47D411yescharacteristic
71Q8×D47—22no—
72Q8×D47—22no—
73D4×D47—22no—
74D4×D47—22no—
75D4×D47—44no—
76C2×D188—21no—
77C2×D188C2311yescharacteristic
78C2×C4×D47—22no—
79C2×C4×D47—22no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47D411yescharacteristic
84C2×C4×D47D411yescharacteristic
85C2×C4×D47C2311yescharacteristic
86C2×C4×D47C2311yescharacteristic
87C2×Dic94—21no—
88C2×Dic94C2311yescharacteristic
89SD16×C47—22no—
90M16×C47—22no—
91C2×C8×C47C2311yescharacteristic
92C2×C8×C47C2311yescharacteristic
93C4⋊C4×C47—21no—
94C4⋊C4×C47C2311yescharacteristic
95C4⋊C4×C47C2311yescharacteristic
96C22⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47—21no—
100#10625336—22no—
101#10625335—22no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47C2311yescharacteristic
108C4⋊Dic47C2311yescharacteristic
109Dic47⋊C4—21no—
110Dic47⋊C4—21no—
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113#10625329—22no—
114C2×C47⋊C8C2311yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116#10625325—22no—
117#10625324—22no—
118#10625324—22no—
119C8×D47—22no—
120C8×D47D414yescomplemented
121C23×C47—21no—
122C23×C47C2×D411yescharacteristic
123C22×D47—22no—
124C22×D47—22no—
125C22×D47—22no—
126C22×D47—21no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47C2×D411yescharacteristic
131C22×D47C2×D411yescharacteristic
132Q8×C47—21no—
133Q8×C47—21no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—42no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2411yescharacteristic
144C22⋊D47—42no—
145C22⋊D47—42no—
146C22⋊D47—42no—
147C2×Dic47—22no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47C2×D411yescharacteristic
152C2×Dic47C2×D411yescharacteristic
153D188—21no—
154D188—21no—
155D188—42no—
156C4×D47—22no—
157C4×D47—21no—
158C4×D47—21no—
159C4×D47—22no—
160C4×D47—42no—
161C4×D47—42no—
162C4×D47—42no—
163C4×D47C2×D412yes—
164C4×D47#4112yes—
165Dic94—21no—
166Dic94—21no—
167Dic94—42no—
168C8×C47—21no—
169C8×C47C2×D412yescomplemented
170C47⋊C8—21no—
171C47⋊C8C2×D412yescomplemented
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47C22×D411yescharacteristic
179C2×D47—21no—
180C2×D47—21no—
181C2×D47—21no—
182C2×D47—44no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—84no—
187C2×D47#12112yes—
188C2×D47AGL(1,ℤ/8)12yes—
189C2×D47#13712yes—
190C4×C47—21no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47C22×D411yescharacteristic
195C4×C47C2×#4111yescharacteristic
196Dic47—21no—
197Dic47—41no—
198Dic47—41no—
199Dic47—41no—
200Dic47#12112yes—
201C2×#468—471nomaximal, Sylow
202C2×C47—41no—
203C2×C47—81no—
204C2×C47C2×#12111yescharacteristic
205C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C47C2×#13711yescharacteristic
207D47—41no—
208D47—81no—
209D47#46814yesdirect product factor
210C22×SD16—471no—
211C22×M16—471no—
212C2×C22⋊Q8—471no—
213C2×#121—471no—
214#468—471no—
215#468—471no—
216#468—471no—
217#468—471no—
218#468—471no—
219#468—471no—
220#468—471no—
221#468D4711yescharacteristic, direct product factor
222C2×#107—471no—
223C2×#103—471no—
224C2×#102—471no—
225C47C2×#46811yescharacteristic, complemented, Sylow
226C22×Q8—471no—
227C22×D4—471no—
228C22×D4—941no—
229C23×C4—471no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×SD16—471no—
233C2×SD16—944no—
234C2×SD16C2×D4711yescharacteristic, complemented
235C2×M16—471no—
236C2×M16—471no—
237C2×M16—471no—
238C2×M16—944no—
239C2×M16C2×D4711yescharacteristic, complemented
240C22×C8—471no—
241C22×C8—471no—
242C22⋊Q8—471no—
243C22⋊Q8—471no—
244C22⋊Q8—471no—
245C22⋊Q8—941no—
246C22⋊Q8—941no—
247C22⋊Q8C2×D4711yescharacteristic, complemented
248#121—471no—
249#121—471no—
250#121—471no—
251#121—941no—
252#121—941no—
253#121C2×D4711yescharacteristic
254C2×C4⋊C4—471no—
255C2×C4⋊C4—471no—
256C2×C4⋊C4—941no—
257C2×C22⋊C4—941no—
258C2×C22⋊C4—941no—
259#107—471no—
260#107—471no—
261#107—471no—
262#107C2×D4711yescharacteristic, complemented
263#103—471no—
264#103—471no—
265#103—471no—
266#103C2×D4711yescharacteristic, complemented
267#102—471no—
268#102—471no—
269#102—471no—
270#102C2×D4711yescharacteristic, complemented
271C24—471no—
272C24—941no—
273C2×Q8—471no—
274C2×Q8—941no—
275C2×Q8—942no—
276C2×Q8—942no—
277C2×Q8C22×D4711yescharacteristic
278C2×D4—21no—
279C2×D4—471no—
280C2×D4—941no—
281C2×D4—942no—
282C2×D4—942no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4—941no—
286C2×D4—1884no—
287C2×D4C22×D4711yescharacteristic
288C22×C4—471no—
289C22×C4—471no—
290C22×C4—471no—
291C22×C4—471no—
292C22×C4—471no—
293C22×C4—942no—
294C22×C4—942no—
295C22×C4—941no—
296C22×C4—941no—
297C22×C4—941no—
298C22×C4C22×D4711yescharacteristic
299SD16—22no—
300SD16—942no—
301SD16—942no—
302SD16—942no—
303M16—22no—
304M16—942no—
305M16—942no—
306M16—942no—
307C2×C8—471no—
308C2×C8—474no—
309C2×C8—471no—
310C2×C8—942no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—471no—
315C4⋊C4—471no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4—941no—
319C4⋊C4—941no—
320C4⋊C4—941no—
321C4⋊C4C22×D4711yescharacteristic
322C4⋊C4C22×D4711yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C22⋊C4—941no—
331C23—21no—
332C23—471no—
333C23—471no—
334C23—942no—
335C23—942no—
336C23—942no—
337C23—941no—
338C23—1882no—
339C23—1882no—
340C23—1882no—
341C23D4×D4711yescharacteristic
342Q8—21no—
343Q8—21no—
344Q8—941no—
345Q8—941no—
346Q8—1882no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—941no—
351D4—941no—
352D4—1882no—
353D4—1882no—
354D4—1882no—
355D4—1882no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—471no—
362C2×C4—472no—
363C2×C4—472no—
364C2×C4—471no—
365C2×C4—942no—
366C2×C4—942no—
367C2×C4—942no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—941no—
373C2×C4—1882no—
374C2×C4—1882no—
375C2×C4—1882no—
376C2×C4D4×D4711yescharacteristic
377C2×C4C23×D4711yescharacteristic
378C8—21no—
379C8—472no—
380C8—941no—
381C8D4×D4712yescomplemented
382C22—21no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—472no—
389C22—472no—
390C22—472no—
391C22—941no—
392C22—941no—
393C22—941no—
394C22—3764no—
395C22—1884no—
396C22—1881no—
397C22—1881no—
398C22—1881no—
399C22C2×D4×D4711yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—472no—
405C4—941no—
406C4—1881no—
407C4—1881no—
408C4—1881no—
409C4C2×D4×D4711yescharacteristic
410C4#41×D4711yescharacteristic
411C2—41no—
412C2—81no—
413C2—474no—
414C2—3761no—
415C2—1881no—
416C2#121×D4711yescharacteristic
417C2AGL(1,ℤ/8)×D4711yescharacteristic
418C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47C2×#468
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D47C2semidirect
2. C2×M16×D47C2semidirect
3. C22⋊Q8×D47C2semidirect
5. #15689372C2semidirect
6. #15689371C2semidirect
7. #15689370C2semidirect
8. #15689369C2semidirect
9. #15689368C2semidirect
10. #15689367C2semidirect
11. #15689366C2semidirect
12. #107×D47C2semidirect
13. #103×D47C2semidirect
14. #102×D47C2semidirect
15. C47×#468C2semidirect
20. C2×#10625325C22semidirect
21. C2×#10625335C22semidirect
22. C2×#10625336C22semidirect
24. C2×#10625329C22semidirect
25. C2×#10625324C22semidirect
26. C2×#10625324C22semidirect
30. #13094004C22semidirect
31. #13094003C22semidirect
34. #13094000C22semidirect
45. #13093958C22semidirect
46. #13093957C22semidirect
47. #13093957C22semidirect
48. #13093949C22semidirect
49. #13093948C22semidirect
50. #13093947C22semidirect
51. #13093946C22semidirect
52. #13093945C22semidirect
53. #13093944C22semidirect
54. C2×SD16×C47C22semidirect
55. C2×M16×C47C22semidirect
56. C22⋊Q8×C47C22semidirect
58. #107×C47C22semidirect
59. #103×C47C22semidirect
60. #102×C47C22semidirect
120. C8×D47D4semidirect
169. C8×C47C2×D4semidirect
171. C47⋊C8C2×D4semidirect
209. D47#468direct (N × H)
221. #468D47direct (N × H)
225. C47C2×#468semidirect
234. C2×SD16C2×D47semidirect
239. C2×M16C2×D47semidirect
247. C22⋊Q8C2×D47semidirect
262. #107C2×D47semidirect
266. #103C2×D47semidirect
270. #102C2×D47semidirect
381. C8D4×D47semidirect