Finite Group Databasebeta

← #20254864

Subgroups — #20254864

Order 6016.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094050C211yesmaximal, characteristic, complemented
2C22×#10625334C211yesmaximal, characteristic, complemented
3#15689769C211yesmaximal, characteristic, complemented
4#15689510C211yesmaximal, characteristic, complemented
5#15689374C211yesmaximal, characteristic, complemented
6#15689350C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689315C211yesmaximal, characteristic, complemented
9#15689274C211yesmaximal, characteristic, complemented
10#15689266C211yesmaximal, characteristic, complemented
11#15689257C211yesmaximal, characteristic, complemented
12#15689256C211yesmaximal, characteristic, complemented
13#15689233C211yesmaximal, characteristic, complemented
14#15689195C211yesmaximal, characteristic, complemented
15D42×C47C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic, complemented
17C22×D188C2211yescharacteristic, complemented
18#13094050—24no—
19C2×#10625335C2211yescharacteristic, complemented
20C2×#10625335C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic, complemented
22C2×#10625334—24no—
23C2×#10625334C2211yescharacteristic
24C2×#10625334C2211yescharacteristic
25C2×#10625334C2211yescharacteristic, complemented
26C2×#10625334C2211yescharacteristic, complemented
27C2×#10625334C2211yescharacteristic, complemented
28C2×#10625334C2211yescharacteristic, complemented
29C2×#10625329C2211yescharacteristic, complemented
30C22×C47⋊C8C2211yescharacteristic, complemented
31#13094012C2211yescharacteristic, complemented
32#13094009—21no—
33#13094003C2211yescharacteristic, complemented
34#13093998C2211yescharacteristic, complemented
35#13093997—21no—
36#13093992—21no—
37C4×D188C2211yescharacteristic, complemented
38C22⋊C4×D47—21no—
39#13093955C2211yescharacteristic, complemented
40C4⋊(C47⋊C8)C2211yescharacteristic, complemented
41#13093947C2211yescharacteristic, complemented
42#13093945C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic, complemented
45#13093944C2211yescharacteristic, complemented
46#13093944C2211yescharacteristic, complemented
47C22⋊(C47⋊C8)C2211yescharacteristic, complemented
48C22⋊(C47⋊C8)C2211yescharacteristic, complemented
49#13093935C2211yescharacteristic, complemented
50C22×D4×C47—21no—
51C22×D4×C47C2211yescharacteristic
52C22×D4×C47C2211yescharacteristic, complemented
53#127×C47C2211yescharacteristic, complemented
54#121×C47—21no—
55#121×C47C2211yescharacteristic
56#121×C47C2211yescharacteristic, complemented
57#120×C47—21no—
58#120×C47—21no—
59C4×D4×C47C2211yescharacteristic
60C4×D4×C47C2211yescharacteristic, complemented
61C24×C47—21no—
62C24×C47—21no—
63C23×D47—21no—
64C2×D4×C47—22no—
65C2×D4×C47—22no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47—21no—
72C2×D4×C47—41no—
73C2×D4×C47—41no—
74C2×D4×C47—44no—
75C2×D4×C47D411yescharacteristic
76C2×D4×C47C2311yescharacteristic
77C2×D4×C47C2311yescharacteristic
78C2×D4×C47C2311yescharacteristic
79C22×C4×C47—21no—
80C22×C4×C47C2311yescharacteristic
81C22×C4×C47C2311yescharacteristic
82C2×C22⋊D47—21no—
83C2×C22⋊D47—21no—
84#10625350—22no—
85#10625350—41no—
86C2×D188—22no—
87C2×D188—21no—
88C2×D188—41no—
89C2×D188C2311yescharacteristic
90C2×D188C2311yescharacteristic
91C2×C4×D47—21no—
92C2×C4×D47—21no—
93C2×Dic94C2311yescharacteristic
94C4⋊C4×C47D411yescharacteristic
95C4⋊C4×C47C2311yescharacteristic
96C22⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C22⋊C4×C47—21no—
99C22⋊C4×C47D411yescharacteristic
100C22⋊C4×C47D411yescharacteristic
101C42×C47C2311yescharacteristic
102C22⋊Dic47—21no—
103#10625335—22no—
104#10625335—22no—
105#10625335—41no—
106#10625334—22no—
107#10625334—22no—
108#10625334—22no—
109#10625334—22no—
110#10625334—41no—
111#10625334D414yescomplemented
112(C2×D47)⋊C4—21no—
113(C2×D47)⋊C4—21no—
114(C2×D47)⋊C4—21no—
115(C2×D47)⋊C4—21no—
116C4⋊Dic47C2311yescharacteristic
117Dic47⋊C4—21no—
118#10625329—22no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122C2×C47⋊C8C2311yescharacteristic
123C2×C47⋊C8C2311yescharacteristic
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—42no—
128C23×C47—42no—
129C23×C47—42no—
130C23×C47—42no—
131C23×C47—81no—
132C23×C47—81no—
133C23×C47C2×D411yescharacteristic
134C23×C47C2×D411yescharacteristic
135C22×D47—21no—
136C22×D47—21no—
137C22×D47—42no—
138C22×D47—42no—
139C22×D47—81no—
140D4×C47—22no—
141D4×C47—21no—
142D4×C47—21no—
143D4×C47—21no—
144D4×C47—21no—
145D4×C47—21no—
146D4×C47—42no—
147D4×C47—42no—
148D4×C47—42no—
149D4×C47—42no—
150D4×C47—42no—
151D4×C47—81no—
152D4×C47C2×D412yes—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—42no—
159C2×C4×C47C2×D411yescharacteristic
160C2×C4×C47C2×D411yescharacteristic
161C2×C4×C47C2×D411yescharacteristic
162C2×C4×C47C2×D411yescharacteristic
163C2×C4×C47C2411yescharacteristic
164C22⋊D47—42no—
165C22⋊D47—81no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168D188—21no—
169D188—21no—
170D188—21no—
171D188—42no—
172D188C2×D412yescomplemented
173C4×D47—42no—
174C4×D47—81no—
175Dic94—21no—
176Dic94—21no—
177C47⋊C8—21no—
178C47⋊C8—21no—
179C47⋊C8—21no—
180C47⋊C8C2×D412yescomplemented
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—22no—
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47—41no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47—84no—
196C22×C47—84no—
197C22×C47AGL(1,ℤ/8)12yescomplemented
198C22×C47C22×D411yescharacteristic
199C2×D47—22no—
200C2×D47—41no—
201C2×D47—41no—
202C2×D47—41no—
203C2×D47—41no—
204C2×D47—41no—
205C2×D47—84no—
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—21no—
209C4×C47—21no—
210C4×C47—41no—
211C4×C47C22×D411yescharacteristic
212C4×C47H(5,𝔽2)11yescharacteristic
213Dic47—41no—
214Dic47—41no—
215#3264—471nomaximal, Sylow
216C2×C47—22no—
217C2×C47—41no—
218C2×C47—42no—
219C2×C47—81no—
220C2×C47—81no—
221C2×C47D4211yescharacteristic
222C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
223C2×C47#57611yescharacteristic
224D47—42no—
225D47—81no—
226C2×AGL(1,ℤ/8)—471no—
227C22×D8—471no—
228#546—471no—
229D42D4711yescharacteristic, complemented
230#496—471no—
231#469—471no—
232#465—471no—
233#463—471no—
234#459—471no—
235#450—471no—
236#449—471no—
237#447—471no—
238#447—471no—
239#442—471no—
240#435—471no—
241C47#326411yescharacteristic, complemented, Sylow
242C2×#41—471no—
243C22×D4—21no—
244C22×D4—471no—
245C22×D4C2×D4711yescharacteristic
246C22×D4C2×D4711yescharacteristic, complemented
247AGL(1,ℤ/8)—944no—
248C2×SD16—471no—
249C2×SD16—471no—
250C2×SD16—471no—
251C2×D8—471no—
252C2×D8—471no—
253C2×D8—471no—
254C2×D8—471no—
255C2×D8—471no—
256C2×D8—471no—
257C2×D8—944no—
258C2×M16—471no—
259C22×C8—471no—
260#127C2×D4711yescharacteristic, complemented
261#124—471no—
262#123—941no—
263C22⋊Q8—471no—
264#121—21no—
265#121—471no—
266#121—941no—
267#121C2×D4711yescharacteristic
268#121C2×D4711yescharacteristic, complemented
269#120—21no—
270#120—21no—
271#120—941no—
272C4×D4—471no—
273C4×D4C2×D4711yescharacteristic
274C4×D4C2×D4711yescharacteristic, complemented
275C2×C22⋊C4—941no—
276#106—471no—
277C4⋊C8—471no—
278#103—471no—
279#102—471no—
280#102—471no—
281#102—471no—
282#102—471no—
283#102—471no—
284C22⋊C8—471no—
285C22⋊C8—471no—
286#97—471no—
287C24—21no—
288C24—21no—
289C24—941no—
290#41—942no—
291#41—1881no—
292C2×Q8—471no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—44no—
304C2×D4—471no—
305C2×D4—471no—
306C2×D4—942no—
307C2×D4—941no—
308C2×D4—941no—
309C2×D4—941no—
310C2×D4—1881no—
311C2×D4C22⋊D4711yescharacteristic
312C2×D4C22×D4711yescharacteristic
313C2×D4C22×D4711yescharacteristic
314C2×D4C22×D4711yescharacteristic
315C22×C4—21no—
316C22×C4—941no—
317C22×C4—941no—
318C22×C4C22×D4711yescharacteristic
319C22×C4C22×D4711yescharacteristic
320SD16—942no—
321SD16—942no—
322SD16—1881no—
323D8—474no—
324D8—942no—
325D8—942no—
326D8—942no—
327D8—942no—
328D8—1881no—
329M16—942no—
330C2×C8—471no—
331C2×C8—471no—
332C2×C8—471no—
333C2×C8—471no—
334C2×C8—942no—
335C4⋊C4—471no—
336C4⋊C4—941no—
337C4⋊C4C22⋊D4711yescharacteristic
338C4⋊C4C22×D4711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—941no—
343C22⋊C4—941no—
344C22⋊C4—941no—
345C22⋊C4—941no—
346C22⋊C4—941no—
347C22⋊C4C22⋊D4711yescharacteristic
348C22⋊C4C22⋊D4711yescharacteristic
349C42C22×D4711yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—81no—
358C23—81no—
359C23—941no—
360C23—941no—
361C23—3761no—
362C23—1882no—
363C23—1882no—
364C23C2×C22⋊D4711yescharacteristic
365C23C2×C22⋊D4711yescharacteristic
366Q8—941no—
367Q8—941no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—42no—
379D4—81no—
380D4—472no—
381D4—941no—
382D4—941no—
383D4—941no—
384D4—3761no—
385D4—1882no—
386D4—1882no—
387D4D4×D4712yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—42no—
394C2×C4—941no—
395C2×C4—941no—
396C2×C4—3761no—
397C2×C4—1882no—
398C2×C4C2×C22⋊D4711yescharacteristic
399C2×C4C2×C22⋊D4711yescharacteristic
400C2×C4C2×C22⋊D4711yescharacteristic
401C2×C4C2×C22⋊D4711yescharacteristic
402C2×C4C23×D4711yescharacteristic
403C8—472no—
404C8—941no—
405C8—941no—
406C8—941no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—942no—
424C22—3764no—
425C22—1881no—
426C22—1881no—
427C22—1881no—
428C22—1881no—
429C22—1881no—
430C22#1309405012yescomplemented
431C22C22×C22⋊D4711yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—1881no—
438C4—1881no—
439C4C2×D4×D4711yescharacteristic
440C4#1309406911yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—3761no—
447C2—1882no—
448C2D4×C22⋊D4711yescharacteristic
449C2C2×#1309405011yescharacteristic
450C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD42×C47C2
socleC22×C47C22×D4
hypercenterD42D47
hypocenterC47#3264
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#13094050C2semidirect
2. C22×#10625334C2semidirect
3. #15689769C2semidirect
4. #15689510C2semidirect
5. #15689374C2semidirect
6. #15689350C2semidirect
7. #15689338C2semidirect
8. #15689315C2semidirect
9. #15689274C2semidirect
10. #15689266C2semidirect
11. #15689257C2semidirect
12. #15689256C2semidirect
13. #15689233C2semidirect
14. #15689195C2semidirect
15. D42×C47C2semidirect
16. C2×#10625350C22semidirect
17. C22×D188C22semidirect
19. C2×#10625335C22semidirect
20. C2×#10625335C22semidirect
21. C2×#10625335C22semidirect
25. C2×#10625334C22semidirect
26. C2×#10625334C22semidirect
27. C2×#10625334C22semidirect
28. C2×#10625334C22semidirect
29. C2×#10625329C22semidirect
30. C22×C47⋊C8C22semidirect
31. #13094012C22semidirect
33. #13094003C22semidirect
34. #13093998C22semidirect
37. C4×D188C22semidirect
39. #13093955C22semidirect
40. C4⋊(C47⋊C8)C22semidirect
41. #13093947C22semidirect
42. #13093945C22semidirect
43. #13093945C22semidirect
44. #13093945C22semidirect
45. #13093944C22semidirect
46. #13093944C22semidirect
47. C22⋊(C47⋊C8)C22semidirect
48. C22⋊(C47⋊C8)C22semidirect
49. #13093935C22semidirect
52. C22×D4×C47C22semidirect
53. #127×C47C22semidirect
56. #121×C47C22semidirect
60. C4×D4×C47C22semidirect
111. #10625334D4semidirect
172. D188C2×D4semidirect
180. C47⋊C8C2×D4semidirect
197. C22×C47AGL(1,ℤ/8)semidirect
229. D42D47semidirect
241. C47#3264semidirect
246. C22×D4C2×D47semidirect
260. #127C2×D47semidirect
268. #121C2×D47semidirect
274. C4×D4C2×D47semidirect
430. C22#13094050semidirect