Finite Group Databasebeta

← #20254863

Subgroups — #20254863

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×#13094048C211yesmaximal, characteristic, complemented
2C2×D8×D47C211yesmaximal, characteristic, complemented
3#15689768C211yesmaximal, characteristic, complemented
4#15689758C211yesmaximal, characteristic, complemented
5#15689510C211yesmaximal, characteristic, complemented
6#15689375C211yesmaximal, characteristic, complemented
7#15689351C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689275C211yesmaximal, characteristic, complemented
10#15689265C211yesmaximal, characteristic, complemented
11#15689258C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13#15689233C211yesmaximal, characteristic, complemented
14#15689193C211yesmaximal, characteristic, complemented
15C47×#459C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic, complemented
17C2×D4×D47—21no—
18C2×D4×D47C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic, complemented
20C2×D4×D47C2211yescharacteristic, complemented
21#13094048—24no—
22C2×#10625325C2211yescharacteristic, complemented
23C2×#10625335C2211yescharacteristic, complemented
24C2×#10625335C2211yescharacteristic, complemented
25C2×D376C2211yescharacteristic
26C2×#10625334C2211yescharacteristic
27C2×#10625334C2211yescharacteristic, complemented
28C2×#10625334C2211yescharacteristic, complemented
29D8×D47—24no—
30C2×#10625324C2211yescharacteristic, complemented
31C2×C8×D47C2211yescharacteristic, complemented
32#13094012C2211yescharacteristic, complemented
33#13094008—21no—
34#13094004C2211yescharacteristic, complemented
35#13093999C2211yescharacteristic, complemented
36#13093998—21no—
37#13093995—21no—
38#13093995C2211yescharacteristic
39#13093995C2211yescharacteristic, complemented
40#13093994—21no—
41#13093992—21no—
42#13093992—21no—
43C4×D188C2211yescharacteristic
44C4×D188C2211yescharacteristic, complemented
45C2×(C2×D47)⋊C4—21no—
46#13093955C2211yescharacteristic, complemented
47#13093949C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic, complemented
49#13093945C2211yescharacteristic, complemented
50#13093944C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093935C2211yescharacteristic, complemented
54C2×D8×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic, complemented
56#127×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic, complemented
58C4⋊C8×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C23×D47—21no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C2×D4×C47C2311yescharacteristic
69C22×C4×C47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C22×Dic47—21no—
77#10625352—22no—
78#10625352—41no—
79D4×D47—22no—
80D4×D47—22no—
81D4×D47—22no—
82D4×D47—41no—
83D4×D47—41no—
84D4×D47—41no—
85D4×D47—44no—
86C2×D188—21no—
87C2×D188D411yescharacteristic
88C2×D188C2311yescharacteristic
89C2×D188C2311yescharacteristic
90C2×C4×D47—21no—
91C2×C4×D47C2311yescharacteristic
92C2×C4×D47C2311yescharacteristic
93C2×Dic94C2311yescharacteristic
94D8×C47—22no—
95D8×C47—22no—
96C2×C8×C47C2311yescharacteristic
97C2×C8×C47C2311yescharacteristic
98C4⋊C4×C47C2311yescharacteristic
99C22⋊C4×C47—21no—
100C42×C47C2311yescharacteristic
101C22⋊Dic47—21no—
102C22⋊Dic47—21no—
103#10625335—22no—
104#10625335—41no—
105#10625334—22no—
106#10625334—41no—
107#10625334D414yescomplemented
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113(C2×D47)⋊C4D411yescharacteristic
114(C2×D47)⋊C4D411yescharacteristic
115C4⋊Dic47—21no—
116C4⋊Dic47D411yescharacteristic
117C4⋊Dic47C2311yescharacteristic
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120D376—22no—
121#10625325—22no—
122#10625324—22no—
123C8×D47—22no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—42no—
133C22×D47—42no—
134C22×D47—42no—
135C22×D47—81no—
136C22×D47—81no—
137C22×D47—81no—
138C22×D47C2×D411yescharacteristic
139C22×D47C2×D411yescharacteristic
140D4×C47—21no—
141D4×C47—21no—
142D4×C47—21no—
143D4×C47—21no—
144D4×C47—21no—
145D4×C47—42no—
146D4×C47—81no—
147D4×C47C2×D412yescomplemented
148C2×C4×C47—21no—
149C2×C4×C47—81no—
150C2×C4×C47C2×D411yescharacteristic
151C2×C4×C47C2×D411yescharacteristic
152C2×C4×C47C2411yescharacteristic
153C22⋊D47—42no—
154C22⋊D47—42no—
155C22⋊D47—42no—
156C22⋊D47—42no—
157C22⋊D47—42no—
158C22⋊D47—42no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—42no—
162C2×Dic47C2×D411yescharacteristic
163C2×Dic47C2×D411yescharacteristic
164D188—22no—
165D188—21no—
166D188—21no—
167D188—21no—
168D188—81no—
169D188C2×D412yes—
170C4×D47—21no—
171C4×D47—21no—
172C4×D47—21no—
173C4×D47—21no—
174C4×D47—42no—
175Dic94—21no—
176Dic94—21no—
177C8×C47—21no—
178C8×C47—21no—
179C47⋊C8—21no—
180C47⋊C8C2×D412yescomplemented
181C22×C47—22no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47C22×D411yescharacteristic
191C2×D47—21no—
192C2×D47—21no—
193C2×D47—21no—
194C2×D47—22no—
195C2×D47—21no—
196C2×D47—21no—
197C2×D47—41no—
198C2×D47—41no—
199C2×D47—41no—
200C2×D47—41no—
201C2×D47—41no—
202C2×D47—84no—
203C2×D47—84no—
204C2×D47—84no—
205C2×D47AGL(1,ℤ/8)12yescomplemented
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—41no—
209C4×C47C22×D411yescharacteristic
210C4×C47H(5,𝔽2)11yescharacteristic
211Dic47—21no—
212Dic47—21no—
213Dic47—41no—
214Dic47—41no—
215#3264—471nomaximal, Sylow
216C2×C47—42no—
217C2×C47—81no—
218C2×C47—81no—
219C2×C47D4211yescharacteristic
220C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
221C2×C47#57611yescharacteristic
222D47—22no—
223D47—41no—
224D47—42no—
225D47—81no—
226C2×AGL(1,ℤ/8)—471no—
227C22×D8—471no—
228#546—471no—
229D42—471no—
230#496—471no—
231#469—471no—
232#465—471no—
233#463—471no—
234#459D4711yescharacteristic, complemented
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—471no—
244C22×D4—471no—
245C22×D4—471no—
246C22×D4—941no—
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—944no—
256C2×D8C2×D4711yescharacteristic, complemented
257C2×D8C2×D4711yescharacteristic, complemented
258C2×M16—471no—
259C22×C8—471no—
260#127C2×D4711yescharacteristic, complemented
261#124—471no—
262#123—941no—
263C22⋊Q8—471no—
264#121—471no—
265#121—471no—
266#121—471no—
267#121—941no—
268#121—941no—
269#120—941no—
270#120—941no—
271#120—941no—
272C4×D4—471no—
273C4×D4—471no—
274C4×D4C2×D4711yescharacteristic, complemented
275C2×C22⋊C4—941no—
276#106—471no—
277C4⋊C8C2×D4711yescharacteristic, complemented
278#103—471no—
279#102—471no—
280#102—471no—
281#102—471no—
282#102C2×D4711yescharacteristic, complemented
283#102C2×D4711yescharacteristic, complemented
284C22⋊C8—471no—
285C22⋊C8—471no—
286#97—471no—
287C24—941no—
288C24—941no—
289C24—941no—
290#41—942no—
291#41—1881no—
292C2×Q8—471no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—471no—
296C2×D4—471no—
297C2×D4—471no—
298C2×D4—941no—
299C2×D4—941no—
300C2×D4—941no—
301C2×D4—941no—
302C2×D4—942no—
303C2×D4—942no—
304C2×D4—942no—
305C2×D4—941no—
306C2×D4—941no—
307C2×D4—941no—
308C2×D4—1881no—
309C2×D4—1881no—
310C2×D4—1881no—
311C2×D4—1884no—
312C2×D4C22×D4711yescharacteristic
313C2×D4C22×D4711yescharacteristic
314C2×D4C22×D4711yescharacteristic
315C22×C4—21no—
316C22×C4—471no—
317C22×C4—471no—
318C22×C4—941no—
319C22×C4—941no—
320SD16—942no—
321SD16—942no—
322SD16—1881no—
323D8—22no—
324D8—22no—
325D8—474no—
326D8—942no—
327D8—942no—
328D8—1881no—
329M16—942no—
330C2×C8—471no—
331C2×C8—471no—
332C2×C8—942no—
333C2×C8C22×D4711yescharacteristic
334C2×C8C22×D4711yescharacteristic
335C4⋊C4—471no—
336C4⋊C4—471no—
337C4⋊C4—941no—
338C4⋊C4C22×D4711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—471no—
341C22⋊C4—471no—
342C22⋊C4—941no—
343C22⋊C4—941no—
344C22⋊C4—941no—
345C22⋊C4—941no—
346C22⋊C4—941no—
347C22⋊C4—941no—
348C22⋊C4—941no—
349C42C22×D4711yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—471no—
354C23—471no—
355C23—941no—
356C23—941no—
357C23—3761no—
358C23—3761no—
359C23—3761no—
360C23—1882no—
361C23—1882no—
362C23—1882no—
363C23—1882no—
364C23—1882no—
365C23—1882no—
366Q8—941no—
367Q8—941no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—42no—
374D4—81no—
375D4—472no—
376D4—942no—
377D4—941no—
378D4—941no—
379D4—941no—
380D4—3761no—
381D4—1882no—
382D4—1882no—
383D4—1882no—
384D4—1882no—
385D4—1882no—
386D4—1882no—
387D4D4×D4712yescomplemented
388C2×C4—21no—
389C2×C4—81no—
390C2×C4—471no—
391C2×C4—471no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—941no—
395C2×C4—941no—
396C2×C4—941no—
397C2×C4—941no—
398C2×C4—1882no—
399C2×C4—1882no—
400C2×C4D4×D4711yescharacteristic
401C2×C4D4×D4711yescharacteristic
402C2×C4C23×D4711yescharacteristic
403C8—21no—
404C8—21no—
405C8—472no—
406C8—941no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—472no—
417C22—941no—
418C22—941no—
419C22—941no—
420C22—942no—
421C22—941no—
422C22—941no—
423C22—3764no—
424C22—3764no—
425C22—3764no—
426C22—1881no—
427C22—1881no—
428C22—1881no—
429C22—1881no—
430C22—1881no—
431C22C2×D4×D4711yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—941no—
436C4—941no—
437C4—1881no—
438C4—1881no—
439C4C2×D4×D4711yescharacteristic
440C4#1309407011yescharacteristic
441C2—42no—
442C2—81no—
443C2—81no—
444C2—942no—
445C2—3761no—
446C2—1881no—
447C2—1882no—
448C2#1568975711yescharacteristic
449C2AGL(1,ℤ/8)×D4711yescharacteristic
450C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47#3264
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C2×D8×D47C2semidirect
3. #15689768C2semidirect
4. #15689758C2semidirect
5. #15689510C2semidirect
6. #15689375C2semidirect
7. #15689351C2semidirect
8. #15689339C2semidirect
9. #15689275C2semidirect
10. #15689265C2semidirect
11. #15689258C2semidirect
12. #15689255C2semidirect
13. #15689233C2semidirect
14. #15689193C2semidirect
15. C47×#459C2semidirect
16. C2×#10625352C22semidirect
19. C2×D4×D47C22semidirect
20. C2×D4×D47C22semidirect
22. C2×#10625325C22semidirect
23. C2×#10625335C22semidirect
24. C2×#10625335C22semidirect
27. C2×#10625334C22semidirect
28. C2×#10625334C22semidirect
30. C2×#10625324C22semidirect
31. C2×C8×D47C22semidirect
32. #13094012C22semidirect
34. #13094004C22semidirect
35. #13093999C22semidirect
39. #13093995C22semidirect
44. C4×D188C22semidirect
46. #13093955C22semidirect
47. #13093949C22semidirect
48. #13093946C22semidirect
49. #13093945C22semidirect
50. #13093944C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093935C22semidirect
54. C2×D8×C47C22semidirect
55. C2×D8×C47C22semidirect
56. #127×C47C22semidirect
57. C4×D4×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #102×C47C22semidirect
60. #102×C47C22semidirect
107. #10625334D4semidirect
147. D4×C47C2×D4semidirect
180. C47⋊C8C2×D4semidirect
205. C2×D47AGL(1,ℤ/8)semidirect
234. #459D47semidirect
241. C47#3264semidirect
256. C2×D8C2×D47semidirect
257. C2×D8C2×D47semidirect
260. #127C2×D47semidirect
274. C4×D4C2×D47semidirect
277. C4⋊C8C2×D47semidirect
282. #102C2×D47semidirect
283. #102C2×D47semidirect
387. D4D4×D47semidirect