Finite Group Databasebeta

← #20254982

Subgroups — #20254982

Order 6016.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C211yesmaximal, characteristic, complemented
2#15689772C211yesmaximal, characteristic, complemented
3D4×C22⋊D47C211yesmaximal, characteristic, complemented
4#15689494C211yesmaximal, characteristic, complemented
5#15689369C211yesmaximal, characteristic, complemented
6#15689366C211yesmaximal, characteristic, complemented
7#15689326C211yesmaximal, characteristic, complemented
8#15689316C211yesmaximal, characteristic, complemented
9#15689274C211yesmaximal, characteristic, complemented
10#15689272C211yesmaximal, characteristic, complemented
11#15689268C211yesmaximal, characteristic, complemented
12#15689265C211yesmaximal, characteristic, complemented
13D8×Dic47C211yesmaximal, characteristic, complemented
14#15689199C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic, complemented
17C22×C22⋊D47—21no—
18C2×D4×D47C2211yescharacteristic
19#13094048—24no—
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic
22C2×#10625335C2211yescharacteristic, complemented
23C2×#10625336C2211yescharacteristic, complemented
24C2×#10625334C2211yescharacteristic, complemented
25C2×#10625324C2211yescharacteristic, complemented
26#13094022C2211yescharacteristic, complemented
27#13094020C2211yescharacteristic
28#13094007—21no—
29#13094005—21no—
30#13094003C2211yescharacteristic, complemented
31#13094000C2211yescharacteristic, complemented
32#13093998C2211yescharacteristic
33#13093996—21no—
34#13093996—21no—
35#13093995C2211yescharacteristic
36#13093993—21no—
37#13093992—21no—
38D4×Dic47C2211yescharacteristic
39D4×Dic47C2211yescharacteristic, complemented
40C4×C22⋊D47C2211yescharacteristic
41C2×Dic47⋊C4—21no—
42#13093958C2211yescharacteristic, complemented
43Dic47⋊C8C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic, complemented
49#13093945C2211yescharacteristic, complemented
50C22⋊(C47⋊C8)C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C8×Dic47C2211yescharacteristic, complemented
53C2×#41×C47C2211yescharacteristic, complemented
54C22×D4×C47C2211yescharacteristic
55AGL(1,ℤ/8)×C47—24no—
56C2×SD16×C47C2211yescharacteristic
57C2×SD16×C47C2211yescharacteristic, complemented
58C2×D8×C47C2211yescharacteristic
59C2×D8×C47C2211yescharacteristic, complemented
60C2×M16×C47C2211yescharacteristic, complemented
61C24×C47—21no—
62C23×D47—21no—
63#41×C47—22no—
64#41×C47—41no—
65C2×Q8×C47C2311yescharacteristic
66C2×D4×C47—22no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—41no—
70C2×D4×C47C2311yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C2×D4×C47C2311yescharacteristic
73C22×C4×C47—21no—
74C22×C4×C47C2311yescharacteristic
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80C2×C22⋊D47—21no—
81C2×C22⋊D47—44no—
82C2×C22⋊D47D411yescharacteristic
83C22×Dic47—21no—
84C22×Dic47—21no—
85C22×Dic47—21no—
86#10625352—22no—
87#10625352—41no—
88D4×D47—22no—
89D4×D47—41no—
90C2×D188C2311yescharacteristic
91C2×C4×D47C2311yescharacteristic
92C2×Dic94C2311yescharacteristic
93SD16×C47—22no—
94SD16×C47—22no—
95D8×C47—22no—
96D8×C47D414yescomplemented
97M16×C47—22no—
98C2×C8×C47C2311yescharacteristic
99C2×C8×C47C2311yescharacteristic
100C22⋊Dic47—21no—
101C22⋊Dic47—21no—
102C22⋊Dic47—21no—
103C22⋊Dic47—21no—
104C22⋊Dic47D411yescharacteristic
105#10625336—41no—
106#10625335—22no—
107#10625335—41no—
108#10625334—22no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4D411yescharacteristic
112C4⋊Dic47C2311yescharacteristic
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117Dic47⋊C4—21no—
118Dic47⋊C4D411yescharacteristic
119C4×Dic47C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122#10625325—22no—
123#10625324—22no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—42no—
128C23×C47—42no—
129C23×C47—81no—
130C23×C47C2×D411yescharacteristic
131C22×D47—21no—
132C22×D47—42no—
133C22×D47—42no—
134C22×D47—81no—
135C22×D47C2×D411yescharacteristic
136Q8×C47—21no—
137Q8×C47—21no—
138D4×C47—21no—
139D4×C47—21no—
140D4×C47—21no—
141D4×C47—21no—
142D4×C47—42no—
143D4×C47—42no—
144D4×C47C2×D412yes—
145D4×C47C2×D412yescomplemented
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—42no—
150C2×C4×C47C2×D411yescharacteristic
151C2×C4×C47C2411yescharacteristic
152C22⋊D47—22no—
153C22⋊D47—42no—
154C22⋊D47—42no—
155C22⋊D47—42no—
156C22⋊D47—42no—
157C22⋊D47—42no—
158C22⋊D47—81no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—42no—
163C2×Dic47—42no—
164C2×Dic47—42no—
165C2×Dic47C2×D411yescharacteristic
166C2×Dic47C2×D411yescharacteristic
167C2×Dic47C2×D411yescharacteristic
168D188—21no—
169D188—21no—
170C4×D47—21no—
171C4×D47—21no—
172Dic94—21no—
173Dic94—21no—
174C8×C47—21no—
175C8×C47C2×D412yescomplemented
176C47⋊C8—21no—
177C47⋊C8—21no—
178C22×C47—22no—
179C22×C47—22no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47—84no—
191C22×C47C22×D411yescharacteristic
192C2×D47—21no—
193C2×D47—21no—
194C2×D47—21no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—41no—
198C2×D47—84no—
199C4×C47—21no—
200C4×C47—41no—
201C4×C47C22×D411yescharacteristic
202C4×C47H(5,𝔽2)11yescharacteristic
203Dic47—21no—
204Dic47—21no—
205Dic47—41no—
206Dic47—41no—
207Dic47—41no—
208Dic47AGL(1,ℤ/8)12yescomplemented
209#3272—471nomaximal, Sylow
210C2×C47—42no—
211C2×C47—41no—
212C2×C47—42no—
213C2×C47—81no—
214C2×C47D4211yescharacteristic
215C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
216C2×C47#57711yescharacteristic
217D47—41no—
218D47—81no—
219C2×AGL(1,ℤ/8)—471no—
220C2×AGL(1,ℤ/8)D4711yescharacteristic, complemented
221#547—471no—
222D42—471no—
223#492—471no—
224#468—471no—
225#468—471no—
226#461—471no—
227#459—471no—
228#450—471no—
229#450—471no—
230#449—471no—
231#449—471no—
232C4×D8—471no—
233#436—471no—
234C47#327211yescharacteristic, complemented, Sylow
235C2×#41—471no—
236C2×#41C2×D4711yescharacteristic, complemented
237C22×D4—471no—
238C22×D4—941no—
239C22×D4C2×D4711yescharacteristic
240AGL(1,ℤ/8)—24no—
241AGL(1,ℤ/8)—944no—
242C2×SD16—471no—
243C2×SD16—471no—
244C2×SD16—471no—
245C2×SD16—471no—
246C2×SD16C2×D4711yescharacteristic
247C2×SD16C2×D4711yescharacteristic, complemented
248C2×D8—471no—
249C2×D8C2×D4711yescharacteristic
250C2×D8C2×D4711yescharacteristic, complemented
251C2×M16—471no—
252C2×M16C2×D4711yescharacteristic, complemented
253C4⋊Q8—471no—
254#127—471no—
255#123—941no—
256#123—941no—
257C22⋊Q8—471no—
258C22⋊Q8—471no—
259#121—471no—
260#121—471no—
261#121—941no—
262#121—941no—
263#120—941no—
264#120—941no—
265C4×D4—471no—
266C4×D4—471no—
267C4×D4—471no—
268C2×C4⋊C4—941no—
269#107—471no—
270C4⋊C8—471no—
271#103—471no—
272#103—471no—
273#102—471no—
274#102—471no—
275#102—471no—
276#102—471no—
277C22⋊C8—471no—
278C22⋊C8—471no—
279C4×C8—471no—
280C24—21no—
281C24—941no—
282#41—22no—
283#41—41no—
284#41—942no—
285#41—1881no—
286C2×Q8—471no—
287C2×Q8C22×D4711yescharacteristic
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—471no—
293C2×D4—471no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—942no—
298C2×D4—941no—
299C2×D4—941no—
300C2×D4—941no—
301C2×D4—1881no—
302C2×D4—1884no—
303C2×D4C22×D4711yescharacteristic
304C2×D4C22×D4711yescharacteristic
305C2×D4C22×D4711yescharacteristic
306C22×C4—21no—
307C22×C4—471no—
308C22×C4—941no—
309C22×C4—941no—
310C22×C4—941no—
311C22×C4C22×D4711yescharacteristic
312SD16—22no—
313SD16—22no—
314SD16—942no—
315SD16—942no—
316SD16—1881no—
317SD16—1881no—
318D8—22no—
319D8—942no—
320D8C22⋊D4714yescomplemented
321M16—22no—
322M16—942no—
323C2×C8—471no—
324C2×C8—471no—
325C2×C8C22×D4711yescharacteristic
326C2×C8C22×D4711yescharacteristic
327C4⋊C4—471no—
328C4⋊C4—471no—
329C4⋊C4—471no—
330C4⋊C4—941no—
331C4⋊C4—941no—
332C4⋊C4—941no—
333C4⋊C4—941no—
334C22⋊C4—471no—
335C22⋊C4—471no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C22⋊C4—941no—
339C22⋊C4—941no—
340C22⋊C4—941no—
341C22⋊C4—941no—
342C42—471no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—471no—
350C23—941no—
351C23—3761no—
352C23—1882no—
353C23—1882no—
354C23D4×D4711yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—941no—
358Q8—941no—
359D4—21no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—942no—
366D4—941no—
367D4—941no—
368D4—3761no—
369D4—1882no—
370D4—1882no—
371D4—1882no—
372D4—1882no—
373D4—1882no—
374D4C2×C22⋊D4712yes—
375D4C2×C22⋊D4712yescomplemented
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—471no—
381C2×C4—471no—
382C2×C4—471no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—1882no—
389C2×C4—1882no—
390C2×C4—1882no—
391C2×C4D4×D4711yescharacteristic
392C2×C4C23×D4711yescharacteristic
393C8—21no—
394C8—941no—
395C8—941no—
396C8C2×C22⋊D4712yescomplemented
397C22—21no—
398C22—22no—
399C22—22no—
400C22—21no—
401C22—21no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—84no—
410C22—941no—
411C22—941no—
412C22—941no—
413C22—3764no—
414C22—1881no—
415C22—1881no—
416C22—1881no—
417C22C2×D4×D4711yescharacteristic
418C4—21no—
419C4—41no—
420C4—472no—
421C4—941no—
422C4—941no—
423C4—1881no—
424C4—1881no—
425C4—1881no—
426C4C22×C22⋊D4711yescharacteristic
427C4#1309406911yescharacteristic
428C2—41no—
429C2—42no—
430C2—42no—
431C2—81no—
432C2—3761no—
433C2—1881no—
434C2D4×C22⋊D4711yescharacteristic
435C2AGL(1,ℤ/8)×D4711yescharacteristic
436C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC22×C47C22×D4
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47#3272
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. #15689772C2semidirect
3. D4×C22⋊D47C2semidirect
4. #15689494C2semidirect
5. #15689369C2semidirect
6. #15689366C2semidirect
7. #15689326C2semidirect
8. #15689316C2semidirect
9. #15689274C2semidirect
10. #15689272C2semidirect
11. #15689268C2semidirect
12. #15689265C2semidirect
13. D8×Dic47C2semidirect
14. #15689199C2semidirect
15. C2×AGL(1,ℤ/8)×C47C2semidirect
16. C2×#10625352C22semidirect
20. C2×#10625325C22semidirect
22. C2×#10625335C22semidirect
23. C2×#10625336C22semidirect
24. C2×#10625334C22semidirect
25. C2×#10625324C22semidirect
26. #13094022C22semidirect
30. #13094003C22semidirect
31. #13094000C22semidirect
39. D4×Dic47C22semidirect
42. #13093958C22semidirect
43. Dic47⋊C8C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093946C22semidirect
48. #13093945C22semidirect
49. #13093945C22semidirect
50. C22⋊(C47⋊C8)C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. C8×Dic47C22semidirect
53. C2×#41×C47C22semidirect
57. C2×SD16×C47C22semidirect
59. C2×D8×C47C22semidirect
60. C2×M16×C47C22semidirect
96. D8×C47D4semidirect
145. D4×C47C2×D4semidirect
175. C8×C47C2×D4semidirect
208. Dic47AGL(1,ℤ/8)semidirect
220. C2×AGL(1,ℤ/8)D47semidirect
234. C47#3272semidirect
236. C2×#41C2×D47semidirect
247. C2×SD16C2×D47semidirect
250. C2×D8C2×D47semidirect
252. C2×M16C2×D47semidirect
320. D8C22⋊D47semidirect
375. D4C2×C22⋊D47semidirect
396. C8C2×C22⋊D47semidirect