Finite Group Databasebeta

← #20254868

Subgroups — #20254868

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
2#15689767C211yesmaximal, characteristic, complemented
3D4×C22⋊D47C211yesmaximal, characteristic, complemented
4#15689511C211yesmaximal, characteristic, complemented
5#15689373C211yesmaximal, characteristic, complemented
6#15689352C211yesmaximal, characteristic, complemented
7#15689336C211yesmaximal, characteristic, complemented
8#15689316C211yesmaximal, characteristic, complemented
9#15689274C211yesmaximal, characteristic, complemented
10#15689265C211yesmaximal, characteristic, complemented
11#15689257C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13#15689235C211yesmaximal, characteristic, complemented
14#15689194C211yesmaximal, characteristic, complemented
15C22×D8×C47C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic, complemented
17C22×C22⋊D47—21no—
18C2×D4×D47C2211yescharacteristic, complemented
19#13094048—24no—
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic, complemented
22C2×#10625335C2211yescharacteristic, complemented
23C2×#10625334C2211yescharacteristic, complemented
24C2×#10625334C2211yescharacteristic, complemented
25C2×#10625324C2211yescharacteristic, complemented
26#13094020C2211yescharacteristic, complemented
27#13094011C2211yescharacteristic, complemented
28#13094005—21no—
29#13094003C2211yescharacteristic, complemented
30#13093998C2211yescharacteristic
31#13093996—21no—
32#13093996—21no—
33#13093995C2211yescharacteristic, complemented
34#13093995C2211yescharacteristic, complemented
35#13093993—21no—
36#13093993—21no—
37#13093992—21no—
38D4×Dic47C2211yescharacteristic, complemented
39D4×Dic47C2211yescharacteristic, complemented
40C4×C22⋊D47C2211yescharacteristic
41C2×C22⋊Dic47—21no—
42#13093956C2211yescharacteristic, complemented
43Dic47⋊C8C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic, complemented
49#13093945C2211yescharacteristic, complemented
50C22⋊(C47⋊C8)C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52#13093934C2211yescharacteristic, complemented
53C22×D4×C47C2211yescharacteristic
54C22×D4×C47C2211yescharacteristic, complemented
55C2×D8×C47—24no—
56C2×D8×C47C2211yescharacteristic
57C2×D8×C47C2211yescharacteristic
58C2×D8×C47C2211yescharacteristic, complemented
59C2×D8×C47C2211yescharacteristic, complemented
60C22×C8×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—41no—
69C2×D4×C47—41no—
70C2×D4×C47C2311yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C2×D4×C47C2311yescharacteristic
73C2×D4×C47C2311yescharacteristic
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—21no—
82C2×C22⋊D47—44no—
83C2×C22⋊D47D411yescharacteristic
84C22×Dic47—21no—
85C22×Dic47—21no—
86C22×Dic47—21no—
87#10625352—22no—
88#10625352—41no—
89D4×D47—22no—
90D4×D47—41no—
91C2×D188C2311yescharacteristic
92C2×C4×D47C2311yescharacteristic
93C2×Dic94C2311yescharacteristic
94D8×C47—22no—
95D8×C47—22no—
96D8×C47—22no—
97D8×C47D414yescomplemented
98C2×C8×C47—22no—
99C2×C8×C47C2311yescharacteristic
100C2×C8×C47C2311yescharacteristic
101C22⋊Dic47—21no—
102C22⋊Dic47—21no—
103C22⋊Dic47—21no—
104C22⋊Dic47—21no—
105C22⋊Dic47—21no—
106C22⋊Dic47—21no—
107C22⋊Dic47—21no—
108C22⋊Dic47D411yescharacteristic
109#10625335—22no—
110#10625335—41no—
111#10625334—22no—
112#10625334—41no—
113(C2×D47)⋊C4—21no—
114(C2×D47)⋊C4D411yescharacteristic
115C4⋊Dic47C2311yescharacteristic
116C4⋊Dic47C2311yescharacteristic
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—21no—
128C23×C47—42no—
129C23×C47—42no—
130C23×C47—42no—
131C23×C47—42no—
132C23×C47—81no—
133C23×C47—81no—
134C23×C47C2×D411yescharacteristic
135C22×D47—21no—
136C22×D47—42no—
137C22×D47—42no—
138C22×D47—81no—
139C22×D47C2×D411yescharacteristic
140D4×C47—21no—
141D4×C47—21no—
142D4×C47—21no—
143D4×C47—21no—
144D4×C47—21no—
145D4×C47—21no—
146D4×C47—42no—
147D4×C47—42no—
148D4×C47C2×D412yes—
149D4×C47C2×D412yescomplemented
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47C2×D411yescharacteristic
153C2×C4×C47C2411yescharacteristic
154C22⋊D47—22no—
155C22⋊D47—42no—
156C22⋊D47—42no—
157C22⋊D47—42no—
158C22⋊D47—42no—
159C22⋊D47—42no—
160C22⋊D47—81no—
161C22⋊D47—81no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—42no—
166C2×Dic47—42no—
167C2×Dic47—81no—
168C2×Dic47C2×D411yescharacteristic
169C2×Dic47C2×D411yescharacteristic
170C2×Dic47C2×D411yescharacteristic
171D188—21no—
172D188—21no—
173C4×D47—21no—
174C4×D47—21no—
175Dic94—21no—
176Dic94—21no—
177C8×C47—21no—
178C8×C47C2×D412yescomplemented
179C47⋊C8—21no—
180C47⋊C8—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—22no—
184C22×C47—22no—
185C22×C47—41no—
186C22×C47—41no—
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—21no—
200C2×D47—21no—
201C2×D47—21no—
202C2×D47—41no—
203C2×D47—41no—
204C2×D47—41no—
205C2×D47—84no—
206C4×C47—21no—
207C4×C47C22×D411yescharacteristic
208C4×C47H(5,𝔽2)11yescharacteristic
209Dic47—21no—
210Dic47—21no—
211Dic47—21no—
212Dic47—41no—
213Dic47—41no—
214Dic47—41no—
215#3264—471nomaximal, Sylow
216C2×C47—22no—
217C2×C47—42no—
218C2×C47—42no—
219C2×C47—81no—
220C2×C47—81no—
221C2×C47D4211yescharacteristic
222C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
223C2×C47#57611yescharacteristic
224D47—41no—
225D47—81no—
226C2×AGL(1,ℤ/8)—471no—
227C22×D8D4711yescharacteristic, complemented
228#546—471no—
229D42—471no—
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—471no—
244C22×D4—941no—
245C22×D4C2×D4711yescharacteristic
246C22×D4C2×D4711yescharacteristic, complemented
247AGL(1,ℤ/8)—944no—
248C2×SD16—471no—
249C2×SD16—471no—
250C2×SD16—471no—
251C2×D8—24no—
252C2×D8—471no—
253C2×D8—471no—
254C2×D8C2×D4711yescharacteristic
255C2×D8C2×D4711yescharacteristic
256C2×D8C2×D4711yescharacteristic, complemented
257C2×D8C2×D4711yescharacteristic, complemented
258C2×M16—471no—
259C22×C8C2×D4711yescharacteristic, complemented
260#127—471no—
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×D4—471no—
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—41no—
298C2×D4—41no—
299C2×D4—471no—
300C2×D4—471no—
301C2×D4—941no—
302C2×D4—941no—
303C2×D4—941no—
304C2×D4—942no—
305C2×D4—941no—
306C2×D4—941no—
307C2×D4—941no—
308C2×D4—941no—
309C2×D4—1881no—
310C2×D4—1884no—
311C2×D4C22×D4711yescharacteristic
312C2×D4C22×D4711yescharacteristic
313C2×D4C22×D4711yescharacteristic
314C2×D4C22×D4711yescharacteristic
315C22×C4—471no—
316C22×C4—941no—
317C22×C4—941no—
318C22×C4—941no—
319C22×C4C22×D4711yescharacteristic
320SD16—942no—
321SD16—942no—
322SD16—1881no—
323D8—22no—
324D8—22no—
325D8—22no—
326D8—942no—
327D8—1881no—
328D8C22⋊D4714yescomplemented
329M16—942no—
330C2×C8—22no—
331C2×C8—471no—
332C2×C8—471no—
333C2×C8C22×D4711yescharacteristic
334C2×C8C22×D4711yescharacteristic
335C4⋊C4—471no—
336C4⋊C4—471no—
337C4⋊C4—471no—
338C4⋊C4—941no—
339C22⋊C4—471no—
340C22⋊C4—471no—
341C22⋊C4—941no—
342C22⋊C4—941no—
343C22⋊C4—941no—
344C22⋊C4—941no—
345C22⋊C4—941no—
346C22⋊C4—941no—
347C22⋊C4—941no—
348C22⋊C4—941no—
349C42—471no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23—471no—
361C23—941no—
362C23—3761no—
363C23—1882no—
364C23—1882no—
365C23D4×D4711yescharacteristic
366Q8—941no—
367Q8—941no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—942no—
377D4—941no—
378D4—941no—
379D4—3761no—
380D4—3761no—
381D4—1882no—
382D4—1882no—
383D4—1882no—
384D4—1882no—
385D4—1882no—
386D4C2×C22⋊D4712yes—
387D4C2×C22⋊D4712yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—471no—
391C2×C4—471no—
392C2×C4—471no—
393C2×C4—941no—
394C2×C4—941no—
395C2×C4—941no—
396C2×C4—941no—
397C2×C4—941no—
398C2×C4—3761no—
399C2×C4—1882no—
400C2×C4—1882no—
401C2×C4D4×D4711yescharacteristic
402C2×C4C23×D4711yescharacteristic
403C8—21no—
404C8—941no—
405C8—941no—
406C8C2×C22⋊D4712yescomplemented
407C22—21no—
408C22—21no—
409C22—22no—
410C22—22no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—941no—
424C22—941no—
425C22—941no—
426C22—3764no—
427C22—1881no—
428C22—1881no—
429C22—1881no—
430C22#1309404812yescomplemented
431C22C2×D4×D4711yescharacteristic
432C4—21no—
433C4—941no—
434C4—941no—
435C4—941no—
436C4—1881no—
437C4—1881no—
438C4—1881no—
439C4C22×C22⋊D4711yescharacteristic
440C4#1309406911yescharacteristic
441C2—22no—
442C2—42no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—3761no—
447C2—1881no—
448C2D4×C22⋊D4711yescharacteristic
449C2C2×#1309404811yescharacteristic
450C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC22×D8×C47C2
socleC22×C47C22×D4
hypercenterC22×D8D47
hypocenterC47#3264
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. #15689767C2semidirect
3. D4×C22⋊D47C2semidirect
4. #15689511C2semidirect
5. #15689373C2semidirect
6. #15689352C2semidirect
7. #15689336C2semidirect
8. #15689316C2semidirect
9. #15689274C2semidirect
10. #15689265C2semidirect
11. #15689257C2semidirect
12. #15689255C2semidirect
13. #15689235C2semidirect
14. #15689194C2semidirect
15. C22×D8×C47C2semidirect
16. C2×#10625352C22semidirect
18. C2×D4×D47C22semidirect
20. C2×#10625325C22semidirect
21. C2×#10625335C22semidirect
22. C2×#10625335C22semidirect
23. C2×#10625334C22semidirect
24. C2×#10625334C22semidirect
25. C2×#10625324C22semidirect
26. #13094020C22semidirect
27. #13094011C22semidirect
29. #13094003C22semidirect
33. #13093995C22semidirect
34. #13093995C22semidirect
38. D4×Dic47C22semidirect
39. D4×Dic47C22semidirect
42. #13093956C22semidirect
43. Dic47⋊C8C22semidirect
44. #13093949C22semidirect
45. #13093946C22semidirect
46. #13093945C22semidirect
47. #13093945C22semidirect
48. #13093945C22semidirect
49. #13093945C22semidirect
50. C22⋊(C47⋊C8)C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. #13093934C22semidirect
54. C22×D4×C47C22semidirect
58. C2×D8×C47C22semidirect
59. C2×D8×C47C22semidirect
60. C22×C8×C47C22semidirect
97. D8×C47D4semidirect
149. D4×C47C2×D4semidirect
178. C8×C47C2×D4semidirect
197. C22×C47AGL(1,ℤ/8)semidirect
227. C22×D8D47semidirect
241. C47#3264semidirect
246. C22×D4C2×D47semidirect
256. C2×D8C2×D47semidirect
257. C2×D8C2×D47semidirect
259. C22×C8C2×D47semidirect
328. D8C22⋊D47semidirect
387. D4C2×C22⋊D47semidirect
406. C8C2×C22⋊D47semidirect
430. C22#13094048semidirect