Finite Group Databasebeta

← #20254869

Subgroups — #20254869

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×#13094049C211yesmaximal, characteristic, complemented
2C22×#10625334C211yesmaximal, characteristic, complemented
3D4×D188C211yesmaximal, characteristic, complemented
4#15689513C211yesmaximal, characteristic, complemented
5#15689374C211yesmaximal, characteristic, complemented
6#15689354C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689318C211yesmaximal, characteristic, complemented
9#15689273C211yesmaximal, characteristic, complemented
10#15689268C211yesmaximal, characteristic, complemented
11#15689257C211yesmaximal, characteristic, complemented
12#15689256C211yesmaximal, characteristic, complemented
13#15689233C211yesmaximal, characteristic, complemented
14#15689195C211yesmaximal, characteristic, complemented
15C47×#546C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic, complemented
18C2×D4×D47—21no—
19#13094049—24no—
20C2×#10625336C2211yescharacteristic, complemented
21C2×#10625336C2211yescharacteristic, complemented
22C2×#10625336C2211yescharacteristic, complemented
23C2×#10625334—24no—
24C2×#10625334C2211yescharacteristic
25C2×#10625334C2211yescharacteristic
26C2×#10625334C2211yescharacteristic, complemented
27C2×#10625334C2211yescharacteristic, complemented
28C2×#10625334C2211yescharacteristic, complemented
29C2×#10625334C2211yescharacteristic, complemented
30C2×#10625329C2211yescharacteristic, complemented
31C22×C47⋊C8C2211yescharacteristic, complemented
32#13094021C2211yescharacteristic, complemented
33#13093999—21no—
34#13093998C2211yescharacteristic
35#13093998C2211yescharacteristic, complemented
36#13093994—21no—
37#13093994—21no—
38C4×D188C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40C4⋊(C47⋊C8)C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093945C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic, complemented
44#13093944C2211yescharacteristic, complemented
45#13093944C2211yescharacteristic, complemented
46#13093944C2211yescharacteristic, complemented
47C22⋊(C47⋊C8)C2211yescharacteristic, complemented
48C22⋊(C47⋊C8)C2211yescharacteristic, complemented
49#13093935C2211yescharacteristic, complemented
50C2×#41×C47C2211yescharacteristic, complemented
51C22×D4×C47C2211yescharacteristic, complemented
52#124×C47C2211yescharacteristic, complemented
53#123×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic, complemented
55#121×C47—21no—
56#121×C47C2211yescharacteristic, complemented
57#120×C47—21no—
58C4×D4×C47C2211yescharacteristic
59C4×D4×C47C2211yescharacteristic, complemented
60C2×C22⋊C4×C47—21no—
61C24×C47—21no—
62C23×D47—21no—
63C23×D47—21no—
64#41×C47—22no—
65#41×C47—41no—
66C2×Q8×C47C2311yescharacteristic
67C2×D4×C47—22no—
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47—41no—
72C2×D4×C47D411yescharacteristic
73C2×D4×C47C2311yescharacteristic
74C2×D4×C47C2311yescharacteristic
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47C2311yescharacteristic
78C22×C4×C47C2311yescharacteristic
79C2×C22⋊D47—21no—
80C2×C22⋊D47—21no—
81D4×D47—44no—
82C2×D188—22no—
83C2×D188—22no—
84C2×D188—21no—
85C2×D188—21no—
86C2×D188—21no—
87C2×D188—21no—
88C2×D188—41no—
89C2×D188—41no—
90C2×D188C2311yescharacteristic
91C2×D188C2311yescharacteristic
92C2×D188C2311yescharacteristic
93C2×C4×D47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47D411yescharacteristic
96C4⋊C4×C47C2311yescharacteristic
97C22⋊C4×C47—21no—
98C22⋊C4×C47—21no—
99C22⋊C4×C47—21no—
100C22⋊C4×C47—21no—
101C22⋊C4×C47—21no—
102C22⋊C4×C47D411yescharacteristic
103C22⋊C4×C47D411yescharacteristic
104C42×C47C2311yescharacteristic
105#10625336—22no—
106#10625336—22no—
107#10625336—41no—
108#10625334—22no—
109#10625334—22no—
110#10625334—22no—
111#10625334—22no—
112#10625334—41no—
113#10625334D414yescomplemented
114(C2×D47)⋊C4—21no—
115(C2×D47)⋊C4—21no—
116(C2×D47)⋊C4—21no—
117C4⋊Dic47C2311yescharacteristic
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—42no—
127C23×C47—42no—
128C23×C47—81no—
129C23×C47C2×D411yescharacteristic
130C23×C47C2×D411yescharacteristic
131C22×D47—21no—
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—42no—
135C22×D47—42no—
136C22×D47—42no—
137C22×D47—42no—
138C22×D47—81no—
139C22×D47—81no—
140Q8×C47—21no—
141Q8×C47—21no—
142D4×C47—22no—
143D4×C47—21no—
144D4×C47—21no—
145D4×C47—21no—
146D4×C47—42no—
147D4×C47—42no—
148D4×C47—81no—
149D4×C47C2×D412yescomplemented
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—42no—
157C2×C4×C47—81no—
158C2×C4×C47C2×D411yescharacteristic
159C2×C4×C47C2×D411yescharacteristic
160C2×C4×C47C2×D411yescharacteristic
161C2×C4×C47C2×D411yescharacteristic
162C2×C4×C47C2411yescharacteristic
163C22⋊D47—42no—
164C22⋊D47—42no—
165C2×Dic47—21no—
166D188—21no—
167D188—21no—
168D188—21no—
169D188—21no—
170D188—21no—
171D188—42no—
172D188—42no—
173D188—42no—
174D188—81no—
175D188C2×D412yes—
176C4×D47—42no—
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—84no—
193C22×C47AGL(1,ℤ/8)12yescomplemented
194C22×C47C22×D411yescharacteristic
195C2×D47—22no—
196C2×D47—41no—
197C2×D47—41no—
198C2×D47—41no—
199C2×D47—41no—
200C2×D47—41no—
201C2×D47—41no—
202C2×D47—41no—
203C2×D47—41no—
204C2×D47—84no—
205C2×D47—84no—
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—21no—
209C4×C47—21no—
210C4×C47—41no—
211C4×C47—41no—
212C4×C47C22×D411yescharacteristic
213C4×C47H(5,𝔽2)11yescharacteristic
214Dic47—41no—
215#3264—471nomaximal, Sylow
216C2×C47—22no—
217C2×C47—41no—
218C2×C47—42no—
219C2×C47—81no—
220C2×C47D4211yescharacteristic
221C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
222C2×C47#57611yescharacteristic
223D47—42no—
224D47—81no—
225D47—81no—
226C2×AGL(1,ℤ/8)—471no—
227C22×D8—471no—
228#546D4711yescharacteristic, complemented
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×#41C2×D4711yescharacteristic, complemented
243C22×D4—471no—
244C22×D4—471no—
245C22×D4—941no—
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#127—471no—
261#124C2×D4711yescharacteristic, complemented
262#123—21no—
263C22⋊Q8C2×D4711yescharacteristic, complemented
264#121—21no—
265#121—471no—
266#121—471no—
267#121—941no—
268#121C2×D4711yescharacteristic, complemented
269#120—21no—
270#120—941no—
271#120—941no—
272C4×D4—471no—
273C4×D4C2×D4711yescharacteristic
274C4×D4C2×D4711yescharacteristic, complemented
275C2×C22⋊C4—21no—
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—941no—
289C24—941no—
290#41—22no—
291#41—41no—
292C2×Q8C22×D4711yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—471no—
299C2×D4—471no—
300C2×D4—471no—
301C2×D4—942no—
302C2×D4—942no—
303C2×D4—941no—
304C2×D4—941no—
305C2×D4—941no—
306C2×D4—941no—
307C2×D4—941no—
308C2×D4—941no—
309C2×D4—1881no—
310C2×D4—1881no—
311C2×D4—1884no—
312C2×D4C22⋊D4711yescharacteristic
313C2×D4C22×D4711yescharacteristic
314C2×D4C22×D4711yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
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—21no—
336C4⋊C4—471no—
337C4⋊C4C22⋊D4711yescharacteristic
338C4⋊C4C22×D4711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—941no—
345C22⋊C4—941no—
346C22⋊C4—941no—
347C22⋊C4C22⋊D4711yescharacteristic
348C22⋊C4C22⋊D4711yescharacteristic
349C42C22×D4711yescharacteristic
350C23—21no—
351C23—21no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—941no—
356C23—941no—
357C23—941no—
358C23—3761no—
359C23—3761no—
360C23—1882no—
361C23—1882no—
362C23—1882no—
363C23—1882no—
364C23C2×C22⋊D4711yescharacteristic
365C23C2×C22⋊D4711yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—42no—
373D4—42no—
374D4—81no—
375D4—472no—
376D4—941no—
377D4—941no—
378D4—941no—
379D4—941no—
380D4—941no—
381D4—3761no—
382D4—1882no—
383D4—1882no—
384D4—1882no—
385D4—1882no—
386D4—1882no—
387D4D4×D4712yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—81no—
396C2×C4—941no—
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—84no—
419C22—942no—
420C22—3764no—
421C22—3764no—
422C22—1881no—
423C22—1881no—
424C22—1881no—
425C22—1881no—
426C22—1881no—
427C22—1881no—
428C22—1881no—
429C22—1881no—
430C22#1309404912yescomplemented
431C22C22×C22⋊D4711yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—1881no—
439C4C2×D4×D4711yescharacteristic
440C4#1309406911yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—3761no—
446C2—3761no—
447C2—1882no—
448C2D4×C22⋊D4711yescharacteristic
449C2C2×#1309404911yescharacteristic
450C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#546C2
socleC22×C47C22×D4
hypercenter#546D47
hypocenterC47#3264
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#13094049C2semidirect
2. C22×#10625334C2semidirect
3. D4×D188C2semidirect
4. #15689513C2semidirect
5. #15689374C2semidirect
6. #15689354C2semidirect
7. #15689335C2semidirect
8. #15689318C2semidirect
9. #15689273C2semidirect
10. #15689268C2semidirect
11. #15689257C2semidirect
12. #15689256C2semidirect
13. #15689233C2semidirect
14. #15689195C2semidirect
15. C47×#546C2semidirect
17. C22×D188C22semidirect
20. C2×#10625336C22semidirect
21. C2×#10625336C22semidirect
22. C2×#10625336C22semidirect
26. C2×#10625334C22semidirect
27. C2×#10625334C22semidirect
28. C2×#10625334C22semidirect
29. C2×#10625334C22semidirect
30. C2×#10625329C22semidirect
31. C22×C47⋊C8C22semidirect
32. #13094021C22semidirect
35. #13093998C22semidirect
38. C4×D188C22semidirect
39. #13093955C22semidirect
40. C4⋊(C47⋊C8)C22semidirect
41. #13093948C22semidirect
42. #13093945C22semidirect
43. #13093945C22semidirect
44. #13093944C22semidirect
45. #13093944C22semidirect
46. #13093944C22semidirect
47. C22⋊(C47⋊C8)C22semidirect
48. C22⋊(C47⋊C8)C22semidirect
49. #13093935C22semidirect
50. C2×#41×C47C22semidirect
51. C22×D4×C47C22semidirect
52. #124×C47C22semidirect
54. C22⋊Q8×C47C22semidirect
56. #121×C47C22semidirect
59. C4×D4×C47C22semidirect
113. #10625334D4semidirect
149. D4×C47C2×D4semidirect
180. C47⋊C8C2×D4semidirect
193. C22×C47AGL(1,ℤ/8)semidirect
228. #546D47semidirect
241. C47#3264semidirect
242. C2×#41C2×D47semidirect
246. C22×D4C2×D47semidirect
261. #124C2×D47semidirect
263. C22⋊Q8C2×D47semidirect
268. #121C2×D47semidirect
274. C4×D4C2×D47semidirect
387. D4D4×D47semidirect
430. C22#13094049semidirect