Finite Group Databasebeta

← #20255058

Subgroups — #20255058

Order 6016.

620 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625334C211yesmaximal, characteristic, complemented
2C2×D8×D47C211yesmaximal, characteristic, complemented
3#15689757C211yesmaximal, characteristic, complemented
4D4×C22⋊D47C211yesmaximal, characteristic, complemented
5#15689498C211yesmaximal, characteristic, complemented
6#15689358C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689317C211yesmaximal, characteristic, complemented
9#15689316C211yesmaximal, characteristic, complemented
10#15689259C211yesmaximal, characteristic, complemented
11#15689258C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
15C47×#447C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic, complemented
17C22×C22⋊D47—21no—
18C2×D4×D47—21no—
19C2×D4×D47C2211yescharacteristic, complemented
20C2×D4×D47C2211yescharacteristic, complemented
21C2×D376C2211yescharacteristic, complemented
22C2×D376C2211yescharacteristic, complemented
23C2×#10625334—24no—
24C2×#10625334C2211yescharacteristic
25C2×#10625334C2211yescharacteristic, complemented
26C2×#10625334C2211yescharacteristic, complemented
27C2×#10625334C2211yescharacteristic, complemented
28C2×#10625334C2211yescharacteristic, complemented
29D8×D47—24no—
30C22×C47⋊C8C2211yescharacteristic, complemented
31C2×C8×D47C2211yescharacteristic, complemented
32#13094020C2211yescharacteristic, complemented
33#13094020C2211yescharacteristic, complemented
34#13093999C2211yescharacteristic, complemented
35#13093998C2211yescharacteristic, complemented
36#13093997—21no—
37#13093996—21no—
38#13093995C2211yescharacteristic, complemented
39#13093994—21no—
40#13093993—21no—
41#13093992—21no—
42#13093992—21no—
43D4×Dic47C2211yescharacteristic, complemented
44#13093986C2211yescharacteristic, complemented
45C4×C22⋊D47C2211yescharacteristic
46#13093957C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic, complemented
50#13093945C2211yescharacteristic, complemented
51#13093944C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53C8×Dic47C2211yescharacteristic, complemented
54C22×D4×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic, complemented
56C2×D8×C47C2211yescharacteristic, complemented
57#121×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic, complemented
60C22⋊C8×C47C2211yescharacteristic, complemented
61C24×C47—21no—
62C23×D47—21no—
63C23×D47—21no—
64C23×D47—21no—
65C2×D4×C47—22no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—41no—
69C2×D4×C47C2311yescharacteristic
70C2×D4×C47C2311yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
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—
84D4×D47—22no—
85D4×D47—22no—
86D4×D47—41no—
87D4×D47—41no—
88D4×D47—44no—
89C2×D188—22no—
90C2×D188—21no—
91C2×D188—21no—
92C2×D188—41no—
93C2×D188C2311yescharacteristic
94C2×D188C2311yescharacteristic
95C2×D188C2311yescharacteristic
96C2×C4×D47—21no—
97C2×C4×D47C2311yescharacteristic
98D8×C47—22no—
99D8×C47—41no—
100C2×C8×C47C2311yescharacteristic
101C2×C8×C47C2311yescharacteristic
102C4⋊C4×C47C2311yescharacteristic
103C22⋊C4×C47—21no—
104C22⋊Dic47—21no—
105C22⋊Dic47—21no—
106C22⋊Dic47D411yescharacteristic
107#10625334—22no—
108#10625334—22no—
109#10625334—22no—
110#10625334—22no—
111#10625334D414yescomplemented
112(C2×D47)⋊C4—21no—
113(C2×D47)⋊C4—21no—
114(C2×D47)⋊C4—21no—
115(C2×D47)⋊C4D411yescharacteristic
116C4⋊Dic47C2311yescharacteristic
117Dic47⋊C4D411yescharacteristic
118C4×Dic47C2311yescharacteristic
119C2×C47⋊C8—22no—
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122D376—22no—
123D376—41no—
124C8×D47—22no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—42no—
129C23×C47—42no—
130C23×C47—81no—
131C23×C47C2×D411yescharacteristic
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—42no—
136C22×D47—42no—
137C22×D47—42no—
138C22×D47—42no—
139C22×D47—42no—
140C22×D47—42no—
141C22×D47—81no—
142C22×D47—81no—
143C22×D47—81no—
144C22×D47C2×D411yescharacteristic
145D4×C47—21no—
146D4×C47—21no—
147D4×C47—21no—
148D4×C47—21no—
149D4×C47—21no—
150D4×C47—42no—
151D4×C47—42no—
152D4×C47C2×D412yescomplemented
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47C2×D411yescharacteristic
157C2×C4×C47C2411yescharacteristic
158C22⋊D47—42no—
159C22⋊D47—42no—
160C22⋊D47—42no—
161C22⋊D47—42no—
162C22⋊D47—42no—
163C22⋊D47—42no—
164C22⋊D47—81no—
165C22⋊D47—81no—
166C22⋊D47D814yescomplemented
167C2×Dic47—21no—
168C2×Dic47—42no—
169C2×Dic47C2×D411yescharacteristic
170C2×Dic47C2×D411yescharacteristic
171C2×Dic47C2×D411yescharacteristic
172D188—21no—
173D188—21no—
174D188—21no—
175D188—21no—
176D188—21no—
177D188—42no—
178D188—42no—
179D188C2×D412yescomplemented
180C4×D47—21no—
181C4×D47—21no—
182C4×D47—42no—
183C8×C47—21no—
184C8×C47—21no—
185C47⋊C8—21no—
186C47⋊C8C2×D412yescomplemented
187C22×C47—21no—
188C22×C47—21no—
189C22×C47—22no—
190C22×C47—41no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—84no—
199C22×C47C2×D812yescomplemented
200C22×C47C22×D411yescharacteristic
201C2×D47—21no—
202C2×D47—21no—
203C2×D47—22no—
204C2×D47—41no—
205C2×D47—41no—
206C2×D47—41no—
207C2×D47—41no—
208C2×D47—41no—
209C2×D47—41no—
210C2×D47—41no—
211C2×D47—41no—
212C2×D47—84no—
213C2×D47—84no—
214C2×D47—84no—
215C2×D47C2×D812yescomplemented
216C4×C47—21no—
217C4×C47—41no—
218C4×C47C22×D411yescharacteristic
219C4×C47H(5,𝔽2)11yescharacteristic
220Dic47—21no—
221Dic47—21no—
222Dic47—41no—
223Dic47C2×D812yescomplemented
224D4×D8—471nomaximal, Sylow
225C2×C47—22no—
226C2×C47—42no—
227C2×C47—81no—
228C2×C47—81no—
229C2×C47D4211yescharacteristic
230C2×C47C22×D811yescharacteristic
231C2×C47#57611yescharacteristic
232D47—22no—
233D47—42no—
234D47—81no—
235D47—81no—
236C22×D8—471no—
237C22×D8—471no—
238D42—471no—
239D42—471no—
240#493—471no—
241#466—471no—
242#466—471no—
243#459—471no—
244#459—471no—
245#447—471no—
246#447—471no—
247#447—471no—
248#447D4711yescharacteristic, complemented
249C4×D8—471no—
250C8×D4—471no—
251C47D4×D811yescharacteristic, complemented, Sylow
252C22×D4—471no—
253C22×D4—471no—
254C22×D4—471no—
255C22×D4—941no—
256C22×D4—941no—
257C22×D4C2×D4711yescharacteristic, complemented
258C2×D8—471no—
259C2×D8—471no—
260C2×D8—471no—
261C2×D8—471no—
262C2×D8—471no—
263C2×D8—471no—
264C2×D8—471no—
265C2×D8—944no—
266C2×D8—944no—
267C2×D8C2×D4711yescharacteristic, complemented
268C2×D8C2×D4711yescharacteristic, complemented
269C22×C8—471no—
270C22×C8—471no—
271#127—471no—
272#127—471no—
273#121—471no—
274#121—471no—
275#121—471no—
276#121—941no—
277#121—941no—
278#121C2×D4711yescharacteristic, complemented
279#120—941no—
280#120—941no—
281#120—941no—
282#120—941no—
283C4×D4—471no—
284C4×D4—471no—
285C4×D4—471no—
286#107—471no—
287C4⋊C8—471no—
288#102—471no—
289#102—471no—
290#102—471no—
291#102—471no—
292#102C2×D4711yescharacteristic, complemented
293#102C2×D4711yescharacteristic, complemented
294C22⋊C8—471no—
295C22⋊C8C2×D4711yescharacteristic, complemented
296C4×C8—471no—
297C24—21no—
298C24—941no—
299C24—941no—
300C24—941no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—471no—
306C2×D4—471no—
307C2×D4—471no—
308C2×D4—471no—
309C2×D4—942no—
310C2×D4—941no—
311C2×D4—941no—
312C2×D4—941no—
313C2×D4—941no—
314C2×D4—941no—
315C2×D4—941no—
316C2×D4—941no—
317C2×D4—942no—
318C2×D4—942no—
319C2×D4—941no—
320C2×D4—941no—
321C2×D4—941no—
322C2×D4—1881no—
323C2×D4—1881no—
324C2×D4—1881no—
325C2×D4—1884no—
326C2×D4—1884no—
327C2×D4C22×D4711yescharacteristic
328C2×D4C22×D4711yescharacteristic
329C2×D4C22×D4711yescharacteristic
330C22×C4—471no—
331C22×C4—941no—
332C22×C4—941no—
333C22×C4C22×D4711yescharacteristic
334D8—22no—
335D8—41no—
336D8—474no—
337D8—942no—
338D8—942no—
339D8—942no—
340D8—942no—
341D8—942no—
342D8—1881no—
343C2×C8—471no—
344C2×C8—471no—
345C2×C8—942no—
346C2×C8—942no—
347C2×C8C22×D4711yescharacteristic
348C2×C8C22×D4711yescharacteristic
349C4⋊C4—471no—
350C4⋊C4—471no—
351C4⋊C4C22×D4711yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—471no—
354C22⋊C4—471no—
355C22⋊C4—941no—
356C22⋊C4—941no—
357C22⋊C4—941no—
358C22⋊C4—941no—
359C22⋊C4—941no—
360C42—471no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—42no—
365C23—42no—
366C23—81no—
367C23—471no—
368C23—941no—
369C23—941no—
370C23—941no—
371C23—3761no—
372C23—3761no—
373C23—3761no—
374C23—1882no—
375C23—1882no—
376C23—1882no—
377C23—1882no—
378C23—1882no—
379C23—1882no—
380C23D4×D4711yescharacteristic
381D4—21no—
382D4—21no—
383D4—21no—
384D4—21no—
385D4—21no—
386D4—42no—
387D4—42no—
388D4—474no—
389D4—472no—
390D4—941no—
391D4—941no—
392D4—941no—
393D4—941no—
394D4—941no—
395D4—3761no—
396D4—3761no—
397D4—1882no—
398D4—1882no—
399D4—1882no—
400D4—1882no—
401D4—1882no—
402D4—1882no—
403D4—1882no—
404D4—1882no—
405D4D4×D4712yescomplemented
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—471no—
410C2×C4—471no—
411C2×C4—471no—
412C2×C4—941no—
413C2×C4—941no—
414C2×C4—941no—
415C2×C4—1882no—
416C2×C4—1882no—
417C2×C4D4×D4711yescharacteristic
418C2×C4C23×D4711yescharacteristic
419C8—21no—
420C8—21no—
421C8—472no—
422C8—941no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—84no—
435C22—472no—
436C22—941no—
437C22—941no—
438C22—942no—
439C22—3764no—
440C22—3764no—
441C22—3764no—
442C22—1881no—
443C22—1881no—
444C22—1881no—
445C22—1881no—
446C22—1881no—
447C22—1881no—
448C22—1881no—
449C22—1881no—
450C22D8×D4712yescomplemented
451C22C2×D4×D4711yescharacteristic
452C4—21no—
453C4—41no—
454C4—472no—
455C4—941no—
456C4—941no—
457C4—1881no—
458C4C2×D4×D4711yescharacteristic
459C4#1309406911yescharacteristic
460C2—22no—
461C2—42no—
462C2—81no—
463C2—81no—
464C2—942no—
465C2—3761no—
466C2—3761no—
467C2—1882no—
468C2#1568975511yescharacteristic
469C2C2×D8×D4711yescharacteristic
470C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47D4×D8
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×#10625334C2semidirect
2. C2×D8×D47C2semidirect
3. #15689757C2semidirect
4. D4×C22⋊D47C2semidirect
5. #15689498C2semidirect
6. #15689358C2semidirect
7. #15689357C2semidirect
8. #15689317C2semidirect
9. #15689316C2semidirect
10. #15689259C2semidirect
11. #15689258C2semidirect
12. #15689255C2semidirect
13. #15689203C2semidirect
14. (C22⋊D47)⋊C8C2semidirect
15. C47×#447C2semidirect
16. C22×D188C22semidirect
19. C2×D4×D47C22semidirect
20. C2×D4×D47C22semidirect
21. C2×D376C22semidirect
22. C2×D376C22semidirect
25. C2×#10625334C22semidirect
26. C2×#10625334C22semidirect
27. C2×#10625334C22semidirect
28. C2×#10625334C22semidirect
30. C22×C47⋊C8C22semidirect
31. C2×C8×D47C22semidirect
32. #13094020C22semidirect
33. #13094020C22semidirect
34. #13093999C22semidirect
35. #13093998C22semidirect
38. #13093995C22semidirect
43. D4×Dic47C22semidirect
44. #13093986C22semidirect
46. #13093957C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093946C22semidirect
49. #13093946C22semidirect
50. #13093945C22semidirect
51. #13093944C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. C8×Dic47C22semidirect
54. C22×D4×C47C22semidirect
55. C2×D8×C47C22semidirect
56. C2×D8×C47C22semidirect
57. #121×C47C22semidirect
58. #102×C47C22semidirect
59. #102×C47C22semidirect
60. C22⋊C8×C47C22semidirect
111. #10625334D4semidirect
152. D4×C47C2×D4semidirect
166. C22⋊D47D8semidirect
179. D188C2×D4semidirect
186. C47⋊C8C2×D4semidirect
199. C22×C47C2×D8semidirect
215. C2×D47C2×D8semidirect
223. Dic47C2×D8semidirect
248. #447D47semidirect
251. C47D4×D8semidirect
257. C22×D4C2×D47semidirect
267. C2×D8C2×D47semidirect
268. C2×D8C2×D47semidirect
278. #121C2×D47semidirect
292. #102C2×D47semidirect
293. #102C2×D47semidirect
295. C22⋊C8C2×D47semidirect
405. D4D4×D47semidirect
450. C22D8×D47semidirect