Finite Group Databasebeta

← #20254870

Subgroups — #20254870

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
4D4×D188C211yesmaximal, characteristic, complemented
5#15689512C211yesmaximal, characteristic, complemented
6#15689377C211yesmaximal, characteristic, complemented
7#15689353C211yesmaximal, characteristic, complemented
8#15689338C211yesmaximal, characteristic, complemented
9#15689318C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11#15689269C211yesmaximal, characteristic, complemented
12#15689258C211yesmaximal, characteristic, complemented
13#15689258C211yesmaximal, characteristic, complemented
14#15689196C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic, complemented
17C22×D188—21no—
18C2×D4×D47C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic, complemented
20C2×D4×D47C2211yescharacteristic, complemented
21#13094048—24no—
22C2×#10625325C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic, complemented
24C2×#10625335C2211yescharacteristic, complemented
25C2×D376C2211yescharacteristic, complemented
26C2×D376C2211yescharacteristic, complemented
27C2×#10625334C2211yescharacteristic
28C2×#10625334C2211yescharacteristic, complemented
29C2×#10625334C2211yescharacteristic, complemented
30D8×D47—24no—
31C2×#10625324C2211yescharacteristic, complemented
32C2×C8×D47C2211yescharacteristic, complemented
33#13094021C2211yescharacteristic, complemented
34#13094012C2211yescharacteristic, complemented
35#13094008—21no—
36#13094004C2211yescharacteristic, complemented
37#13093999C2211yescharacteristic
38#13093999C2211yescharacteristic, complemented
39#13093999C2211yescharacteristic, complemented
40#13093998—21no—
41#13093998—21no—
42#13093994—21no—
43#13093994—21no—
44#13093994—21no—
45C4×D188C2211yescharacteristic
46C2×(C2×D47)⋊C4—21no—
47C4⋊(C47⋊C8)C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic, complemented
50#13093944C2211yescharacteristic, complemented
51#13093944C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54C2×D8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic, complemented
56C4×D4×C47C2211yescharacteristic, complemented
57#106×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic, complemented
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C23×D47—21no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C22×Dic47—21no—
73#10625352—22no—
74#10625352—41no—
75D4×D47—22no—
76D4×D47—22no—
77D4×D47—22no—
78D4×D47—41no—
79D4×D47—41no—
80D4×D47—41no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188—21no—
84C2×D188—21no—
85C2×D188—21no—
86C2×D188—44no—
87C2×D188D411yescharacteristic
88C2×D188C2311yescharacteristic
89C2×D188C2311yescharacteristic
90C2×D188C2311yescharacteristic
91C2×C4×D47C2311yescharacteristic
92C2×C4×D47C2311yescharacteristic
93C2×Dic94C2311yescharacteristic
94D8×C47D414yescomplemented
95C2×C8×C47C2311yescharacteristic
96C2×C8×C47C2311yescharacteristic
97C4⋊C4×C47C2311yescharacteristic
98C4⋊C4×C47C2311yescharacteristic
99C22⋊C4×C47—21no—
100C22⋊C4×C47—21no—
101C42×C47C2311yescharacteristic
102#10625335—22no—
103#10625334—22no—
104#10625334—22no—
105#10625334—22no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4D411yescharacteristic
113(C2×D47)⋊C4D411yescharacteristic
114C4⋊Dic47—21no—
115C4⋊Dic47D411yescharacteristic
116C2×C47⋊C8C2311yescharacteristic
117C2×C47⋊C8C2311yescharacteristic
118D376—22no—
119D376—41no—
120#10625325—22no—
121#10625325—41no—
122#10625324—22no—
123C8×D47—22no—
124C23×C47—21no—
125C23×C47—21no—
126C22×D47—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×C47C2×D412yes—
143D4×C47C2×D412yescomplemented
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—42no—
147C2×C4×C47—81no—
148C2×C4×C47C2×D411yescharacteristic
149C2×C4×C47C2×D411yescharacteristic
150C2×C4×C47C2411yescharacteristic
151C22⋊D47—42no—
152C22⋊D47—42no—
153C22⋊D47—42no—
154C22⋊D47—42no—
155C2×Dic47—21no—
156C2×Dic47—42no—
157C2×Dic47C2×D411yescharacteristic
158C2×Dic47C2×D411yescharacteristic
159D188—22no—
160D188—21no—
161D188—21no—
162D188—21no—
163D188—21no—
164D188—21no—
165D188—21no—
166D188—42no—
167D188—42no—
168D188—42no—
169D188—81no—
170D188—81no—
171C4×D47—21no—
172C4×D47—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—22no—
182C22×C47—22no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47C22×D411yescharacteristic
188C2×D47—21no—
189C2×D47—21no—
190C2×D47—21no—
191C2×D47—21no—
192C2×D47—21no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C2×D47—41no—
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×C47—41no—
210C4×C47C22×D411yescharacteristic
211C4×C47H(5,𝔽2)11yescharacteristic
212Dic47—21no—
213Dic47—21no—
214Dic47—41no—
215#3264—471nomaximal, Sylow
216C2×C47—42no—
217C2×C47—42no—
218C2×C47D4211yescharacteristic
219C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C47#57611yescharacteristic
221D47—22no—
222D47—41no—
223D47—81no—
224D47—81no—
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#459—471no—
235#450—471no—
236#449—471no—
237#447—471no—
238#447—471no—
239#442D4711yescharacteristic, complemented
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—471no—
256C2×D8—944no—
257C2×D8C2×D4711yescharacteristic
258C2×M16—471no—
259C22×C8—471no—
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×D4C2×D4711yescharacteristic, complemented
274C4×D4C2×D4711yescharacteristic, complemented
275C2×C22⋊C4—941no—
276#106C2×D4711yescharacteristic, complemented
277C4⋊C8—471no—
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#97C2×D4711yescharacteristic, complemented
287C24—941no—
288C24—941no—
289C24—941no—
290#41—942no—
291#41—1881no—
292C2×Q8—471no—
293C2×D4—471no—
294C2×D4—471no—
295C2×D4—471no—
296C2×D4—471no—
297C2×D4—941no—
298C2×D4—941no—
299C2×D4—941no—
300C2×D4—941no—
301C2×D4—941no—
302C2×D4—941no—
303C2×D4—942no—
304C2×D4—942no—
305C2×D4—942no—
306C2×D4—941no—
307C2×D4—941no—
308C2×D4—941no—
309C2×D4—1884no—
310C2×D4—1881no—
311C2×D4—1881no—
312C2×D4—1881no—
313C2×D4C22×D4711yescharacteristic
314C2×D4C22×D4711yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—471no—
318C22×C4—471no—
319C22×C4—941no—
320SD16—942no—
321SD16—942no—
322SD16—1881no—
323D8—942no—
324D8—942no—
325D8—942no—
326D8—942no—
327D8—1881no—
328D8D18814yescomplemented
329M16—942no—
330C2×C8—471no—
331C2×C8—471no—
332C2×C8—942no—
333C2×C8C22×D4711yescharacteristic
334C2×C8C22×D4711yescharacteristic
335C4⋊C4—471no—
336C4⋊C4—941no—
337C4⋊C4C22×D4711yescharacteristic
338C4⋊C4C22×D4711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—471no—
342C22⋊C4—471no—
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—471no—
353C23—471no—
354C23—941no—
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—942no—
371D4—941no—
372D4—941no—
373D4—941no—
374D4—941no—
375D4—941no—
376D4—941no—
377D4—3761no—
378D4—3761no—
379D4—1882no—
380D4—1882no—
381D4—1882no—
382D4—1882no—
383D4—1882no—
384D4—1882no—
385D4—1882no—
386D4C2×D18812yes—
387D4C2×D18812yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—471no—
393C2×C4—471no—
394C2×C4—941no—
395C2×C4—941no—
396C2×C4—941no—
397C2×C4—941no—
398C2×C4—941no—
399C2×C4—1882no—
400C2×C4D4×D4711yescharacteristic
401C2×C4D4×D4711yescharacteristic
402C2×C4C23×D4711yescharacteristic
403C8—21no—
404C8—941no—
405C8—941no—
406C8C2×D18812yescomplemented
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—472no—
414C22—941no—
415C22—941no—
416C22—941no—
417C22—941no—
418C22—941no—
419C22—3764no—
420C22—3764no—
421C22—3764no—
422C22—1881no—
423C22—1881no—
424C22—1881no—
425C22—1881no—
426C22—1881no—
427C22—1881no—
428C22—1881no—
429C22—1881no—
430C22—1881no—
431C22C2×D4×D4711yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—941no—
437C4—941no—
438C4—1881no—
439C4C22×D18811yescharacteristic
440C4#1309407011yescharacteristic
441C2—42no—
442C2—42no—
443C2—942no—
444C2—3761no—
445C2—3761no—
446C2—3761no—
447C2—1881no—
448C2D4×D18811yescharacteristic
449C2AGL(1,ℤ/8)×D4711yescharacteristic
450C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3264
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C2×D8×D47C2semidirect
3. #15689768C2semidirect
4. D4×D188C2semidirect
5. #15689512C2semidirect
6. #15689377C2semidirect
7. #15689353C2semidirect
8. #15689338C2semidirect
9. #15689318C2semidirect
10. #15689275C2semidirect
11. #15689269C2semidirect
12. #15689258C2semidirect
13. #15689258C2semidirect
14. #15689196C2semidirect
15. C47×#442C2semidirect
16. C2×#10625352C22semidirect
19. C2×D4×D47C22semidirect
20. C2×D4×D47C22semidirect
22. C2×#10625325C22semidirect
23. C2×#10625325C22semidirect
24. C2×#10625335C22semidirect
25. C2×D376C22semidirect
26. C2×D376C22semidirect
28. C2×#10625334C22semidirect
29. C2×#10625334C22semidirect
31. C2×#10625324C22semidirect
32. C2×C8×D47C22semidirect
33. #13094021C22semidirect
34. #13094012C22semidirect
36. #13094004C22semidirect
38. #13093999C22semidirect
39. #13093999C22semidirect
47. C4⋊(C47⋊C8)C22semidirect
48. #13093947C22semidirect
49. #13093944C22semidirect
50. #13093944C22semidirect
51. #13093944C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. (C2×D47)⋊C8C22semidirect
55. C4×D4×C47C22semidirect
56. C4×D4×C47C22semidirect
57. #106×C47C22semidirect
58. #102×C47C22semidirect
59. #102×C47C22semidirect
60. #97×C47C22semidirect
94. D8×C47D4semidirect
143. D4×C47C2×D4semidirect
178. C8×C47C2×D4semidirect
205. C2×D47AGL(1,ℤ/8)semidirect
239. #442D47semidirect
241. C47#3264semidirect
273. C4×D4C2×D47semidirect
274. C4×D4C2×D47semidirect
276. #106C2×D47semidirect
282. #102C2×D47semidirect
283. #102C2×D47semidirect
286. #97C2×D47semidirect
328. D8D188semidirect
387. D4C2×D188semidirect
406. C8C2×D188semidirect