Finite Group Databasebeta

← #20254865

Subgroups — #20254865

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×#13094051C211yesmaximal, characteristic, complemented
2C22×D376C211yesmaximal, characteristic, complemented
3#15689764C211yesmaximal, characteristic, complemented
4#15689757C211yesmaximal, characteristic, complemented
5#15689509C211yesmaximal, characteristic, complemented
6#15689377C211yesmaximal, characteristic, complemented
7#15689341C211yesmaximal, characteristic, complemented
8#15689317C211yesmaximal, characteristic, complemented
9#15689273C211yesmaximal, characteristic, complemented
10#15689271C211yesmaximal, characteristic, complemented
11#15689258C211yesmaximal, characteristic, complemented
12#15689256C211yesmaximal, characteristic, complemented
13#15689234C211yesmaximal, characteristic, complemented
14#15689194C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic, complemented
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic, complemented
19C2×D4×D47—21no—
20C2×D4×D47C2211yescharacteristic, complemented
21#13094051—24no—
22C2×#10625336C2211yescharacteristic, complemented
23C2×#10625336C2211yescharacteristic, complemented
24C2×D376—24no—
25C2×D376C2211yescharacteristic
26C2×D376C2211yescharacteristic
27C2×D376C2211yescharacteristic, complemented
28C2×D376C2211yescharacteristic, complemented
29C2×#10625334C2211yescharacteristic, complemented
30C2×#10625334C2211yescharacteristic, complemented
31C2×#10625324C2211yescharacteristic, complemented
32#13094020C2211yescharacteristic, complemented
33#13094013C2211yescharacteristic, complemented
34#13094009—21no—
35#13093999—21no—
36#13093999C2211yescharacteristic, complemented
37#13093999C2211yescharacteristic, complemented
38#13093997—21no—
39#13093994—21no—
40#13093994—21no—
41#13093992—21no—
42#13093986C2211yescharacteristic, complemented
43#13093986C2211yescharacteristic, complemented
44C4×C22⋊D47C2211yescharacteristic
45C22⋊C4×D47—21no—
46Dic47⋊C8C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic, complemented
50#13093944C2211yescharacteristic, complemented
51C22⋊(C47⋊C8)C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093934C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C22×C8×C47C2211yescharacteristic, complemented
56C22⋊Q8×C47C2211yescharacteristic, complemented
57#121×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C23×D47—21no—
64C2×Q8×C47C2311yescharacteristic
65C2×D4×C47—21no—
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47D411yescharacteristic
72#10625354—22no—
73#10625354—41no—
74D4×D47—22no—
75D4×D47—41no—
76D4×D47—44no—
77C2×D188—22no—
78C2×D188—22no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188—21no—
84C2×D188—41no—
85C2×D188—41no—
86C2×D188C2311yescharacteristic
87C2×D188C2311yescharacteristic
88C2×D188C2311yescharacteristic
89C2×D188C2311yescharacteristic
90C2×C4×D47—21no—
91C2×C4×D47—21no—
92C2×C4×D47—21no—
93C2×C4×D47C2311yescharacteristic
94SD16×C47—22no—
95C2×C8×C47—22no—
96C2×C8×C47C2311yescharacteristic
97C2×C8×C47C2311yescharacteristic
98C4⋊C4×C47—21no—
99C4⋊C4×C47C2311yescharacteristic
100C4⋊C4×C47C2311yescharacteristic
101C22⋊C4×C47—21no—
102C22⋊C4×C47—21no—
103C22⋊Dic47D411yescharacteristic
104#10625336—22no—
105#10625336—41no—
106#10625334—22no—
107#10625334—41no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113(C2×D47)⋊C4—21no—
114(C2×D47)⋊C4D411yescharacteristic
115Dic47⋊C4D411yescharacteristic
116C4×Dic47C2311yescharacteristic
117C2×C47⋊C8C2311yescharacteristic
118C2×C47⋊C8C2311yescharacteristic
119D376—22no—
120D376—22no—
121D376—22no—
122D376D414yescomplemented
123#10625324—22no—
124C23×C47—21no—
125C23×C47C2×D411yescharacteristic
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—42no—
133C22×D47—42no—
134C22×D47—42no—
135C22×D47—42no—
136C22×D47—81no—
137C22×D47—81no—
138C22×D47—81no—
139C22×D47C2×D411yescharacteristic
140Q8×C47—21no—
141Q8×C47—21no—
142D4×C47—21no—
143D4×C47—21no—
144D4×C47—42no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47C2×D411yescharacteristic
151C2×C4×C47C2411yescharacteristic
152C22⋊D47—22no—
153C22⋊D47—42no—
154C22⋊D47—42no—
155C22⋊D47—81no—
156C2×Dic47C2×D411yescharacteristic
157C2×Dic47C2×D411yescharacteristic
158C2×Dic47C2×D411yescharacteristic
159D188—21no—
160D188—21no—
161D188—21no—
162D188—21no—
163D188—21no—
164D188—21no—
165D188—42no—
166D188—42no—
167D188—42no—
168D188—42no—
169D188—81no—
170D188C2×D412yes—
171D188C2×D412yescomplemented
172C4×D47—21no—
173C4×D47—21no—
174C4×D47—42no—
175C4×D47—42no—
176C4×D47—81no—
177C8×C47—21no—
178C8×C47C2×D412yescomplemented
179C47⋊C8—21no—
180C47⋊C8—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47AGL(1,ℤ/8)12yescomplemented
187C22×C47C22×D411yescharacteristic
188C2×D47—21no—
189C2×D47—22no—
190C2×D47—22no—
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—41no—
203C2×D47—84no—
204C2×D47—84no—
205C2×D47—84no—
206C4×C47—21no—
207C4×C47—41no—
208C4×C47—41no—
209C4×C47—41no—
210C4×C47C22×D411yescharacteristic
211C4×C47H(5,𝔽2)11yescharacteristic
212Dic47—21no—
213Dic47—21no—
214Dic47—21no—
215#3264—471nomaximal, Sylow
216C2×C47—22no—
217C2×C47—81no—
218C2×C47D4211yescharacteristic
219C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C47#57611yescharacteristic
221D47—41no—
222D47—42no—
223D47—42no—
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#465D4711yescharacteristic, complemented
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—471no—
245C22×D4—471no—
246C22×D4—941no—
247AGL(1,ℤ/8)—944no—
248C2×SD16—471no—
249C2×SD16—471no—
250C2×SD16C2×D4711yescharacteristic, complemented
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×C8C2×D4711yescharacteristic, complemented
260#127—471no—
261#124—471no—
262#123—941no—
263C22⋊Q8C2×D4711yescharacteristic, complemented
264#121—471no—
265#121—471no—
266#121—941no—
267#121—941no—
268#121C2×D4711yescharacteristic
269#120—941no—
270#120—941no—
271#120—941no—
272C4×D4—471no—
273C4×D4—471no—
274C4×D4—471no—
275C2×C22⋊C4—941no—
276#106C2×D4711yescharacteristic, complemented
277C4⋊C8—471no—
278#103C2×D4711yescharacteristic, complemented
279#102—471no—
280#102—471no—
281#102—471no—
282#102—471no—
283#102C2×D4711yescharacteristic, complemented
284C22⋊C8—471no—
285C22⋊C8—471no—
286#97—471no—
287C24—941no—
288C24—941no—
289C24—941no—
290#41—942no—
291#41—1881no—
292C2×Q8C22×D4711yescharacteristic
293C2×D4—21no—
294C2×D4—471no—
295C2×D4—471no—
296C2×D4—471no—
297C2×D4—471no—
298C2×D4—471no—
299C2×D4—942no—
300C2×D4—942no—
301C2×D4—941no—
302C2×D4—941no—
303C2×D4—941no—
304C2×D4—941no—
305C2×D4—941no—
306C2×D4—941no—
307C2×D4—942no—
308C2×D4—941no—
309C2×D4—941no—
310C2×D4—1881no—
311C2×D4—1881no—
312C2×D4—1881no—
313C2×D4—1884no—
314C2×D4C22×D4711yescharacteristic
315C22×C4—471no—
316C22×C4—941no—
317C22×C4—941no—
318C22×C4—941no—
319C22×C4C22×D4711yescharacteristic
320SD16—22no—
321SD16—942no—
322SD16—1881no—
323D8—474no—
324D8—942no—
325D8—942no—
326D8—942no—
327D8—942no—
328D8—1881no—
329M16—942no—
330C2×C8—22no—
331C2×C8—471no—
332C2×C8—471no—
333C2×C8C22×D4711yescharacteristic
334C2×C8C22×D4711yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—471no—
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—
349C42—471no—
350C23—21no—
351C23—471no—
352C23—941no—
353C23—941no—
354C23—941no—
355C23—941no—
356C23—3761no—
357C23—3761no—
358C23—3761no—
359C23—1882no—
360C23—1882no—
361C23—1882no—
362C23—1882no—
363C23—1882no—
364C23—1882no—
365C23D4×D4711yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—42no—
371D4—472no—
372D4—472no—
373D4—942no—
374D4—941no—
375D4—941no—
376D4—941no—
377D4—941no—
378D4—941no—
379D4—941no—
380D4—3761no—
381D4—3761no—
382D4—1882no—
383D4—1882no—
384D4—1882no—
385D4—1882no—
386D4—1882no—
387D4—1882no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—471no—
394C2×C4—471no—
395C2×C4—471no—
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—
406C8D4×D4712yescomplemented
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—941no—
413C22—942no—
414C22—942no—
415C22—941no—
416C22—941no—
417C22—3764no—
418C22—3764no—
419C22—3764no—
420C22—1881no—
421C22—1881no—
422C22—1881no—
423C22—1881no—
424C22—1881no—
425C22—1881no—
426C22—1881no—
427C22—1881no—
428C22—1881no—
429C22—1881no—
430C22#1309405112yescomplemented
431C22C2×D4×D4711yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—941no—
437C4—941no—
438C4—941no—
439C4C2×D4×D4711yescharacteristic
440C4#1309407011yescharacteristic
441C2—22no—
442C2—81no—
443C2—3761no—
444C2—3761no—
445C2—1881no—
446C2—1882no—
447C2—1882no—
448C2#1568975711yescharacteristic
449C2C2×#1309405111yescharacteristic
450C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3264
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. C22×D376C2semidirect
3. #15689764C2semidirect
4. #15689757C2semidirect
5. #15689509C2semidirect
6. #15689377C2semidirect
7. #15689341C2semidirect
8. #15689317C2semidirect
9. #15689273C2semidirect
10. #15689271C2semidirect
11. #15689258C2semidirect
12. #15689256C2semidirect
13. #15689234C2semidirect
14. #15689194C2semidirect
15. C47×#465C2semidirect
16. C2×#10625354C22semidirect
18. C22×D188C22semidirect
20. C2×D4×D47C22semidirect
22. C2×#10625336C22semidirect
23. C2×#10625336C22semidirect
27. C2×D376C22semidirect
28. C2×D376C22semidirect
29. C2×#10625334C22semidirect
30. C2×#10625334C22semidirect
31. C2×#10625324C22semidirect
32. #13094020C22semidirect
33. #13094013C22semidirect
36. #13093999C22semidirect
37. #13093999C22semidirect
42. #13093986C22semidirect
43. #13093986C22semidirect
46. Dic47⋊C8C22semidirect
47. #13093944C22semidirect
48. #13093944C22semidirect
49. #13093944C22semidirect
50. #13093944C22semidirect
51. C22⋊(C47⋊C8)C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093934C22semidirect
54. C2×SD16×C47C22semidirect
55. C22×C8×C47C22semidirect
56. C22⋊Q8×C47C22semidirect
58. #106×C47C22semidirect
59. #103×C47C22semidirect
60. #102×C47C22semidirect
122. D376D4semidirect
171. D188C2×D4semidirect
178. C8×C47C2×D4semidirect
186. C22×C47AGL(1,ℤ/8)semidirect
232. #465D47semidirect
241. C47#3264semidirect
250. C2×SD16C2×D47semidirect
259. C22×C8C2×D47semidirect
263. C22⋊Q8C2×D47semidirect
276. #106C2×D47semidirect
278. #103C2×D47semidirect
283. #102C2×D47semidirect
406. C8D4×D47semidirect
430. C22#13094051semidirect