Finite Group Databasebeta

← #20254874

Subgroups — #20254874

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
2C2×D8×D47C211yesmaximal, characteristic, complemented
3#15689766C211yesmaximal, characteristic, complemented
4D4×D188C211yesmaximal, characteristic, complemented
5#15689513C211yesmaximal, characteristic, complemented
6#15689375C211yesmaximal, characteristic, complemented
7#15689355C211yesmaximal, characteristic, complemented
8#15689319C211yesmaximal, characteristic, complemented
9#15689272C211yesmaximal, characteristic, complemented
10#15689271C211yesmaximal, characteristic, complemented
11#15689258C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13#15689233C211yesmaximal, characteristic, complemented
14#15689193C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic, complemented
17C22×D188—21no—
18C2×D4×D47C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic, complemented
20C2×D4×D47C2211yescharacteristic, complemented
21#13094051—24no—
22C2×#10625336C2211yescharacteristic, complemented
23C2×#10625336C2211yescharacteristic, complemented
24C2×D376C2211yescharacteristic, complemented
25C2×D376C2211yescharacteristic, complemented
26C2×#10625334C2211yescharacteristic
27C2×#10625334C2211yescharacteristic, complemented
28C2×#10625334C2211yescharacteristic, complemented
29D8×D47—24no—
30C2×#10625324C2211yescharacteristic, complemented
31C2×C8×D47C2211yescharacteristic, complemented
32#13094021C2211yescharacteristic, complemented
33#13094006—21no—
34#13094000C2211yescharacteristic, complemented
35#13093999C2211yescharacteristic
36#13093999C2211yescharacteristic, complemented
37#13093998—21no—
38#13093997—21no—
39#13093995C2211yescharacteristic, complemented
40#13093994—21no—
41#13093994—21no—
42#13093994—21no—
43C4×D188C2211yescharacteristic
44C4×D188C2211yescharacteristic, complemented
45C22⋊C4×D47—21no—
46#13093955C2211yescharacteristic, complemented
47#13093946C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic, complemented
49#13093945C2211yescharacteristic, complemented
50#13093944C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093935C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic, complemented
58C4⋊C8×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C23×D47—21no—
64C2×Q8×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72#10625354—22no—
73#10625354—41no—
74D4×D47—22no—
75D4×D47—22no—
76D4×D47—22no—
77D4×D47—41no—
78D4×D47—41no—
79D4×D47—41no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188—21no—
84C2×D188—21no—
85C2×D188—44no—
86C2×D188D411yescharacteristic
87C2×D188C2311yescharacteristic
88C2×D188C2311yescharacteristic
89C2×D188C2311yescharacteristic
90C2×C4×D47—21no—
91C2×C4×D47—21no—
92C2×C4×D47C2311yescharacteristic
93C2×C4×D47C2311yescharacteristic
94SD16×C47—22no—
95D8×C47—22no—
96C2×C8×C47C2311yescharacteristic
97C2×C8×C47C2311yescharacteristic
98C4⋊C4×C47C2311yescharacteristic
99C22⋊C4×C47—21no—
100C22⋊C4×C47—21no—
101C22⋊C4×C47—21no—
102C42×C47C2311yescharacteristic
103C22⋊Dic47—21no—
104#10625336—22no—
105#10625336—41no—
106#10625334—22no—
107#10625334—41no—
108#10625334D414yescomplemented
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113(C2×D47)⋊C4D411yescharacteristic
114(C2×D47)⋊C4D411yescharacteristic
115C4⋊Dic47D411yescharacteristic
116C4⋊Dic47C2311yescharacteristic
117Dic47⋊C4—21no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120D376—22no—
121D376—22no—
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
140Q8×C47—21no—
141Q8×C47—21no—
142D4×C47—21no—
143D4×C47—21no—
144D4×C47—21no—
145D4×C47C2×D412yes—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—42no—
149C2×C4×C47C2×D411yescharacteristic
150C2×C4×C47C2×D411yescharacteristic
151C2×C4×C47C2411yescharacteristic
152C22⋊D47—42no—
153C22⋊D47—42no—
154C22⋊D47—42no—
155C22⋊D47—81no—
156C2×Dic47—21no—
157C2×Dic47C2×D411yescharacteristic
158C2×Dic47C2×D411yescharacteristic
159D188—22no—
160D188—21no—
161D188—21no—
162D188—21no—
163D188—21no—
164D188—21no—
165D188—42no—
166D188—42no—
167D188—42no—
168D188—42no—
169D188—81no—
170D188C2×D412yescomplemented
171C4×D47—21no—
172C4×D47—21no—
173C4×D47—21no—
174C4×D47—21no—
175C4×D47—42no—
176C4×D47—81no—
177C8×C47—21no—
178C8×C47—21no—
179C47⋊C8—21no—
180C47⋊C8C2×D412yescomplemented
181C22×C47—22no—
182C22×C47—41no—
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—22no—
192C2×D47—21no—
193C2×D47—21no—
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—81no—
218C2×C47D4211yescharacteristic
219C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C47#57611yescharacteristic
221D47—22no—
222D47—41no—
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#465—471no—
233#463D4711yescharacteristic, complemented
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—944no—
257C2×D8C2×D4711yescharacteristic
258C2×M16—471no—
259C22×C8—471no—
260#127—471no—
261#124C2×D4711yescharacteristic, complemented
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×D4C2×D4711yescharacteristic, complemented
275C2×C22⋊C4—941no—
276#106—471no—
277C4⋊C8C2×D4711yescharacteristic, complemented
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—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—471no—
317C22×C4—471no—
318C22×C4—941no—
319C22×C4—941no—
320SD16—22no—
321SD16—942no—
322SD16—1881no—
323D8—22no—
324D8—474no—
325D8—942no—
326D8—942no—
327D8—942no—
328D8—1881no—
329M16—942no—
330C2×C8—471no—
331C2×C8—471no—
332C2×C8—942no—
333C2×C8C22×D4711yescharacteristic
334C2×C8C22×D4711yescharacteristic
335C4⋊C4—471no—
336C4⋊C4—471no—
337C4⋊C4—941no—
338C4⋊C4C22×D4711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—471no—
343C22⋊C4—471no—
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—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—472no—
372D4—942no—
373D4—941no—
374D4—941no—
375D4—941no—
376D4—941no—
377D4—941no—
378D4—3761no—
379D4—3761no—
380D4—1882no—
381D4—1882no—
382D4—1882no—
383D4—1882no—
384D4—1882no—
385D4—1882no—
386D4—1882no—
387D4D4×D4712yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
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×C4D4×D4711yescharacteristic
401C2×C4D4×D4711yescharacteristic
402C2×C4C23×D4711yescharacteristic
403C8—21no—
404C8—21no—
405C8—472no—
406C8—941no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—472no—
414C22—941no—
415C22—941no—
416C22—941no—
417C22—942no—
418C22—941no—
419C22—941no—
420C22—3764no—
421C22—3764no—
422C22—3764no—
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—
439C4C2×D4×D4711yescharacteristic
440C4#1309407011yescharacteristic
441C2—42no—
442C2—81no—
443C2—942no—
444C2—3761no—
445C2—3761no—
446C2—1881no—
447C2—1882no—
448C2#1568975711yescharacteristic
449C2AGL(1,ℤ/8)×D4711yescharacteristic
450C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3264
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. C2×D8×D47C2semidirect
3. #15689766C2semidirect
4. D4×D188C2semidirect
5. #15689513C2semidirect
6. #15689375C2semidirect
7. #15689355C2semidirect
8. #15689319C2semidirect
9. #15689272C2semidirect
10. #15689271C2semidirect
11. #15689258C2semidirect
12. #15689255C2semidirect
13. #15689233C2semidirect
14. #15689193C2semidirect
15. C47×#463C2semidirect
16. C2×#10625354C22semidirect
19. C2×D4×D47C22semidirect
20. C2×D4×D47C22semidirect
22. C2×#10625336C22semidirect
23. C2×#10625336C22semidirect
24. C2×D376C22semidirect
25. C2×D376C22semidirect
27. C2×#10625334C22semidirect
28. C2×#10625334C22semidirect
30. C2×#10625324C22semidirect
31. C2×C8×D47C22semidirect
32. #13094021C22semidirect
34. #13094000C22semidirect
36. #13093999C22semidirect
39. #13093995C22semidirect
44. C4×D188C22semidirect
46. #13093955C22semidirect
47. #13093946C22semidirect
48. #13093946C22semidirect
49. #13093945C22semidirect
50. #13093944C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093935C22semidirect
54. C2×SD16×C47C22semidirect
56. #124×C47C22semidirect
57. C4×D4×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #103×C47C22semidirect
60. #102×C47C22semidirect
108. #10625334D4semidirect
170. D188C2×D4semidirect
180. C47⋊C8C2×D4semidirect
205. C2×D47AGL(1,ℤ/8)semidirect
233. #463D47semidirect
241. C47#3264semidirect
250. C2×SD16C2×D47semidirect
261. #124C2×D47semidirect
274. C4×D4C2×D47semidirect
277. C4⋊C8C2×D47semidirect
278. #103C2×D47semidirect
283. #102C2×D47semidirect