Finite Group Databasebeta

← #20254882

Subgroups — #20254882

Order 6016.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C211yesmaximal, characteristic, complemented
2C2×SD16×D47C211yesmaximal, characteristic, complemented
3#15689781C211yesmaximal, characteristic, complemented
4#15689758C211yesmaximal, characteristic, complemented
5#15689366C211yesmaximal, characteristic, complemented
6#15689356C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689320C211yesmaximal, characteristic, complemented
9#15689272C211yesmaximal, characteristic, complemented
10#15689265C211yesmaximal, characteristic, complemented
11#15689260C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13#15689225C211yesmaximal, characteristic, complemented
14#15689196C211yesmaximal, characteristic, complemented
15C47×#496C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic, complemented
17C2×Q8×D47C2211yescharacteristic, complemented
18C2×D4×D47—21no—
19C2×D4×D47C2211yescharacteristic
20C2×D4×D47C2211yescharacteristic
21#13094048—24no—
22C2×#10625325C2211yescharacteristic
23C2×#10625335C2211yescharacteristic, complemented
24C2×#10625335C2211yescharacteristic, complemented
25C2×#10625336C2211yescharacteristic
26SD16×D47—24no—
27C2×#10625334C2211yescharacteristic
28C2×#10625324C2211yescharacteristic, complemented
29C2×C8×D47C2211yescharacteristic, complemented
30#13094010—21no—
31#13094001—21no—
32#13094000C2211yescharacteristic, complemented
33#13093997—21no—
34#13093995—21no—
35#13093995C2211yescharacteristic
36#13093995C2211yescharacteristic
37#13093995C2211yescharacteristic, complemented
38#13093992—21no—
39#13093992—21no—
40C4×Dic94C2211yescharacteristic, complemented
41C4×D188C2211yescharacteristic
42C4×D188C2211yescharacteristic
43(C22⋊D47)⋊C4—21no—
44#13093958C2211yescharacteristic, complemented
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46#13093949C2211yescharacteristic, complemented
47#13093948C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic
49#13093945C2211yescharacteristic, complemented
50#13093945C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×SD16×C47C2211yescharacteristic, complemented
56C2×D8×C47C2211yescharacteristic, complemented
57C2×D8×C47C2211yescharacteristic, complemented
58#127×C47C2211yescharacteristic
59#124×C47C2211yescharacteristic, complemented
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C2×D4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C22×Dic47—21no—
76Q8×D47—22no—
77Q8×D47—41no—
78#10625352—22no—
79#10625352—41no—
80D4×D47—22no—
81D4×D47—22no—
82D4×D47—41no—
83D4×D47—41no—
84D4×D47—44no—
85C2×D188D411yescharacteristic
86C2×D188C2311yescharacteristic
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47C2311yescharacteristic
90C2×C4×D47C2311yescharacteristic
91C2×Dic94—21no—
92C2×Dic94C2311yescharacteristic
93SD16×C47—22no—
94SD16×C47—41no—
95D8×C47—22no—
96D8×C47—41no—
97C2×C8×C47C2311yescharacteristic
98C2×C8×C47C2311yescharacteristic
99C22⋊C4×C47—21no—
100C22⋊C4×C47—21no—
101C42×C47C2311yescharacteristic
102C22⋊Dic47—21no—
103C22⋊Dic47—21no—
104C22⋊Dic47—21no—
105#10625336—22no—
106#10625335—22no—
107#10625335—22no—
108#10625334—22no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4D411yescharacteristic
112(C2×D47)⋊C4D411yescharacteristic
113C4⋊Dic47D411yescharacteristic
114C4⋊Dic47C2311yescharacteristic
115C4⋊Dic47C2311yescharacteristic
116Dic47⋊C4—21no—
117Dic47⋊C4—21no—
118C4×Dic47—21no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121#10625325D414yescomplemented
122#10625324—22no—
123C8×D47—22no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C22×D47—21no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—81no—
133C22×D47—81no—
134C22×D47C2×D411yescharacteristic
135C22×D47C2×D411yescharacteristic
136Q8×C47—21no—
137Q8×C47—21no—
138D4×C47—21no—
139D4×C47—21no—
140D4×C47—21no—
141D4×C47—21no—
142D4×C47—21no—
143D4×C47—21no—
144D4×C47—42no—
145D4×C47—81no—
146C2×C4×C47—21no—
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2×D411yescharacteristic
149C2×C4×C47C2411yescharacteristic
150C22⋊D47—42no—
151C22⋊D47—42no—
152C22⋊D47—42no—
153C22⋊D47—42no—
154C22⋊D47—42no—
155C22⋊D47—42no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—42no—
160C2×Dic47C2×D411yescharacteristic
161C2×Dic47C2×D411yescharacteristic
162D188—22no—
163D188—21no—
164D188C2×D412yes—
165C4×D47—21no—
166C4×D47—21no—
167C4×D47—21no—
168C4×D47—21no—
169C4×D47—42no—
170C4×D47—42no—
171Dic94—21no—
172Dic94—42no—
173Dic94C2×D412yescomplemented
174C8×C47—21no—
175C8×C47C2×D412yescomplemented
176C47⋊C8—21no—
177C47⋊C8—21no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
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—84no—
197C2×D47—84no—
198C2×D47AGL(1,ℤ/8)12yescomplemented
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—41no—
202C4×C47C22×D411yescharacteristic
203C4×C47H(5,𝔽2)11yescharacteristic
204Dic47—22no—
205Dic47—21no—
206Dic47—21no—
207Dic47—41no—
208Dic47—41no—
209#3265—471nomaximal, Sylow
210C2×C47—81no—
211C2×C47—81no—
212C2×C47—81no—
213C2×C47D4211yescharacteristic
214C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C47#57711yescharacteristic
216D47—22no—
217D47—41no—
218D47—42no—
219C2×AGL(1,ℤ/8)—471no—
220C22×SD16—471no—
221#548—471no—
222D42—471no—
223#496D4711yescharacteristic, complemented
224#468—471no—
225#466—471no—
226#463—471no—
227#460—471no—
228#450—471no—
229#449—471no—
230#448—471no—
231#447—471no—
232#440—471no—
233#435—471no—
234C47#326511yescharacteristic, complemented, Sylow
235C2×#41—471no—
236C22×Q8—471no—
237C22×D4—471no—
238C22×D4—471no—
239C22×D4—941no—
240AGL(1,ℤ/8)—944no—
241C2×SD16—471no—
242C2×SD16—471no—
243C2×SD16—471no—
244C2×SD16—471no—
245C2×SD16—944no—
246C2×SD16C2×D4711yescharacteristic, complemented
247C2×SD16C2×D4711yescharacteristic, complemented
248C2×D8—471no—
249C2×D8C2×D4711yescharacteristic, complemented
250C2×D8C2×D4711yescharacteristic, complemented
251C2×M16—471no—
252C22×C8—471no—
253#127C2×D4711yescharacteristic
254#124—941no—
255#124C2×D4711yescharacteristic, complemented
256C22⋊Q8—471no—
257C22⋊Q8—941no—
258#121—471no—
259#121—471no—
260#121—471no—
261#121—941no—
262#121—941no—
263#120—941no—
264#120—941no—
265C4×Q8—471no—
266C4×D4—471no—
267C4×D4—471no—
268C4×D4—941no—
269#107—471no—
270C4⋊C8—471no—
271#103—471no—
272#103—471no—
273#102—471no—
274#102—471no—
275#102—471no—
276#102—471no—
277C22⋊C8—471no—
278C22⋊C8—471no—
279#97C2×D4711yescharacteristic, complemented
280C24—941no—
281C24—941no—
282#41—942no—
283#41—1881no—
284C2×Q8—471no—
285C2×Q8—941no—
286C2×Q8—942no—
287C2×Q8—1881no—
288C2×Q8C22×D4711yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—471no—
292C2×D4—471no—
293C2×D4—941no—
294C2×D4—941no—
295C2×D4—942no—
296C2×D4—942no—
297C2×D4—941no—
298C2×D4—941no—
299C2×D4—941no—
300C2×D4—941no—
301C2×D4—1881no—
302C2×D4—1881no—
303C2×D4—1884no—
304C2×D4C22×D4711yescharacteristic
305C2×D4C22×D4711yescharacteristic
306C2×D4C22×D4711yescharacteristic
307C22×C4—471no—
308C22×C4—471no—
309C22×C4—941no—
310C22×C4—941no—
311C22×C4—941no—
312SD16—22no—
313SD16—41no—
314SD16—474no—
315SD16—942no—
316SD16—942no—
317SD16—942no—
318D8—22no—
319D8—41no—
320D8—942no—
321M16—942no—
322C2×C8—471no—
323C2×C8—471no—
324C2×C8—942no—
325C2×C8C22×D4711yescharacteristic
326C2×C8C22×D4711yescharacteristic
327C4⋊C4—471no—
328C4⋊C4—471no—
329C4⋊C4—471no—
330C4⋊C4—941no—
331C4⋊C4—941no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—471no—
335C22⋊C4—471no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C22⋊C4—941no—
339C22⋊C4—941no—
340C22⋊C4—941no—
341C42—941no—
342C42C22×D4711yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—471no—
347C23—471no—
348C23—941no—
349C23—3761no—
350C23—3761no—
351C23—1882no—
352C23—1882no—
353C23—1882no—
354C23—1882no—
355Q8—21no—
356Q8—21no—
357Q8—472no—
358Q8—941no—
359Q8—1882no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—81no—
368D4—472no—
369D4—942no—
370D4—941no—
371D4—1882no—
372D4—1882no—
373D4—1882no—
374D4—1882no—
375D4—1882no—
376D4—1882no—
377C2×C4—21no—
378C2×C4—471no—
379C2×C4—471no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—1882no—
388C2×C4—1882no—
389C2×C4—1882no—
390C2×C4D4×D4711yescharacteristic
391C2×C4D4×D4711yescharacteristic
392C2×C4C23×D4711yescharacteristic
393C8—21no—
394C8—941no—
395C8—941no—
396C8D4×D4712yescomplemented
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—472no—
407C22—941no—
408C22—941no—
409C22—941no—
410C22—942no—
411C22—941no—
412C22—941no—
413C22—3764no—
414C22—3764no—
415C22—1881no—
416C22—1881no—
417C22C2×D4×D4711yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—941no—
422C4—941no—
423C4—942no—
424C4—1881no—
425C4—1881no—
426C4C2×D4×D4711yescharacteristic
427C4#1309406911yescharacteristic
428C2—81no—
429C2—81no—
430C2—81no—
431C2—942no—
432C2—1881no—
433C2—1882no—
434C2#1568975811yescharacteristic
435C2AGL(1,ℤ/8)×D4711yescharacteristic
436C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#496C2
socleC22×C47C22×D4
hypercenter#496D47
hypocenterC47#3265
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C2×SD16×D47C2semidirect
3. #15689781C2semidirect
4. #15689758C2semidirect
5. #15689366C2semidirect
6. #15689356C2semidirect
7. #15689335C2semidirect
8. #15689320C2semidirect
9. #15689272C2semidirect
10. #15689265C2semidirect
11. #15689260C2semidirect
12. #15689255C2semidirect
13. #15689225C2semidirect
14. #15689196C2semidirect
15. C47×#496C2semidirect
16. C2×#10625352C22semidirect
17. C2×Q8×D47C22semidirect
23. C2×#10625335C22semidirect
24. C2×#10625335C22semidirect
28. C2×#10625324C22semidirect
29. C2×C8×D47C22semidirect
32. #13094000C22semidirect
37. #13093995C22semidirect
40. C4×Dic94C22semidirect
44. #13093958C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. #13093949C22semidirect
47. #13093948C22semidirect
49. #13093945C22semidirect
50. #13093945C22semidirect
51. #13093945C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. (C2×D47)⋊C8C22semidirect
54. C2×SD16×C47C22semidirect
55. C2×SD16×C47C22semidirect
56. C2×D8×C47C22semidirect
57. C2×D8×C47C22semidirect
59. #124×C47C22semidirect
60. #97×C47C22semidirect
121. #10625325D4semidirect
173. Dic94C2×D4semidirect
175. C8×C47C2×D4semidirect
198. C2×D47AGL(1,ℤ/8)semidirect
223. #496D47semidirect
234. C47#3265semidirect
246. C2×SD16C2×D47semidirect
247. C2×SD16C2×D47semidirect
249. C2×D8C2×D47semidirect
250. C2×D8C2×D47semidirect
255. #124C2×D47semidirect
279. #97C2×D47semidirect
396. C8D4×D47semidirect