Finite Group Databasebeta

← #20254889

Subgroups — #20254889

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
4D4×D188C211yesmaximal, characteristic, complemented
5#15689513C211yesmaximal, characteristic, complemented
6#15689372C211yesmaximal, characteristic, complemented
7#15689358C211yesmaximal, characteristic, complemented
8#15689324C211yesmaximal, characteristic, complemented
9#15689272C211yesmaximal, characteristic, complemented
10#15689269C211yesmaximal, characteristic, complemented
11#15689263C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic, complemented
14#15689193C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic, complemented
17C2×Q8×D47C2211yescharacteristic, complemented
18C22×D188—21no—
19C2×D4×D47C2211yescharacteristic
20C2×D4×D47C2211yescharacteristic
21#13094048—24no—
22C2×#10625325C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic, complemented
24C2×#10625335C2211yescharacteristic
25C2×#10625336C2211yescharacteristic, complemented
26C2×#10625336C2211yescharacteristic, complemented
27SD16×D47—24no—
28C2×#10625334C2211yescharacteristic, complemented
29C2×#10625334C2211yescharacteristic, complemented
30C2×#10625324C2211yescharacteristic, complemented
31C2×C8×D47C2211yescharacteristic, complemented
32#13094021C2211yescharacteristic
33#13094010—21no—
34#13094001—21no—
35#13094000C2211yescharacteristic, complemented
36#13093999C2211yescharacteristic
37#13093999C2211yescharacteristic
38#13093998—21no—
39#13093997—21no—
40#13093995C2211yescharacteristic, complemented
41#13093994—21no—
42#13093994—21no—
43C4×Dic94C2211yescharacteristic, complemented
44C4×D188C2211yescharacteristic
45(C22⋊D47)⋊C4—21no—
46#13093957C2211yescharacteristic, complemented
47#13093947C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic, complemented
50#13093945C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093935C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic
55C2×D8×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic
58C4⋊C8×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C22×Dic47—21no—
72Q8×D47—22no—
73Q8×D47—41no—
74#10625352—22no—
75#10625352—41no—
76D4×D47—22no—
77D4×D47—22no—
78D4×D47—41no—
79D4×D47—41no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188—21no—
84C2×D188—44no—
85C2×D188D411yescharacteristic
86C2×D188C2311yescharacteristic
87C2×D188C2311yescharacteristic
88C2×C4×D47—21no—
89C2×C4×D47C2311yescharacteristic
90C2×C4×D47C2311yescharacteristic
91C2×Dic94—21no—
92C2×Dic94C2311yescharacteristic
93SD16×C47—22no—
94D8×C47—22no—
95C2×C8×C47C2311yescharacteristic
96C2×C8×C47C2311yescharacteristic
97C4⋊C4×C47C2311yescharacteristic
98C22⋊C4×C47—21no—
99C22⋊C4×C47—21no—
100C22⋊C4×C47—21no—
101C42×C47C2311yescharacteristic
102C22⋊Dic47—21no—
103#10625336—22no—
104#10625336—41no—
105#10625335D414yescomplemented
106#10625334—22no—
107#10625334—41no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4D411yescharacteristic
112(C2×D47)⋊C4D411yescharacteristic
113C4⋊Dic47D411yescharacteristic
114C4⋊Dic47C2311yescharacteristic
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117C4×Dic47—21no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120#10625325—22no—
121#10625325—22no—
122#10625324—22no—
123C8×D47—22no—
124C23×C47—21no—
125C23×C47—21no—
126C22×D47—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×C47C2×D412yes—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—42no—
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2411yescharacteristic
148C22⋊D47—42no—
149C22⋊D47—42no—
150C22⋊D47—42no—
151C22⋊D47—42no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—42no—
155C2×Dic47C2×D411yescharacteristic
156C2×Dic47C2×D411yescharacteristic
157D188—22no—
158D188—21no—
159D188—21no—
160D188—21no—
161D188—21no—
162D188—42no—
163D188—42no—
164D188—42no—
165D188—81no—
166C4×D47—21no—
167C4×D47—21no—
168C4×D47—21no—
169C4×D47—21no—
170C4×D47—42no—
171Dic94—21no—
172Dic94—42no—
173Dic94C2×D412yescomplemented
174C8×C47—21no—
175C8×C47—21no—
176C47⋊C8—21no—
177C47⋊C8C2×D412yescomplemented
178C22×C47—22no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47C22×D411yescharacteristic
185C2×D47—21no—
186C2×D47—21no—
187C2×D47—21no—
188C2×D47—21no—
189C2×D47—21no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
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×C47—41no—
203C4×C47C22×D411yescharacteristic
204C4×C47H(5,𝔽2)11yescharacteristic
205Dic47—22no—
206Dic47—21no—
207Dic47—21no—
208Dic47—41no—
209#3265—471nomaximal, Sylow
210C2×C47—42no—
211C2×C47—81no—
212C2×C47D4211yescharacteristic
213C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C47#57711yescharacteristic
215D47—22no—
216D47—41no—
217D47—81no—
218D47—81no—
219C2×AGL(1,ℤ/8)—471no—
220C22×SD16—471no—
221#548—471no—
222D42—471no—
223#496—471no—
224#468—471no—
225#466—471no—
226#463D4711yescharacteristic, complemented
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—471no—
246C2×SD16—944no—
247C2×SD16C2×D4711yescharacteristic
248C2×D8—471no—
249C2×D8—471no—
250C2×D8C2×D4711yescharacteristic
251C2×M16—471no—
252C22×C8—471no—
253#127—471no—
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—941no—
268C4×D4C2×D4711yescharacteristic
269#107—471no—
270C4⋊C8C2×D4711yescharacteristic, complemented
271#103—471no—
272#103C2×D4711yescharacteristic, complemented
273#102—471no—
274#102—471no—
275#102—471no—
276#102C2×D4711yescharacteristic, complemented
277C22⋊C8—471no—
278C22⋊C8—471no—
279#97—471no—
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—471no—
290C2×D4—471no—
291C2×D4—471no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4—942no—
297C2×D4—942no—
298C2×D4—941no—
299C2×D4—941no—
300C2×D4—941no—
301C2×D4—941no—
302C2×D4—1884no—
303C2×D4—1881no—
304C2×D4—1881no—
305C2×D4C22×D4711yescharacteristic
306C2×D4C22×D4711yescharacteristic
307C22×C4—21no—
308C22×C4—471no—
309C22×C4—471no—
310C22×C4—941no—
311C22×C4—941no—
312SD16—22no—
313SD16—474no—
314SD16—942no—
315SD16—942no—
316SD16—942no—
317SD16—1881no—
318D8—22no—
319D8—942no—
320D8—1881no—
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—941no—
330C4⋊C4—941no—
331C4⋊C4C22×D4711yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—471no—
336C22⋊C4—471no—
337C22⋊C4—941no—
338C22⋊C4—941no—
339C22⋊C4—941no—
340C22⋊C4—941no—
341C42—941no—
342C42C22×D4711yescharacteristic
343C23—21no—
344C23—21no—
345C23—471no—
346C23—471no—
347C23—941no—
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—942no—
364D4—941no—
365D4—941no—
366D4—941no—
367D4—941no—
368D4—3761no—
369D4—1882no—
370D4—1882no—
371D4—1882no—
372D4—1882no—
373D4—1882no—
374D4—1882no—
375D4—1882no—
376D4D4×D4712yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—471no—
381C2×C4—471no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—1882no—
389C2×C4—1882no—
390C2×C4D4×D4711yescharacteristic
391C2×C4D4×D4711yescharacteristic
392C2×C4C23×D4711yescharacteristic
393C8—21no—
394C8—21no—
395C8—472no—
396C8—941no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—472no—
404C22—941no—
405C22—941no—
406C22—941no—
407C22—941no—
408C22—941no—
409C22—3764no—
410C22—3764no—
411C22—1881no—
412C22—1881no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22—1881no—
417C22C2×D4×D4711yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—941no—
423C4—941no—
424C4—942no—
425C4—1881no—
426C4C2×D4×D4711yescharacteristic
427C4#1309407011yescharacteristic
428C2—42no—
429C2—81no—
430C2—942no—
431C2—3761no—
432C2—3761no—
433C2—1881no—
434C2#1568975711yescharacteristic
435C2AGL(1,ℤ/8)×D4711yescharacteristic
436C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3265
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×#13094048C2semidirect
2. C2×SD16×D47C2semidirect
3. #15689781C2semidirect
4. D4×D188C2semidirect
5. #15689513C2semidirect
6. #15689372C2semidirect
7. #15689358C2semidirect
8. #15689324C2semidirect
9. #15689272C2semidirect
10. #15689269C2semidirect
11. #15689263C2semidirect
12. #15689255C2semidirect
13. #15689223C2semidirect
14. #15689193C2semidirect
15. C47×#463C2semidirect
16. C2×#10625352C22semidirect
17. C2×Q8×D47C22semidirect
22. C2×#10625325C22semidirect
23. C2×#10625325C22semidirect
25. C2×#10625336C22semidirect
26. C2×#10625336C22semidirect
28. C2×#10625334C22semidirect
29. C2×#10625334C22semidirect
30. C2×#10625324C22semidirect
31. C2×C8×D47C22semidirect
35. #13094000C22semidirect
40. #13093995C22semidirect
43. C4×Dic94C22semidirect
46. #13093957C22semidirect
47. #13093947C22semidirect
48. #13093946C22semidirect
49. #13093946C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093935C22semidirect
56. #124×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #103×C47C22semidirect
60. #102×C47C22semidirect
105. #10625335D4semidirect
173. Dic94C2×D4semidirect
177. C47⋊C8C2×D4semidirect
198. C2×D47AGL(1,ℤ/8)semidirect
226. #463D47semidirect
234. C47#3265semidirect
255. #124C2×D47semidirect
270. C4⋊C8C2×D47semidirect
272. #103C2×D47semidirect
276. #102C2×D47semidirect