Finite Group Databasebeta

← #20254879

Subgroups — #20254879

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×#13094050C211yesmaximal, characteristic, complemented
2C22×#10625335C211yesmaximal, characteristic, complemented
3#15689782C211yesmaximal, characteristic, complemented
4#15689510C211yesmaximal, characteristic, complemented
5#15689367C211yesmaximal, characteristic, complemented
6#15689357C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689320C211yesmaximal, characteristic, complemented
9#15689274C211yesmaximal, characteristic, complemented
10#15689266C211yesmaximal, characteristic, complemented
11#15689261C211yesmaximal, characteristic, complemented
12#15689257C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic, complemented
14#15689195C211yesmaximal, characteristic, complemented
15D42×C47C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic, complemented
17C22×Dic94C2211yescharacteristic, complemented
18#13094050—24no—
19C2×#10625335—24no—
20C2×#10625335C2211yescharacteristic
21C2×#10625335C2211yescharacteristic
22C2×#10625335C2211yescharacteristic, complemented
23C2×#10625335C2211yescharacteristic, complemented
24C2×#10625335C2211yescharacteristic, complemented
25C2×#10625335C2211yescharacteristic, complemented
26C2×#10625334C2211yescharacteristic
27C2×#10625334C2211yescharacteristic, complemented
28C2×#10625334C2211yescharacteristic, complemented
29C2×#10625329C2211yescharacteristic, complemented
30C22×C47⋊C8C2211yescharacteristic, complemented
31#13094012C2211yescharacteristic, complemented
32#13094010—21no—
33#13094003C2211yescharacteristic, complemented
34#13094002—21no—
35#13093998C2211yescharacteristic, complemented
36#13093996—21no—
37C4×Dic94C2211yescharacteristic, complemented
38(C22⋊D47)⋊C4—21no—
39#13093957C2211yescharacteristic, complemented
40C4⋊(C47⋊C8)C2211yescharacteristic, complemented
41#13093947C2211yescharacteristic, complemented
42#13093947C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic
44#13093945C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic, complemented
46#13093944C2211yescharacteristic, complemented
47C22⋊(C47⋊C8)C2211yescharacteristic, complemented
48C22⋊(C47⋊C8)C2211yescharacteristic, complemented
49#13093935C2211yescharacteristic, complemented
50C22×D4×C47—21no—
51C22×D4×C47C2211yescharacteristic
52C22×D4×C47C2211yescharacteristic
53#127×C47C2211yescharacteristic
54#121×C47—21no—
55#121×C47C2211yescharacteristic
56#121×C47C2211yescharacteristic
57#120×C47—21no—
58#120×C47—21no—
59C4×D4×C47C2211yescharacteristic
60C4×D4×C47C2211yescharacteristic
61C24×C47—21no—
62C24×C47—21no—
63C2×D4×C47—22no—
64C2×D4×C47—22no—
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C2×D4×C47—44no—
74C2×D4×C47D411yescharacteristic
75C2×D4×C47C2311yescharacteristic
76C2×D4×C47C2311yescharacteristic
77C2×D4×C47C2311yescharacteristic
78C22×C4×C47—21no—
79C22×C4×C47C2311yescharacteristic
80C22×C4×C47C2311yescharacteristic
81C2×C22⋊D47—21no—
82C2×C22⋊D47—21no—
83C22×Dic47—21no—
84#10625350—22no—
85#10625350—41no—
86C2×D188C2311yescharacteristic
87C2×C4×D47—21no—
88C2×Dic94—22no—
89C2×Dic94—21no—
90C2×Dic94—41no—
91C2×Dic94C2311yescharacteristic
92C2×Dic94C2311yescharacteristic
93C4⋊C4×C47D411yescharacteristic
94C4⋊C4×C47C2311yescharacteristic
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C22⋊C4×C47D411yescharacteristic
99C22⋊C4×C47D411yescharacteristic
100C42×C47C2311yescharacteristic
101C22⋊Dic47—21no—
102#10625335—22no—
103#10625335—22no—
104#10625335—22no—
105#10625335—22no—
106#10625335—41no—
107#10625335D414yescomplemented
108#10625334—22no—
109#10625334—22no—
110#10625334—41no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113(C2×D47)⋊C4—21no—
114C4⋊Dic47C2311yescharacteristic
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117C4×Dic47—21no—
118#10625329—22no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122C2×C47⋊C8C2311yescharacteristic
123C2×C47⋊C8C2311yescharacteristic
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—42no—
128C23×C47—42no—
129C23×C47—42no—
130C23×C47—42no—
131C23×C47—81no—
132C23×C47—81no—
133C23×C47C2×D411yescharacteristic
134C23×C47C2×D411yescharacteristic
135C22×D47—21no—
136D4×C47—22no—
137D4×C47—21no—
138D4×C47—21no—
139D4×C47—21no—
140D4×C47—21no—
141D4×C47—21no—
142D4×C47—42no—
143D4×C47—42no—
144D4×C47—42no—
145D4×C47—42no—
146D4×C47—42no—
147D4×C47—81no—
148D4×C47C2×D412yes—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—42no—
155C2×C4×C47C2×D411yescharacteristic
156C2×C4×C47C2×D411yescharacteristic
157C2×C4×C47C2×D411yescharacteristic
158C2×C4×C47C2×D411yescharacteristic
159C2×C4×C47C2411yescharacteristic
160C22⋊D47—42no—
161C22⋊D47—42no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—42no—
166D188—21no—
167D188—21no—
168C4×D47—42no—
169Dic94—21no—
170Dic94—21no—
171Dic94—21no—
172Dic94—42no—
173Dic94C2×D412yescomplemented
174C47⋊C8—21no—
175C47⋊C8—21no—
176C47⋊C8—21no—
177C47⋊C8C2×D412yescomplemented
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—22no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47—41no—
191C22×C47—41no—
192C22×C47—84no—
193C22×C47—84no—
194C22×C47AGL(1,ℤ/8)12yescomplemented
195C22×C47C22×D411yescharacteristic
196C2×D47—41no—
197C2×D47—41no—
198C2×D47—41no—
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—21no—
202C4×C47—21no—
203C4×C47—41no—
204C4×C47C22×D411yescharacteristic
205C4×C47H(5,𝔽2)11yescharacteristic
206Dic47—22no—
207Dic47—41no—
208Dic47—41no—
209#3265—471nomaximal, Sylow
210C2×C47—22no—
211C2×C47—41no—
212C2×C47—42no—
213C2×C47—81no—
214C2×C47—81no—
215C2×C47D4211yescharacteristic
216C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
217C2×C47#57711yescharacteristic
218D47—81no—
219C2×AGL(1,ℤ/8)—471no—
220C22×SD16—471no—
221#548—471no—
222D42D4711yescharacteristic, complemented
223#496—471no—
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—21no—
238C22×D4C2×D4711yescharacteristic
239C22×D4C2×D4711yescharacteristic
240AGL(1,ℤ/8)—944no—
241C2×SD16—471no—
242C2×SD16—471no—
243C2×SD16—471no—
244C2×SD16—471no—
245C2×SD16—471no—
246C2×SD16—471no—
247C2×SD16—944no—
248C2×D8—471no—
249C2×D8—471no—
250C2×D8—471no—
251C2×M16—471no—
252C22×C8—471no—
253#127C2×D4711yescharacteristic
254#124—471no—
255#124—941no—
256C22⋊Q8—471no—
257C22⋊Q8—941no—
258#121—21no—
259#121—471no—
260#121—941no—
261#121C2×D4711yescharacteristic
262#121C2×D4711yescharacteristic
263#120—21no—
264#120—21no—
265C4×Q8—471no—
266C4×D4—941no—
267C4×D4C2×D4711yescharacteristic
268C4×D4C2×D4711yescharacteristic
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#97—471no—
280C24—21no—
281C24—21no—
282#41—942no—
283#41—1881no—
284C2×Q8—471no—
285C2×Q8—471no—
286C2×Q8—942no—
287C2×Q8—941no—
288C2×Q8—1881no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—471no—
301C2×D4—941no—
302C2×D4—941no—
303C2×D4C22⋊D4711yescharacteristic
304C2×D4C22×D4711yescharacteristic
305C2×D4C22×D4711yescharacteristic
306C2×D4C22×D4711yescharacteristic
307C22×C4—21no—
308C22×C4—941no—
309C22×C4—941no—
310C22×C4C22×D4711yescharacteristic
311C22×C4C22×D4711yescharacteristic
312SD16—474no—
313SD16—942no—
314SD16—942no—
315SD16—942no—
316SD16—942no—
317SD16—1881no—
318D8—942no—
319D8—942no—
320D8—1881no—
321M16—942no—
322C2×C8—471no—
323C2×C8—471no—
324C2×C8—471no—
325C2×C8—471no—
326C2×C8—942no—
327C4⋊C4—471no—
328C4⋊C4—941no—
329C4⋊C4—941no—
330C4⋊C4C22⋊D4711yescharacteristic
331C4⋊C4C22×D4711yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—941no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C22⋊C4—941no—
339C22⋊C4C22⋊D4711yescharacteristic
340C22⋊C4C22⋊D4711yescharacteristic
341C42—941no—
342C42C22×D4711yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—941no—
353C23C2×C22⋊D4711yescharacteristic
354C23C2×C22⋊D4711yescharacteristic
355Q8—472no—
356Q8—941no—
357Q8—941no—
358Q8—941no—
359Q8—1882no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—941no—
373D4—941no—
374D4—1882no—
375D4—1882no—
376D4D4×D4712yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—1882no—
387C2×C4—1882no—
388C2×C4C2×C22⋊D4711yescharacteristic
389C2×C4C2×C22⋊D4711yescharacteristic
390C2×C4C2×C22⋊D4711yescharacteristic
391C2×C4C2×C22⋊D4711yescharacteristic
392C2×C4C23×D4711yescharacteristic
393C8—472no—
394C8—941no—
395C8—941no—
396C8—941no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22#1309405012yescomplemented
417C22C22×C22⋊D4711yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—942no—
424C4—1881no—
425C4—1881no—
426C4C2×D4×D4711yescharacteristic
427C4#1309406911yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—3761no—
434C2D4×C22⋊D4711yescharacteristic
435C2C2×#1309405011yescharacteristic
436C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD42×C47C2
socleC22×C47C22×D4
hypercenterD42D47
hypocenterC47#3265
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#13094050C2semidirect
2. C22×#10625335C2semidirect
3. #15689782C2semidirect
4. #15689510C2semidirect
5. #15689367C2semidirect
6. #15689357C2semidirect
7. #15689338C2semidirect
8. #15689320C2semidirect
9. #15689274C2semidirect
10. #15689266C2semidirect
11. #15689261C2semidirect
12. #15689257C2semidirect
13. #15689223C2semidirect
14. #15689195C2semidirect
15. D42×C47C2semidirect
16. C2×#10625350C22semidirect
17. C22×Dic94C22semidirect
22. C2×#10625335C22semidirect
23. C2×#10625335C22semidirect
24. C2×#10625335C22semidirect
25. C2×#10625335C22semidirect
27. C2×#10625334C22semidirect
28. C2×#10625334C22semidirect
29. C2×#10625329C22semidirect
30. C22×C47⋊C8C22semidirect
31. #13094012C22semidirect
33. #13094003C22semidirect
35. #13093998C22semidirect
37. C4×Dic94C22semidirect
39. #13093957C22semidirect
40. C4⋊(C47⋊C8)C22semidirect
41. #13093947C22semidirect
42. #13093947C22semidirect
44. #13093945C22semidirect
45. #13093945C22semidirect
46. #13093944C22semidirect
47. C22⋊(C47⋊C8)C22semidirect
48. C22⋊(C47⋊C8)C22semidirect
49. #13093935C22semidirect
107. #10625335D4semidirect
173. Dic94C2×D4semidirect
177. C47⋊C8C2×D4semidirect
194. C22×C47AGL(1,ℤ/8)semidirect
222. D42D47semidirect
234. C47#3265semidirect
416. C22#13094050semidirect