Finite Group Databasebeta

← #20255015

Subgroups — #20255015

Order 6016.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094054C211yesmaximal, characteristic, complemented
2C2×#13094050C211yesmaximal, characteristic, complemented
3#15689782C211yesmaximal, characteristic, complemented
4#15689505C211yesmaximal, characteristic, complemented
5#15689379C211yesmaximal, characteristic, complemented
6#15689374C211yesmaximal, characteristic, complemented
7#15689342C211yesmaximal, characteristic, complemented
8#15689338C211yesmaximal, characteristic, complemented
9#15689283C211yesmaximal, characteristic, complemented
10#15689274C211yesmaximal, characteristic, complemented
11#15689268C211yesmaximal, characteristic, complemented
12#15689261C211yesmaximal, characteristic, complemented
13C4×#10625335C211yesmaximal, characteristic, complemented
14#15689201C211yesmaximal, characteristic, complemented
15C47×#546C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×Dic94C2211yescharacteristic, complemented
18#13094054—24no—
19#13094050—24no—
20C2×#10625337C2211yescharacteristic, complemented
21C2×#10625337C2211yescharacteristic, complemented
22C2×#10625335C2211yescharacteristic
23C2×#10625335C2211yescharacteristic
24C2×#10625335C2211yescharacteristic
25C2×#10625335C2211yescharacteristic
26C2×#10625336C2211yescharacteristic, complemented
27C2×#10625334C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C2×#10625329C2211yescharacteristic
30C2×#10625329C2211yescharacteristic, complemented
31#13094012C2211yescharacteristic, complemented
32#13094010—21no—
33#13094003C2211yescharacteristic
34#13094002—21no—
35#13093998C2211yescharacteristic, complemented
36#13093996—21no—
37C4×Dic94C2211yescharacteristic, complemented
38(C22⋊D47)⋊C4—21no—
39#13093955C2211yescharacteristic, complemented
40C4⋊(C47⋊C8)C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093947C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic, complemented
47C22⋊(C47⋊C8)C2211yescharacteristic
48C22⋊(C47⋊C8)C2211yescharacteristic, complemented
49C4×C47⋊C8C2211yescharacteristic, complemented
50C2×#41×C47C2211yescharacteristic
51C22×D4×C47C2211yescharacteristic
52#124×C47C2211yescharacteristic
53#123×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47—21no—
56#121×C47C2211yescharacteristic
57#120×C47—21no—
58C4×D4×C47C2211yescharacteristic
59C4×D4×C47C2211yescharacteristic
60C2×C22⋊C4×C47—21no—
61C24×C47—21no—
62#41×C47—22no—
63#41×C47—41no—
64C2×Q8×C47C2311yescharacteristic
65C2×D4×C47—22no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—41no—
70C2×D4×C47D411yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C2×D4×C47C2311yescharacteristic
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C22×Dic47—21no—
80#10625350—22no—
81#10625350—41no—
82C2×D188C2311yescharacteristic
83C2×C4×D47—21no—
84C2×Dic94—22no—
85C2×Dic94—21no—
86C2×Dic94—41no—
87C2×Dic94C2311yescharacteristic
88C2×Dic94C2311yescharacteristic
89C4⋊C4×C47—21no—
90C4⋊C4×C47D411yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47D411yescharacteristic
98C22⋊C4×C47D411yescharacteristic
99C42×C47C2311yescharacteristic
100C22⋊Dic47—21no—
101#10625337—22no—
102#10625337—22no—
103#10625336—41no—
104#10625335—22no—
105#10625335—22no—
106#10625335—41no—
107#10625335D414yescomplemented
108#10625334—22no—
109#10625334—22no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—21no—
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116C4×Dic47—21no—
117#10625329—22no—
118#10625329—22no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121C2×C47⋊C8C2311yescharacteristic
122C2×C47⋊C8C2311yescharacteristic
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—42no—
126C23×C47—42no—
127C23×C47—81no—
128C23×C47C2×D411yescharacteristic
129C23×C47C2×D411yescharacteristic
130C22×D47—21no—
131Q8×C47—21no—
132Q8×C47—21no—
133D4×C47—21no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—41no—
137D4×C47—42no—
138D4×C47—42no—
139D4×C47—81no—
140D4×C47C2×D412yes—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—42no—
148C2×C4×C47—81no—
149C2×C4×C47C2×D411yescharacteristic
150C2×C4×C47C2×D411yescharacteristic
151C2×C4×C47C2×D411yescharacteristic
152C2×C4×C47C2×D411yescharacteristic
153C2×C4×C47C2411yescharacteristic
154C22⋊D47—42no—
155C22⋊D47—42no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—42no—
160D188—21no—
161D188—21no—
162C4×D47—42no—
163Dic94—21no—
164Dic94—21no—
165Dic94—21no—
166Dic94—42no—
167Dic94C2×D412yes—
168C47⋊C8—21no—
169C47⋊C8—21no—
170C47⋊C8—21no—
171C47⋊C8C2×D412yes—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—22no—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—84no—
185C22×C47C22×D411yescharacteristic
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—21no—
192C4×C47—21no—
193C4×C47—41no—
194C4×C47—41no—
195C4×C47C22×D411yescharacteristic
196C4×C47H(5,𝔽2)11yescharacteristic
197Dic47—22no—
198Dic47—41no—
199Dic47—41no—
200#3275—471nomaximal, Sylow
201C2×C47—41no—
202C2×C47—41no—
203C2×C47—42no—
204C2×C47—81no—
205C2×C47D4211yescharacteristic
206C2×C47#57511yescharacteristic
207C2×C47#57711yescharacteristic
208D47—81no—
209C2×#137—471no—
210C2×AGL(1,ℤ/8)—471no—
211#548—471no—
212#546D4711yescharacteristic, complemented
213#495—471no—
214#470—471no—
215#469—471no—
216#464—471no—
217#463—471no—
218#452—471no—
219#450—471no—
220#449—471no—
221#448—471no—
222C4×SD16—471no—
223#436—471no—
224C47#327511yescharacteristic, complemented, Sylow
225C2×#41—471no—
226C2×#41C2×D4711yescharacteristic
227C22×Q8—471no—
228C22×D4C2×D4711yescharacteristic
229#137—944no—
230AGL(1,ℤ/8)—944no—
231C2×Q16—471no—
232C2×Q16—471no—
233C2×SD16—471no—
234C2×SD16—471no—
235C2×SD16—471no—
236C2×SD16—471no—
237C2×SD16—471no—
238C2×D8—471no—
239C2×D8—471no—
240C2×M16—471no—
241C2×M16—471no—
242#124—471no—
243#124—941no—
244#124C2×D4711yescharacteristic
245#123—21no—
246C22⋊Q8—471no—
247C22⋊Q8—941no—
248C22⋊Q8C2×D4711yescharacteristic
249#121—21no—
250#121—471no—
251#121—941no—
252#121C2×D4711yescharacteristic
253#120—21no—
254C4×Q8—471no—
255C4×D4—941no—
256C4×D4C2×D4711yescharacteristic
257C4×D4C2×D4711yescharacteristic
258C2×C22⋊C4—21no—
259#106—471no—
260C4⋊C8—471no—
261#103—471no—
262#103—471no—
263#103—471no—
264#102—471no—
265#102—471no—
266#102—471no—
267C22⋊C8—471no—
268C22⋊C8—471no—
269C4×C8—471no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—942no—
274#41—1881no—
275C2×Q8—471no—
276C2×Q8—471no—
277C2×Q8—942no—
278C2×Q8—941no—
279C2×Q8—1881no—
280C2×Q8C22×D4711yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—471no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4C22⋊D4711yescharacteristic
290C2×D4C22×D4711yescharacteristic
291C2×D4C22×D4711yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4C22×D4711yescharacteristic
297C22×C4C22×D4711yescharacteristic
298Q16—942no—
299Q16—942no—
300SD16—474no—
301SD16—942no—
302SD16—942no—
303SD16—1881no—
304SD16—1881no—
305D8—942no—
306D8—942no—
307M16—942no—
308M16—942no—
309C2×C8—471no—
310C2×C8—471no—
311C2×C8—471no—
312C2×C8—471no—
313C4⋊C4—21no—
314C4⋊C4—471no—
315C4⋊C4—941no—
316C4⋊C4—941no—
317C4⋊C4C22⋊D4711yescharacteristic
318C4⋊C4C22×D4711yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4C22⋊D4711yescharacteristic
329C22⋊C4C22⋊D4711yescharacteristic
330C42—941no—
331C42C22×D4711yescharacteristic
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—941no—
338C23C2×C22⋊D4711yescharacteristic
339C23C2×C22⋊D4711yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—472no—
343Q8—941no—
344Q8—941no—
345Q8—941no—
346Q8—1882no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—81no—
354D4—941no—
355D4—941no—
356D4—1882no—
357D4—1882no—
358D4D4×D4712yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—1882no—
371C2×C4—1882no—
372C2×C4C2×C22⋊D4711yescharacteristic
373C2×C4C2×C22⋊D4711yescharacteristic
374C2×C4C2×C22⋊D4711yescharacteristic
375C2×C4C2×C22⋊D4711yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C8—472no—
378C8—941no—
379C8—941no—
380C8—941no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22C22×C22⋊D4711yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—942no—
405C4—1881no—
406C4—1881no—
407C4C2×D4×D4711yescharacteristic
408C4#1309406911yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—81no—
413C2—3761no—
414C2D4×C22⋊D4711yescharacteristic
415C2#1568992111yescharacteristic
416C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#546C2
socleC22×C47C22×D4
hypercenter#546D47
hypocenterC47#3275
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#13094054C2semidirect
2. C2×#13094050C2semidirect
3. #15689782C2semidirect
4. #15689505C2semidirect
5. #15689379C2semidirect
6. #15689374C2semidirect
7. #15689342C2semidirect
8. #15689338C2semidirect
9. #15689283C2semidirect
10. #15689274C2semidirect
11. #15689268C2semidirect
12. #15689261C2semidirect
13. C4×#10625335C2semidirect
14. #15689201C2semidirect
15. C47×#546C2semidirect
17. C22×Dic94C22semidirect
20. C2×#10625337C22semidirect
21. C2×#10625337C22semidirect
26. C2×#10625336C22semidirect
30. C2×#10625329C22semidirect
31. #13094012C22semidirect
35. #13093998C22semidirect
37. C4×Dic94C22semidirect
39. #13093955C22semidirect
40. C4⋊(C47⋊C8)C22semidirect
41. #13093948C22semidirect
42. #13093947C22semidirect
43. #13093947C22semidirect
46. #13093944C22semidirect
48. C22⋊(C47⋊C8)C22semidirect
49. C4×C47⋊C8C22semidirect
107. #10625335D4semidirect
212. #546D47semidirect
224. C47#3275semidirect