Finite Group Databasebeta

← #20255018

Subgroups — #20255018

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×#13094056C211yesmaximal, characteristic, complemented
2C2×#13094048C211yesmaximal, characteristic, complemented
3#15689781C211yesmaximal, characteristic, complemented
4#15689766C211yesmaximal, characteristic, complemented
5#15689378C211yesmaximal, characteristic, complemented
6#15689373C211yesmaximal, characteristic, complemented
7#15689342C211yesmaximal, characteristic, complemented
8#15689335C211yesmaximal, characteristic, complemented
9#15689282C211yesmaximal, characteristic, complemented
10#15689272C211yesmaximal, characteristic, complemented
11#15689267C211yesmaximal, characteristic, complemented
12#15689260C211yesmaximal, characteristic, complemented
13C4×#10625325C211yesmaximal, characteristic, complemented
14#15689202C211yesmaximal, characteristic, complemented
15C47×#495C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic, complemented
19C2×D4×D47C2211yescharacteristic
20#13094056—24no—
21#13094048—24no—
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic
24C2×#10625335C2211yescharacteristic
25C2×#10625336C2211yescharacteristic
26C2×#10625334C2211yescharacteristic
27C2×#10625324C2211yescharacteristic
28C2×#10625324C2211yescharacteristic, complemented
29#13094010—21no—
30#13094006—21no—
31#13094001—21no—
32#13094000C2211yescharacteristic
33#13094000C2211yescharacteristic
34#13093997—21no—
35#13093997—21no—
36#13093995C2211yescharacteristic
37#13093995C2211yescharacteristic, complemented
38#13093994—21no—
39C4×Dic94C2211yescharacteristic, complemented
40C4×D188C2211yescharacteristic
41C4×D188C2211yescharacteristic
42(C22⋊D47)⋊C4—21no—
43C22⋊C4×D47—21no—
44#13093956C2211yescharacteristic, complemented
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46#13093949C2211yescharacteristic, complemented
47#13093948C2211yescharacteristic, complemented
48#13093948C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic
50#13093945C2211yescharacteristic
51#13093945C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54C2×Q16×C47C2211yescharacteristic, complemented
55C2×SD16×C47C2211yescharacteristic
56C2×SD16×C47C2211yescharacteristic, complemented
57C2×D8×C47C2211yescharacteristic
58#124×C47C2211yescharacteristic
59#124×C47C2211yescharacteristic, complemented
60C4×C8×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C22×Dic47—21no—
71#10625354—22no—
72#10625354—41no—
73Q8×D47—22no—
74Q8×D47—41no—
75#10625352—22no—
76#10625352—41no—
77D4×D47—22no—
78D4×D47—41no—
79C2×D188—21no—
80C2×D188D411yescharacteristic
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47C2311yescharacteristic
86C2×C4×D47C2311yescharacteristic
87C2×Dic94—21no—
88C2×Dic94C2311yescharacteristic
89Q16×C47—22no—
90SD16×C47—41no—
91SD16×C47—41no—
92D8×C47—22no—
93C2×C8×C47C2311yescharacteristic
94C2×C8×C47C2311yescharacteristic
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C22⋊C4×C47—21no—
99C42×C47C2311yescharacteristic
100C22⋊Dic47—21no—
101C22⋊Dic47—21no—
102#10625337—22no—
103#10625336—22no—
104#10625335—22no—
105#10625334—22no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4D411yescharacteristic
110(C2×D47)⋊C4D411yescharacteristic
111C4⋊Dic47D411yescharacteristic
112C4⋊Dic47C2311yescharacteristic
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117C4×Dic47—21no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120#10625325D414yescomplemented
121#10625324—22no—
122#10625324—22no—
123C23×C47—21no—
124C23×C47—21no—
125C22×D47—21no—
126C22×D47—42no—
127C22×D47—42no—
128C22×D47—81no—
129C22×D47C2×D411yescharacteristic
130C22×D47C2×D411yescharacteristic
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135D4×C47—21no—
136D4×C47—21no—
137D4×C47—21no—
138D4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2411yescharacteristic
144C22⋊D47—42no—
145C22⋊D47—42no—
146C22⋊D47—42no—
147C22⋊D47—81no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—42no—
152C2×Dic47C2×D411yescharacteristic
153C2×Dic47C2×D411yescharacteristic
154D188—21no—
155D188—41no—
156D188—42no—
157D188C2×D412yes—
158C4×D47—21no—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—21no—
162C4×D47—42no—
163C4×D47—42no—
164C4×D47—81no—
165Dic94—21no—
166Dic94—42no—
167Dic94C2×D412yes—
168C8×C47—21no—
169C8×C47C2×D412yes—
170C47⋊C8—21no—
171C47⋊C8—21no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47C22×D411yescharacteristic
179C2×D47—21no—
180C2×D47—21no—
181C2×D47—22no—
182C2×D47—21no—
183C2×D47—21no—
184C2×D47—21no—
185C2×D47—21no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—84no—
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47C22×D411yescharacteristic
194C4×C47H(5,𝔽2)11yescharacteristic
195Dic47—22no—
196Dic47—21no—
197Dic47—21no—
198Dic47—41no—
199Dic47—41no—
200#3275—471nomaximal, Sylow
201C2×C47—81no—
202C2×C47—81no—
203C2×C47D4211yescharacteristic
204C2×C47#57511yescharacteristic
205C2×C47#57711yescharacteristic
206D47—41no—
207D47—41no—
208D47—42no—
209C2×#137—471no—
210C2×AGL(1,ℤ/8)—471no—
211#548—471no—
212#546—471no—
213#495D4711yescharacteristic, complemented
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×#41—471no—
227C22×Q8—471no—
228C22×D4—471no—
229#137—944no—
230AGL(1,ℤ/8)—944no—
231C2×Q16—471no—
232C2×Q16C2×D4711yescharacteristic, complemented
233C2×SD16—471no—
234C2×SD16—471no—
235C2×SD16—471no—
236C2×SD16C2×D4711yescharacteristic
237C2×SD16C2×D4711yescharacteristic, complemented
238C2×D8—471no—
239C2×D8C2×D4711yescharacteristic
240C2×M16—471no—
241C2×M16—471no—
242#124—941no—
243#124C2×D4711yescharacteristic
244#124C2×D4711yescharacteristic, complemented
245#123—941no—
246C22⋊Q8—471no—
247C22⋊Q8—471no—
248C22⋊Q8—941no—
249#121—471no—
250#121—471no—
251#121—941no—
252#121—941no—
253#120—941no—
254C4×Q8—471no—
255C4×D4—471no—
256C4×D4—471no—
257C4×D4—941no—
258C2×C22⋊C4—941no—
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×C8C2×D4711yescharacteristic, complemented
270C24—941no—
271#41—942no—
272#41—942no—
273#41—1881no—
274#41—1881no—
275C2×Q8—471no—
276C2×Q8—941no—
277C2×Q8—942no—
278C2×Q8—1881no—
279C2×Q8C22×D4711yescharacteristic
280C2×Q8C22×D4711yescharacteristic
281C2×D4—471no—
282C2×D4—471no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4—942no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4—1881no—
290C2×D4C22×D4711yescharacteristic
291C2×D4C22×D4711yescharacteristic
292C22×C4—471no—
293C22×C4—471no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4—941no—
297C22×C4—941no—
298Q16—22no—
299Q16—942no—
300SD16—41no—
301SD16—41no—
302SD16—474no—
303SD16—942no—
304SD16—942no—
305D8—22no—
306D8—942no—
307M16—942no—
308M16—942no—
309C2×C8—471no—
310C2×C8—471no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—471no—
314C4⋊C4—471no—
315C4⋊C4—471no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4—941no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—471no—
324C22⋊C4—471no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C42—941no—
331C42C22×D4711yescharacteristic
332C23—21no—
333C23—21no—
334C23—471no—
335C23—471no—
336C23—941no—
337C23—3761no—
338C23—1882no—
339C23—1882no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—472no—
345Q8—941no—
346Q8—1882no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—472no—
352D4—941no—
353D4—3761no—
354D4—1881no—
355D4—1882no—
356D4—1882no—
357D4—1882no—
358D4—1882no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—471no—
362C2×C4—471no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—3761no—
371C2×C4—1882no—
372C2×C4—1882no—
373C2×C4—1882no—
374C2×C4D4×D4711yescharacteristic
375C2×C4D4×D4711yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C8—21no—
378C8—941no—
379C8—941no—
380C8D4×D4712yes—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—941no—
388C22—941no—
389C22—942no—
390C22—941no—
391C22—941no—
392C22—941no—
393C22—941no—
394C22—3764no—
395C22—1881no—
396C22—1881no—
397C22C2×D4×D4711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—941no—
403C4—941no—
404C4—942no—
405C4—1881no—
406C4—1881no—
407C4C2×D4×D4711yescharacteristic
408C4#1309406911yescharacteristic
409C2—81no—
410C2—81no—
411C2—1881no—
412C2—1881no—
413C2—1882no—
414C2#1568975811yescharacteristic
415C2#1568992011yescharacteristic
416C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#495C2
socleC22×C47C22×D4
hypercenter#495D47
hypocenterC47#3275
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#13094056C2semidirect
2. C2×#13094048C2semidirect
3. #15689781C2semidirect
4. #15689766C2semidirect
5. #15689378C2semidirect
6. #15689373C2semidirect
7. #15689342C2semidirect
8. #15689335C2semidirect
9. #15689282C2semidirect
10. #15689272C2semidirect
11. #15689267C2semidirect
12. #15689260C2semidirect
13. C4×#10625325C2semidirect
14. #15689202C2semidirect
15. C47×#495C2semidirect
18. C2×Q8×D47C22semidirect
22. C2×#10625337C22semidirect
28. C2×#10625324C22semidirect
37. #13093995C22semidirect
39. C4×Dic94C22semidirect
44. #13093956C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. #13093949C22semidirect
47. #13093948C22semidirect
48. #13093948C22semidirect
51. #13093945C22semidirect
53. (C2×D47)⋊C8C22semidirect
54. C2×Q16×C47C22semidirect
56. C2×SD16×C47C22semidirect
59. #124×C47C22semidirect
60. C4×C8×C47C22semidirect
120. #10625325D4semidirect
213. #495D47semidirect
224. C47#3275semidirect
232. C2×Q16C2×D47semidirect
237. C2×SD16C2×D47semidirect
244. #124C2×D47semidirect
269. C4×C8C2×D47semidirect