Finite Group Databasebeta

← #20255016

Subgroups — #20255016

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×#13094052C211yesmaximal, characteristic, complemented
3#15689783C211yesmaximal, characteristic, complemented
4#15689764C211yesmaximal, characteristic, complemented
5#15689508C211yesmaximal, characteristic, complemented
6#15689377C211yesmaximal, characteristic, complemented
7#15689348C211yesmaximal, characteristic, complemented
8#15689341C211yesmaximal, characteristic, complemented
9#15689283C211yesmaximal, characteristic, complemented
10#15689273C211yesmaximal, characteristic, complemented
11#15689271C211yesmaximal, characteristic, complemented
12#15689263C211yesmaximal, characteristic, complemented
13#15689210C211yesmaximal, characteristic, complemented
14#15689199C211yesmaximal, characteristic, complemented
15C47×#470C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625350C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic, complemented
19C22×D188C2211yescharacteristic
20#13094056—24no—
21#13094052—24no—
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic
24C2×#10625325C2211yescharacteristic
25C2×#10625336C2211yescharacteristic
26C2×#10625336C2211yescharacteristic
27C2×#10625336C2211yescharacteristic, complemented
28C2×D376C2211yescharacteristic
29C2×D376C2211yescharacteristic
30C2×#10625324C2211yescharacteristic, complemented
31#13094013C2211yescharacteristic
32#13094013C2211yescharacteristic, complemented
33#13094010—21no—
34#13094009—21no—
35#13094002—21no—
36#13093999—21no—
37#13093999C2211yescharacteristic
38#13093999C2211yescharacteristic, complemented
39#13093997—21no—
40#13093994—21no—
41#13093989C2211yescharacteristic, complemented
42#13093986—21no—
43#13093986C2211yescharacteristic
44C4×C22⋊D47C2211yescharacteristic
45C22⋊C4×D47—21no—
46Dic47⋊C8C2211yescharacteristic, complemented
47#13093947C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093944C2211yescharacteristic, complemented
51C22⋊(C47⋊C8)C2211yescharacteristic
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53C8×Dic47C2211yescharacteristic, complemented
54C2×Q16×C47C2211yescharacteristic, complemented
55C2×M16×C47C2211yescharacteristic
56C22⋊Q8×C47C2211yescharacteristic
57C22⋊Q8×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#103×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47D411yescharacteristic
67#10625354—22no—
68#10625354—41no—
69Q8×D47—22no—
70Q8×D47—41no—
71#10625350—22no—
72#10625350—41no—
73C2×D188—22no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—41no—
79C2×D188C2311yescharacteristic
80C2×D188C2311yescharacteristic
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47C2311yescharacteristic
87C2×Dic94—21no—
88C2×Dic94C2311yescharacteristic
89Q16×C47—22no—
90M16×C47—22no—
91C2×C8×C47C2311yescharacteristic
92C2×C8×C47C2311yescharacteristic
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47C2311yescharacteristic
96C4⋊C4×C47C2311yescharacteristic
97C22⋊C4×C47—21no—
98C22⋊C4×C47—21no—
99C22⋊Dic47D411yescharacteristic
100#10625337—22no—
101#10625336—22no—
102#10625336—41no—
103#10625336—41no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4D411yescharacteristic
112Dic47⋊C4—21no—
113Dic47⋊C4D411yescharacteristic
114C4×Dic47—21no—
115C4×Dic47C2311yescharacteristic
116C2×C47⋊C8C2311yescharacteristic
117C2×C47⋊C8C2311yescharacteristic
118D376—22no—
119D376—22no—
120#10625325—22no—
121#10625325D414yescomplemented
122#10625324—22no—
123C23×C47C2×D411yescharacteristic
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—81no—
130C22×D47C2×D411yescharacteristic
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2411yescharacteristic
143C22⋊D47—41no—
144C22⋊D47—42no—
145C2×Dic47—21no—
146C2×Dic47C2×D411yescharacteristic
147C2×Dic47C2×D411yescharacteristic
148C2×Dic47C2×D411yescharacteristic
149D188—21no—
150D188—21no—
151D188—21no—
152D188—21no—
153D188—21no—
154D188—42no—
155D188—42no—
156D188—42no—
157D188—81no—
158D188C2×D412yes—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—42no—
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—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47C22×D411yescharacteristic
176C2×D47—21no—
177C2×D47—22no—
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—84no—
189C4×C47—21no—
190C4×C47—41no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47C22×D411yescharacteristic
195C4×C47H(5,𝔽2)11yescharacteristic
196Dic47—22no—
197Dic47—21no—
198Dic47—21no—
199Dic47—21no—
200#3275—471nomaximal, Sylow
201C2×C47—41no—
202C2×C47D4211yescharacteristic
203C2×C47#57511yescharacteristic
204C2×C47#57711yescharacteristic
205D47—41no—
206D47—42no—
207D47—81no—
208D47—81no—
209C2×#137—471no—
210C2×AGL(1,ℤ/8)—471no—
211#548—471no—
212#546—471no—
213#495—471no—
214#470D4711yescharacteristic, complemented
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×SD16—471no—
237C2×SD16—471no—
238C2×D8—471no—
239C2×D8—471no—
240C2×M16—471no—
241C2×M16C2×D4711yescharacteristic
242#124—471no—
243#124—471no—
244#124—941no—
245#123—941no—
246C22⋊Q8—941no—
247C22⋊Q8C2×D4711yescharacteristic
248C22⋊Q8C2×D4711yescharacteristic
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#106C2×D4711yescharacteristic, complemented
260C4⋊C8—471no—
261#103—471no—
262#103C2×D4711yescharacteristic, complemented
263#103C2×D4711yescharacteristic, complemented
264#102—471no—
265#102—471no—
266#102—471no—
267C22⋊C8—471no—
268C22⋊C8—471no—
269C4×C8—471no—
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—471no—
284C2×D4—471no—
285C2×D4—942no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4—941no—
290C2×D4—941no—
291C2×D4—1881no—
292C22×C4—471no—
293C22×C4—941no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4—941no—
297C22×C4C22×D4711yescharacteristic
298Q16—22no—
299Q16—942no—
300SD16—474no—
301SD16—942no—
302SD16—942no—
303SD16—1881no—
304SD16—1881no—
305D8—942no—
306D8—942no—
307M16—22no—
308M16—942no—
309C2×C8—471no—
310C2×C8—471no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—471no—
316C4⋊C4—941no—
317C4⋊C4C22×D4711yescharacteristic
318C4⋊C4C22×D4711yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—471no—
322C22⋊C4—471no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C42—471no—
331C42—941no—
332C23—471no—
333C23—941no—
334C23—941no—
335C23—941no—
336C23—3761no—
337C23—1882no—
338C23—1882no—
339C23D4×D4711yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—472no—
345Q8—941no—
346Q8—1882no—
347D4—472no—
348D4—941no—
349D4—941no—
350D4—941no—
351D4—941no—
352D4—941no—
353D4—3761no—
354D4—1882no—
355D4—1882no—
356D4—1882no—
357D4—1881no—
358D4—1882no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—471no—
366C2×C4—471no—
367C2×C4—471no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—3761no—
372C2×C4—1882no—
373C2×C4—1882no—
374C2×C4—1882no—
375C2×C4D4×D4711yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C8—21no—
378C8—941no—
379C8—941no—
380C8D4×D4712yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—941no—
385C22—942no—
386C22—941no—
387C22—941no—
388C22—3764no—
389C22—1881no—
390C22—1881no—
391C22—1881no—
392C22—1881no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22C2×D4×D4711yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—941no—
404C4—942no—
405C4—941no—
406C4—941no—
407C4C2×D4×D4711yescharacteristic
408C4#1309407011yescharacteristic
409C2—41no—
410C2—3761no—
411C2—3761no—
412C2—1881no—
413C2—1882no—
414C2#1568975711yescharacteristic
415C2#1568992211yescharacteristic
416C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3275
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#13094056C2semidirect
2. C2×#13094052C2semidirect
3. #15689783C2semidirect
4. #15689764C2semidirect
5. #15689508C2semidirect
6. #15689377C2semidirect
7. #15689348C2semidirect
8. #15689341C2semidirect
9. #15689283C2semidirect
10. #15689273C2semidirect
11. #15689271C2semidirect
12. #15689263C2semidirect
13. #15689210C2semidirect
14. #15689199C2semidirect
15. C47×#470C2semidirect
18. C2×Q8×D47C22semidirect
22. C2×#10625337C22semidirect
27. C2×#10625336C22semidirect
30. C2×#10625324C22semidirect
32. #13094013C22semidirect
38. #13093999C22semidirect
41. #13093989C22semidirect
46. Dic47⋊C8C22semidirect
47. #13093947C22semidirect
50. #13093944C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. C8×Dic47C22semidirect
54. C2×Q16×C47C22semidirect
58. #106×C47C22semidirect
59. #103×C47C22semidirect
60. #103×C47C22semidirect
121. #10625325D4semidirect
214. #470D47semidirect
224. C47#3275semidirect
232. C2×Q16C2×D47semidirect
259. #106C2×D47semidirect
262. #103C2×D47semidirect
263. #103C2×D47semidirect