Finite Group Databasebeta

← #20255097

Subgroups — #20255097

Order 6016.

504 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×#13094045C211yesmaximal, characteristic, complemented
2C2×SD16×D47C211yesmaximal, characteristic, complemented
3#15689785C211yesmaximal, characteristic, complemented
4#15689768C211yesmaximal, characteristic, complemented
5#15689507C211yesmaximal, characteristic, complemented
6#15689353C211yesmaximal, characteristic, complemented
7#15689353C211yesmaximal, characteristic, complemented
8#15689345C211yesmaximal, characteristic, complemented
9#15689338C211yesmaximal, characteristic, complemented
10#15689286C211yesmaximal, characteristic, complemented
11#15689280C211yesmaximal, characteristic, complemented
12#15689271C211yesmaximal, characteristic, complemented
13#15689258C211yesmaximal, characteristic, complemented
14C8×D188C211yesmaximal, characteristic, complemented
15C4×SD16×C47C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic, complemented
17C2×#10625352C2211yescharacteristic
18C2×Q8×D47C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic
20#13094045—24no—
21C2×Dic188C2211yescharacteristic, complemented
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic
24C2×#10625325C2211yescharacteristic, complemented
25C2×#10625335C2211yescharacteristic
26C2×#10625336C2211yescharacteristic
27SD16×D47—24no—
28C2×D376C2211yescharacteristic
29C2×#10625334C2211yescharacteristic
30C2×C8×D47C2211yescharacteristic
31C2×C8×D47C2211yescharacteristic, complemented
32#13094012—21no—
33#13094012C2211yescharacteristic
34#13094012C2211yescharacteristic, complemented
35#13094008—21no—
36#13094004—21no—
37#13094004C2211yescharacteristic
38#13094004C2211yescharacteristic, complemented
39#13093999—21no—
40#13093999C2211yescharacteristic
41#13093999C2211yescharacteristic
42#13093998—21no—
43#13093994—21no—
44C4×D188—21no—
45C4×D188C2211yescharacteristic
46C2×(C2×D47)⋊C4—21no—
47C4⋊(C47⋊C8)C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093947C2211yescharacteristic, complemented
50#13093944C2211yescharacteristic
51#13093944C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic, complemented
56C4×D4×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic, complemented
58#103×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic
60C4×C8×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47—21no—
68#10625354—22no—
69#10625354—41no—
70Q8×D47—22no—
71Q8×D47—41no—
72#10625352—22no—
73#10625352—41no—
74D4×D47—22no—
75D4×D47—41no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188D411yescharacteristic
80C2×D188C2311yescharacteristic
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47C2311yescharacteristic
85C2×C4×D47C2311yescharacteristic
86C2×Dic94—21no—
87C2×Dic94C2311yescharacteristic
88C2×Dic94C2311yescharacteristic
89SD16×C47D414yescomplemented
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47—21no—
93C4⋊C4×C47C2311yescharacteristic
94C4⋊C4×C47C2311yescharacteristic
95C22⋊C4×C47—21no—
96C42×C47—21no—
97C42×C47C2311yescharacteristic
98#10625337—22no—
99#10625336—22no—
100#10625335—22no—
101#10625334—22no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
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)⋊C4D411yescharacteristic
111(C2×D47)⋊C4D411yescharacteristic
112C4⋊Dic47—21no—
113C4⋊Dic47—21no—
114C4⋊Dic47D411yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116C2×C47⋊C8C2311yescharacteristic
117Dic188—41no—
118D376—41no—
119#10625325—22no—
120#10625325—22no—
121C8×D47—22no—
122C8×D47—22no—
123C23×C47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—42no—
127C22×D47—42no—
128C22×D47—81no—
129C22×D47C2×D411yescharacteristic
130C22×D47C2×D411yescharacteristic
131Q8×C47—21no—
132Q8×C47C2×D412yes—
133D4×C47—21no—
134D4×C47C2×D412yes—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—81no—
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2411yescharacteristic
142C22⋊D47—42no—
143C22⋊D47—42no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—42no—
147C2×Dic47C2×D411yescharacteristic
148C2×Dic47C2×D411yescharacteristic
149D188—22no—
150D188—21no—
151D188—21no—
152D188—21no—
153D188—21no—
154D188—42no—
155D188—42no—
156D188—81no—
157C4×D47—21no—
158C4×D47—21no—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—42no—
162C4×D47—42no—
163Dic94—21no—
164Dic94—21no—
165Dic94—21no—
166Dic94—21no—
167Dic94—42no—
168C8×C47—21no—
169C8×C47C2×D412yes—
170C47⋊C8—21no—
171C47⋊C8—21no—
172C22×C47—22no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47C22×D411yescharacteristic
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—21no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—84no—
188C2×D47#13512yescomplemented
189C4×C47—22no—
190C4×C47—21no—
191C4×C47—21no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47C22×D411yescharacteristic
195C4×C47H(5,𝔽2)11yescharacteristic
196Dic47—21no—
197Dic47—21no—
198Dic47—41no—
199Dic47—41no—
200#3282—471nomaximal, Sylow
201C2×C47—42no—
202C2×C47D4211yescharacteristic
203C2×C47C2×#13511yescharacteristic
204C2×C47#57711yescharacteristic
205D47—22no—
206D47—41no—
207D47—81no—
208D47—81no—
209C2×#135—471no—
210C22×SD16—471no—
211#548—471no—
212#546—471no—
213#495—471no—
214#465—471no—
215#465—471no—
216#464—471no—
217#463—471no—
218#452—471no—
219#451—471no—
220#449—471no—
221#447—471no—
222C4×SD16D4711yescharacteristic, complemented
223C8×D4—471no—
224C47#328211yescharacteristic, complemented, Sylow
225C2×#41—471no—
226C2×#41—471no—
227C22×Q8—471no—
228C22×D4—471no—
229#135—944no—
230C2×Q16—471no—
231C2×Q16—471no—
232C2×SD16—471no—
233C2×SD16—471no—
234C2×SD16—471no—
235C2×SD16—471no—
236C2×SD16—944no—
237C2×SD16C2×D4711yescharacteristic
238C2×D8—471no—
239C2×D8—471no—
240C22×C8—471no—
241C22×C8—471no—
242#124—471no—
243#124—471no—
244#124—941no—
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×Q8C2×D4711yescharacteristic, complemented
255C4×D4—471no—
256C4×D4—941no—
257C4×D4C2×D4711yescharacteristic
258C2×C22⋊C4—941no—
259#106C2×D4711yescharacteristic, complemented
260C4⋊C8—471no—
261#103—471no—
262#103—471no—
263#103C2×D4711yescharacteristic, complemented
264#102—471no—
265#102—471no—
266#102C2×D4711yescharacteristic
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—471no—
277C2×Q8—941no—
278C2×Q8—942no—
279C2×Q8—1881no—
280C2×Q8C22×D4711yescharacteristic
281C2×D4—471no—
282C2×D4—471no—
283C2×D4—471no—
284C2×D4—941no—
285C2×D4—941no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—942no—
289C2×D4—941no—
290C2×D4—1881no—
291C2×D4C22×D4711yescharacteristic
292C22×C4—21no—
293C22×C4—471no—
294C22×C4—471no—
295C22×C4—941no—
296C22×C4—941no—
297C22×C4—941no—
298Q16—942no—
299Q16—1881no—
300SD16—942no—
301SD16—942no—
302SD16—942no—
303SD16—942no—
304SD16D18814yescomplemented
305D8—942no—
306D8—1881no—
307C2×C8—471no—
308C2×C8—471no—
309C2×C8—942no—
310C2×C8—942no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—471no—
315C4⋊C4—941no—
316C4⋊C4—941no—
317C4⋊C4C22×D4711yescharacteristic
318C4⋊C4C22×D4711yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—471no—
321C22⋊C4—471no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C42—21no—
331C42C22×D4711yescharacteristic
332C23—21no—
333C23—471no—
334C23—471no—
335C23—941no—
336C23—941no—
337C23—3761no—
338C23—1882no—
339C23—1882no—
340Q8—21no—
341Q8—941no—
342Q8—941no—
343Q8—941no—
344Q8—941no—
345Q8—1882no—
346Q8C2×D18812yes—
347D4—21no—
348D4—942no—
349D4—941no—
350D4—941no—
351D4—941no—
352D4—941no—
353D4—3761no—
354D4—1882no—
355D4—1882no—
356D4—1882no—
357D4—1882no—
358D4C2×D18812yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—81no—
363C2×C4—471no—
364C2×C4—471no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—1882no—
372C2×C4—1882no—
373C2×C4—1882no—
374C2×C4D4×D4711yescharacteristic
375C2×C4D4×D4711yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C8—21no—
378C8—941no—
379C8—941no—
380C8C2×D18812yes—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—472no—
385C22—941no—
386C22—941no—
387C22—941no—
388C22—941no—
389C22—941no—
390C22—3764no—
391C22—1881no—
392C22—1881no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22C2×D4×D4711yescharacteristic
398C4—22no—
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—941no—
404C4—941no—
405C4—1881no—
406C4—1881no—
407C4C22×D18811yescharacteristic
408C4#1309407011yescharacteristic
409C2—42no—
410C2—942no—
411C2—3761no—
412C2—3761no—
413C2—1881no—
414C2D4×D18811yescharacteristic
415C2#135×D4711yescharacteristic
416C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×SD16×C47C2
socleC22×C47C22×D4
hypercenterC4×SD16D47
hypocenterC47#3282
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13094045C2semidirect
2. C2×SD16×D47C2semidirect
3. #15689785C2semidirect
4. #15689768C2semidirect
5. #15689507C2semidirect
6. #15689353C2semidirect
7. #15689353C2semidirect
8. #15689345C2semidirect
9. #15689338C2semidirect
10. #15689286C2semidirect
11. #15689280C2semidirect
12. #15689271C2semidirect
13. #15689258C2semidirect
14. C8×D188C2semidirect
15. C4×SD16×C47C2semidirect
16. C2×#10625354C22semidirect
21. C2×Dic188C22semidirect
22. C2×#10625337C22semidirect
24. C2×#10625325C22semidirect
31. C2×C8×D47C22semidirect
34. #13094012C22semidirect
38. #13094004C22semidirect
47. C4⋊(C47⋊C8)C22semidirect
48. #13093947C22semidirect
49. #13093947C22semidirect
51. #13093944C22semidirect
53. (C2×D47)⋊C8C22semidirect
55. C4×Q8×C47C22semidirect
57. #106×C47C22semidirect
58. #103×C47C22semidirect
60. C4×C8×C47C22semidirect
89. SD16×C47D4semidirect
188. C2×D47#135semidirect
222. C4×SD16D47semidirect
224. C47#3282semidirect
254. C4×Q8C2×D47semidirect
259. #106C2×D47semidirect
263. #103C2×D47semidirect
269. C4×C8C2×D47semidirect
304. SD16D188semidirect