Finite Group Databasebeta

← #20254915

Subgroups — #20254915

Order 6016.

500 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×#13094048C211yesmaximal, characteristic, complemented
2C2×#13094043C211yesmaximal, characteristic, complemented
3#15689777C211yesmaximal, characteristic, complemented
4#15689768C211yesmaximal, characteristic, complemented
5#15689517C211yesmaximal, characteristic, complemented
6#15689382C211yesmaximal, characteristic, complemented
7#15689353C211yesmaximal, characteristic, complemented
8#15689338C211yesmaximal, characteristic, complemented
9#15689328C211yesmaximal, characteristic, complemented
10#15689286C211yesmaximal, characteristic, complemented
11#15689286C211yesmaximal, characteristic, complemented
12#15689275C211yesmaximal, characteristic, complemented
13#15689269C211yesmaximal, characteristic, complemented
14#15689196C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×#10625352C2211yescharacteristic, complemented
19C2×D4×D47C2211yescharacteristic
20#13094048—24no—
21#13094043—24no—
22C2×Dic188C2211yescharacteristic, complemented
23C2×Dic188C2211yescharacteristic, complemented
24C2×#10625325C2211yescharacteristic
25C2×#10625325C2211yescharacteristic
26C2×#10625335C2211yescharacteristic
27C2×#10625335C2211yescharacteristic
28C2×#10625335C2211yescharacteristic, complemented
29C2×#10625334C2211yescharacteristic
30C2×#10625324C2211yescharacteristic
31C2×C8×D47C2211yescharacteristic, complemented
32#13094024C2211yescharacteristic, complemented
33#13094012C2211yescharacteristic
34#13094008—21no—
35#13094008—21no—
36#13094008—21no—
37#13094004C2211yescharacteristic
38#13094004C2211yescharacteristic
39#13094004C2211yescharacteristic, complemented
40#13093999C2211yescharacteristic
41#13093998—21no—
42#13093998—21no—
43#13093994—21no—
44C4×D188C2211yescharacteristic
45C2×C4⋊Dic47—21no—
46C2×(C2×D47)⋊C4—21no—
47C4⋊(C47⋊C8)C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093947C2211yescharacteristic, complemented
50#13093947C2211yescharacteristic, complemented
51#13093944C2211yescharacteristic
52(C2×D47)⋊C8C2211yescharacteristic
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54C2×D8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic, complemented
57#106×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59#102×C47C2211yescharacteristic, complemented
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C22×Dic47—21no—
71C22×Dic47—21no—
72C22×Dic47—21no—
73#10625352—22no—
74#10625352—22no—
75#10625352—22no—
76#10625352—41no—
77#10625352—41no—
78#10625352—41no—
79D4×D47—22no—
80D4×D47—41no—
81C2×D188—21no—
82C2×D188D411yescharacteristic
83C2×D188C2311yescharacteristic
84C2×C4×D47C2311yescharacteristic
85C2×C4×D47C2311yescharacteristic
86C2×Dic94C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88C2×Dic94C2311yescharacteristic
89D8×C47D414yescomplemented
90C2×C8×C47C2311yescharacteristic
91C2×C8×C47C2311yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C4⋊C4×C47C2311yescharacteristic
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C42×C47C2311yescharacteristic
97#10625335—22no—
98#10625335—22no—
99#10625335—22no—
100#10625334—22no—
101(C2×D47)⋊C4—21no—
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)⋊C4D411yescharacteristic
108(C2×D47)⋊C4D411yescharacteristic
109C4⋊Dic47—21no—
110C4⋊Dic47—21no—
111C4⋊Dic47—21no—
112C4⋊Dic47—21no—
113C4⋊Dic47—21no—
114C4⋊Dic47D411yescharacteristic
115C2×C47⋊C8C2311yescharacteristic
116C2×C47⋊C8C2311yescharacteristic
117Dic188—22no—
118Dic188—41no—
119#10625325—22no—
120#10625325—41no—
121#10625324—22no—
122C8×D47—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
131D4×C47—21no—
132D4×C47—21no—
133D4×C47C2×D412yes—
134D4×C47C2×D412yes—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—42no—
138C2×C4×C47—81no—
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2411yescharacteristic
142C22⋊D47—42no—
143C22⋊D47—42no—
144C22⋊D47—42no—
145C22⋊D47—42no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—42no—
150C2×Dic47—42no—
151C2×Dic47—42no—
152C2×Dic47C2×D411yescharacteristic
153C2×Dic47C2×D411yescharacteristic
154D188—21no—
155D188—21no—
156D188—41no—
157D188—81no—
158C4×D47—21no—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—21no—
162Dic94—21no—
163Dic94—21no—
164Dic94—21no—
165Dic94—21no—
166Dic94—21no—
167Dic94—21no—
168C8×C47—21no—
169C8×C47C2×D412yes—
170C47⋊C8—21no—
171C47⋊C8—21no—
172C22×C47—22no—
173C22×C47—22no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47C22×D411yescharacteristic
179C2×D47—21no—
180C2×D47—21no—
181C2×D47—21no—
182C2×D47—21no—
183C2×D47—21no—
184C2×D47—21no—
185C2×D47—41no—
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—21no—
196Dic47—21no—
197Dic47—41no—
198Dic47—41no—
199Dic47—41no—
200#3267—471nomaximal, Sylow
201C2×C47—42no—
202C2×C47—42no—
203C2×C47D4211yescharacteristic
204C2×C47#57511yescharacteristic
205C2×C47#57711yescharacteristic
206D47—41no—
207D47—41no—
208D47—81no—
209C2×AGL(1,ℤ/8)—471no—
210C2×#135—471no—
211#547—471no—
212#546—471no—
213#497—471no—
214#470—471no—
215#465—471no—
216#463—471no—
217#461—471no—
218#452—471no—
219#452—471no—
220#450—471no—
221#449—471no—
222#442D4711yescharacteristic, complemented
223#435—471no—
224C47#326711yescharacteristic, complemented, Sylow
225C2×#41—471no—
226C2×#41—471no—
227C2×#41—471no—
228C22×D4—471no—
229AGL(1,ℤ/8)—944no—
230#135—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×D8C2×D4711yescharacteristic
240C2×M16—471no—
241C22×C8—471no—
242C4⋊Q8—471no—
243#124—471no—
244#123—941no—
245#123—941no—
246#123—941no—
247C22⋊Q8—471no—
248C22⋊Q8—471no—
249C22⋊Q8—471no—
250#121—471no—
251#121—941no—
252#121—941no—
253#120—941no—
254C4×D4—471no—
255C4×D4C2×D4711yescharacteristic
256C4×D4C2×D4711yescharacteristic, complemented
257C2×C4⋊C4—941no—
258C2×C22⋊C4—941no—
259#106C2×D4711yescharacteristic, complemented
260C4⋊C8—471no—
261#103—471no—
262#103—471no—
263#103—471no—
264#102—471no—
265#102C2×D4711yescharacteristic
266#102C2×D4711yescharacteristic, complemented
267C22⋊C8—471no—
268C22⋊C8—471no—
269#97C2×D4711yescharacteristic, complemented
270C24—941no—
271#41—942no—
272#41—942no—
273#41—942no—
274#41—1881no—
275#41—1881no—
276#41—1881no—
277C2×Q8—471no—
278C2×Q8—471no—
279C2×Q8—471no—
280C2×D4—471no—
281C2×D4—471no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—942no—
285C2×D4—941no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—1881no—
289C2×D4C22×D4711yescharacteristic
290C2×D4C22×D4711yescharacteristic
291C22×C4—21no—
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—
304SD16—1881no—
305D8—942no—
306D8D18814yescomplemented
307M16—942no—
308C2×C8—471no—
309C2×C8—471no—
310C2×C8—942no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—471no—
314C4⋊C4—941no—
315C4⋊C4—941no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4—941no—
319C4⋊C4C22×D4711yescharacteristic
320C4⋊C4C22×D4711yescharacteristic
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—
330C22⋊C4—941no—
331C42C22×D4711yescharacteristic
332C23—21no—
333C23—21no—
334C23—471no—
335C23—471no—
336C23—941no—
337C23—3761no—
338C23—1882no—
339C23—1882no—
340Q8—941no—
341Q8—941no—
342Q8—941no—
343Q8—941no—
344Q8—941no—
345Q8—941no—
346D4—21no—
347D4—21no—
348D4—941no—
349D4—941no—
350D4—3761no—
351D4—1881no—
352D4—1882no—
353D4—1882no—
354D4—1882no—
355D4—1882no—
356D4C2×D18812yes—
357D4C2×D18812yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—471no—
363C2×C4—471no—
364C2×C4—941no—
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—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—941no—
388C22—941no—
389C22—941no—
390C22—941no—
391C22—941no—
392C22—941no—
393C22—3764no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22C2×D4×D4711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—941no—
403C4—941no—
404C4—1881no—
405C4—1881no—
406C4—1881no—
407C4C22×D18811yescharacteristic
408C4#1309407011yescharacteristic
409C2—42no—
410C2—42no—
411C2—3761no—
412C2—1881no—
413C2—1881no—
414C2D4×D18811yescharacteristic
415C2#1568991911yescharacteristic
416C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3267
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C2×#13094043C2semidirect
3. #15689777C2semidirect
4. #15689768C2semidirect
5. #15689517C2semidirect
6. #15689382C2semidirect
7. #15689353C2semidirect
8. #15689338C2semidirect
9. #15689328C2semidirect
10. #15689286C2semidirect
11. #15689286C2semidirect
12. #15689275C2semidirect
13. #15689269C2semidirect
14. #15689196C2semidirect
15. C47×#442C2semidirect
18. C2×#10625352C22semidirect
22. C2×Dic188C22semidirect
23. C2×Dic188C22semidirect
28. C2×#10625335C22semidirect
31. C2×C8×D47C22semidirect
32. #13094024C22semidirect
39. #13094004C22semidirect
47. C4⋊(C47⋊C8)C22semidirect
48. #13093947C22semidirect
49. #13093947C22semidirect
50. #13093947C22semidirect
53. (C2×D47)⋊C8C22semidirect
56. C4×D4×C47C22semidirect
57. #106×C47C22semidirect
59. #102×C47C22semidirect
60. #97×C47C22semidirect
89. D8×C47D4semidirect
222. #442D47semidirect
224. C47#3267semidirect
256. C4×D4C2×D47semidirect
259. #106C2×D47semidirect
266. #102C2×D47semidirect
269. #97C2×D47semidirect
306. D8D188semidirect