Finite Group Databasebeta

← #20255100

Subgroups — #20255100

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×#13094046C211yesmaximal, characteristic, complemented
2C22×#10625325C211yesmaximal, characteristic, complemented
3#15689782C211yesmaximal, characteristic, complemented
4#15689769C211yesmaximal, characteristic, complemented
5#15689507C211yesmaximal, characteristic, complemented
6#15689352C211yesmaximal, characteristic, complemented
7#15689352C211yesmaximal, characteristic, complemented
8#15689346C211yesmaximal, characteristic, complemented
9#15689339C211yesmaximal, characteristic, complemented
10#15689287C211yesmaximal, characteristic, complemented
11#15689281C211yesmaximal, characteristic, complemented
12#15689270C211yesmaximal, characteristic, complemented
13#15689259C211yesmaximal, characteristic, complemented
14C4×#10625325C211yesmaximal, characteristic, complemented
15C8×D4×C47C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625350C2211yescharacteristic, complemented
18C22×Dic94C2211yescharacteristic
19C22×D188C2211yescharacteristic
20#13094046—24no—
21C2×Dic188C2211yescharacteristic, complemented
22C2×Dic188C2211yescharacteristic, complemented
23C2×#10625325—24no—
24C2×#10625325C2211yescharacteristic
25C2×#10625325C2211yescharacteristic
26C2×#10625325C2211yescharacteristic
27C2×#10625325C2211yescharacteristic
28C2×#10625325C2211yescharacteristic, complemented
29C2×D376C2211yescharacteristic
30C2×D376C2211yescharacteristic
31#13094012C2211yescharacteristic
32#13094012C2211yescharacteristic, complemented
33#13094010—21no—
34#13094009—21no—
35#13094003C2211yescharacteristic
36#13094003C2211yescharacteristic, complemented
37#13094002—21no—
38#13093998C2211yescharacteristic
39#13093998C2211yescharacteristic
40#13093997—21no—
41#13093996—21no—
42#13093992—21no—
43C4×Dic94C2211yescharacteristic, complemented
44C4×D188C2211yescharacteristic
45(C22⋊D47)⋊C4—21no—
46C22⋊C4×D47—21no—
47#13093956C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093949C2211yescharacteristic, complemented
50#13093949C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic
52#13093946C2211yescharacteristic
53#13093946C2211yescharacteristic, complemented
54C22×C8×C47C2211yescharacteristic
55C22×C8×C47C2211yescharacteristic, complemented
56C4×D4×C47C2211yescharacteristic
57C4⋊C8×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C22⋊C8×C47C2211yescharacteristic, complemented
60C4×C8×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×D4×C47D411yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C22×Dic47—21no—
70#10625350—22no—
71#10625350—22no—
72#10625350—41no—
73#10625350—41no—
74C2×D188—22no—
75C2×D188—21no—
76C2×D188—41no—
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×D188C2311yescharacteristic
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×Dic94—22no—
84C2×Dic94—21no—
85C2×Dic94—41no—
86C2×Dic94C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88C2×Dic94C2311yescharacteristic
89C2×C8×C47—22no—
90C2×C8×C47—22no—
91C2×C8×C47C2311yescharacteristic
92C2×C8×C47C2311yescharacteristic
93C2×C8×C47C2311yescharacteristic
94C2×C8×C47C2311yescharacteristic
95C4⋊C4×C47D411yescharacteristic
96C22⋊C4×C47D411yescharacteristic
97C22⋊C4×C47D411yescharacteristic
98C42×C47C2311yescharacteristic
99C22⋊Dic47—21no—
100C22⋊Dic47—21no—
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)⋊C4—21no—
108C4⋊Dic47C2311yescharacteristic
109C4⋊Dic47C2311yescharacteristic
110Dic47⋊C4—21no—
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113C4×Dic47—21no—
114Dic188—22no—
115Dic188—41no—
116D376—22no—
117D376—41no—
118#10625325—22no—
119#10625325—22no—
120#10625325—22no—
121#10625325—22no—
122#10625325D414yescomplemented
123C23×C47C2×D411yescharacteristic
124C23×C47C2×D411yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47—81no—
131D4×C47—22no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2411yescharacteristic
141C22⋊D47—42no—
142C22⋊D47—42no—
143C22⋊D47—42no—
144C22⋊D47—81no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—42no—
151D188—21no—
152D188—21no—
153D188—21no—
154D188—21no—
155D188—21no—
156D188—42no—
157D188C2×D412yes—
158C4×D47—42no—
159C4×D47—42no—
160C4×D47—81no—
161Dic94—21no—
162Dic94—21no—
163Dic94—21no—
164Dic94—21no—
165Dic94—21no—
166Dic94—42no—
167Dic94C2×D412yes—
168C8×C47—21no—
169C8×C47—21no—
170C8×C47—21no—
171C8×C47C2×D412yes—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47#13512yescomplemented
178C22×C47C22×D411yescharacteristic
179C2×D47—22no—
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—21no—
191C4×C47—21no—
192C4×C47—21no—
193C4×C47C22×D411yescharacteristic
194C4×C47H(5,𝔽2)11yescharacteristic
195Dic47—22no—
196Dic47—41no—
197Dic47—41no—
198Dic47—41no—
199Dic47—41no—
200#3282—471nomaximal, Sylow
201C2×C47—22no—
202C2×C47—41no—
203C2×C47D4211yescharacteristic
204C2×C47C2×#13511yescharacteristic
205C2×C47#57711yescharacteristic
206D47—42no—
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×SD16—471no—
223C8×D4D4711yescharacteristic, complemented
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—471no—
237C2×SD16—944no—
238C2×D8—471no—
239C2×D8—471no—
240C22×C8C2×D4711yescharacteristic
241C22×C8C2×D4711yescharacteristic, complemented
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×Q8—471no—
255C4×D4—471no—
256C4×D4—941no—
257C4×D4C2×D4711yescharacteristic
258C2×C22⋊C4—941no—
259#106—471no—
260C4⋊C8C2×D4711yescharacteristic, complemented
261#103—471no—
262#103—471no—
263#103—471no—
264#102—471no—
265#102—471no—
266#102—471no—
267C22⋊C8C2×D4711yescharacteristic
268C22⋊C8C2×D4711yescharacteristic, complemented
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—471no—
278C2×Q8—942no—
279C2×Q8—941no—
280C2×Q8—1881no—
281C2×D4—471no—
282C2×D4—471no—
283C2×D4—471no—
284C2×D4—942no—
285C2×D4—941no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4—941no—
290C2×D4—1881no—
291C2×D4D18811yescharacteristic
292C22×C4—941no—
293C22×C4—941no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4C22×D4711yescharacteristic
297C22×C4C22×D4711yescharacteristic
298Q16—942no—
299Q16—1881no—
300SD16—474no—
301SD16—942no—
302SD16—942no—
303SD16—942no—
304SD16—942no—
305D8—942no—
306D8—1881no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C22×D4711yescharacteristic
310C2×C8C22×D4711yescharacteristic
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—471no—
314C4⋊C4—471no—
315C4⋊C4—941no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4D18811yescharacteristic
319C22⋊C4—941no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4D18811yescharacteristic
329C22⋊C4D18811yescharacteristic
330C42—941no—
331C42C22×D4711yescharacteristic
332C23—941no—
333C23—941no—
334C23—941no—
335C23—3761no—
336C23—1882no—
337C23—1882no—
338C23C2×D18811yescharacteristic
339C23C2×D18811yescharacteristic
340Q8—472no—
341Q8—941no—
342Q8—941no—
343Q8—941no—
344Q8—941no—
345Q8—941no—
346Q8—1882no—
347D4—22no—
348D4—472no—
349D4—941no—
350D4—941no—
351D4—941no—
352D4—941no—
353D4—941no—
354D4—3761no—
355D4—1882no—
356D4—1882no—
357D4—1882no—
358D4—1882no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—3761no—
369C2×C4—1882no—
370C2×C4—1882no—
371C2×C4—1882no—
372C2×C4C2×D18811yescharacteristic
373C2×C4C2×D18811yescharacteristic
374C2×C4C2×D18811yescharacteristic
375C2×C4C2×D18811yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D4712yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—942no—
387C22—3764no—
388C22—1881no—
389C22—1881no—
390C22—1881no—
391C22—1881no—
392C22—1881no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22#1309404612yescomplemented
397C22C22×D18811yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—942no—
403C4—1881no—
404C4—1881no—
405C4—1881no—
406C4—1881no—
407C4C2×D4×D4711yescharacteristic
408C4#1309407011yescharacteristic
409C2—22no—
410C2—41no—
411C2—3761no—
412C2—3761no—
413C2—1882no—
414C2D4×D18811yescharacteristic
415C2C2×#1309404611yescharacteristic
416C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC8×D4×C47C2
socleC22×C47C22×D4
hypercenterC8×D4D47
hypocenterC47#3282
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13094046C2semidirect
2. C22×#10625325C2semidirect
3. #15689782C2semidirect
4. #15689769C2semidirect
5. #15689507C2semidirect
6. #15689352C2semidirect
7. #15689352C2semidirect
8. #15689346C2semidirect
9. #15689339C2semidirect
10. #15689287C2semidirect
11. #15689281C2semidirect
12. #15689270C2semidirect
13. #15689259C2semidirect
14. C4×#10625325C2semidirect
15. C8×D4×C47C2semidirect
17. C2×#10625350C22semidirect
21. C2×Dic188C22semidirect
22. C2×Dic188C22semidirect
28. C2×#10625325C22semidirect
32. #13094012C22semidirect
36. #13094003C22semidirect
43. C4×Dic94C22semidirect
47. #13093956C22semidirect
48. #13093949C22semidirect
49. #13093949C22semidirect
50. #13093949C22semidirect
53. #13093946C22semidirect
55. C22×C8×C47C22semidirect
57. C4⋊C8×C47C22semidirect
59. C22⋊C8×C47C22semidirect
60. C4×C8×C47C22semidirect
122. #10625325D4semidirect
177. C22×C47#135semidirect
223. C8×D4D47semidirect
224. C47#3282semidirect
241. C22×C8C2×D47semidirect
260. C4⋊C8C2×D47semidirect
268. C22⋊C8C2×D47semidirect
269. C4×C8C2×D47semidirect
396. C22#13094046semidirect