Finite Group Databasebeta

← #20254919

Subgroups — #20254919

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×#13094051C211yesmaximal, characteristic, complemented
2C2×#13094045C211yesmaximal, characteristic, complemented
3#15689776C211yesmaximal, characteristic, complemented
4#15689768C211yesmaximal, characteristic, complemented
5#15689515C211yesmaximal, characteristic, complemented
6#15689380C211yesmaximal, characteristic, complemented
7#15689355C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689288C211yesmaximal, characteristic, complemented
10#15689282C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689271C211yesmaximal, characteristic, complemented
13#15689233C211yesmaximal, characteristic, complemented
14#15689193C211yesmaximal, characteristic, complemented
15C47×#461C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625354C2211yescharacteristic, complemented
18C2×#10625352C2211yescharacteristic
19C2×D4×D47C2211yescharacteristic
20#13094051—24no—
21#13094045—24no—
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625337C2211yescharacteristic, complemented
24C2×#10625325C2211yescharacteristic, complemented
25C2×#10625336C2211yescharacteristic
26C2×#10625336C2211yescharacteristic
27C2×D376C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C2×#10625324C2211yescharacteristic
30C2×C8×D47C2211yescharacteristic, complemented
31#13094012C2211yescharacteristic
32#13094009—21no—
33#13094009—21no—
34#13094008—21no—
35#13094004C2211yescharacteristic
36#13094000C2211yescharacteristic
37#13094000C2211yescharacteristic, complemented
38#13093999—21no—
39#13093999C2211yescharacteristic
40#13093998—21no—
41#13093994—21no—
42C4×D188C2211yescharacteristic
43C4×D188C2211yescharacteristic, complemented
44C4⋊C4×D47—21no—
45C2×(C2×D47)⋊C4—21no—
46#13093955C2211yescharacteristic, complemented
47#13093949C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093944C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093935C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic
55C2×SD16×C47C2211yescharacteristic
56C4⋊Q8×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic
58C4⋊C8×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#103×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69#10625354—22no—
70#10625354—22no—
71#10625354—41no—
72#10625354—41no—
73#10625352—22no—
74#10625352—41no—
75D4×D47—22no—
76D4×D47—41no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188D411yescharacteristic
81C2×D188C2311yescharacteristic
82C2×D188C2311yescharacteristic
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47C2311yescharacteristic
87C2×C4×D47C2311yescharacteristic
88C2×Dic94C2311yescharacteristic
89SD16×C47—22no—
90SD16×C47—22no—
91C2×C8×C47C2311yescharacteristic
92C2×C8×C47C2311yescharacteristic
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47C2311yescharacteristic
96C22⋊C4×C47—21no—
97C42×C47C2311yescharacteristic
98#10625337—22no—
99#10625337—41no—
100#10625336—22no—
101#10625336—41no—
102#10625334D414yescomplemented
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⋊Dic47D411yescharacteristic
114C4⋊Dic47C2311yescharacteristic
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117C2×C47⋊C8C2311yescharacteristic
118C2×C47⋊C8C2311yescharacteristic
119D376—22no—
120#10625325—22no—
121#10625324—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×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135D4×C47—21no—
136D4×C47C2×D412yes—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—81no—
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2411yescharacteristic
144C22⋊D47—42no—
145C22⋊D47—42no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—42no—
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151D188—21no—
152D188—21no—
153D188—21no—
154D188—41no—
155D188—42no—
156D188—42no—
157D188—81no—
158D188C2×D412yes—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—21no—
162C4×D47—21no—
163C4×D47—42no—
164C4×D47—42no—
165C4×D47—42no—
166Dic94—21no—
167Dic94—21no—
168C8×C47—21no—
169C8×C47—21no—
170C47⋊C8—21no—
171C47⋊C8C2×D412yes—
172C22×C47—22no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47C22×D411yescharacteristic
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—22no—
179C2×D47—21no—
180C2×D47—21no—
181C2×D47—21no—
182C2×D47—21no—
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—41no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47C22×D411yescharacteristic
195C4×C47H(5,𝔽2)11yescharacteristic
196Dic47—21no—
197Dic47—21no—
198Dic47—41no—
199Dic47—41no—
200#3267—471nomaximal, Sylow
201C2×C47—42no—
202C2×C47D4211yescharacteristic
203C2×C47#57511yescharacteristic
204C2×C47#57711yescharacteristic
205D47—41no—
206D47—41no—
207D47—42no—
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#461D4711yescharacteristic, complemented
218#452—471no—
219#452—471no—
220#450—471no—
221#449—471no—
222#442—471no—
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×SD16C2×D4711yescharacteristic
237C2×SD16C2×D4711yescharacteristic
238C2×D8—471no—
239C2×D8—471no—
240C2×M16—471no—
241C22×C8—471no—
242C4⋊Q8C2×D4711yescharacteristic, complemented
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×D4—471no—
256C4×D4C2×D4711yescharacteristic
257C2×C4⋊C4—941no—
258C2×C22⋊C4—941no—
259#106—471no—
260C4⋊C8C2×D4711yescharacteristic, complemented
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—
269#97—471no—
270C24—941no—
271#41—942no—
272#41—942no—
273#41—942no—
274#41—1881no—
275#41—1881no—
276#41—1881no—
277C2×Q8—471no—
278C2×Q8C22×D4711yescharacteristic
279C2×Q8C22×D4711yescharacteristic
280C2×D4—471no—
281C2×D4—471no—
282C2×D4—471no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4—941no—
286C2×D4—941no—
287C2×D4—942no—
288C2×D4—941no—
289C2×D4—1881no—
290C2×D4C22×D4711yescharacteristic
291C22×C4—21no—
292C22×C4—471no—
293C22×C4—471no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4—941no—
297C22×C4—941no—
298Q16—942no—
299Q16—1881no—
300SD16—22no—
301SD16—22no—
302SD16—942no—
303SD16—942no—
304SD16—1881no—
305D8—474no—
306D8—942no—
307M16—942no—
308C2×C8—471no—
309C2×C8—471no—
310C2×C8—942no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—471no—
316C4⋊C4—471no—
317C4⋊C4—941no—
318C4⋊C4—941no—
319C4⋊C4—941no—
320C4⋊C4C22×D4711yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—471no—
323C22⋊C4—471no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C22⋊C4—941no—
331C42C22×D4711yescharacteristic
332C23—21no—
333C23—471no—
334C23—471no—
335C23—941no—
336C23—941no—
337C23—3761no—
338C23—1882no—
339C23—1882no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—941no—
345Q8—941no—
346D4—21no—
347D4—472no—
348D4—941no—
349D4—941no—
350D4—941no—
351D4—3761no—
352D4—1881no—
353D4—1882no—
354D4—1882no—
355D4—1882no—
356D4—1882no—
357D4D4×D4712yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
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—1882no—
371C2×C4—1882no—
372C2×C4—1882no—
373C2×C4—1882no—
374C2×C4D4×D4711yescharacteristic
375C2×C4D4×D4711yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C8—21no—
378C8—21no—
379C8—472no—
380C8—941no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—941no—
385C22—941no—
386C22—942no—
387C22—941no—
388C22—941no—
389C22—941no—
390C22—941no—
391C22—3764no—
392C22—1881no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22C2×D4×D4711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—941no—
404C4—941no—
405C4—1881no—
406C4—1881no—
407C4C2×D4×D4711yescharacteristic
408C4#1309407011yescharacteristic
409C2—42no—
410C2—3761no—
411C2—1881no—
412C2—1881no—
413C2—1882no—
414C2#1568975711yescharacteristic
415C2#1568992211yescharacteristic
416C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3267
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. C2×#13094045C2semidirect
3. #15689776C2semidirect
4. #15689768C2semidirect
5. #15689515C2semidirect
6. #15689380C2semidirect
7. #15689355C2semidirect
8. #15689339C2semidirect
9. #15689288C2semidirect
10. #15689282C2semidirect
11. #15689272C2semidirect
12. #15689271C2semidirect
13. #15689233C2semidirect
14. #15689193C2semidirect
15. C47×#461C2semidirect
17. C2×#10625354C22semidirect
22. C2×#10625337C22semidirect
23. C2×#10625337C22semidirect
24. C2×#10625325C22semidirect
30. C2×C8×D47C22semidirect
37. #13094000C22semidirect
43. C4×D188C22semidirect
46. #13093955C22semidirect
47. #13093949C22semidirect
50. #13093944C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093935C22semidirect
56. C4⋊Q8×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #103×C47C22semidirect
60. #103×C47C22semidirect
102. #10625334D4semidirect
217. #461D47semidirect
224. C47#3267semidirect
242. C4⋊Q8C2×D47semidirect
260. C4⋊C8C2×D47semidirect
262. #103C2×D47semidirect
263. #103C2×D47semidirect