Finite Group Databasebeta

← #20252641

Subgroups — #20252641

Order 6016.

806 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D47C211yesmaximal, characteristic, complemented
2C2×#13094052C211yesmaximal, characteristic, complemented
3C2×#13094049C211yesmaximal, characteristic, complemented
4C2×#13093999C211yesmaximal, characteristic, complemented
5#15689271C212yesmaximal, complemented
6#15689269C212yesmaximal, complemented
7#15689263C212yesmaximal, complemented
8#15689258C212yesmaximal, complemented
9#15689122C211yesmaximal, characteristic, complemented
10#15689086C211yesmaximal, characteristic, complemented
11C47×#417C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic, complemented
13C2×#10625350—21no—
14C2×#10625350C2211yescharacteristic
15C2×#10625352—21no—
16C2×#10625352C2211yescharacteristic, complemented
17#41×D47—24no—
18#41×D47—24no—
19C2×Q8×D47C2211yescharacteristic, complemented
20C22×D188—21no—
21C22×D188C2211yescharacteristic, complemented
22C2×D4×D47—21no—
23C2×D4×D47C2211yescharacteristic, complemented
24C22×C4×D47—21no—
25C22×C4×D47C2211yescharacteristic
26#13094052—24no—
27#13094049—24no—
28C2×#10625325C2212yescomplemented
29C2×#10625336C2212yescomplemented
30C2×D376C2212yescomplemented
31C2×#10625334C2212yescomplemented
32C2×#10625329C2211yescharacteristic, complemented
33#13093999—21no—
34#13093999—21no—
35#13093999C2212yes—
36#13093999C2212yescomplemented
37C2×(C2×D47)⋊C4—21no—
38#13093947C2212yescomplemented
39#13093944C2212yescomplemented
40(C2×D47)⋊C8C2212yescomplemented
41(C2×D47)⋊C8C2212yescomplemented
42C2×#41×C47C2211yescharacteristic
43C2×M16×C47C2211yescharacteristic, complemented
44C2×C4⋊C4×C47C2211yescharacteristic, complemented
45#103×C47C2212yescomplemented
46#102×C47C2212yescomplemented
47C23×D47—21no—
48C23×D47—21no—
49C23×D47D411yescharacteristic
50#41×C47—22no—
51#41×C47D414yescomplemented
52C2×Q8×C47C2311yescharacteristic
53C2×D4×C47—21no—
54C2×D4×C47C2311yescharacteristic
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47C2311yescharacteristic
58C2×C22⋊D47—21no—
59C2×C22⋊D47—21no—
60C2×C22⋊D47—21no—
61C22×Dic47—21no—
62C22×Dic47D411yescharacteristic
63#10625354—22no—
64#10625354—22no—
65Q8×D47—22no—
66Q8×D47—22no—
67#10625352—28no—
68#10625352—22no—
69#10625352—22no—
70D4×D47—28no—
71D4×D47—22no—
72D4×D47—22no—
73#10625350—28no—
74#10625350—22no—
75#10625350D414yescomplemented
76C2×D188—21no—
77C2×D188—22no—
78C2×D188—22no—
79C2×D188—22no—
80C2×D188—22no—
81C2×D188—21no—
82C2×D188—44no—
83C2×D188C2312yes—
84C2×D188C2311yescharacteristic
85C2×C4×D47—28no—
86C2×C4×D47—21no—
87C2×C4×D47—21no—
88C2×C4×D47—22no—
89C2×C4×D47—22no—
90C2×C4×D47—21no—
91C2×C4×D47D411yescharacteristic
92C2×C4×D47D411yescharacteristic
93C2×C4×D47C2311yescharacteristic
94C2×C4×D47C2311yescharacteristic
95C2×Dic94—21no—
96C2×Dic94C2311yescharacteristic
97M16×C47—22no—
98C2×C8×C47C2312yes—
99C4⋊C4×C47—21no—
100C4⋊C4×C47C2312yes—
101#10625336—24no—
102#10625334—24no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—22no—
105#10625329—22no—
106C2×C47⋊C8C2312yes—
107D376—24no—
108#10625325—24no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—24no—
112C22×D47—22no—
113C22×D47—21no—
114C22×D47—22no—
115C22×D47—22no—
116C22×D47—41no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—42no—
121C22×D47—42no—
122C22×D47C2×D411yescharacteristic
123C22×D47C2×D411yescharacteristic
124Q8×C47—21no—
125Q8×C47C2×D412yescomplemented
126D4×C47—24no—
127D4×C47—21no—
128D4×C47C2×D412yescomplemented
129C2×C4×C47—21no—
130C2×C4×C47—24no—
131C2×C4×C47—22no—
132C2×C4×C47—42no—
133C2×C4×C47C2×D412yes—
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D412yes—
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—24no—
138C22⋊D47—24no—
139C22⋊D47—24no—
140C2×Dic47—24no—
141C2×Dic47—22no—
142C2×Dic47—21no—
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145D188—24no—
146D188—21no—
147D188—22no—
148D188—22no—
149D188—44no—
150D188—44no—
151D188—42no—
152D188C2×D412yescomplemented
153C4×D47—24no—
154C4×D47—24no—
155C4×D47—22no—
156C4×D47—24no—
157C4×D47—22no—
158C4×D47—21no—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—21no—
162Dic94—24no—
163Dic94—21no—
164Dic94C2×D412yescomplemented
165C8×C47—22no—
166C47⋊C8—22no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—22no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47#12012yes—
173C22×C47C22×D411yescharacteristic
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—22no—
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—44no—
181C2×D47—48no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—42no—
185C2×D47—42no—
186C2×D47—42no—
187C2×D47—84no—
188C2×D47AGL(1,ℤ/8)12yescomplemented
189C4×C47—22no—
190C4×C47—42no—
191C4×C47#12012yes—
192C4×C47C22×D411yescharacteristic
193C4×C47C22×D411yescharacteristic
194Dic47—21no—
195Dic47—22no—
196Dic47—21no—
197#3006—471nomaximal, Sylow
198C2×C47—22no—
199C2×C47—42no—
200C2×C47C2×#12011yescharacteristic
201C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
202C2×C47#57511yescharacteristic
203D47—22no—
204D47—41no—
205D47—42no—
206D47—82no—
207C22×#41—471no—
208C2×AGL(1,ℤ/8)—471no—
209C2×AGL(1,ℤ/8)—471no—
210C2×#121—471no—
211#449—472no—
212#449—472no—
213#448—472no—
214#447—472no—
215#417—471no—
216#417D4711yescharacteristic, complemented
217#407—471no—
218C47#300611yescharacteristic, complemented, Sylow
219C2×#41—471no—
220C2×#41—471no—
221C2×#41—471no—
222C2×#41—941no—
223C2×#41—941no—
224C2×#41—944no—
225C2×#41—944no—
226C2×#41C2×D4711yescharacteristic
227C22×Q8—471no—
228C22×D4—471no—
229C22×D4—471no—
230C22×D4—941no—
231C22×D4—941no—
232C23×C4—471no—
233C23×C4—941no—
234AGL(1,ℤ/8)—944no—
235AGL(1,ℤ/8)—944no—
236C2×SD16—472no—
237C2×SD16—472no—
238C2×D8—472no—
239C2×D8—472no—
240C2×M16—471no—
241C2×M16C2×D4711yescharacteristic, complemented
242#121—472no—
243#121—472no—
244#121—941no—
245#121—941no—
246C2×C4⋊C4C2×D4711yescharacteristic, complemented
247C2×C22⋊C4—941no—
248#103—472no—
249#103C2×D4712yescomplemented
250#102—472no—
251#102C2×D4712yescomplemented
252C22⋊C8—472no—
253C22⋊C8—472no—
254C24—471no—
255C24—941no—
256C24—941no—
257#41—22no—
258#41—474no—
259#41—948no—
260#41—942no—
261#41—948no—
262#41—942no—
263#41—942no—
264#41—942no—
265#41—942no—
266#41D18814yescomplemented
267C2×Q8—471no—
268C2×Q8—941no—
269C2×Q8—942no—
270C2×Q8—942no—
271C2×Q8C22×D4711yescharacteristic
272C2×D4—21no—
273C2×D4—471no—
274C2×D4—472no—
275C2×D4—941no—
276C2×D4—942no—
277C2×D4—942no—
278C2×D4—941no—
279C2×D4—942no—
280C2×D4—948no—
281C2×D4—941no—
282C2×D4—941no—
283C2×D4—942no—
284C2×D4—942no—
285C2×D4—942no—
286C2×D4—941no—
287C2×D4—1884no—
288C2×D4C22×D4711yescharacteristic
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—471no—
292C22×C4—471no—
293C22×C4—471no—
294C22×C4—471no—
295C22×C4—471no—
296C22×C4—941no—
297C22×C4—941no—
298C22×C4—948no—
299C22×C4—941no—
300C22×C4—942no—
301C22×C4—942no—
302C22×C4—941no—
303C22×C4C22×D4711yescharacteristic
304SD16—944no—
305SD16—944no—
306D8—944no—
307D8—944no—
308M16—22no—
309M16—942no—
310C2×C8—472no—
311C2×C8C22×D4712yes—
312C4⋊C4—21no—
313C4⋊C4C22×D4712yes—
314C22⋊C4—942no—
315C22⋊C4—942no—
316C23—21no—
317C23—471no—
318C23—471no—
319C23—942no—
320C23—944no—
321C23—942no—
322C23—941no—
323C23—942no—
324C23—1881no—
325C23—1882no—
326C23—1882no—
327C23—1882no—
328C23—1882no—
329C23—1882no—
330C23D4×D4711yescharacteristic
331Q8—21no—
332Q8—472no—
333Q8—944no—
334Q8—941no—
335Q8C2×D18812yescomplemented
336D4—24no—
337D4—21no—
338D4—472no—
339D4—944no—
340D4—944no—
341D4—944no—
342D4—944no—
343D4—942no—
344D4—941no—
345D4—942no—
346D4—1884no—
347D4—1884no—
348D4—1882no—
349D4C2×D18812yescomplemented
350C2×C4—21no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—471no—
355C2×C4—471no—
356C2×C4—944no—
357C2×C4—944no—
358C2×C4—944no—
359C2×C4—942no—
360C2×C4—941no—
361C2×C4—942no—
362C2×C4—942no—
363C2×C4—944no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4C2×D18812yes—
369C2×C4D4×D4711yescharacteristic
370C2×C4D4×D4712yes—
371C2×C4C23×D4711yescharacteristic
372C8—22no—
373C8—942no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—41no—
378C22—41no—
379C22—472no—
380C22—941no—
381C22—941no—
382C22—942no—
383C22—941no—
384C22—941no—
385C22—941no—
386C22—3764no—
387C22—1884no—
388C22—1888no—
389C22—1882no—
390C22—1882no—
391C22—1882no—
392C22—1881no—
393C22—1881no—
394C22#1309399412yes—
395C22C2×D4×D4711yescharacteristic
396C4—22no—
397C4—42no—
398C4—941no—
399C4—941no—
400C4—942no—
401C4#1309399412yes—
402C4C2×D4×D4711yescharacteristic
403C4C22×D18811yescharacteristic
404C2—22no—
405C2—42no—
406C2—942no—
407C2—3762no—
408C2—1881no—
409C2—1882no—
410C2C2×#1309399411yescharacteristic
411C2AGL(1,ℤ/8)×D4711yescharacteristic
412C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#417C2
socleC22×C47C22×D4
hypercenter#417D47
hypocenterC47#3006
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#41×D47C2semidirect
2. C2×#13094052C2semidirect
3. C2×#13094049C2semidirect
4. C2×#13093999C2semidirect
5. #15689271C2semidirect
6. #15689269C2semidirect
7. #15689263C2semidirect
8. #15689258C2semidirect
9. #15689122C2semidirect
10. #15689086C2semidirect
11. C47×#417C2semidirect
12. C2×#10625354C22semidirect
16. C2×#10625352C22semidirect
19. C2×Q8×D47C22semidirect
21. C22×D188C22semidirect
23. C2×D4×D47C22semidirect
28. C2×#10625325C22semidirect
29. C2×#10625336C22semidirect
30. C2×D376C22semidirect
31. C2×#10625334C22semidirect
32. C2×#10625329C22semidirect
36. #13093999C22semidirect
38. #13093947C22semidirect
39. #13093944C22semidirect
40. (C2×D47)⋊C8C22semidirect
41. (C2×D47)⋊C8C22semidirect
43. C2×M16×C47C22semidirect
44. C2×C4⋊C4×C47C22semidirect
45. #103×C47C22semidirect
46. #102×C47C22semidirect
51. #41×C47D4semidirect
75. #10625350D4semidirect
125. Q8×C47C2×D4semidirect
128. D4×C47C2×D4semidirect
152. D188C2×D4semidirect
164. Dic94C2×D4semidirect
188. C2×D47AGL(1,ℤ/8)semidirect
216. #417D47semidirect
218. C47#3006semidirect
241. C2×M16C2×D47semidirect
246. C2×C4⋊C4C2×D47semidirect
249. #103C2×D47semidirect
251. #102C2×D47semidirect
266. #41D188semidirect
335. Q8C2×D188semidirect
349. D4C2×D188semidirect