Finite Group Databasebeta

← #20253022

Subgroups — #20253022

Order 6016.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D47C211yesmaximal, characteristic, complemented
2C2×#13094030C211yesmaximal, characteristic, complemented
3#15689696C211yesmaximal, characteristic, complemented
4#15689689C211yesmaximal, characteristic
5#15689372C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689368C211yesmaximal, characteristic, complemented
8#15689367C211yesmaximal, characteristic, complemented
9#15689353C211yesmaximal, characteristic, complemented
10#15689352C211yesmaximal, characteristic, complemented
11#15689349C211yesmaximal, characteristic, complemented
12#15689158C211yesmaximal, characteristic, complemented
13#15689130C211yesmaximal, characteristic, complemented
14#15689126C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625336C2211yescharacteristic
22SD16×D47—24no—
23#13094030—24no—
24C2×#10625329C2211yescharacteristic, complemented
25C2×#10625324C2211yescharacteristic
26C2×#10625324C2211yescharacteristic, complemented
27C2×C8×D47C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic, complemented
29#13094023—21no—
30#13094020—21no—
31#13094010—21no—
32#13094010—21no—
33#13094009—21no—
34#13094006—21no—
35#13094004C2211yescharacteristic, complemented
36#13094003C2211yescharacteristic, complemented
37#13094000C2211yescharacteristic, complemented
38#13093999C2211yescharacteristic
39#13093998C2211yescharacteristic
40#13093995C2211yescharacteristic
41#13093994—21no—
42#13093992—21no—
43#13093982C2211yescharacteristic
44#13093982C2211yescharacteristic
45#13093957C2211yescharacteristic, complemented
46#13093957C2211yescharacteristic, complemented
47#13093956C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093948C2211yescharacteristic, complemented
50#13093947C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic
52#13093945C2211yescharacteristic
53#13093944C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22×C8×C47C2211yescharacteristic, complemented
56C22⋊Q8×C47C2211yescharacteristic, complemented
57#121×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47D411yescharacteristic
70C2×C22⋊D47D411yescharacteristic
71Q8×D47—22no—
72Q8×D47—22no—
73D4×D47—22no—
74D4×D47—22no—
75#10625350—22no—
76#10625350—22no—
77C2×D188—21no—
78C2×D188D411yescharacteristic
79C2×D188C2311yescharacteristic
80C2×C4×D47—21no—
81C2×C4×D47C2311yescharacteristic
82C2×C4×D47C2311yescharacteristic
83C2×Dic94—21no—
84C2×Dic94D411yescharacteristic
85C2×Dic94C2311yescharacteristic
86SD16×C47—22no—
87C2×C8×C47—22no—
88C2×C8×C47C2311yescharacteristic
89C2×C8×C47C2311yescharacteristic
90C4⋊C4×C47—21no—
91C4⋊C4×C47C2311yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97#10625336—22no—
98#10625335—22no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105C4⋊Dic47—21no—
106C4⋊Dic47C2311yescharacteristic
107C4⋊Dic47C2311yescharacteristic
108Dic47⋊C4—21no—
109Dic47⋊C4—21no—
110C4×Dic47—21no—
111C4×Dic47—21no—
112#10625329—22no—
113C2×C47⋊C8C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115#10625325—22no—
116#10625324—22no—
117#10625324—22no—
118C8×D47—22no—
119C8×D47D414yescomplemented
120C23×C47—21no—
121C23×C47C2×D411yescharacteristic
122C22×D47—21no—
123C22×D47—42no—
124C22×D47—81no—
125C22×D47—81no—
126C22×D47C2×D411yescharacteristic
127C22×D47C2×D411yescharacteristic
128Q8×C47—21no—
129Q8×C47—21no—
130D4×C47—21no—
131D4×C47—21no—
132D4×C47—81no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2411yescharacteristic
140C22⋊D47—22no—
141C22⋊D47—22no—
142C22⋊D47—42no—
143C22⋊D47—81no—
144C22⋊D47—81no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47C2×D411yescharacteristic
149C2×Dic47C2×D411yescharacteristic
150D188—22no—
151D188—21no—
152D188—21no—
153D188—81no—
154C4×D47—21no—
155C4×D47—21no—
156C4×D47—42no—
157C4×D47C2×D412yes—
158C4×D47#4112yes—
159Dic94—22no—
160Dic94—21no—
161Dic94—21no—
162Dic94—42no—
163C8×C47—21no—
164C8×C47C2×D412yes—
165C47⋊C8—21no—
166C47⋊C8C2×D412yes—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47C22×D411yescharacteristic
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—21no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—84no—
183C2×D47#12112yes—
184C4×C47—21no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47C22×D411yescharacteristic
189C4×C47C2×#4111yescharacteristic
190Dic47—21no—
191Dic47—41no—
192Dic47—41no—
193Dic47—41no—
194Dic47#12112yes—
195#3057—471nomaximal, Sylow
196C2×C47—41no—
197C2×C47—81no—
198C2×C47C2×#12111yescharacteristic
199C2×C47#57711yescharacteristic
200C2×C47#57711yescharacteristic
201D47—22no—
202D47—41no—
203D47—81no—
204C22×SD16—471no—
205C2×#131—471no—
206#536—471no—
207#535—471no—
208#468—471no—
209#468—471no—
210#468—471no—
211#468—471no—
212#465—471no—
213#465—471no—
214#465—471no—
215#465D4711yescharacteristic, complemented
216#427—471no—
217#419—471no—
218#418—471no—
219C47#305711yescharacteristic, complemented, Sylow
220C2×#41—471no—
221C22×Q8—471no—
222C22×D4—471no—
223C2×SD16—471no—
224C2×SD16—471no—
225C2×SD16—471no—
226C2×SD16—944no—
227C2×SD16C2×D4711yescharacteristic
228#131—944no—
229C2×M16—471no—
230C2×M16—471no—
231C2×M16—471no—
232C22×C8—471no—
233C22×C8—471no—
234C22×C8C2×D4711yescharacteristic, complemented
235C4⋊Q8—941no—
236#127—941no—
237#124—941no—
238#124—941no—
239#123—941no—
240#123—941no—
241C22⋊Q8—471no—
242C22⋊Q8—471no—
243C22⋊Q8—471no—
244C22⋊Q8C2×D4711yescharacteristic, complemented
245#121—471no—
246#121—471no—
247#121—471no—
248#121C2×D4711yescharacteristic
249#120—941no—
250#120—941no—
251#117—471no—
252#117—471no—
253#107—471no—
254#107—471no—
255#106—471no—
256#106C2×D4711yescharacteristic, complemented
257#103—471no—
258#103—471no—
259#103—471no—
260#103C2×D4711yescharacteristic, complemented
261#102—471no—
262#102—471no—
263#102—471no—
264#102C2×D4711yescharacteristic
265C24—941no—
266#41—942no—
267#41—942no—
268C2×Q8—471no—
269C2×Q8—471no—
270C2×Q8—941no—
271C2×Q8—942no—
272C2×Q8—942no—
273C2×Q8C22×D4711yescharacteristic
274C2×D4—21no—
275C2×D4—471no—
276C2×D4—471no—
277C2×D4—471no—
278C2×D4—471no—
279C2×D4—941no—
280C2×D4—942no—
281C2×D4—942no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4C22×D4711yescharacteristic
286C22×C4—471no—
287C22×C4—471no—
288C22×C4—941no—
289C22×C4C22×D4711yescharacteristic
290SD16—22no—
291SD16—942no—
292SD16—942no—
293SD16—942no—
294M16—942no—
295M16—942no—
296M16—942no—
297C2×C8—22no—
298C2×C8—471no—
299C2×C8—474no—
300C2×C8—471no—
301C2×C8—942no—
302C2×C8C22×D4711yescharacteristic
303C2×C8C22×D4711yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—471no—
306C4⋊C4—471no—
307C4⋊C4—941no—
308C4⋊C4—941no—
309C4⋊C4—941no—
310C4⋊C4C22×D4711yescharacteristic
311C4⋊C4C22×D4711yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C42—941no—
323C42—941no—
324C23—21no—
325C23—471no—
326C23—471no—
327C23—941no—
328C23—3761no—
329C23—3761no—
330C23—1882no—
331C23D4×D4711yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—942no—
335Q8—941no—
336Q8—941no—
337Q8—1882no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—942no—
342D4—942no—
343D4—942no—
344D4—941no—
345D4—941no—
346D4—3761no—
347D4—3761no—
348D4—3761no—
349D4—1882no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—471no—
356C2×C4—472no—
357C2×C4—472no—
358C2×C4—471no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—1882no—
365C2×C4D4×D4711yescharacteristic
366C2×C4C23×D4711yescharacteristic
367C8—21no—
368C8—472no—
369C8—941no—
370C8D4×D4712yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—472no—
378C22—941no—
379C22—941no—
380C22—941no—
381C22—941no—
382C22—941no—
383C22—3764no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22C2×D4×D4711yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—472no—
393C4—941no—
394C4—1881no—
395C4—1881no—
396C4—1881no—
397C4C2×D4×D4711yescharacteristic
398C4#41×D4711yescharacteristic
399C2—41no—
400C2—81no—
401C2—942no—
402C2—3761no—
403C2—1881no—
404C2#121×D4711yescharacteristic
405C2#1568992911yescharacteristic
406C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3057
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D47C2semidirect
2. C2×#13094030C2semidirect
3. #15689696C2semidirect
5. #15689372C2semidirect
6. #15689371C2semidirect
7. #15689368C2semidirect
8. #15689367C2semidirect
9. #15689353C2semidirect
10. #15689352C2semidirect
11. #15689349C2semidirect
12. #15689158C2semidirect
13. #15689130C2semidirect
14. #15689126C2semidirect
15. C47×#465C2semidirect
24. C2×#10625329C22semidirect
26. C2×#10625324C22semidirect
28. C2×C8×D47C22semidirect
35. #13094004C22semidirect
36. #13094003C22semidirect
37. #13094000C22semidirect
45. #13093957C22semidirect
46. #13093957C22semidirect
47. #13093956C22semidirect
48. #13093949C22semidirect
49. #13093948C22semidirect
50. #13093947C22semidirect
55. C22×C8×C47C22semidirect
56. C22⋊Q8×C47C22semidirect
58. #106×C47C22semidirect
59. #103×C47C22semidirect
119. C8×D47D4semidirect
215. #465D47semidirect
219. C47#3057semidirect
234. C22×C8C2×D47semidirect
244. C22⋊Q8C2×D47semidirect
256. #106C2×D47semidirect
260. #103C2×D47semidirect