Finite Group Databasebeta

← #20254437

Subgroups — #20254437

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689724C211yesmaximal, characteristic, complemented
2#15689686C211yesmaximal, characteristic, complemented
3#15689511C211yesmaximal, characteristic, complemented
4#15689498C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689476C211yesmaximal, characteristic, complemented
7#15689339C211yesmaximal, characteristic, complemented
8#15689338C211yesmaximal, characteristic, complemented
9#15689315C211yesmaximal, characteristic, complemented
10#15689269C211yesmaximal, characteristic, complemented
11#15689265C211yesmaximal, characteristic, complemented
12#15689258C211yesmaximal, characteristic, complemented
13#15689255C211yesmaximal, characteristic, complemented
14#15689183C211yesmaximal, characteristic, complemented
15C47×#459C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625325C2211yescharacteristic, complemented
19C2×#10625335C2211yescharacteristic, complemented
20C2×D376C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23C2×#10625334C2211yescharacteristic, complemented
24#13094020C2211yescharacteristic
25#13094020C2211yescharacteristic, complemented
26#13094015C2211yescharacteristic, complemented
27#13094012C2211yescharacteristic
28#13094011C2211yescharacteristic
29#13094007—21no—
30#13094006—21no—
31#13093999C2211yescharacteristic
32#13093998—21no—
33#13093997—21no—
34#13093996—21no—
35#13093996—21no—
36#13093995C2211yescharacteristic
37#13093992—21no—
38#13093992—21no—
39C4×D188C2211yescharacteristic, complemented
40#13093981C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×D8×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic, complemented
54#127×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C22×Dic47—21no—
74#10625352—41no—
75#10625352—41no—
76D4×D47—41no—
77D4×D47—41no—
78C2×D188—21no—
79C2×D188C2311yescharacteristic
80C2×D188C2311yescharacteristic
81C2×C4×D47—21no—
82C2×C4×D47C2311yescharacteristic
83C2×Dic94C2311yescharacteristic
84D8×C47—41no—
85D8×C47—41no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94#10625335—41no—
95#10625334—41no—
96#10625334—41no—
97#10625334—41no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4D411yescharacteristic
103(C2×D47)⋊C4D411yescharacteristic
104C4⋊Dic47—21no—
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4D411yescharacteristic
108Dic47⋊C4D411yescharacteristic
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112D376—41no—
113#10625325—41no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C22×D47C2×D411yescharacteristic
123D4×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—81no—
130D4×C47—81no—
131C2×C4×C47—21no—
132C2×C4×C47—81no—
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2411yescharacteristic
136C22⋊D47—42no—
137C22⋊D47—42no—
138C22⋊D47—81no—
139C22⋊D47—81no—
140C22⋊D47—81no—
141C22⋊D47—81no—
142C22⋊D47—81no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—42no—
146C2×Dic47C2×D411yescharacteristic
147C2×Dic47C2×D411yescharacteristic
148C2×Dic47C2×D411yescharacteristic
149D188—21no—
150D188—21no—
151D188—21no—
152D188—21no—
153D188—81no—
154C4×D47—21no—
155C4×D47—21no—
156C4×D47—81no—
157Dic94—21no—
158Dic94—21no—
159C8×C47—21no—
160C8×C47—21no—
161C47⋊C8—21no—
162C47⋊C8—21no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47C22×D411yescharacteristic
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—84no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—41no—
186C4×C47H(5,𝔽2)11yescharacteristic
187C4×C47H(5,𝔽2)11yescharacteristic
188Dic47—21no—
189Dic47—21no—
190Dic47—21no—
191Dic47—41no—
192Dic47—41no—
193#3220—471nomaximal, Sylow
194C2×C47—81no—
195C2×C47—81no—
196C2×C47—81no—
197C2×C47#53511yescharacteristic
198C2×C47#57611yescharacteristic
199C2×C47#57611yescharacteristic
200D47—41no—
201D47—81no—
202D47—81no—
203#540—471no—
204#535—471no—
205#496—471no—
206#493—471no—
207#490—471no—
208#488—471no—
209#463—471no—
210#463—471no—
211#459—471no—
212#459D4711yescharacteristic, complemented
213#449—471no—
214#449—471no—
215#447—471no—
216#447—471no—
217#433—471no—
218C47#322011yescharacteristic, complemented, Sylow
219C2×#41—471no—
220C22×D4—471no—
221C2×SD16—471no—
222C2×SD16—471no—
223C2×D8—471no—
224C2×D8—471no—
225C2×D8—471no—
226C2×D8—471no—
227C2×D8C2×D4711yescharacteristic
228C2×D8C2×D4711yescharacteristic, complemented
229#127—471no—
230#127—471no—
231#127C2×D4711yescharacteristic
232#125—471no—
233#124—471no—
234#124—471no—
235#123—941no—
236#123—941no—
237#121—471no—
238#121—471no—
239#121—941no—
240#121—941no—
241#121—941no—
242#121—941no—
243#120—941no—
244#120—941no—
245C4×D4—471no—
246C4×D4C2×D4711yescharacteristic, complemented
247#117—471no—
248C4⋊C8—471no—
249C4⋊C8C2×D4711yescharacteristic, complemented
250#103—471no—
251#103—471no—
252#102—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102C2×D4711yescharacteristic
257#102C2×D4711yescharacteristic, complemented
258C22⋊C8—471no—
259C22⋊C8—471no—
260#97—471no—
261C4×C8—471no—
262C24—941no—
263#41—1881no—
264#41—1881no—
265C2×Q8—471no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—471no—
269C2×D4—471no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—1881no—
279C2×D4—1881no—
280C2×D4C22×D4711yescharacteristic
281C2×D4C22×D4711yescharacteristic
282C2×D4C22×D4711yescharacteristic
283C22×C4—21no—
284C22×C4—471no—
285C22×C4—941no—
286C22×C4—941no—
287SD16—1881no—
288SD16—1881no—
289D8—41no—
290D8—41no—
291D8—1881no—
292D8—1881no—
293D8—1881no—
294D8—1881no—
295C2×C8—471no—
296C2×C8—471no—
297C2×C8C22×D4711yescharacteristic
298C2×C8C22×D4711yescharacteristic
299C4⋊C4—471no—
300C4⋊C4—471no—
301C4⋊C4—471no—
302C4⋊C4—941no—
303C4⋊C4—941no—
304C4⋊C4C22×D4711yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—471no—
307C22⋊C4—471no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4—941no—
311C22⋊C4—941no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C42—471no—
316C42C22×D4711yescharacteristic
317C23—21no—
318C23—21no—
319C23—21no—
320C23—471no—
321C23—941no—
322C23—941no—
323C23—3761no—
324C23—3761no—
325C23—1882no—
326Q8—941no—
327Q8—941no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—941no—
337D4—941no—
338D4—941no—
339D4—941no—
340D4—3761no—
341D4—3761no—
342D4—3761no—
343D4—3761no—
344D4—3761no—
345D4—3761no—
346D4—1882no—
347D4—1882no—
348C2×C4—21no—
349C2×C4—81no—
350C2×C4—471no—
351C2×C4—471no—
352C2×C4—471no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—3761no—
358C2×C4—1882no—
359C2×C4D4×D4711yescharacteristic
360C2×C4D4×D4711yescharacteristic
361C2×C4C23×D4711yescharacteristic
362C8—21no—
363C8—21no—
364C8—941no—
365C8—941no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—941no—
376C22—941no—
377C22—941no—
378C22—3764no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22—1881no—
385C22C2×D4×D4711yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—941no—
390C4—941no—
391C4—941no—
392C4—1881no—
393C4—1881no—
394C4#1309406911yescharacteristic
395C4#1309407011yescharacteristic
396C2—81no—
397C2—81no—
398C2—81no—
399C2—3761no—
400C2—3761no—
401C2—1881no—
402C2#1568968911yescharacteristic
403C2#1568992411yescharacteristic
404C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47#3220
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #15689724C2semidirect
2. #15689686C2semidirect
3. #15689511C2semidirect
4. #15689498C2semidirect
5. #15689486C2semidirect
6. #15689476C2semidirect
7. #15689339C2semidirect
8. #15689338C2semidirect
9. #15689315C2semidirect
10. #15689269C2semidirect
11. #15689265C2semidirect
12. #15689258C2semidirect
13. #15689255C2semidirect
14. #15689183C2semidirect
15. C47×#459C2semidirect
18. C2×#10625325C22semidirect
19. C2×#10625335C22semidirect
23. C2×#10625334C22semidirect
25. #13094020C22semidirect
26. #13094015C22semidirect
39. C4×D188C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093949C22semidirect
43. #13093947C22semidirect
46. #13093945C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
53. C2×D8×C47C22semidirect
55. C4×D4×C47C22semidirect
56. C4⋊C8×C47C22semidirect
58. #102×C47C22semidirect
212. #459D47semidirect
218. C47#3220semidirect
228. C2×D8C2×D47semidirect
246. C4×D4C2×D47semidirect
249. C4⋊C8C2×D47semidirect
257. #102C2×D47semidirect