Finite Group Databasebeta

← #20254436

Subgroups — #20254436

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#15689726C211yesmaximal, characteristic, complemented
2#15689687C211yesmaximal, characteristic, complemented
3#15689509C211yesmaximal, characteristic, complemented
4#15689498C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689479C211yesmaximal, characteristic, complemented
7#15689341C211yesmaximal, characteristic, complemented
8#15689340C211yesmaximal, characteristic, complemented
9#15689317C211yesmaximal, characteristic, complemented
10#15689316C211yesmaximal, characteristic, complemented
11#15689268C211yesmaximal, characteristic, complemented
12#15689259C211yesmaximal, characteristic, complemented
13#15689256C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×#10625336C2211yescharacteristic, complemented
18C2×D376C2211yescharacteristic
19C2×D376C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C2×#10625334C2211yescharacteristic, complemented
23#13094020C2211yescharacteristic
24#13094020C2211yescharacteristic
25#13094020C2211yescharacteristic, complemented
26#13094015C2211yescharacteristic, complemented
27#13094013C2211yescharacteristic
28#13094013C2211yescharacteristic
29#13094008—21no—
30#13094006—21no—
31#13093998—21no—
32#13093998—21no—
33#13093998C2211yescharacteristic
34#13093996—21no—
35#13093995—21no—
36#13093992—21no—
37#13093992—21no—
38D4×Dic47C2211yescharacteristic, complemented
39#13093986C2211yescharacteristic, complemented
40#13093983C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093948C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×#41×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic, complemented
54C2×D8×C47C2211yescharacteristic, complemented
55#121×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C23×D47—21no—
60#41×C47—41no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C22×Dic47—21no—
77C2×D188—21no—
78C2×D188—41no—
79C2×D188—41no—
80C2×D188C2311yescharacteristic
81C2×D188C2311yescharacteristic
82C2×D188C2311yescharacteristic
83C2×C4×D47—21no—
84SD16×C47—41no—
85D8×C47—41no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47D411yescharacteristic
92C22⋊Dic47D411yescharacteristic
93#10625336—41no—
94#10625334—41no—
95#10625334—41no—
96#10625334—41no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103C4⋊Dic47—21no—
104C4⋊Dic47D411yescharacteristic
105C4⋊Dic47D411yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107Dic47⋊C4—21no—
108C4×Dic47C2311yescharacteristic
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112D376—41no—
113D376—41no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47C2×D411yescharacteristic
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—42no—
121C22×D47—81no—
122C22×D47—81no—
123Q8×C47—21no—
124Q8×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—42no—
130D4×C47—81no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—42no—
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2411yescharacteristic
138C22⋊D47—81no—
139C22⋊D47—81no—
140C22⋊D47—81no—
141C22⋊D47—81no—
142C22⋊D47—81no—
143C22⋊D47—81no—
144C22⋊D47—81no—
145C2×Dic47—21no—
146C2×Dic47—81no—
147C2×Dic47C2×D411yescharacteristic
148C2×Dic47C2×D411yescharacteristic
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151D188—21no—
152D188—21no—
153D188—21no—
154D188—21no—
155D188—21no—
156D188—21no—
157D188—42no—
158C4×D47—81no—
159C8×C47—21no—
160C8×C47—21no—
161C47⋊C8—21no—
162C47⋊C8—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47C22×D411yescharacteristic
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
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—41no—
185C4×C47—41no—
186C4×C47H(5,𝔽2)11yescharacteristic
187C4×C47H(5,𝔽2)11yescharacteristic
188Dic47—21no—
189Dic47—21no—
190Dic47—21no—
191Dic47—21no—
192Dic47—41no—
193#3220—471nomaximal, Sylow
194C2×C47—41no—
195C2×C47—81no—
196C2×C47—81no—
197C2×C47#53511yescharacteristic
198C2×C47#57611yescharacteristic
199C2×C47#57611yescharacteristic
200D47—81no—
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#459—471no—
213#449—471no—
214#449D4711yescharacteristic, complemented
215#447—471no—
216#447—471no—
217#433—471no—
218C47#322011yescharacteristic, complemented, Sylow
219C2×#41C2×D4711yescharacteristic
220C22×D4—471no—
221C2×SD16—471no—
222C2×SD16C2×D4711yescharacteristic, complemented
223C2×D8—471no—
224C2×D8—471no—
225C2×D8—471no—
226C2×D8—471no—
227C2×D8—471no—
228C2×D8C2×D4711yescharacteristic, complemented
229#127—471no—
230#127—471no—
231#127—471no—
232#125—471no—
233#124—471no—
234#124—471no—
235#123—941no—
236#123—941no—
237#121—471no—
238#121—941no—
239#121—941no—
240#121—941no—
241#121—941no—
242#121C2×D4711yescharacteristic
243#120—941no—
244#120—941no—
245C4×D4—471no—
246C4×D4—471no—
247#117—471no—
248C4⋊C8—471no—
249C4⋊C8—471no—
250#103—471no—
251#103C2×D4711yescharacteristic, complemented
252#102—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102—471no—
257#102C2×D4711yescharacteristic, complemented
258C22⋊C8—471no—
259C22⋊C8C2×D4711yescharacteristic
260#97—471no—
261C4×C8—471no—
262C24—941no—
263#41—41no—
264#41—41no—
265C2×Q8C22×D4711yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—471no—
269C2×D4—471no—
270C2×D4—471no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C2×D4—1881no—
280C2×D4—1881no—
281C2×D4C22×D4711yescharacteristic
282C2×D4C22×D4711yescharacteristic
283C22×C4—21no—
284C22×C4—941no—
285C22×C4—941no—
286C22×C4C22×D4711yescharacteristic
287SD16—41no—
288SD16—1881no—
289D8—41no—
290D8—1881no—
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—
316C42—471no—
317C23—21no—
318C23—21no—
319C23—941no—
320C23—941no—
321C23—941no—
322C23—3761no—
323C23—3761no—
324C23—1882no—
325C23D4×D4711yescharacteristic
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—941no—
335D4—941no—
336D4—941no—
337D4—941no—
338D4—941no—
339D4—941no—
340D4—3761no—
341D4—3761no—
342D4—3761no—
343D4—3761no—
344D4—3761no—
345D4—3761no—
346D4—3761no—
347D4—1882no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—471no—
354C2×C4—471no—
355C2×C4—471no—
356C2×C4—471no—
357C2×C4—941no—
358C2×C4—3761no—
359C2×C4—3761no—
360C2×C4D4×D4711yescharacteristic
361C2×C4C23×D4711yescharacteristic
362C8—21no—
363C8—21no—
364C8—941no—
365C8—941no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—3764no—
376C22—1881no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22—1881no—
385C22C2×D4×D4711yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—941no—
390C4—941no—
391C4—941no—
392C4—941no—
393C4—1881no—
394C4#1309406911yescharacteristic
395C4#1309406911yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—3761no—
400C2—3761no—
401C2—3761no—
402C2#1568968811yescharacteristic
403C2#1568992511yescharacteristic
404C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3220
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #15689726C2semidirect
2. #15689687C2semidirect
3. #15689509C2semidirect
4. #15689498C2semidirect
5. #15689486C2semidirect
6. #15689479C2semidirect
7. #15689341C2semidirect
8. #15689340C2semidirect
9. #15689317C2semidirect
10. #15689316C2semidirect
11. #15689268C2semidirect
12. #15689259C2semidirect
13. #15689256C2semidirect
14. #15689181C2semidirect
15. C47×#449C2semidirect
17. C2×#10625336C22semidirect
22. C2×#10625334C22semidirect
25. #13094020C22semidirect
26. #13094015C22semidirect
38. D4×Dic47C22semidirect
39. #13093986C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093948C22semidirect
46. #13093945C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
53. C2×SD16×C47C22semidirect
54. C2×D8×C47C22semidirect
56. #103×C47C22semidirect
57. #102×C47C22semidirect
214. #449D47semidirect
218. C47#3220semidirect
222. C2×SD16C2×D47semidirect
228. C2×D8C2×D47semidirect
251. #103C2×D47semidirect
257. #102C2×D47semidirect