Finite Group Databasebeta

← #20254434

Subgroups — #20254434

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#15689690C211yesmaximal, characteristic, complemented
3#15689511C211yesmaximal, characteristic, complemented
4#15689498C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689476C211yesmaximal, characteristic, complemented
7#15689337C211yesmaximal, characteristic, complemented
8#15689336C211yesmaximal, characteristic, complemented
9#15689317C211yesmaximal, characteristic, complemented
10#15689316C211yesmaximal, characteristic, complemented
11#15689270C211yesmaximal, characteristic, complemented
12#15689266C211yesmaximal, characteristic, complemented
13#15689257C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#447C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625325C2211yescharacteristic, complemented
18C2×#10625335C2211yescharacteristic, complemented
19C2×D376C2211yescharacteristic, complemented
20C2×#10625334C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C2×#10625334C2211yescharacteristic, complemented
23#13094020C2211yescharacteristic
24#13094020C2211yescharacteristic
25#13094020C2211yescharacteristic, complemented
26#13094015C2211yescharacteristic, complemented
27#13094011C2211yescharacteristic
28#13094011C2211yescharacteristic
29#13094008—21no—
30#13094006—21no—
31#13093998C2211yescharacteristic
32#13093996—21no—
33#13093995—21no—
34#13093995—21no—
35#13093995—21no—
36#13093993—21no—
37#13093993—21no—
38D4×Dic47C2211yescharacteristic, complemented
39#13093986C2211yescharacteristic, complemented
40#13093983C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C24×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—41no—
63C2×D4×C47—41no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
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—
77#10625350—41no—
78#10625350—41no—
79C2×D188C2311yescharacteristic
80C2×D188C2311yescharacteristic
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×Dic94C2311yescharacteristic
84D8×C47—41no—
85D8×C47—41no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47D411yescharacteristic
96C22⋊Dic47D411yescharacteristic
97#10625335—41no—
98#10625334—41no—
99#10625334—41no—
100#10625334—41no—
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—
113#10625325—41no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—42no—
118C23×C47—81no—
119C23×C47—81no—
120C23×C47C2×D411yescharacteristic
121C22×D47—21no—
122C22×D47—21no—
123D4×C47—21no—
124D4×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×C47C2×D411yescharacteristic
135C2×C4×C47C2411yescharacteristic
136C22⋊D47—42no—
137C22⋊D47—81no—
138C22⋊D47—81no—
139C22⋊D47—81no—
140C22⋊D47—81no—
141C22⋊D47—81no—
142C22⋊D47—81no—
143C22⋊D47—81no—
144C2×Dic47—21no—
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—
155C4×D47—42no—
156C4×D47—81no—
157Dic94—21no—
158Dic94—21no—
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×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—84no—
176C22×C47C22×D411yescharacteristic
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C4×C47—21no—
184C4×C47—41no—
185C4×C47H(5,𝔽2)11yescharacteristic
186C4×C47H(5,𝔽2)11yescharacteristic
187Dic47—21no—
188Dic47—21no—
189Dic47—21no—
190Dic47—21no—
191Dic47—41no—
192Dic47—41no—
193#3220—471nomaximal, Sylow
194C2×C47—41no—
195C2×C47—81no—
196C2×C47—81no—
197C2×C47—81no—
198C2×C47#53511yescharacteristic
199C2×C47#57611yescharacteristic
200C2×C47#57611yescharacteristic
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#449—471no—
215#447—471no—
216#447D4711yescharacteristic, complemented
217#433—471no—
218C47#322011yescharacteristic, complemented, Sylow
219C2×#41—471no—
220C22×D4C2×D4711yescharacteristic
221C2×SD16—471no—
222C2×SD16—471no—
223C2×D8—471no—
224C2×D8—471no—
225C2×D8—471no—
226C2×D8—471no—
227C2×D8C2×D4711yescharacteristic
228C2×D8C2×D4711yescharacteristic
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#103—471no—
252#102—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102C2×D4711yescharacteristic
257#102C2×D4711yescharacteristic
258C22⋊C8—471no—
259C22⋊C8C2×D4711yescharacteristic
260#97—471no—
261C4×C8—471no—
262C24—21no—
263#41—1881no—
264#41—1881no—
265C2×Q8—471no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—471no—
271C2×D4—471no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C2×D4—941no—
280C2×D4C22×D4711yescharacteristic
281C2×D4C22×D4711yescharacteristic
282C2×D4C22×D4711yescharacteristic
283C22×C4—941no—
284C22×C4—941no—
285C22×C4—941no—
286C22×C4C22×D4711yescharacteristic
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—
316C42—471no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—941no—
324C23—941no—
325C23D4×D4711yescharacteristic
326Q8—941no—
327Q8—941no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
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—471no—
352C2×C4—471no—
353C2×C4—471no—
354C2×C4—471no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—3761no—
358C2×C4—3761no—
359C2×C4—1882no—
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—41no—
376C22—41no—
377C22—41no—
378C22—84no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22—1881no—
385C22C2×D4×D4711yescharacteristic
386C4—21no—
387C4—41no—
388C4—941no—
389C4—941no—
390C4—941no—
391C4—941no—
392C4—1881no—
393C4—1881no—
394C4#1309406911yescharacteristic
395C4#1309406911yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—81no—
400C2—3761no—
401C2—3761no—
402C2#1568968811yescharacteristic
403C2#1568992411yescharacteristic
404C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3220
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #15689726C2semidirect
2. #15689690C2semidirect
3. #15689511C2semidirect
4. #15689498C2semidirect
5. #15689486C2semidirect
6. #15689476C2semidirect
7. #15689337C2semidirect
8. #15689336C2semidirect
9. #15689317C2semidirect
10. #15689316C2semidirect
11. #15689270C2semidirect
12. #15689266C2semidirect
13. #15689257C2semidirect
14. #15689181C2semidirect
15. C47×#447C2semidirect
17. C2×#10625325C22semidirect
18. C2×#10625335C22semidirect
19. C2×D376C22semidirect
22. C2×#10625334C22semidirect
25. #13094020C22semidirect
26. #13094015C22semidirect
38. D4×Dic47C22semidirect
39. #13093986C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093947C22semidirect
45. #13093946C22semidirect
48. #13093944C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
216. #447D47semidirect
218. C47#3220semidirect