Finite Group Databasebeta

← #20255232

Subgroups — #20255232

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689769C211yesmaximal, characteristic, complemented
2#15689480C211yesmaximal, characteristic, complemented
3#15689458C211yesmaximal, characteristic, complemented
4#15689447C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689357C211yesmaximal, characteristic, complemented
7#15689350C211yesmaximal, characteristic, complemented
8#15689338C211yesmaximal, characteristic, complemented
9#15689266C211yesmaximal, characteristic, complemented
10#15689256C211yesmaximal, characteristic, complemented
11C4×#10625334C211yesmaximal, characteristic, complemented
12D4×C47⋊C8C211yesmaximal, characteristic, complemented
13#15689117C211yesmaximal, characteristic, complemented
14C2×#13093944C211yesmaximal, characteristic, complemented
15C47×#553C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×#10625335C2211yescharacteristic, complemented
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C22×C47⋊C8C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic, complemented
23#13094012C2211yescharacteristic
24#13094009—21no—
25#13094003C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093997—21no—
28#13093992—21no—
29C4×D188C2211yescharacteristic
30C22⋊C4×D47—21no—
31#13093957C2211yescharacteristic, complemented
32#13093957C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35#13093947C2211yescharacteristic, complemented
36#13093947C2211yescharacteristic, complemented
37#13093947C2211yescharacteristic, complemented
38#13093945C2211yescharacteristic, complemented
39#13093944C2211yescharacteristic
40#13093944C2211yescharacteristic
41#13093944C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47C4×C47⋊C8C2211yescharacteristic, complemented
48#126×C47—21no—
49#125×C47C2211yescharacteristic, complemented
50#123×C47—21no—
51#121×C47—21no—
52#121×C47C2211yescharacteristic
53#121×C47C2211yescharacteristic, complemented
54C4×D4×C47—21no—
55C4×D4×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic, complemented
57#117×C47C2211yescharacteristic, complemented
58C2×C4⋊C4×C47C2211yescharacteristic
59C23×D47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47D411yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70#10625350—22no—
71#10625350—41no—
72C2×D188—22no—
73C2×D188—21no—
74C2×D188—41no—
75C2×D188C2311yescharacteristic
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×Dic94C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47D411yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊C4×C47D411yescharacteristic
92C22⋊C4×C47D411yescharacteristic
93C42×C47—21no—
94C42×C47C2311yescharacteristic
95C22⋊Dic47—21no—
96#10625335—41no—
97#10625334—22no—
98#10625334—41no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—81no—
119D4×C47—22no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—42no—
123D4×C47—81no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—81no—
132C2×C4×C47—81no—
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2411yescharacteristic
138C22⋊D47—42no—
139C22⋊D47—81no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142D188—21no—
143D188—21no—
144D188—21no—
145D188—42no—
146D188#4112yes—
147C4×D47—42no—
148C4×D47—81no—
149Dic94—21no—
150Dic94—21no—
151C47⋊C8—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47#13512yes—
164C22×C47C22×D411yescharacteristic
165C2×D47—22no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—84no—
172C4×C47—21no—
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47C2×#4111yescharacteristic
180C4×C47H(5,𝔽2)11yescharacteristic
181Dic47—41no—
182Dic47—41no—
183#3297—471nomaximal, Sylow
184C2×C47—22no—
185C2×C47—41no—
186C2×C47—81no—
187C2×C47#54611yescharacteristic
188C2×C47C2×#13511yescharacteristic
189C2×C47#57611yescharacteristic
190D47—42no—
191D47—81no—
192#553D4711yescharacteristic, complemented
193#546—471no—
194#488—471no—
195#484—471no—
196#482—471no—
197#478—471no—
198#466—471no—
199#465—471no—
200#463—471no—
201#449—471no—
202#447—471no—
203C4×D8—471no—
204C8×D4—471no—
205#416—471no—
206C2×#102—471no—
207C47#329711yescharacteristic, complemented, Sylow
208C2×#41—471no—
209C22×D4—471no—
210C2×SD16—471no—
211C2×D8—471no—
212C2×D8—471no—
213C22×C8—471no—
214C22×C8—471no—
215#126—21no—
216#125C2×D4711yescharacteristic, complemented
217#124—471no—
218#123—21no—
219#123—941no—
220C22⋊Q8—471no—
221#121—21no—
222#121—471no—
223#121—941no—
224#121C2×D4711yescharacteristic
225#121C2×D4711yescharacteristic, complemented
226#120—941no—
227C4×D4—21no—
228C4×D4—471no—
229C4×D4C2×D4711yescharacteristic
230C4×D4C2×D4711yescharacteristic, complemented
231#117C2×D4711yescharacteristic, complemented
232C2×C4⋊C4C2×D4711yescharacteristic
233C2×C22⋊C4—941no—
234#107—471no—
235#107—471no—
236#106—471no—
237C4⋊C8—471no—
238#103—471no—
239#103—471no—
240#103—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248C22⋊C8—471no—
249C22⋊C8—471no—
250C4×C8—471no—
251C24—941no—
252#41—942no—
253#41—1881no—
254C2×Q8—471no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—471no—
258C2×D4—471no—
259C2×D4—942no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—1881no—
264C2×D4C22⋊D4711yescharacteristic
265C2×D4C22×D4711yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272SD16—1881no—
273D8—942no—
274D8—1881no—
275C2×C8—471no—
276C2×C8—471no—
277C2×C8—471no—
278C2×C8—471no—
279C2×C8—1881no—
280C2×C8—1881no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—471no—
285C4⋊C4—941no—
286C4⋊C4C22⋊D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C4⋊C4C22×D4711yescharacteristic
289C4⋊C4C22×D4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4C22⋊D4711yescharacteristic
300C22⋊C4C22⋊D4711yescharacteristic
301C42—21no—
302C42C22×D4711yescharacteristic
303C23—21no—
304C23—941no—
305C23—941no—
306C23—3761no—
307C23—1882no—
308C23—1882no—
309C23C2×C22⋊D4711yescharacteristic
310C23C2×C22⋊D4711yescharacteristic
311Q8—941no—
312Q8—941no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—472no—
319D4—941no—
320D4—941no—
321D4—941no—
322D4—3761no—
323D4—1882no—
324D4—1882no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—3761no—
337C2×C4—1882no—
338C2×C4C2×C22⋊D4711yescharacteristic
339C2×C4C2×C22⋊D4711yescharacteristic
340C2×C4C2×C22⋊D4711yescharacteristic
341C2×C4C2×C22⋊D4711yescharacteristic
342C2×C4C23×D4711yescharacteristic
343C8—941no—
344C8—941no—
345C8—941no—
346C8—941no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—942no—
356C22—3764no—
357C22—1881no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22—1881no—
362C22#1309404412yes—
363C22C22×C22⋊D4711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—1881no—
372C4—1881no—
373C4#41×D4711yescharacteristic
374C4#1309407011yescharacteristic
375C2—22no—
376C2—41no—
377C2—81no—
378C2—3761no—
379C2—1882no—
380C2#1568976111yescharacteristic
381C2C2×#1309404411yescharacteristic
382C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#553C2
socleC22×C47C22×D4
hypercenter#553D47
hypocenterC47#3297
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #15689769C2semidirect
2. #15689480C2semidirect
3. #15689458C2semidirect
4. #15689447C2semidirect
5. #15689420C2semidirect
6. #15689357C2semidirect
7. #15689350C2semidirect
8. #15689338C2semidirect
9. #15689266C2semidirect
10. #15689256C2semidirect
11. C4×#10625334C2semidirect
12. D4×C47⋊C8C2semidirect
13. #15689117C2semidirect
14. C2×#13093944C2semidirect
15. C47×#553C2semidirect
18. C2×#10625335C22semidirect
22. C22×C47⋊C8C22semidirect
31. #13093957C22semidirect
32. #13093957C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. #13093947C22semidirect
36. #13093947C22semidirect
37. #13093947C22semidirect
38. #13093945C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. C4×C47⋊C8C22semidirect
49. #125×C47C22semidirect
53. #121×C47C22semidirect
56. C4×D4×C47C22semidirect
57. #117×C47C22semidirect
192. #553D47semidirect
207. C47#3297semidirect
216. #125C2×D47semidirect
225. #121C2×D47semidirect
230. C4×D4C2×D47semidirect
231. #117C2×D47semidirect