Finite Group Databasebeta

← #20254252

Subgroups — #20254252

Order 6016.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689692C211yesmaximal, characteristic, complemented
2#15689689C211yesmaximal, characteristic, complemented
3#15689450C211yesmaximal, characteristic, complemented
4#15689449C211yesmaximal, characteristic, complemented
5#15689447C211yesmaximal, characteristic, complemented
6#15689377C211yesmaximal, characteristic, complemented
7#15689375C211yesmaximal, characteristic, complemented
8#15689360C211yesmaximal, characteristic, complemented
9#15689358C211yesmaximal, characteristic, complemented
10#15689259C211yesmaximal, characteristic, complemented
11#15689258C211yesmaximal, characteristic, complemented
12#15689258C211yesmaximal, characteristic, complemented
13#15689256C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic, complemented
18C2×D4×D47C2211yescharacteristic, complemented
19C2×D376C2211yescharacteristic
20C2×D376C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23C2×#10625324C2211yescharacteristic, complemented
24C2×C8×D47C2211yescharacteristic, complemented
25#13094021—21no—
26#13094020—21no—
27#13094012—21no—
28#13094010—21no—
29#13093999C2211yescharacteristic
30#13093999C2211yescharacteristic
31#13093999C2211yescharacteristic, complemented
32#13093999C2211yescharacteristic, complemented
33#13093999C2211yescharacteristic, complemented
34#13093998C2211yescharacteristic
35#13093995C2211yescharacteristic, complemented
36#13093994—21no—
37#13093994—21no—
38#13093994—21no—
39#13093992—21no—
40#13093982C2211yescharacteristic, complemented
41#13093957C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093944C2211yescharacteristic, complemented
46#13093944C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic, complemented
54#107×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47D411yescharacteristic
68C2×C22⋊D47D411yescharacteristic
69D4×D47—41no—
70D4×D47—41no—
71#10625350—41no—
72#10625350—41no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—41no—
80C2×D188—41no—
81C2×D188D411yescharacteristic
82C2×D188C2311yescharacteristic
83C2×D188C2311yescharacteristic
84C2×D188C2311yescharacteristic
85C2×C4×D47C2311yescharacteristic
86C2×C4×D47C2311yescharacteristic
87C2×Dic94D411yescharacteristic
88C2×C8×C47C2311yescharacteristic
89C2×C8×C47C2311yescharacteristic
90C4⋊C4×C47C2311yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C4⋊C4×C47C2311yescharacteristic
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C42×C47—21no—
96C22⋊Dic47—21no—
97#10625334—41no—
98#10625334—41no—
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—
105(C2×D47)⋊C4—21no—
106C4⋊Dic47C2311yescharacteristic
107C4×Dic47—21no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110D376—41no—
111D376—41no—
112#10625324—41no—
113C8×D47—41no—
114C23×C47—21no—
115C23×C47C2×D411yescharacteristic
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—42no—
120C22×D47—42no—
121C22×D47—81no—
122C22×D47—81no—
123C22×D47—81no—
124C22×D47—81no—
125C22×D47C2×D411yescharacteristic
126C22×D47C2×D411yescharacteristic
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—81no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—41no—
138C22⋊D47—41no—
139C22⋊D47—42no—
140C22⋊D47—81no—
141C22⋊D47—81no—
142C2×Dic47—21no—
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145D188—21no—
146D188—21no—
147D188—21no—
148D188—21no—
149D188—21no—
150D188—21no—
151D188—41no—
152D188—42no—
153D188—81no—
154D188—81no—
155D188—81no—
156D188—81no—
157D188—81no—
158C4×D47—21no—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—21no—
162Dic94—41no—
163C8×C47—21no—
164C8×C47—21no—
165C47⋊C8—21no—
166C47⋊C8—21no—
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—21no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—84no—
190C2×D47—84no—
191C4×C47—21no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47—41no—
195C4×C47H(5,𝔽2)11yescharacteristic
196C4×C47H(5,𝔽2)11yescharacteristic
197Dic47—21no—
198Dic47—21no—
199Dic47—41no—
200#3199—471nomaximal, Sylow
201C2×C47—41no—
202C2×C47—81no—
203C2×C47#53411yescharacteristic
204C2×C47#57611yescharacteristic
205C2×C47#57611yescharacteristic
206D47—41no—
207D47—41no—
208D47—81no—
209D47—81no—
210D47—81no—
211#535—471no—
212#535—471no—
213#482—471no—
214#482—471no—
215#482—471no—
216#482D4711yescharacteristic, complemented
217#469—471no—
218#469—471no—
219#466—471no—
220#466—471no—
221#447—471no—
222#447—471no—
223#447—471no—
224#447—471no—
225#408—471no—
226C47#319911yescharacteristic, complemented, Sylow
227C2×#41—471no—
228C22×D4—471no—
229C22×D4—471no—
230C2×D8—471no—
231C2×D8—471no—
232C2×D8—471no—
233C2×D8—471no—
234C2×M16—471no—
235C22×C8—471no—
236#127—941no—
237#127—941no—
238#124—941no—
239#124—941no—
240#121—471no—
241#121—471no—
242#121—471no—
243#121—471no—
244#121—471no—
245#121—471no—
246#121—471no—
247#121C2×D4711yescharacteristic
248#120—941no—
249#120—941no—
250#120—941no—
251#120—941no—
252#117—471no—
253#117C2×D4711yescharacteristic, complemented
254#107—471no—
255#107C2×D4711yescharacteristic, complemented
256#106—471no—
257#106C2×D4711yescharacteristic, complemented
258#102—471no—
259#102—471no—
260#102—471no—
261#102—471no—
262#102—471no—
263#102—471no—
264#102C2×D4711yescharacteristic, complemented
265#102C2×D4711yescharacteristic, complemented
266C22⋊C8—471no—
267C22⋊C8—471no—
268C22⋊C8—471no—
269C22⋊C8C2×D4711yescharacteristic, complemented
270C24—941no—
271C24—941no—
272#41—1881no—
273#41—1881no—
274C2×Q8—471no—
275C2×D4—21no—
276C2×D4—471no—
277C2×D4—471no—
278C2×D4—471no—
279C2×D4—471no—
280C2×D4—471no—
281C2×D4—471no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4—941no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4—941no—
290C2×D4—941no—
291C2×D4—1881no—
292C2×D4—1881no—
293C2×D4—1881no—
294C2×D4—1881no—
295C2×D4C22×D4711yescharacteristic
296C22×C4—471no—
297C22×C4—471no—
298C22×C4C22×D4711yescharacteristic
299D8—1881no—
300D8—1881no—
301D8—1881no—
302D8—1881no—
303M16—1881no—
304C2×C8—471no—
305C2×C8—471no—
306C2×C8—1881no—
307C2×C8C22×D4711yescharacteristic
308C2×C8C22×D4711yescharacteristic
309C4⋊C4—471no—
310C4⋊C4C22×D4711yescharacteristic
311C4⋊C4C22×D4711yescharacteristic
312C4⋊C4C22×D4711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C22⋊C4—941no—
318C22⋊C4—941no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C42—21no—
324C42—941no—
325C23—21no—
326C23—471no—
327C23—471no—
328C23—941no—
329C23—941no—
330C23—941no—
331C23—3761no—
332C23—3761no—
333C23—3761no—
334C23—3761no—
335C23—1882no—
336C23—1882no—
337C23D4×D4711yescharacteristic
338Q8—1881no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—941no—
343D4—941no—
344D4—941no—
345D4—941no—
346D4—941no—
347D4—941no—
348D4—3761no—
349D4—3761no—
350D4—3761no—
351D4—3761no—
352D4—3761no—
353D4—3761no—
354D4—3761no—
355D4—1881no—
356D4—1882no—
357D4—1881no—
358D4—1881no—
359D4—1882no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—471no—
366C2×C4—471no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4D4×D4711yescharacteristic
373C2×C4C23×D4711yescharacteristic
374C8—21no—
375C8—21no—
376C8—941no—
377C8—941no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—941no—
385C22—941no—
386C22—941no—
387C22—941no—
388C22—941no—
389C22—941no—
390C22—3764no—
391C22—3764no—
392C22—1881no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22—1881no—
398C22—1881no—
399C22—1881no—
400C22—1881no—
401C22C2×D4×D4711yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—941no—
407C4—941no—
408C4—1881no—
409C4#1309407011yescharacteristic
410C4#1309407011yescharacteristic
411C2—41no—
412C2—81no—
413C2—3761no—
414C2—3761no—
415C2—3761no—
416C2—1881no—
417C2—1881no—
418C2#1568968411yescharacteristic
419C2#1568992511yescharacteristic
420C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3199
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #15689692C2semidirect
2. #15689689C2semidirect
3. #15689450C2semidirect
4. #15689449C2semidirect
5. #15689447C2semidirect
6. #15689377C2semidirect
7. #15689375C2semidirect
8. #15689360C2semidirect
9. #15689358C2semidirect
10. #15689259C2semidirect
11. #15689258C2semidirect
12. #15689258C2semidirect
13. #15689256C2semidirect
14. #15689088C2semidirect
15. C47×#482C2semidirect
17. C22×D188C22semidirect
18. C2×D4×D47C22semidirect
23. C2×#10625324C22semidirect
24. C2×C8×D47C22semidirect
31. #13093999C22semidirect
32. #13093999C22semidirect
33. #13093999C22semidirect
35. #13093995C22semidirect
40. #13093982C22semidirect
41. #13093957C22semidirect
42. #13093955C22semidirect
43. #13093946C22semidirect
44. #13093946C22semidirect
45. #13093944C22semidirect
46. #13093944C22semidirect
47. #13093944C22semidirect
48. #13093944C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. (C2×D47)⋊C8C22semidirect
53. #117×C47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. #102×C47C22semidirect
57. #102×C47C22semidirect
58. C22⋊C8×C47C22semidirect
216. #482D47semidirect
226. C47#3199semidirect
253. #117C2×D47semidirect
255. #107C2×D47semidirect
257. #106C2×D47semidirect
264. #102C2×D47semidirect
265. #102C2×D47semidirect
269. C22⋊C8C2×D47semidirect