Finite Group Databasebeta

← #20255628

Subgroups — #20255628

Order 6016.

460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689836C211yesmaximal, characteristic, complemented
2#15689757C211yesmaximal, characteristic, complemented
3#15689468C211yesmaximal, characteristic, complemented
4#15689450C211yesmaximal, characteristic, complemented
5#15689412C211yesmaximal, characteristic, complemented
6#15689377C211yesmaximal, characteristic, complemented
7#15689374C211yesmaximal, characteristic, complemented
8#15689317C211yesmaximal, characteristic, complemented
9#15689259C211yesmaximal, characteristic, complemented
10#15689258C211yesmaximal, characteristic, complemented
11#15689205C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689127C211yesmaximal, characteristic, complemented
14#15689126C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×D4×D47—21no—
18C2×D4×D47C2211yescharacteristic
19C2×D376C2211yescharacteristic
20C2×D376C2211yescharacteristic, complemented
21C2×#10625334C2211yescharacteristic, complemented
22C2×#10625329C2211yescharacteristic, complemented
23C2×#10625324C2211yescharacteristic, complemented
24#13094023C2211yescharacteristic, complemented
25#13094020C2211yescharacteristic
26#13094012—21no—
27#13094010—21no—
28#13093999C2211yescharacteristic
29#13093999C2211yescharacteristic, complemented
30#13093998C2211yescharacteristic, complemented
31#13093997—21no—
32#13093997—21no—
33#13093994—21no—
34#13093992—21no—
35#13093986C2211yescharacteristic
36#13093986C2211yescharacteristic, complemented
37C4×C22⋊D47C2211yescharacteristic
38#13093982C2211yescharacteristic, complemented
39#13093981—21no—
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic, complemented
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, 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⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69D4×D47—22no—
70D4×D47—41no—
71D4×D47—44no—
72C2×D188—22no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—41no—
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×D188C2311yescharacteristic
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47C2311yescharacteristic
83C2×Dic94—21no—
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C42×C47—21no—
92C22⋊Dic47D411yescharacteristic
93#10625334—41no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4D411yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47C2311yescharacteristic
106#10625329—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109D376—22no—
110D376—41no—
111#10625324—41no—
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—42no—
121C22×D47—81no—
122C22×D47—81no—
123C22×D47C2×D411yescharacteristic
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—42no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2411yescharacteristic
134C22⋊D47—22no—
135C22⋊D47—42no—
136C22⋊D47—42no—
137C22⋊D47—81no—
138C22⋊D47—81no—
139C2×Dic47—21no—
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143D188—21no—
144D188—21no—
145D188—21no—
146D188—21no—
147D188—21no—
148D188—42no—
149D188—42no—
150D188—81no—
151D188#4112yes—
152C4×D47—21no—
153C4×D47—21no—
154C4×D47—42no—
155C4×D47—42no—
156Dic94—81no—
157C8×C47—21no—
158C8×C47—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47C22×D411yescharacteristic
168C2×D47—21no—
169C2×D47—22no—
170C2×D47—21no—
171C2×D47—21no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—84no—
181C2×D47—84no—
182C4×C47—21no—
183C4×C47—41no—
184C4×C47—41no—
185C4×C47—41no—
186C4×C47C2×#4111yescharacteristic
187C4×C47H(5,𝔽2)11yescharacteristic
188Dic47—21no—
189Dic47—21no—
190Dic47—41no—
191Dic47AGL(1,ℤ/8)12yes—
192#3325—471nomaximal, Sylow
193C2×C47—41no—
194C2×C47—81no—
195C2×C47#54611yescharacteristic
196C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C47#57611yescharacteristic
198D47—41no—
199D47—42no—
200D47—81no—
201D47—81no—
202#555—471no—
203D42—471no—
204#486—471no—
205#482—471no—
206#482D4711yescharacteristic, complemented
207#476—471no—
208#469—471no—
209#469—471no—
210#459—471no—
211#447—471no—
212#447—471no—
213C4×D8—471no—
214#436—471no—
215#418—471no—
216#418—471no—
217C47#332511yescharacteristic, complemented, Sylow
218C22×D4—471no—
219C22×D4—471no—
220C22×D4—941no—
221C2×D8—471no—
222C2×D8—471no—
223C2×D8—471no—
224C2×M16—471no—
225C2×M16—471no—
226C4⋊Q8—471no—
227#127—471no—
228#124—941no—
229#124—941no—
230#121—471no—
231#121—471no—
232#121—471no—
233#121—941no—
234#121—941no—
235#121C2×D4711yescharacteristic
236#120—941no—
237#120—941no—
238C4×D4—471no—
239C4×D4—471no—
240C4×D4—471no—
241#117—471no—
242#117—941no—
243#117C2×D4711yescharacteristic, complemented
244#107C2×D4711yescharacteristic, complemented
245#106—471no—
246#106C2×D4711yescharacteristic, complemented
247C4⋊C8—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252#102—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102C2×D4711yescharacteristic, complemented
257#102C2×D4711yescharacteristic, complemented
258C22⋊C8—471no—
259C22⋊C8C2×D4711yescharacteristic, complemented
260C4×C8—471no—
261C24—941no—
262C24—941no—
263C2×Q8—941no—
264C2×D4—21no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—471no—
268C2×D4—471no—
269C2×D4—942no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—942no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—1881no—
279C2×D4—1881no—
280C2×D4—1884no—
281C2×D4C22×D4711yescharacteristic
282C22×C4—471no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4C22×D4711yescharacteristic
286D8—942no—
287D8—1881no—
288D8—1881no—
289M16—1881no—
290M16—1881no—
291C2×C8—471no—
292C2×C8—471no—
293C2×C8C22×D4711yescharacteristic
294C2×C8C22×D4711yescharacteristic
295C4⋊C4—471no—
296C4⋊C4—471no—
297C4⋊C4—941no—
298C4⋊C4C22×D4711yescharacteristic
299C4⋊C4C22×D4711yescharacteristic
300C4⋊C4C22×D4711yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—471no—
304C22⋊C4—471no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4—941no—
311C42—21no—
312C42—471no—
313C42—941no—
314C23—21no—
315C23—471no—
316C23—941no—
317C23—941no—
318C23—941no—
319C23—3761no—
320C23—3761no—
321C23—1882no—
322C23—1882no—
323C23—1882no—
324C23—1882no—
325C23D4×D4711yescharacteristic
326Q8—3761no—
327D4—21no—
328D4—21no—
329D4—42no—
330D4—472no—
331D4—942no—
332D4—941no—
333D4—941no—
334D4—941no—
335D4—941no—
336D4—941no—
337D4—3761no—
338D4—3761no—
339D4—3761no—
340D4—1882no—
341D4—1882no—
342D4—1882no—
343D4—1882no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—471no—
350C2×C4—471no—
351C2×C4—471no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4D4×D4711yescharacteristic
358C2×C4C23×D4711yescharacteristic
359C8—21no—
360C8—21no—
361C8—941no—
362C8—941no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—941no—
370C22—942no—
371C22—941no—
372C22—941no—
373C22—3764no—
374C22—3764no—
375C22—1881no—
376C22—1881no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22C2×D4×D4711yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—472no—
389C4—941no—
390C4—941no—
391C4—1881no—
392C4#41×D4711yescharacteristic
393C4#1309407011yescharacteristic
394C2—41no—
395C2—81no—
396C2—3761no—
397C2—3761no—
398C2—1881no—
399C2—1882no—
400C2#1568976511yescharacteristic
401C2AGL(1,ℤ/8)×D4711yescharacteristic
402C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3325
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. #15689836C2semidirect
2. #15689757C2semidirect
3. #15689468C2semidirect
4. #15689450C2semidirect
5. #15689412C2semidirect
6. #15689377C2semidirect
7. #15689374C2semidirect
8. #15689317C2semidirect
9. #15689259C2semidirect
10. #15689258C2semidirect
11. #15689205C2semidirect
12. #15689198C2semidirect
13. #15689127C2semidirect
14. #15689126C2semidirect
15. C47×#482C2semidirect
20. C2×D376C22semidirect
21. C2×#10625334C22semidirect
22. C2×#10625329C22semidirect
23. C2×#10625324C22semidirect
24. #13094023C22semidirect
29. #13093999C22semidirect
30. #13093998C22semidirect
36. #13093986C22semidirect
38. #13093982C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
43. #13093946C22semidirect
44. #13093945C22semidirect
47. #13093944C22semidirect
48. #13093944C22semidirect
49. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
53. #117×C47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. #102×C47C22semidirect
57. #102×C47C22semidirect
58. C22⋊C8×C47C22semidirect
206. #482D47semidirect
217. C47#3325semidirect
243. #117C2×D47semidirect
244. #107C2×D47semidirect
246. #106C2×D47semidirect
256. #102C2×D47semidirect
257. #102C2×D47semidirect
259. C22⋊C8C2×D47semidirect