Finite Group Databasebeta

← #20255626

Subgroups — #20255626

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
2D4×C22⋊D47C211yesmaximal, characteristic, complemented
3#15689468C211yesmaximal, characteristic, complemented
4#15689447C211yesmaximal, characteristic, complemented
5#15689446C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689376C211yesmaximal, characteristic, complemented
8#15689375C211yesmaximal, characteristic, complemented
9#15689317C211yesmaximal, characteristic, complemented
10#15689258C211yesmaximal, characteristic, complemented
11#15689257C211yesmaximal, characteristic, complemented
12#15689203C211yesmaximal, characteristic, complemented
13#15689199C211yesmaximal, characteristic, complemented
14#15689126C211yesmaximal, characteristic, complemented
15C47×#418C211yesmaximal, characteristic, complemented
16C22×C22⋊D47—21no—
17C2×D4×D47C2211yescharacteristic
18C2×D376C2211yescharacteristic, complemented
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic, complemented
21C2×#10625324C2211yescharacteristic, complemented
22#13094023C2211yescharacteristic, complemented
23#13094020C2211yescharacteristic
24#13094012—21no—
25#13094010—21no—
26#13093999C2211yescharacteristic, complemented
27#13093998C2211yescharacteristic
28#13093998C2211yescharacteristic, complemented
29#13093997—21no—
30#13093996—21no—
31#13093995C2211yescharacteristic
32#13093993—21no—
33#13093992—21no—
34D4×Dic47C2211yescharacteristic
35#13093986C2211yescharacteristic, complemented
36C4×C22⋊D47C2211yescharacteristic
37#13093982C2211yescharacteristic, complemented
38#13093981—21no—
39#13093957C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic, complemented
54#117×C47C2211yescharacteristic, complemented
55#102×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59C24×C47—21no—
60C23×D47—21no—
61C2×D4×C47—22no—
62C2×D4×C47—21no—
63C2×D4×C47—41no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—44no—
74C2×C22⋊D47D411yescharacteristic
75C22×Dic47—21no—
76D4×D47—22no—
77D4×D47—41no—
78C2×D188—21no—
79C2×D188C2311yescharacteristic
80C2×D188C2311yescharacteristic
81C2×C4×D47—21no—
82C2×C4×D47C2311yescharacteristic
83C2×Dic94—21no—
84M16×C47—41no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C42×C47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47D411yescharacteristic
94#10625334—22no—
95#10625334—41no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4D411yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105Dic47⋊C4D411yescharacteristic
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110D376—41no—
111#10625324—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—42no—
115C23×C47—42no—
116C23×C47—81no—
117C23×C47C2×D411yescharacteristic
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—42no—
121C22×D47—42no—
122C22×D47—81no—
123C22×D47C2×D411yescharacteristic
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—42no—
128D4×C47#4112yes—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—22no—
136C22⋊D47—42no—
137C22⋊D47—42no—
138C22⋊D47—42no—
139C22⋊D47—42no—
140C22⋊D47—81no—
141C22⋊D47—81no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—42no—
145C2×Dic47C2×D411yescharacteristic
146C2×Dic47C2×D411yescharacteristic
147C2×Dic47C2×D411yescharacteristic
148D188—21no—
149D188—21no—
150D188—21no—
151D188—21no—
152D188—81no—
153C4×D47—21no—
154C4×D47—21no—
155C4×D47—42no—
156Dic94—81no—
157C8×C47—21no—
158C8×C47—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—22no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—84no—
171C22×C47C22×D411yescharacteristic
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—84no—
182C4×C47—21no—
183C4×C47—41no—
184C4×C47—41no—
185C4×C47C2×#4111yescharacteristic
186C4×C47H(5,𝔽2)11yescharacteristic
187Dic47—21no—
188Dic47—21no—
189Dic47—41no—
190Dic47—41no—
191Dic47AGL(1,ℤ/8)12yes—
192#3325—471nomaximal, Sylow
193C2×C47—42no—
194C2×C47—41no—
195C2×C47—81no—
196C2×C47#54611yescharacteristic
197C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C47#57611yescharacteristic
199D47—41no—
200D47—81no—
201D47—81no—
202#555—471no—
203D42—471no—
204#486—471no—
205#482—471no—
206#482—471no—
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#418D4711yescharacteristic, complemented
217C47#332511yescharacteristic, complemented, Sylow
218C22×D4—471no—
219C22×D4—941no—
220C22×D4C2×D4711yescharacteristic
221C2×D8—471no—
222C2×D8—471no—
223C2×D8—471no—
224C2×M16—471no—
225C2×M16C2×D4711yescharacteristic, complemented
226C4⋊Q8—471no—
227#127—471no—
228#124—941no—
229#124—941no—
230#121—471no—
231#121—471no—
232#121—471no—
233#121—471no—
234#121—941no—
235#121—941no—
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#107—471no—
245#106—471no—
246#106—471no—
247C4⋊C8—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252#102—471no—
253#102—471no—
254#102C2×D4711yescharacteristic
255#102C2×D4711yescharacteristic
256#102C2×D4711yescharacteristic, complemented
257#102C2×D4711yescharacteristic, complemented
258C22⋊C8—471no—
259C22⋊C8—471no—
260C4×C8—471no—
261C24—21no—
262C24—941no—
263C2×Q8—941no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—471no—
268C2×D4—471no—
269C2×D4—471no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—942no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—1881no—
279C2×D4—1884no—
280C2×D4C22×D4711yescharacteristic
281C2×D4C22×D4711yescharacteristic
282C22×C4—471no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4C22×D4711yescharacteristic
286D8—942no—
287D8—1881no—
288D8—1881no—
289M16—41no—
290M16—1881no—
291C2×C8—471no—
292C2×C8—471no—
293C2×C8C22×D4711yescharacteristic
294C2×C8C22×D4711yescharacteristic
295C4⋊C4—471no—
296C4⋊C4—471no—
297C4⋊C4—471no—
298C4⋊C4—941no—
299C4⋊C4C22×D4711yescharacteristic
300C4⋊C4C22×D4711yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—471no—
303C22⋊C4—471no—
304C22⋊C4—941no—
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—21no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—471no—
320C23—941no—
321C23—941no—
322C23—3761no—
323C23—1882no—
324C23—1882no—
325C23D4×D4711yescharacteristic
326Q8—3761no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—942no—
332D4—941no—
333D4—941no—
334D4—941no—
335D4—941no—
336D4—3761no—
337D4—3761no—
338D4—3761no—
339D4—1882no—
340D4—1882no—
341D4—1882no—
342D4—1882no—
343D4#1062535012yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—471no—
349C2×C4—471no—
350C2×C4—471no—
351C2×C4—941no—
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—22no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—84no—
373C22—941no—
374C22—941no—
375C22—941no—
376C22—3764no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22C2×D4×D4711yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—472no—
388C4—941no—
389C4—941no—
390C4—1881no—
391C4—1881no—
392C4C2×#1062535011yescharacteristic
393C4#1309406911yescharacteristic
394C2—41no—
395C2—42no—
396C2—81no—
397C2—3761no—
398C2—3761no—
399C2—1881no—
400C2#1568976311yescharacteristic
401C2AGL(1,ℤ/8)×D4711yescharacteristic
402C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#418C2
socleC22×C47C22×D4
hypercenter#418D47
hypocenterC47#3325
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #15689836C2semidirect
2. D4×C22⋊D47C2semidirect
3. #15689468C2semidirect
4. #15689447C2semidirect
5. #15689446C2semidirect
6. #15689411C2semidirect
7. #15689376C2semidirect
8. #15689375C2semidirect
9. #15689317C2semidirect
10. #15689258C2semidirect
11. #15689257C2semidirect
12. #15689203C2semidirect
13. #15689199C2semidirect
14. #15689126C2semidirect
15. C47×#418C2semidirect
18. C2×D376C22semidirect
20. C2×#10625334C22semidirect
21. C2×#10625324C22semidirect
22. #13094023C22semidirect
26. #13093999C22semidirect
28. #13093998C22semidirect
35. #13093986C22semidirect
37. #13093982C22semidirect
39. #13093957C22semidirect
40. #13093956C22semidirect
41. #13093955C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093946C22semidirect
44. #13093946C22semidirect
46. #13093945C22semidirect
47. #13093944C22semidirect
48. #13093944C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
53. C2×M16×C47C22semidirect
54. #117×C47C22semidirect
57. #102×C47C22semidirect
58. #102×C47C22semidirect
216. #418D47semidirect
217. C47#3325semidirect
225. C2×M16C2×D47semidirect
243. #117C2×D47semidirect
256. #102C2×D47semidirect
257. #102C2×D47semidirect