Finite Group Databasebeta

← #20255536

Subgroups — #20255536

Order 6016.

462 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#15689823C211yesmaximal, characteristic, complemented
2#15689758C211yesmaximal, characteristic, complemented
3#15689487C211yesmaximal, characteristic, complemented
4#15689445C211yesmaximal, characteristic, complemented
5#15689440C211yesmaximal, characteristic, complemented
6#15689424C211yesmaximal, characteristic, complemented
7#15689373C211yesmaximal, characteristic, complemented
8#15689356C211yesmaximal, characteristic, complemented
9#15689255C211yesmaximal, characteristic, complemented
10#15689255C211yesmaximal, characteristic, complemented
11#15689233C211yesmaximal, characteristic, complemented
12#15689193C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#459C211yesmaximal, characteristic, complemented
16C2×D4×D47—21no—
17C2×D4×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625324C2211yescharacteristic, complemented
21C2×C8×D47C2211yescharacteristic, complemented
22#13094017—21no—
23#13094016C2211yescharacteristic, complemented
24#13094007—21no—
25#13093997—21no—
26#13093995—21no—
27#13093995C2211yescharacteristic
28#13093995C2211yescharacteristic
29#13093995C2211yescharacteristic, complemented
30#13093995C2211yescharacteristic, complemented
31#13093992—21no—
32#13093992—21no—
33C4×D188C2211yescharacteristic
34C4×D188C2211yescharacteristic
35C4×C22⋊D47—21no—
36#13093982C2211yescharacteristic, complemented
37C4⋊C4×D47C2211yescharacteristic, complemented
38#13093958C2211yescharacteristic, complemented
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41#13093946C2211yescharacteristic
42#13093946C2211yescharacteristic
43#13093945C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093935C2211yescharacteristic, complemented
52C2×D8×C47C2211yescharacteristic, complemented
53C2×D8×C47C2211yescharacteristic, complemented
54#127×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73D4×D47—22no—
74D4×D47—22no—
75D4×D47—41no—
76D4×D47—41no—
77D4×D47—44no—
78C2×D188D411yescharacteristic
79C2×D188C2311yescharacteristic
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47C2311yescharacteristic
83C2×C4×D47C2311yescharacteristic
84D8×C47—41no—
85D8×C47—41no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95#10625334—22no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4D411yescharacteristic
99(C2×D47)⋊C4D411yescharacteristic
100C4⋊Dic47D411yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107C4×Dic47—21no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C8×D47—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C22×D47C2×D411yescharacteristic
123C22×D47C2×D411yescharacteristic
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—21no—
130D4×C47—42no—
131D4×C47—81no—
132C2×C4×C47—21no—
133C2×C4×C47—81no—
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—42no—
138C22⋊D47—42no—
139C22⋊D47—42no—
140C22⋊D47—42no—
141C22⋊D47—42no—
142C22⋊D47—81no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47C2×D411yescharacteristic
147C2×Dic47C2×D411yescharacteristic
148D188—22no—
149D188—21no—
150D188#4112yes—
151C4×D47—21no—
152C4×D47—21no—
153C4×D47—21no—
154C4×D47—21no—
155C4×D47—42no—
156C4×D47—81no—
157C8×C47—21no—
158C8×C47—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47C22×D411yescharacteristic
171C2×D47—21no—
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—22no—
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—84no—
180C2×D47—84no—
181C2×D47AGL(1,ℤ/8)12yes—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—41no—
185C4×C47C2×#4111yescharacteristic
186C4×C47H(5,𝔽2)11yescharacteristic
187Dic47—21no—
188Dic47—21no—
189Dic47—41no—
190Dic47—41no—
191Dic47—41no—
192#3318—471nomaximal, Sylow
193C2×C47—81no—
194C2×C47—81no—
195C2×C47—81no—
196C2×C47#54611yescharacteristic
197C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C47#57611yescharacteristic
199D47—22no—
200D47—41no—
201D47—42no—
202#553—471no—
203D42—471no—
204#490—471no—
205#482—471no—
206#481—471no—
207#478—471no—
208#469—471no—
209#466—471no—
210#459D4711yescharacteristic, complemented
211#447—471no—
212#447—471no—
213#442—471no—
214#435—471no—
215#418—471no—
216C2×#102—471no—
217C47#331811yescharacteristic, complemented, Sylow
218C22×D4—471no—
219C22×D4—471no—
220C22×D4—941no—
221C2×D8—471no—
222C2×D8C2×D4711yescharacteristic, complemented
223C2×D8C2×D4711yescharacteristic, complemented
224C2×M16—471no—
225C22×C8—471no—
226#127C2×D4711yescharacteristic
227#126—941no—
228#125—471no—
229#123—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—941no—
241C4×D4C2×D4711yescharacteristic, complemented
242#117—471no—
243C2×C4⋊C4—471no—
244#107—471no—
245#106—471no—
246#106—471no—
247C4⋊C8C2×D4711yescharacteristic, complemented
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⋊C8—471no—
260#97—471no—
261C24—941no—
262C24—941no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—942no—
270C2×D4—942no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—1881no—
276C2×D4—1881no—
277C2×D4—1884no—
278C2×D4C22×D4711yescharacteristic
279C2×D4C22×D4711yescharacteristic
280C2×D4C22×D4711yescharacteristic
281C22×C4—21no—
282C22×C4—471no—
283C22×C4—471no—
284C22×C4—941no—
285C22×C4—941no—
286D8—41no—
287D8—41no—
288D8—942no—
289M16—1881no—
290C2×C8—471no—
291C2×C8—471no—
292C2×C8—1881no—
293C2×C8C22×D4711yescharacteristic
294C2×C8C22×D4711yescharacteristic
295C4⋊C4—471no—
296C4⋊C4—471no—
297C4⋊C4—471no—
298C4⋊C4—471no—
299C4⋊C4—941no—
300C4⋊C4—941no—
301C4⋊C4—941no—
302C4⋊C4C22×D4711yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—471no—
305C22⋊C4—471no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4—941no—
311C22⋊C4—941no—
312C42—941no—
313C42C22×D4711yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—471no—
318C23—471no—
319C23—941no—
320C23—3761no—
321C23—3761no—
322C23—1882no—
323C23—1882no—
324C23—1882no—
325C23—1882no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—472no—
335D4—942no—
336D4—941no—
337D4—3761no—
338D4—1882no—
339D4—1882no—
340D4—1882no—
341D4—1882no—
342D4—1882no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—471no—
346C2×C4—471no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—3761no—
355C2×C4—1882no—
356C2×C4D4×D4711yescharacteristic
357C2×C4D4×D4711yescharacteristic
358C2×C4C23×D4711yescharacteristic
359C8—21no—
360C8—21no—
361C8—941no—
362C8—941no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—472no—
373C22—941no—
374C22—941no—
375C22—941no—
376C22—942no—
377C22—941no—
378C22—941no—
379C22—3764no—
380C22—3764no—
381C22—1881no—
382C22—1881no—
383C22C2×D4×D4711yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—941no—
388C4—941no—
389C4—1881no—
390C4—1881no—
391C4—1881no—
392C4#41×D4711yescharacteristic
393C4#1309406911yescharacteristic
394C2—81no—
395C2—81no—
396C2—81no—
397C2—942no—
398C2—1881no—
399C2—1882no—
400C2#1568977011yescharacteristic
401C2AGL(1,ℤ/8)×D4711yescharacteristic
402C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#459C2
socleC22×C47C22×D4
hypercenter#459D47
hypocenterC47#3318
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #15689823C2semidirect
2. #15689758C2semidirect
3. #15689487C2semidirect
4. #15689445C2semidirect
5. #15689440C2semidirect
6. #15689424C2semidirect
7. #15689373C2semidirect
8. #15689356C2semidirect
9. #15689255C2semidirect
10. #15689255C2semidirect
11. #15689233C2semidirect
12. #15689193C2semidirect
13. #15689126C2semidirect
14. #102×D47C2semidirect
15. C47×#459C2semidirect
20. C2×#10625324C22semidirect
21. C2×C8×D47C22semidirect
23. #13094016C22semidirect
29. #13093995C22semidirect
30. #13093995C22semidirect
36. #13093982C22semidirect
37. C4⋊C4×D47C22semidirect
38. #13093958C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
43. #13093945C22semidirect
44. #13093945C22semidirect
45. #13093945C22semidirect
46. #13093945C22semidirect
47. #13093945C22semidirect
49. (C2×D47)⋊C8C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093935C22semidirect
52. C2×D8×C47C22semidirect
53. C2×D8×C47C22semidirect
55. C4×D4×C47C22semidirect
56. C4⋊C8×C47C22semidirect
57. #102×C47C22semidirect
58. #102×C47C22semidirect
210. #459D47semidirect
217. C47#3318semidirect
222. C2×D8C2×D47semidirect
223. C2×D8C2×D47semidirect
241. C4×D4C2×D47semidirect
247. C4⋊C8C2×D47semidirect
256. #102C2×D47semidirect
257. #102C2×D47semidirect