Finite Group Databasebeta

← #20255528

Subgroups — #20255528

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#15689826C211yesmaximal, characteristic, complemented
2#15689758C211yesmaximal, characteristic, complemented
3#15689446C211yesmaximal, characteristic, complemented
4#15689440C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689375C211yesmaximal, characteristic, complemented
7#15689358C211yesmaximal, characteristic, complemented
8#15689315C211yesmaximal, characteristic, complemented
9#15689258C211yesmaximal, characteristic, complemented
10#15689258C211yesmaximal, characteristic, complemented
11#15689236C211yesmaximal, characteristic, complemented
12#15689196C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#490C211yesmaximal, characteristic, complemented
16C2×D4×D47—21no—
17C2×D4×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19C2×D376C2211yescharacteristic
20C2×#10625334C2211yescharacteristic, complemented
21C2×#10625334C2211yescharacteristic, complemented
22C2×#10625324C2211yescharacteristic, complemented
23C2×C8×D47C2211yescharacteristic, complemented
24#13094019—21no—
25#13094009—21no—
26#13093999—21no—
27#13093999C2211yescharacteristic, complemented
28#13093999C2211yescharacteristic, complemented
29#13093995—21no—
30#13093995C2211yescharacteristic
31#13093995C2211yescharacteristic
32#13093992—21no—
33#13093992—21no—
34C4×D188C2211yescharacteristic
35C4×D188C2211yescharacteristic
36C4×D188C2211yescharacteristic, complemented
37#13093986—21no—
38#13093982C2211yescharacteristic, complemented
39C4⋊C4×D47C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43C4⋊(C47⋊C8)C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52#127×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic, complemented
54#102×C47C2211yescharacteristic, complemented
55#102×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58#97×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69D4×D47—22no—
70D4×D47—22no—
71D4×D47—41no—
72D4×D47—41no—
73D4×D47—44no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188D411yescharacteristic
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47C2311yescharacteristic
83C2×C4×D47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2311yescharacteristic
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93#10625334—41no—
94#10625334—41no—
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
101(C2×D47)⋊C4D411yescharacteristic
102C4⋊Dic47D411yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109D376—22no—
110#10625324—41no—
111C8×D47—41no—
112C23×C47—21no—
113C23×C47—21no—
114C22×D47—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—42no—
129D4×C47—81no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—42no—
136C22⋊D47—42no—
137C22⋊D47—42no—
138C22⋊D47—42no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143D188—22no—
144D188—21no—
145D188—21no—
146D188—21no—
147D188—42no—
148D188—81no—
149D188#4112yes—
150C4×D47—21no—
151C4×D47—21no—
152C4×D47—21no—
153C4×D47—21no—
154C4×D47—42no—
155C4×D47—81no—
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×C47C22×D411yescharacteristic
168C2×D47—21no—
169C2×D47—21no—
170C2×D47—21no—
171C2×D47—22no—
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
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×C47—41no—
186C4×C47C2×#4111yescharacteristic
187C4×C47H(5,𝔽2)11yescharacteristic
188Dic47—21no—
189Dic47—21no—
190Dic47—41no—
191Dic47—41no—
192#3318—471nomaximal, Sylow
193C2×C47—81no—
194C2×C47—81no—
195C2×C47#54611yescharacteristic
196C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C47#57611yescharacteristic
198D47—22no—
199D47—41no—
200D47—42no—
201D47—81no—
202#553—471no—
203D42—471no—
204#490D4711yescharacteristic, complemented
205#482—471no—
206#481—471no—
207#478—471no—
208#469—471no—
209#466—471no—
210#459—471no—
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×D8—471no—
223C2×D8—471no—
224C2×M16—471no—
225C22×C8—471no—
226#127C2×D4711yescharacteristic
227#126—941no—
228#125C2×D4711yescharacteristic, complemented
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—471no—
241C4×D4—941no—
242#117—471no—
243C2×C4⋊C4—471no—
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, complemented
255#102C2×D4711yescharacteristic, complemented
256#102C2×D4711yescharacteristic, complemented
257#102C2×D4711yescharacteristic, complemented
258C22⋊C8—471no—
259C22⋊C8—471no—
260#97C2×D4711yescharacteristic, complemented
261C24—941no—
262C24—941no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—471no—
268C2×D4—941no—
269C2×D4—941no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—942no—
273C2×D4—942no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—1881no—
277C2×D4—1881no—
278C2×D4—1884no—
279C2×D4C22×D4711yescharacteristic
280C2×D4C22×D4711yescharacteristic
281C22×C4—471no—
282C22×C4—471no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4—941no—
286D8—942no—
287D8—1881no—
288D8—1881no—
289M16—1881no—
290C2×C8—471no—
291C2×C8—471no—
292C2×C8—1881no—
293C2×C8C22×D4711yescharacteristic
294C2×C8C22×D4711yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—471no—
298C4⋊C4—471no—
299C4⋊C4—471no—
300C4⋊C4—941no—
301C4⋊C4C22×D4711yescharacteristic
302C4⋊C4C22×D4711yescharacteristic
303C22⋊C4—471no—
304C22⋊C4—471no—
305C22⋊C4—941no—
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—471no—
317C23—471no—
318C23—941no—
319C23—941no—
320C23—3761no—
321C23—3761no—
322C23—1882no—
323C23—1882no—
324C23—1882no—
325C23—1882no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—81no—
332D4—472no—
333D4—942no—
334D4—941no—
335D4—941no—
336D4—941no—
337D4—3761no—
338D4—1882no—
339D4—1882no—
340D4—1882no—
341D4—1882no—
342D4—1882no—
343C2×C4—21no—
344C2×C4—21no—
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—3761no—
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—472no—
370C22—941no—
371C22—941no—
372C22—941no—
373C22—942no—
374C22—941no—
375C22—941no—
376C22—3764no—
377C22—3764no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22C2×D4×D4711yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—941no—
389C4—941no—
390C4—1881no—
391C4—1881no—
392C4#41×D4711yescharacteristic
393C4#1309407011yescharacteristic
394C2—81no—
395C2—81no—
396C2—942no—
397C2—3761no—
398C2—1881no—
399C2—1882no—
400C2#1568976611yescharacteristic
401C2AGL(1,ℤ/8)×D4711yescharacteristic
402C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#490C2
socleC22×C47C22×D4
hypercenter#490D47
hypocenterC47#3318
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #15689826C2semidirect
2. #15689758C2semidirect
3. #15689446C2semidirect
4. #15689440C2semidirect
5. #15689420C2semidirect
6. #15689375C2semidirect
7. #15689358C2semidirect
8. #15689315C2semidirect
9. #15689258C2semidirect
10. #15689258C2semidirect
11. #15689236C2semidirect
12. #15689196C2semidirect
13. #15689126C2semidirect
14. #102×D47C2semidirect
15. C47×#490C2semidirect
20. C2×#10625334C22semidirect
21. C2×#10625334C22semidirect
22. C2×#10625324C22semidirect
23. C2×C8×D47C22semidirect
27. #13093999C22semidirect
28. #13093999C22semidirect
36. C4×D188C22semidirect
38. #13093982C22semidirect
39. C4⋊C4×D47C22semidirect
40. #13093957C22semidirect
41. #13093956C22semidirect
42. #13093955C22semidirect
43. C4⋊(C47⋊C8)C22semidirect
45. #13093946C22semidirect
46. #13093945C22semidirect
47. #13093945C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. (C2×D47)⋊C8C22semidirect
53. #125×C47C22semidirect
54. #102×C47C22semidirect
55. #102×C47C22semidirect
56. #102×C47C22semidirect
57. #102×C47C22semidirect
58. #97×C47C22semidirect
204. #490D47semidirect
217. C47#3318semidirect
228. #125C2×D47semidirect
254. #102C2×D47semidirect
255. #102C2×D47semidirect
256. #102C2×D47semidirect
257. #102C2×D47semidirect
260. #97C2×D47semidirect