Finite Group Databasebeta

← #20255533

Subgroups — #20255533

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#15689825C211yesmaximal, characteristic, complemented
2D4×C22⋊D47C211yesmaximal, characteristic, complemented
3#15689486C211yesmaximal, characteristic, complemented
4#15689446C211yesmaximal, characteristic, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689425C211yesmaximal, characteristic, complemented
7#15689373C211yesmaximal, characteristic, complemented
8#15689357C211yesmaximal, characteristic, complemented
9#15689316C211yesmaximal, characteristic, complemented
10#15689255C211yesmaximal, characteristic, complemented
11#15689235C211yesmaximal, characteristic, complemented
12#15689191C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14C2×#13093945C211yesmaximal, characteristic, complemented
15C47×#447C211yesmaximal, characteristic, complemented
16C22×C22⋊D47—21no—
17C2×D4×D47C2211yescharacteristic
18C2×#10625334C2211yescharacteristic, complemented
19C2×#10625324C2211yescharacteristic, complemented
20C22×C47⋊C8C2211yescharacteristic, complemented
21#13094020C2211yescharacteristic
22#13094017—21no—
23#13094015C2211yescharacteristic, complemented
24#13094008—21no—
25#13093998C2211yescharacteristic
26#13093996—21no—
27#13093996—21no—
28#13093995C2211yescharacteristic
29#13093995C2211yescharacteristic, complemented
30#13093993—21no—
31#13093992—21no—
32D4×Dic47—21no—
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic, complemented
35C4×C22⋊D47C2211yescharacteristic
36#13093982C2211yescharacteristic, complemented
37C2×C4⋊Dic47C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093956C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093946C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic, complemented
55#121×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C24×C47—21no—
60C23×D47—21no—
61C2×D4×C47—22no—
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47—41no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C2×C22⋊D47—44no—
76C2×C22⋊D47D411yescharacteristic
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47—21no—
80D4×D47—22no—
81D4×D47—41no—
82C2×D188C2311yescharacteristic
83C2×C4×D47C2311yescharacteristic
84D8×C47—22no—
85D8×C47—41no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47D411yescharacteristic
95#10625334—41no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4D411yescharacteristic
99C4⋊Dic47—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105Dic47⋊C4D411yescharacteristic
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8—41no—
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111#10625324—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—42no—
116C23×C47—42no—
117C23×C47—81no—
118C23×C47C2×D411yescharacteristic
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—21no—
128D4×C47—21no—
129D4×C47—42no—
130D4×C47—42no—
131D4×C47#4112yes—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—22no—
138C22⋊D47—42no—
139C22⋊D47—42no—
140C22⋊D47—42no—
141C22⋊D47—42no—
142C22⋊D47—81no—
143C22⋊D47—81no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—42no—
148C2×Dic47—81no—
149C2×Dic47—81no—
150C2×Dic47C2×D411yescharacteristic
151C2×Dic47C2×D411yescharacteristic
152C2×Dic47C2×D411yescharacteristic
153D188—21no—
154D188—21no—
155C4×D47—21no—
156C4×D47—21no—
157C8×C47—21no—
158C8×C47—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—22no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—84no—
173C22×C47AGL(1,ℤ/8)12yes—
174C22×C47C22×D411yescharacteristic
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—84no—
182C4×C47—21no—
183C4×C47—41no—
184C4×C47C2×#4111yescharacteristic
185C4×C47H(5,𝔽2)11yescharacteristic
186Dic47—21no—
187Dic47—21no—
188Dic47—21no—
189Dic47—41no—
190Dic47—41no—
191Dic47—41no—
192#3318—471nomaximal, Sylow
193C2×C47—22no—
194C2×C47—42no—
195C2×C47—81no—
196C2×C47—81no—
197C2×C47#54611yescharacteristic
198C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C47#57611yescharacteristic
200D47—41no—
201D47—81no—
202#553—471no—
203D42—471no—
204#490—471no—
205#482—471no—
206#481—471no—
207#478—471no—
208#469—471no—
209#466—471no—
210#459—471no—
211#447—471no—
212#447D4711yescharacteristic, complemented
213#442—471no—
214#435—471no—
215#418—471no—
216C2×#102—471no—
217C47#331811yescharacteristic, complemented, Sylow
218C22×D4—471no—
219C22×D4—941no—
220C22×D4C2×D4711yescharacteristic
221C2×D8—471no—
222C2×D8C2×D4711yescharacteristic
223C2×D8C2×D4711yescharacteristic, complemented
224C2×M16—471no—
225C22×C8—471no—
226#127—471no—
227#126—941no—
228#125—471no—
229#123—941no—
230#121—471no—
231#121—471no—
232#121—471no—
233#121—941no—
234#121—941no—
235#121C2×D4711yescharacteristic, complemented
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#102—471no—
255#102—471no—
256#102C2×D4711yescharacteristic
257#102C2×D4711yescharacteristic, complemented
258C22⋊C8—471no—
259C22⋊C8C2×D4711yescharacteristic, complemented
260#97—471no—
261C24—21no—
262C24—941no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—471no—
268C2×D4—471no—
269C2×D4—941no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—942no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—1881no—
277C2×D4—1884no—
278C2×D4C22×D4711yescharacteristic
279C2×D4C22×D4711yescharacteristic
280C2×D4C22×D4711yescharacteristic
281C22×C4—471no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4C22×D4711yescharacteristic
286D8—22no—
287D8—41no—
288D8—1881no—
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—471no—
313C42—941no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—471no—
321C23—941no—
322C23—3761no—
323C23—1882no—
324C23—1882no—
325C23D4×D4711yescharacteristic
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—42no—
332D4—42no—
333D4—942no—
334D4—941no—
335D4—941no—
336D4—3761no—
337D4—3761no—
338D4—1882no—
339D4—1882no—
340D4—1882no—
341D4—1882no—
342D4#1062535212yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—471no—
347C2×C4—471no—
348C2×C4—471no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—3761no—
355C2×C4—3761no—
356C2×C4—1882no—
357C2×C4D4×D4711yescharacteristic
358C2×C4C23×D4711yescharacteristic
359C8—21no—
360C8—21no—
361C8—941no—
362C8—941no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—84no—
375C22—941no—
376C22—941no—
377C22—941no—
378C22—3764no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22#1309404812yes—
383C22C2×D4×D4711yescharacteristic
384C4—21no—
385C4—41no—
386C4—941no—
387C4—941no—
388C4—941no—
389C4—1881no—
390C4—1881no—
391C4—1881no—
392C4C2×#1062535211yescharacteristic
393C4#1309406911yescharacteristic
394C2—22no—
395C2—42no—
396C2—81no—
397C2—81no—
398C2—3761no—
399C2—1881no—
400C2#1568976011yescharacteristic
401C2C2×#1309404811yescharacteristic
402C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3318
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #15689825C2semidirect
2. D4×C22⋊D47C2semidirect
3. #15689486C2semidirect
4. #15689446C2semidirect
5. #15689442C2semidirect
6. #15689425C2semidirect
7. #15689373C2semidirect
8. #15689357C2semidirect
9. #15689316C2semidirect
10. #15689255C2semidirect
11. #15689235C2semidirect
12. #15689191C2semidirect
13. #15689126C2semidirect
14. C2×#13093945C2semidirect
15. C47×#447C2semidirect
18. C2×#10625334C22semidirect
19. C2×#10625324C22semidirect
20. C22×C47⋊C8C22semidirect
23. #13094015C22semidirect
29. #13093995C22semidirect
34. D4×Dic47C22semidirect
36. #13093982C22semidirect
37. C2×C4⋊Dic47C22semidirect
38. #13093957C22semidirect
39. #13093956C22semidirect
40. #13093956C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093946C22semidirect
43. #13093946C22semidirect
46. #13093945C22semidirect
47. #13093945C22semidirect
48. #13093945C22semidirect
49. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093934C22semidirect
54. C2×D8×C47C22semidirect
55. #121×C47C22semidirect
57. #102×C47C22semidirect
58. C22⋊C8×C47C22semidirect
212. #447D47semidirect
217. C47#3318semidirect
223. C2×D8C2×D47semidirect
235. #121C2×D47semidirect
257. #102C2×D47semidirect
259. C22⋊C8C2×D47semidirect