Finite Group Databasebeta

← #482×D47 #20253268

Subgroups — #482×D47 #20253268

Order 6016.

468 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D47C211yesmaximal, characteristic
2#117×D47C211yesmaximal, characteristic, complemented
3#15689450C211yesmaximal, characteristic, complemented
4#15689449C211yesmaximal, characteristic, complemented
5#15689448C211yesmaximal, characteristic, complemented
6#15689447C211yesmaximal, characteristic, complemented
7#15689446C211yesmaximal, characteristic, complemented
8#15689445C211yesmaximal, characteristic, complemented
9#15689444C211yesmaximal, characteristic, complemented
10#107×D47C211yesmaximal, characteristic, complemented
11#106×D47C211yesmaximal, characteristic, complemented
12#102×D47C211yesmaximal, characteristic, complemented
13#102×D47C211yesmaximal, characteristic, complemented
14C22⋊C8×D47C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C2×D4×D47—21no—
17C2×D4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13093999C2211yescharacteristic
22#13093998C2211yescharacteristic
23#13093997—21no—
24#13093996—21no—
25#13093995C2211yescharacteristic
26#13093983C2211yescharacteristic, complemented
27#13093982C2211yescharacteristic, complemented
28#13093982C2211yescharacteristic, complemented
29#13093981—21no—
30#13093980—21no—
31C4⋊C4×D47C2211yescharacteristic
32C4⋊C4×D47C2211yescharacteristic
33C4⋊C4×D47C2211yescharacteristic
34C22⋊C4×D47—21no—
35C22⋊C4×D47—21no—
36C42×D47—21no—
37#13093958C2211yescharacteristic, complemented
38#13093957C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic, complemented
46#13093945C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, 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×D47D411yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C22×Dic47D411yescharacteristic
68D4×D47—22no—
69D4×D47—22no—
70D4×D47—44no—
71C2×D188—21no—
72C2×D188C2311yescharacteristic
73C2×C4×D47—22no—
74C2×C4×D47—22no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47D411yescharacteristic
79C2×C4×D47D411yescharacteristic
80C2×C4×D47C2311yescharacteristic
81C2×C4×D47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C42×C47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C8×D47—22no—
108C8×D47—22no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—22no—
112C22×D47—22no—
113C22×D47—22no—
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47C2×D411yescharacteristic
119C22×D47C2×D411yescharacteristic
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—42no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—42no—
131C22⋊D47—42no—
132C22⋊D47—42no—
133C2×Dic47—22no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139D188—21no—
140D188—21no—
141D188—42no—
142C4×D47—22no—
143C4×D47—21no—
144C4×D47—21no—
145C4×D47—22no—
146C4×D47—42no—
147C4×D47—42no—
148C4×D47—42no—
149C4×D47#4112yes—
150C4×D47#4112yes—
151C8×C47—21no—
152C8×C47—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47C22×D411yescharacteristic
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—21no—
165C2×D47—44no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—84no—
170C2×D47#12312yes—
171C2×D47#13512yes—
172C2×D47AGL(1,ℤ/8)12yes—
173C4×C47—21no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47C2×#4111yescharacteristic
178C4×C47C2×#4111yescharacteristic
179Dic47—21no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183Dic47#12312yes—
184C2×#482—471nomaximal, Sylow
185C2×C47—41no—
186C2×C47—81no—
187C2×C47C2×#12311yescharacteristic
188C2×C47C2×#13511yescharacteristic
189C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
190D47—41no—
191D47—81no—
192D47#48214yesdirect product factor
193C2×#121—471no—
194C2×#117—471no—
195#482—471no—
196#482—471no—
197#482—471no—
198#482—471no—
199#482—471no—
200#482—471no—
201#482—471no—
202#482D4711yescharacteristic, direct product factor
203C2×#107—471no—
204C2×#106—471no—
205C2×#102—471no—
206C2×#102—471no—
207C2×C22⋊C8—471no—
208C47C2×#48211yescharacteristic, complemented, Sylow
209C22×D4—471no—
210C22×D4—941no—
211C23×C4—471no—
212C22×C8—471no—
213C22×C8—471no—
214#121—471no—
215#121—471no—
216#121—471no—
217#121—941no—
218#121—941no—
219#121C2×D4711yescharacteristic
220#117—471no—
221#117—471no—
222#117—471no—
223#117—941no—
224#117—941no—
225#117C2×D4711yescharacteristic, complemented
226C2×C4⋊C4—471no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C22⋊C4—941no—
230C2×C22⋊C4—941no—
231C2×C42—941no—
232#107—471no—
233#107—471no—
234#107—471no—
235#107C2×D4711yescharacteristic, complemented
236#106—471no—
237#106—471no—
238#106—471no—
239#106C2×D4711yescharacteristic, complemented
240#102—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102C2×D4711yescharacteristic, complemented
247#102C2×D4711yescharacteristic, complemented
248C22⋊C8—471no—
249C22⋊C8—471no—
250C22⋊C8—471no—
251C22⋊C8C2×D4711yescharacteristic, complemented
252C24—471no—
253C24—941no—
254C2×D4—21no—
255C2×D4—471no—
256C2×D4—941no—
257C2×D4—942no—
258C2×D4—942no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—1884no—
263C2×D4C22×D4711yescharacteristic
264C22×C4—471no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—942no—
270C22×C4—942no—
271C22×C4—941no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4C22×D4711yescharacteristic
275C2×C8—471no—
276C2×C8—471no—
277C2×C8—942no—
278C2×C8—942no—
279C2×C8C22×D4711yescharacteristic
280C2×C8C22×D4711yescharacteristic
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—471no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4C22×D4711yescharacteristic
288C4⋊C4C22×D4711yescharacteristic
289C4⋊C4C22×D4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C42—21no—
299C42—941no—
300C42—941no—
301C42—941no—
302C23—21no—
303C23—471no—
304C23—471no—
305C23—942no—
306C23—942no—
307C23—942no—
308C23—941no—
309C23—1882no—
310C23—1882no—
311C23—1882no—
312C23D4×D4711yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—941no—
317D4—941no—
318D4—1882no—
319D4—1882no—
320D4—1882no—
321D4—1882no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—471no—
328C2×C4—472no—
329C2×C4—472no—
330C2×C4—471no—
331C2×C4—942no—
332C2×C4—942no—
333C2×C4—942no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—1882no—
340C2×C4—1882no—
341C2×C4—1882no—
342C2×C4D4×D4711yescharacteristic
343C2×C4C23×D4711yescharacteristic
344C8—21no—
345C8—21no—
346C8—941no—
347C8—941no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—472no—
355C22—472no—
356C22—472no—
357C22—941no—
358C22—941no—
359C22—941no—
360C22—3764no—
361C22—1884no—
362C22—1881no—
363C22—1881no—
364C22—1881no—
365C22C2×D4×D4711yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—472no—
371C4—941no—
372C4—1881no—
373C4—1881no—
374C4—1881no—
375C4#41×D4711yescharacteristic
376C4#41×D4711yescharacteristic
377C2—41no—
378C2—81no—
379C2—474no—
380C2—3761no—
381C2—1881no—
382C2#123×D4711yescharacteristic
383C2#135×D4711yescharacteristic
384C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47C2×#482
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
2. #117×D47C2semidirect
3. #15689450C2semidirect
4. #15689449C2semidirect
5. #15689448C2semidirect
6. #15689447C2semidirect
7. #15689446C2semidirect
8. #15689445C2semidirect
9. #15689444C2semidirect
10. #107×D47C2semidirect
11. #106×D47C2semidirect
12. #102×D47C2semidirect
13. #102×D47C2semidirect
14. C22⋊C8×D47C2semidirect
15. C47×#482C2semidirect
26. #13093983C22semidirect
27. #13093982C22semidirect
28. #13093982C22semidirect
37. #13093958C22semidirect
38. #13093957C22semidirect
39. #13093957C22semidirect
40. #13093956C22semidirect
41. #13093955C22semidirect
42. #13093955C22semidirect
43. #13093946C22semidirect
44. #13093946C22semidirect
45. #13093945C22semidirect
46. #13093945C22semidirect
47. #13093944C22semidirect
48. #13093944C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. (C2×D47)⋊C8C22semidirect
53. #117×C47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. #102×C47C22semidirect
57. #102×C47C22semidirect
58. C22⋊C8×C47C22semidirect
192. D47#482direct (N × H)
202. #482D47direct (N × H)
208. C47C2×#482semidirect
225. #117C2×D47semidirect
235. #107C2×D47semidirect
239. #106C2×D47semidirect
246. #102C2×D47semidirect
247. #102C2×D47semidirect
251. C22⋊C8C2×D47semidirect