Finite Group Databasebeta

← #440×D47 #20252163

Subgroups — #440×D47 #20252163

Order 6016.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D47C211yesmaximal, characteristic
2C4×Q8×D47C211yesmaximal, characteristic, complemented
3C4×D4×D47C211yesmaximal, characteristic
4#15689226C211yesmaximal, characteristic, complemented
5#15689225C211yesmaximal, characteristic, complemented
6#15689224C211yesmaximal, characteristic, complemented
7#15689223C211yesmaximal, characteristic, complemented
8#15689222C211yesmaximal, characteristic, complemented
9#15689221C211yesmaximal, characteristic, complemented
10#15689220C211yesmaximal, characteristic, complemented
11#107×D47C211yesmaximal, characteristic, complemented
12#103×D47C211yesmaximal, characteristic, complemented
13#102×D47C211yesmaximal, characteristic
14#97×D47C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C22×C4×D47—21no—
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625336C2211yescharacteristic
22SD16×D47C418yescomplemented
23C2×C8×D47C2211yescharacteristic
24C2×C8×D47C2211yescharacteristic
25Q8×Dic47C2211yescharacteristic, complemented
26C4×Dic94—21no—
27C4×Dic94C2211yescharacteristic, complemented
28#13093989—21no—
29#13093989C2211yescharacteristic, complemented
30C4×D188C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32#13093986C2211yescharacteristic
33C4×C22⋊D47—21no—
34(C22⋊D47)⋊C4—21no—
35C4⋊C4×D47—21no—
36C4⋊C4×D47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38C22⋊C4×D47—21no—
39C42×D47—21no—
40C42×D47C2211yescharacteristic
41#13093958C2211yescharacteristic, complemented
42#13093957C2211yescharacteristic, complemented
43#13093957C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093947C2211yescharacteristic, complemented
47#13093946C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093935C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52#13093934C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic, complemented
55C4×D4×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59#97×C47C2211yescharacteristic, complemented
60C23×D47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66Q8×D47—22no—
67Q8×D47C2×C414yescomplemented
68D4×D47—22no—
69D4×D47C2×C414yes—
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—44no—
77C2×C4×D47D411yescharacteristic
78C2×C4×D47D411yescharacteristic
79C2×C4×D47C2311yescharacteristic
80C2×Dic94—21no—
81C2×Dic94C2311yescharacteristic
82SD16×C47C2×C414yescomplemented
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47—21no—
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47—21no—
89C42×C47—21no—
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92#10625336C2×C414yescomplemented
93#10625335C2×C414yescomplemented
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47D411yescharacteristic
107C4×Dic47D411yescharacteristic
108C4×Dic47C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111#10625325C2×C414yescomplemented
112C8×D47—22no—
113C8×D47C2×C414yescomplemented
114C23×C47—21no—
115C22×D47—21no—
116C22×D47—24no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47C2×D411yescharacteristic
120Q8×C47—21no—
121Q8×C47C22×C412yescomplemented
122D4×C47—21no—
123D4×C47C22×C412yes—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—42no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—24no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—42no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139D188—21no—
140D188C22×C412yes—
141C4×D47—24no—
142C4×D47—22no—
143C4×D47—22no—
144C4×D47—42no—
145C4×D47—42no—
146C4×D47—42no—
147C4×D47—42no—
148C4×D47C22×C412yes—
149C4×D47#4112yes—
150Dic94—21no—
151Dic94—24no—
152Dic94C22×C412yescomplemented
153C8×C47—21no—
154C8×C47C22×C412yescomplemented
155C47⋊C8—21no—
156C47⋊C8C22×C412yescomplemented
157C22×C47—22no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47C22×D411yescharacteristic
161C2×D47—22no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—48no—
165C2×D47C4×D412yes—
166C2×D47AGL(1,ℤ/8)12yes—
167C2×D47#13712yes—
168C4×C47—22no—
169C4×C47—21no—
170C4×C47—21no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47C23×C411yescharacteristic
174C4×C47C2×#4111yescharacteristic
175Dic47—22no—
176Dic47—21no—
177Dic47—21no—
178Dic47—41no—
179Dic47—41no—
180Dic47C4×D412yes—
181C2×#440—471nomaximal, Sylow
182C2×C47—42no—
183C2×C47C2×C4×D411yescharacteristic
184C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C47C2×#13711yescharacteristic
186D47—42no—
187D47#44014yesdirect product factor
188C22×SD16—471no—
189C2×C4×Q8—471no—
190C2×C4×D4—471no—
191#440—471no—
192#440—471no—
193#440—471no—
194#440—471no—
195#440—471no—
196#440—471no—
197#440—471no—
198#440D4711yescharacteristic, direct product factor
199C2×#107—471no—
200C2×#103—471no—
201C2×#102—471no—
202C2×#97—471no—
203C47C2×#44011yescharacteristic, complemented, Sylow
204C22×Q8—471no—
205C22×D4—471no—
206C23×C4—941no—
207C2×SD16—471no—
208C2×SD16—471no—
209C2×SD16—478no—
210C2×SD16—471no—
211C2×SD16C2×D4711yescharacteristic
212C22×C8—471no—
213C22×C8—471no—
214C4×Q8—471no—
215C4×Q8—471no—
216C4×Q8—471no—
217C4×Q8—941no—
218C4×Q8—941no—
219C4×Q8C2×D4711yescharacteristic, complemented
220C4×D4—471no—
221C4×D4—471no—
222C4×D4—471no—
223C4×D4—941no—
224C4×D4—941no—
225C4×D4C2×D4711yescharacteristic
226C2×C4⋊C4—471no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—941no—
229C2×C22⋊C4—941no—
230C2×C42—471no—
231C2×C42—941no—
232#107—471no—
233#107—471no—
234#107—471no—
235#107C2×D4711yescharacteristic, complemented
236#103—471no—
237#103—471no—
238#103—471no—
239#103C2×D4711yescharacteristic, complemented
240#102—471no—
241#102—471no—
242#102—471no—
243#102C2×D4711yescharacteristic
244#97—471no—
245#97—471no—
246#97—471no—
247#97C2×D4711yescharacteristic, complemented
248C24—941no—
249C2×Q8—474no—
250C2×Q8—471no—
251C2×Q8—941no—
252C2×Q8—942no—
253C2×Q8C22×D4711yescharacteristic
254C2×D4—474no—
255C2×D4—471no—
256C2×D4—942no—
257C2×D4—941no—
258C2×D4C22×D4711yescharacteristic
259C22×C4—21no—
260C22×C4—471no—
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4—1884no—
270SD16—474no—
271SD16—474no—
272SD16—474no—
273SD16C4×D4714yescomplemented
274C2×C8—471no—
275C2×C8—474no—
276C2×C8—471no—
277C2×C8—942no—
278C2×C8C22×D4711yescharacteristic
279C2×C8C22×D4711yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4C22×D4711yescharacteristic
289C4⋊C4C22×D4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C42—21no—
295C42—471no—
296C42—471no—
297C42—471no—
298C42—941no—
299C42—941no—
300C42—941no—
301C42C22×D4711yescharacteristic
302C23—21no—
303C23—471no—
304C23—944no—
305C23—941no—
306C23—1882no—
307C23—1882no—
308Q8—21no—
309Q8—472no—
310Q8—944no—
311Q8—941no—
312Q8C2×C4×D4712yescomplemented
313D4—21no—
314D4—472no—
315D4—944no—
316D4—941no—
317D4C2×C4×D4712yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—471no—
323C2×C4—472no—
324C2×C4—472no—
325C2×C4—471no—
326C2×C4—471no—
327C2×C4—942no—
328C2×C4—942no—
329C2×C4—944no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—1882no—
334C2×C4—1882no—
335C2×C4—1882no—
336C2×C4—1882no—
337C2×C4—1882no—
338C2×C4D4×D4711yescharacteristic
339C2×C4D4×D4711yescharacteristic
340C2×C4C23×D4711yescharacteristic
341C8—21no—
342C8—472no—
343C8—941no—
344C8C2×C4×D4712yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—472no—
349C22—472no—
350C22—472no—
351C22—942no—
352C22—1888no—
353C22—1881no—
354C22—1881no—
355C22C2×D4×D4711yescharacteristic
356C4—22no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—472no—
362C4—942no—
363C4—941no—
364C4—941no—
365C4—1881no—
366C4—1881no—
367C4C22×C4×D4711yescharacteristic
368C4#41×D4711yescharacteristic
369C2—42no—
370C2—474no—
371C2—1882no—
372C2C4×D4×D4711yescharacteristic
373C2AGL(1,ℤ/8)×D4711yescharacteristic
374C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47C2×#440
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D47C2semidirect
4. #15689226C2semidirect
5. #15689225C2semidirect
6. #15689224C2semidirect
7. #15689223C2semidirect
8. #15689222C2semidirect
9. #15689221C2semidirect
10. #15689220C2semidirect
11. #107×D47C2semidirect
12. #103×D47C2semidirect
14. #97×D47C2semidirect
15. C47×#440C2semidirect
22. SD16×D47C4semidirect
25. Q8×Dic47C22semidirect
27. C4×Dic94C22semidirect
29. #13093989C22semidirect
41. #13093958C22semidirect
42. #13093957C22semidirect
43. #13093957C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093947C22semidirect
50. #13093935C22semidirect
51. #13093934C22semidirect
52. #13093934C22semidirect
54. C4×Q8×C47C22semidirect
56. #107×C47C22semidirect
57. #103×C47C22semidirect
59. #97×C47C22semidirect
67. Q8×D47C2×C4semidirect
82. SD16×C47C2×C4semidirect
92. #10625336C2×C4semidirect
93. #10625335C2×C4semidirect
111. #10625325C2×C4semidirect
113. C8×D47C2×C4semidirect
121. Q8×C47C22×C4semidirect
152. Dic94C22×C4semidirect
154. C8×C47C22×C4semidirect
156. C47⋊C8C22×C4semidirect
187. D47#440direct (N × H)
198. #440D47direct (N × H)
203. C47C2×#440semidirect
219. C4×Q8C2×D47semidirect
235. #107C2×D47semidirect
239. #103C2×D47semidirect
247. #97C2×D47semidirect
273. SD16C4×D47semidirect
312. Q8C2×C4×D47semidirect
344. C8C2×C4×D47semidirect