Finite Group Databasebeta

← #481×D47 #20253284

Subgroups — #481×D47 #20253284

Order 6016.

512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D47C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3#15689443C212yesmaximal, complemented
4#15689442C211yesmaximal, characteristic, complemented
5#15689441C211yesmaximal, characteristic, complemented
6#15689440C212yesmaximal, complemented
7#15689439C211yesmaximal, characteristic, complemented
8#106×D47C212yesmaximal, complemented
9#102×D47C212yesmaximal, complemented
10C22⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#481C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47C2211yescharacteristic
14C22×C4×D47—21no—
15C22×C4×D47C2211yescharacteristic
16C2×C8×D47C2212yes—
17#13093999C2211yescharacteristic
18#13093998C2211yescharacteristic
19#13093997—21no—
20#13093996—21no—
21#13093995C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic, complemented
23C2×Dic47⋊C4—21no—
24C4⋊C4×D47—21no—
25C4⋊C4×D47—21no—
26C4⋊C4×D47C2212yes—
27C4⋊C4×D47C2211yescharacteristic
28C4⋊C4×D47C2212yescomplemented
29C22⋊C4×D47—21no—
30#13093956C2212yescomplemented
31#13093955C2212yescomplemented
32#13093955C2212yescomplemented
33#13093946C2212yescomplemented
34#13093945C2212yescomplemented
35#13093944C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic, complemented
37(C2×D47)⋊C8C2212yescomplemented
38#121×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic, complemented
40#106×C47C2212yescomplemented
41#102×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic, complemented
43C23×D47—21no—
44C23×D47D411yescharacteristic
45C2×D4×C47—21no—
46C2×D4×C47C2311yescharacteristic
47C22×C4×C47—21no—
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—21no—
50C2×C22⋊D47—21no—
51C2×C22⋊D47—21no—
52C22×Dic47—21no—
53C22×Dic47D411yescharacteristic
54D4×D47—24no—
55D4×D47—44no—
56C2×D188—21no—
57C2×D188C2311yescharacteristic
58C2×C4×D47—24no—
59C2×C4×D47—21no—
60C2×C4×D47—22no—
61C2×C4×D47—22no—
62C2×C4×D47—44no—
63C2×C4×D47D411yescharacteristic
64C2×C4×D47D411yescharacteristic
65C2×C4×D47C2311yescharacteristic
66C2×C4×D47C2311yescharacteristic
67C2×C8×C47C2312yes—
68C4⋊C4×C47—21no—
69C4⋊C4×C47C2311yescharacteristic
70C4⋊C4×C47C2312yes—
71C22⋊C4×C47—21no—
72C22⋊Dic47—21no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—21no—
75C4⋊Dic47—21no—
76C4⋊Dic47C2312yes—
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—22no—
79Dic47⋊C4—22no—
80Dic47⋊C4—21no—
81C2×C47⋊C8C2312yes—
82C8×D47—24no—
83C23×C47—21no—
84C23×C47C2×D411yescharacteristic
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—21no—
88C22×D47—42no—
89C22×D47—42no—
90C22×D47—42no—
91C22×D47SD1614yes—
92C22×D47C2×D411yescharacteristic
93C22×D47C2×D411yescharacteristic
94D4×C47—22no—
95D4×C47—42no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—21no—
99C2×C4×C47—42no—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2411yescharacteristic
102C22⋊D47—42no—
103C22⋊D47—42no—
104C22⋊D47—42no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—21no—
108C2×Dic47—42no—
109C2×Dic47C2×D411yescharacteristic
110C2×Dic47C2×D411yescharacteristic
111D188—22no—
112D188—42no—
113C4×D47—22no—
114C4×D47—22no—
115C4×D47—22no—
116C4×D47—44no—
117C4×D47—42no—
118C4×D47—44no—
119C4×D47#4114yes—
120C8×C47—22no—
121C47⋊C8—22no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—41no—
125C22×C47—41no—
126C22×C47—41no—
127C22×C47C2×SD1612yes—
128C22×C47C22×D411yescharacteristic
129C2×D47—21no—
130C2×D47—21no—
131C2×D47—28no—
132C2×D47—41no—
133C2×D47—41no—
134C2×D47—41no—
135C2×D47—84no—
136C2×D47#12312yes—
137C2×D47C2×SD1612yes—
138C2×D47C2×SD1612yes—
139C2×D47AGL(1,ℤ/8)12yes—
140C4×C47—21no—
141C4×C47—41no—
142C4×C47—42no—
143C4×C47C2×#4112yes—
144Dic47—21no—
145Dic47—41no—
146Dic47—42no—
147Dic47#12312yes—
148C2×#481—471nomaximal, Sylow
149C2×C47—22no—
150C2×C47—81no—
151C2×C47C2×#12311yescharacteristic
152C2×C47C22×SD1611yescharacteristic
153C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
154D47—22no—
155D47—81no—
156D47#48114yesdirect product factor
157C2×#121—471no—
158C22×C4⋊C4—471no—
159#481—471no—
160#481—471no—
161#481—472no—
162#481—472no—
163#481—471no—
164#481D4711yescharacteristic, direct product factor
165C2×#106—472no—
166C2×#102—472no—
167C2×C22⋊C8—471no—
168C47C2×#48111yescharacteristic, complemented, Sylow
169C22×D4—471no—
170C22×D4—941no—
171C23×C4—471no—
172C23×C4—941no—
173C22×C8—472no—
174#121—471no—
175#121—471no—
176#121—471no—
177#121—941no—
178#121—941no—
179#121C2×D4711yescharacteristic
180C2×C4⋊C4—471no—
181C2×C4⋊C4—472no—
182C2×C4⋊C4—472no—
183C2×C4⋊C4—471no—
184C2×C4⋊C4—941no—
185C2×C4⋊C4—941no—
186C2×C4⋊C4—941no—
187C2×C4⋊C4C2×D4711yescharacteristic, complemented
188C2×C22⋊C4—941no—
189#106—472no—
190#106—472no—
191#106—472no—
192#106C2×D4712yescomplemented
193#102—472no—
194#102—472no—
195#102—472no—
196#102C2×D4712yescomplemented
197C22⋊C8—471no—
198C22⋊C8—472no—
199C22⋊C8C2×D4711yescharacteristic, complemented
200C24—471no—
201C24—941no—
202C2×D4—21no—
203C2×D4—471no—
204C2×D4—941no—
205C2×D4—944no—
206C2×D4—941no—
207C2×D4—941no—
208C2×D4—941no—
209C2×D4—1884no—
210C2×D4C22×D4711yescharacteristic
211C22×C4—21no—
212C22×C4—471no—
213C22×C4—471no—
214C22×C4—471no—
215C22×C4—471no—
216C22×C4—471no—
217C22×C4—944no—
218C22×C4—941no—
219C22×C4—942no—
220C22×C4—942no—
221C22×C4—941no—
222C22×C4—1884no—
223C22×C4C22×D4711yescharacteristic
224C2×C8—472no—
225C2×C8—944no—
226C2×C8C22×D4712yes—
227C4⋊C4—21no—
228C4⋊C4—472no—
229C4⋊C4—471no—
230C4⋊C4—942no—
231C4⋊C4—942no—
232C4⋊C4—941no—
233C4⋊C4—941no—
234C4⋊C4C22×D4712yes—
235C4⋊C4C22×D4711yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—941no—
238C22⋊C4—941no—
239C22⋊C4—941no—
240C23—21no—
241C23—471no—
242C23—474no—
243C23—471no—
244C23—942no—
245C23—942no—
246C23—941no—
247C23—1882no—
248C23—1882no—
249C23—1882no—
250C23D4×D4711yescharacteristic
251D4—22no—
252D4—42no—
253D4—942no—
254D4—1882no—
255D4—1882no—
256D4—1882no—
257D4—1882no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—471no—
263C2×C4—474no—
264C2×C4—471no—
265C2×C4—942no—
266C2×C4—942no—
267C2×C4—942no—
268C2×C4—942no—
269C2×C4—941no—
270C2×C4—942no—
271C2×C4—1884no—
272C2×C4—1882no—
273C2×C4—1884no—
274C2×C4—1882no—
275C2×C4D4×D4711yescharacteristic
276C2×C4C23×D4711yescharacteristic
277C8—22no—
278C8—942no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—472no—
285C22—472no—
286C22—472no—
287C22—472no—
288C22—948no—
289C22—941no—
290C22—941no—
291C22—3764no—
292C22—1881no—
293C22—1881no—
294C22—1881no—
295C22SD16×D4712yes—
296C22C2×D4×D4711yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—472no—
301C4—941no—
302C4—1881no—
303C4—1882no—
304C4#41×D4712yes—
305C2—22no—
306C2—81no—
307C2—474no—
308C2—942no—
309C2—3761no—
310C2#123×D4711yescharacteristic
311C2C2×SD16×D4711yescharacteristic
312C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#481C2
socleC22×C47C22×D4
hypercenter#481D47
hypocenterC47C2×#481
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D47C2semidirect
3. #15689443C2semidirect
4. #15689442C2semidirect
5. #15689441C2semidirect
6. #15689440C2semidirect
7. #15689439C2semidirect
8. #106×D47C2semidirect
9. #102×D47C2semidirect
10. C22⋊C8×D47C2semidirect
11. C47×#481C2semidirect
22. C2×C4⋊Dic47C22semidirect
28. C4⋊C4×D47C22semidirect
30. #13093956C22semidirect
31. #13093955C22semidirect
32. #13093955C22semidirect
33. #13093946C22semidirect
34. #13093945C22semidirect
35. #13093944C22semidirect
36. C22⋊(C47⋊C8)C22semidirect
37. (C2×D47)⋊C8C22semidirect
39. C2×C4⋊C4×C47C22semidirect
40. #106×C47C22semidirect
41. #102×C47C22semidirect
42. C22⋊C8×C47C22semidirect
156. D47#481direct (N × H)
164. #481D47direct (N × H)
168. C47C2×#481semidirect
187. C2×C4⋊C4C2×D47semidirect
192. #106C2×D47semidirect
196. #102C2×D47semidirect
199. C22⋊C8C2×D47semidirect