Finite Group Databasebeta

← #20253330

Subgroups — #20253330

Order 6016.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#13093999C211yesmaximal, characteristic
2#117×D47C211yesmaximal, characteristic, complemented
3#15689450C212yesmaximal, complemented
4#15689449C212yesmaximal, complemented
5#15689443C212yesmaximal, complemented
6#15689438C212yesmaximal, complemented
7#15689163C211yesmaximal, characteristic, complemented
8#15689129C211yesmaximal, characteristic, complemented
9#15689127C211yesmaximal, characteristic, complemented
10#15689086C211yesmaximal, characteristic, complemented
11C47×#428C211yesmaximal, characteristic, complemented
12C22×D188—21no—
13C22×D188C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15C2×#10625329C2211yescharacteristic
16#13093999—21no—
17#13093999—21no—
18#13093999C2212yes—
19#13093999C2212yes—
20#13093983C2211yescharacteristic
21#13093982C2211yescharacteristic, complemented
22#13093982C2211yescharacteristic, complemented
23#13093981—21no—
24#13093980—21no—
25C4⋊C4×D47C2211yescharacteristic, complemented
26C4⋊C4×D47C2211yescharacteristic, complemented
27C2×(C2×D47)⋊C4—21no—
28C22⋊C4×D47—21no—
29C42×D47—21no—
30#13093957C2212yescomplemented
31#13093955C2212yescomplemented
32#13093946C2212yescomplemented
33#13093946C2212yescomplemented
34#13093944C2212yescomplemented
35#13093944C2212yescomplemented
36(C2×D47)⋊C8C2212yescomplemented
37(C2×D47)⋊C8C2212yescomplemented
38C2×M16×C47C2211yescharacteristic
39#117×C47C2211yescharacteristic
40C2×C4⋊C4×C47C2211yescharacteristic
41#107×C47C2212yescomplemented
42#106×C47C2212yescomplemented
43C23×D47—21no—
44C23×D47D411yescharacteristic
45C22×C4×C47—21no—
46C22×C4×C47C2311yescharacteristic
47C22×Dic47D411yescharacteristic
48C2×D188—22no—
49C2×D188—22no—
50C2×D188—22no—
51C2×D188—22no—
52C2×D188—21no—
53C2×D188—44no—
54C2×D188C2312yes—
55C2×C4×D47—22no—
56C2×C4×D47—22no—
57C2×C4×D47—21no—
58C2×C4×D47—21no—
59C2×C4×D47D411yescharacteristic
60C2×C4×D47D411yescharacteristic
61C2×C4×D47C2311yescharacteristic
62C2×C4×D47C2311yescharacteristic
63M16×C47—22no—
64C2×C8×C47C2312yes—
65C4⋊C4×C47—21no—
66C4⋊C4×C47C2311yescharacteristic
67C4⋊C4×C47C2312yes—
68C4⋊C4×C47C2311yescharacteristic
69C22⋊C4×C47—21no—
70C42×C47—21no—
71C22⋊Dic47—21no—
72(C2×D47)⋊C4—21no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—22no—
75(C2×D47)⋊C4—22no—
76C4⋊Dic47C2311yescharacteristic
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—21no—
79Dic47⋊C4—21no—
80C4×Dic47—21no—
81C4×Dic47—21no—
82C4×Dic47—21no—
83#10625329—22no—
84C2×C47⋊C8C2312yes—
85C23×C47C2×D411yescharacteristic
86C22×D47—22no—
87C22×D47—22no—
88C22×D47—22no—
89C22×D47—41no—
90C22×D47—42no—
91C22×D47—42no—
92C22×D47—42no—
93C22×D47C2×D411yescharacteristic
94C22×D47C2×D411yescharacteristic
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—42no—
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47#4112yes—
101C2×C4×C47#4112yes—
102C2×C4×C47C2411yescharacteristic
103C2×Dic47—22no—
104C2×Dic47—21no—
105C2×Dic47—21no—
106C2×Dic47C2×D411yescharacteristic
107C2×Dic47C2×D411yescharacteristic
108D188—22no—
109D188—22no—
110D188—44no—
111D188—44no—
112D188—42no—
113C4×D47—22no—
114C4×D47—22no—
115C4×D47—21no—
116C4×D47—21no—
117C4×D47—21no—
118C4×D47—21no—
119C4×D47—42no—
120C4×D47—42no—
121C8×C47—22no—
122C47⋊C8—22no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47#12312yes—
126C22×C47C22×D411yescharacteristic
127C2×D47—21no—
128C2×D47—21no—
129C2×D47—21no—
130C2×D47—21no—
131C2×D47—21no—
132C2×D47—44no—
133C2×D47—42no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—84no—
137C2×D47AGL(1,ℤ/8)12yes—
138C4×C47—41no—
139C4×C47—42no—
140C4×C47—41no—
141C4×C47#12312yes—
142C4×C47C2×#4111yescharacteristic
143C4×C47C2×#4111yescharacteristic
144Dic47—21no—
145Dic47—21no—
146Dic47—41no—
147Dic47—41no—
148#3094—471nomaximal, Sylow
149C2×C47—22no—
150C2×C47C2×#12311yescharacteristic
151C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C47#57511yescharacteristic
153D47—22no—
154D47—41no—
155D47—82no—
156C2×#121—471no—
157C2×#117—471no—
158#482—472no—
159#482—472no—
160#481—472no—
161#480—472no—
162#428—471no—
163#428D4711yescharacteristic, complemented
164#418—471no—
165#418—471no—
166#407—471no—
167C47#309411yescharacteristic, complemented, Sylow
168C22×D4—471no—
169C22×D4—941no—
170C23×C4—471no—
171C2×M16—471no—
172C2×M16C2×D4711yescharacteristic
173#121—472no—
174#121—472no—
175#121—941no—
176#121—941no—
177#117—471no—
178#117—471no—
179#117—471no—
180#117—941no—
181#117—941no—
182#117C2×D4711yescharacteristic
183C2×C4⋊C4—471no—
184C2×C4⋊C4—471no—
185C2×C4⋊C4C2×D4711yescharacteristic
186C2×C22⋊C4—941no—
187C2×C22⋊C4—941no—
188C2×C42—941no—
189#107—472no—
190#107C2×D4712yescomplemented
191#106—472no—
192#106C2×D4712yescomplemented
193#102—472no—
194#102—472no—
195#102—472no—
196#102—472no—
197C22⋊C8—472no—
198C22⋊C8—472no—
199C24—471no—
200C24—941no—
201C2×D4—472no—
202C2×D4—942no—
203C2×D4—942no—
204C2×D4—942no—
205C2×D4—941no—
206C2×D4—942no—
207C2×D4—1884no—
208C22×C4—21no—
209C22×C4—471no—
210C22×C4—471no—
211C22×C4—471no—
212C22×C4—471no—
213C22×C4—471no—
214C22×C4—941no—
215C22×C4—941no—
216C22×C4—942no—
217C22×C4—942no—
218C22×C4C22×D4711yescharacteristic
219M16—22no—
220M16—942no—
221C2×C8—472no—
222C2×C8C22×D4712yes—
223C4⋊C4—21no—
224C4⋊C4—471no—
225C4⋊C4—471no—
226C4⋊C4—941no—
227C4⋊C4—941no—
228C4⋊C4C22×D4711yescharacteristic
229C4⋊C4C22×D4711yescharacteristic
230C4⋊C4C22×D4712yes—
231C22⋊C4—21no—
232C22⋊C4—942no—
233C22⋊C4—942no—
234C22⋊C4—941no—
235C22⋊C4—941no—
236C22⋊C4—941no—
237C42—21no—
238C42—941no—
239C42—941no—
240C42—941no—
241C23—471no—
242C23—471no—
243C23—942no—
244C23—942no—
245C23—942no—
246C23—1881no—
247C23—1882no—
248C23—1882no—
249C23—1882no—
250C23D4×D4711yescharacteristic
251D4—942no—
252D4—942no—
253D4—1884no—
254D4—1884no—
255D4—1882no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—471no—
261C2×C4—471no—
262C2×C4—942no—
263C2×C4—942no—
264C2×C4—942no—
265C2×C4—941no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—941no—
269C2×C4—941no—
270C2×C4—941no—
271C2×C4—1882no—
272C2×C4—1882no—
273C2×C4#1062535012yes—
274C2×C4D4×D4711yescharacteristic
275C2×C4#1062535412yes—
276C2×C4C23×D4711yescharacteristic
277C8—22no—
278C8—942no—
279C22—21no—
280C22—21no—
281C22—472no—
282C22—941no—
283C22—941no—
284C22—941no—
285C22—941no—
286C22—941no—
287C22—3764no—
288C22—1884no—
289C22—1882no—
290C22—1882no—
291C22—1882no—
292C22#1309400912yes—
293C22C2×D4×D4711yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—941no—
298C4—941no—
299C4—1881no—
300C4—1881no—
301C4#1309400912yes—
302C4C2×#1062535011yescharacteristic
303C4C2×#1062535411yescharacteristic
304C2—22no—
305C2—942no—
306C2—3762no—
307C2—1881no—
308C2C2×#1309400911yescharacteristic
309C2AGL(1,ℤ/8)×D4711yescharacteristic
310C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#428C2
socleC22×C47C22×D4
hypercenter#428D47
hypocenterC47#3094
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #117×D47C2semidirect
3. #15689450C2semidirect
4. #15689449C2semidirect
5. #15689443C2semidirect
6. #15689438C2semidirect
7. #15689163C2semidirect
8. #15689129C2semidirect
9. #15689127C2semidirect
10. #15689086C2semidirect
11. C47×#428C2semidirect
21. #13093982C22semidirect
22. #13093982C22semidirect
25. C4⋊C4×D47C22semidirect
26. C4⋊C4×D47C22semidirect
30. #13093957C22semidirect
31. #13093955C22semidirect
32. #13093946C22semidirect
33. #13093946C22semidirect
34. #13093944C22semidirect
35. #13093944C22semidirect
36. (C2×D47)⋊C8C22semidirect
37. (C2×D47)⋊C8C22semidirect
41. #107×C47C22semidirect
42. #106×C47C22semidirect
163. #428D47semidirect
167. C47#3094semidirect
190. #107C2×D47semidirect
192. #106C2×D47semidirect