Finite Group Databasebeta

← #20255996

Subgroups — #20255996

Order 6016.

342 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689844C211yesmaximal, characteristic
2#15689828C211yesmaximal, characteristic
3#15689520C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689465C211yesmaximal, characteristic, complemented
6#15689452C211yesmaximal, characteristic, complemented
7#15689416C211yesmaximal, characteristic, complemented
8#15689407C211yesmaximal, characteristic, complemented
9#15689380C211yesmaximal, characteristic, complemented
10#15689379C211yesmaximal, characteristic, complemented
11#15689215C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic
13#15689163C211yesmaximal, characteristic, complemented
14#15689162C211yesmaximal, characteristic, complemented
15C47×#483C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094019—21no—
22#13094017—21no—
23#13094014—21no—
24#13094010—21no—
25#13094004C2211yescharacteristic
26#13094003—21no—
27#13094003C2211yescharacteristic
28#13094002—21no—
29#13094000C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31#13093989—21no—
32#13093989C2211yescharacteristic
33C4×C22⋊D47—21no—
34C4×C22⋊D47C2211yescharacteristic
35#13093983C2211yescharacteristic
36#13093982C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093955C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093947C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47D411yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47C2311yescharacteristic
65C2×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C22⋊C4×C47—21no—
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78C22⋊Dic47D411yescharacteristic
79#10625337—22no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4D411yescharacteristic
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47C2311yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4D411yescharacteristic
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47C2311yescharacteristic
101#10625329—22no—
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625324—22no—
105C23×C47C2×D411yescharacteristic
106C22×D47C2×D411yescharacteristic
107Q8×C47—21no—
108Q8×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—81no—
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C22⋊D47—22no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C4×D47—21no—
127C4×D47—21no—
128C4×D47—81no—
129Dic94—21no—
130Dic94—21no—
131Dic94—42no—
132Dic94—81no—
133C8×C47—21no—
134C8×C47—21no—
135C47⋊C8—21no—
136C47⋊C8#4112yes—
137C22×C47—21no—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47C22×D411yescharacteristic
141C2×D47—21no—
142C2×D47—21no—
143C2×D47—21no—
144C4×C47—21no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47C2×#4111yescharacteristic
150C4×C472−1+411yescharacteristic
151Dic47—21no—
152Dic47—21no—
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47#13712yes—
158#3356—471nomaximal, Sylow
159C2×C47—41no—
160C2×C47#54711yescharacteristic
161C2×C47C2×#13711yescharacteristic
162C2×C47#57711yescharacteristic
163D47—41no—
164#556—471no—
165#554—471no—
166#498—471no—
167#485—471no—
168#485—471no—
169#483—471no—
170#483D4711yescharacteristic, complemented
171#477—471no—
172#475—471no—
173#470—471no—
174#470—471no—
175C4×Q16—471no—
176#436—471no—
177#428—471no—
178#428—471no—
179C47#335611yescharacteristic, complemented, Sylow
180C2×Q16—471no—
181C2×M16—471no—
182C2×M16—471no—
183C4⋊Q8—471no—
184C4⋊Q8—471no—
185#126—941no—
186#126—941no—
187#125—941no—
188#124—941no—
189C22⋊Q8—471no—
190C22⋊Q8—471no—
191C22⋊Q8—471no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194C22⋊Q8C2×D4711yescharacteristic
195C4×Q8—471no—
196C4×Q8—471no—
197C4×Q8—941no—
198C4×D4—471no—
199C4×D4—941no—
200#117—471no—
201#117—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4C2×D4711yescharacteristic
204#107—471no—
205#107—471no—
206#107—471no—
207#106—471no—
208#106—471no—
209#106—471no—
210#106—471no—
211#106C2×D4711yescharacteristic
212#106C2×D4711yescharacteristic
213C4⋊C8—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103C2×D4711yescharacteristic
219#103C2×D4711yescharacteristic
220C22⋊C8—471no—
221C22⋊C8C2×D4711yescharacteristic
222C4×C8—471no—
223C2×Q8—471no—
224C2×Q8—941no—
225C2×Q8—941no—
226C2×Q8C22×D4711yescharacteristic
227C2×D4—471no—
228C22×C4—21no—
229C22×C4—471no—
230C22×C4—941no—
231C22×C4C22×D4711yescharacteristic
232Q16—942no—
233M16—942no—
234M16—942no—
235C2×C8—471no—
236C2×C8—471no—
237C2×C8C22×D4711yescharacteristic
238C2×C8C22×D4711yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4C22×D4711yescharacteristic
254C4⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—471no—
258C22⋊C4—471no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C42—471no—
265C42—941no—
266C42—941no—
267C42—941no—
268C42—941no—
269C23—471no—
270C23D4×D4711yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—941no—
274Q8—941no—
275Q8—3761no—
276Q8—1882no—
277D4—942no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—3761no—
295C2×C4D4×D4711yescharacteristic
296C2×C4C23×D4711yescharacteristic
297C8—21no—
298C8—21no—
299C8—472no—
300C8—941no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—941no—
305C22—941no—
306C22—941no—
307C22C2×D4×D4711yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—472no—
314C4—941no—
315C4—941no—
316C4—1881no—
317C4—1881no—
318C4—1881no—
319C4—1881no—
320C4#41×D4711yescharacteristic
321C4#1309407111yescharacteristic
322C2—41no—
323C2—1881no—
324C2#1568977111yescharacteristic
325C2#137×D4711yescharacteristic
326C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47#3356
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #15689520C2semidirect
4. #15689467C2semidirect
5. #15689465C2semidirect
6. #15689452C2semidirect
7. #15689416C2semidirect
8. #15689407C2semidirect
9. #15689380C2semidirect
10. #15689379C2semidirect
11. #15689215C2semidirect
13. #15689163C2semidirect
14. #15689162C2semidirect
15. C47×#483C2semidirect
170. #483D47semidirect
179. C47#3356semidirect