Finite Group Databasebeta

← #20255998

Subgroups — #20255998

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#15689831C211yesmaximal, characteristic
3#15689520C211yesmaximal, characteristic, complemented
4#15689463C211yesmaximal, characteristic, complemented
5#15689461C211yesmaximal, characteristic, complemented
6#15689452C211yesmaximal, characteristic, complemented
7#15689451C211yesmaximal, characteristic, complemented
8#15689416C211yesmaximal, characteristic, complemented
9#15689406C211yesmaximal, characteristic, complemented
10#15689378C211yesmaximal, characteristic, complemented
11Q16×Dic47C211yesmaximal, characteristic, complemented
12#15689199C211yesmaximal, characteristic
13#15689165C211yesmaximal, characteristic, complemented
14#15689162C211yesmaximal, characteristic, complemented
15C47×#470C211yesmaximal, characteristic, complemented
16C2×#10625324C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094019—21no—
20#13094017—21no—
21#13094014—21no—
22#13094010—21no—
23#13094004—21no—
24#13094001—21no—
25#13094000C2211yescharacteristic
26#13094000C2211yescharacteristic
27Q8×Dic47C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29#13093989—21no—
30C4×C22⋊D47C2211yescharacteristic
31(C22⋊D47)⋊C4—21no—
32#13093983C2211yescharacteristic
33#13093982C2211yescharacteristic
34C2×C4⋊Dic47C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093955C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093948C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47D411yescharacteristic
63C22×Dic47—21no—
64C2×C4×D47—21no—
65C2×C4×D47C2311yescharacteristic
66C2×Dic94—21no—
67C2×Dic94—21no—
68Q16×C47—22no—
69M16×C47—22no—
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C22⋊Dic47—21no—
79C22⋊Dic47D411yescharacteristic
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⋊Dic47—21no—
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625324—22no—
105C23×C47C2×D411yescharacteristic
106C22×D47C2×D411yescharacteristic
107Q8×C47—21no—
108Q8×C47—21no—
109Q8×C47—21no—
110Q8×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C22⋊D47—22no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—81no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C4×D47—21no—
129C4×D47—21no—
130C4×D47—81no—
131Dic94—42no—
132Dic94—81no—
133C8×C47—21no—
134C8×C47#4112yes—
135C47⋊C8—21no—
136C47⋊C8—21no—
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#483—471no—
171#477—471no—
172#475—471no—
173#470—471no—
174#470D4711yescharacteristic, complemented
175C4×Q16—471no—
176#436—471no—
177#428—471no—
178#428—471no—
179C47#335611yescharacteristic, complemented, Sylow
180C2×Q16C2×D4711yescharacteristic
181C2×M16—471no—
182C2×M16C2×D4711yescharacteristic
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—941no—
192C22⋊Q8—941no—
193C22⋊Q8C2×D4711yescharacteristic
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⋊C4—471no—
204#107—471no—
205#107—471no—
206#107—471no—
207#106—471no—
208#106—471no—
209#106—471no—
210#106—471no—
211#106—471no—
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⋊C8—471no—
222C4×C8—471no—
223C2×Q8—941no—
224C2×Q8—941no—
225C2×Q8C22×D4711yescharacteristic
226C2×Q8C22×D4711yescharacteristic
227C2×D4—471no—
228C22×C4—471no—
229C22×C4—941no—
230C22×C4—941no—
231C22×C4C22×D4711yescharacteristic
232Q16—22no—
233M16—22no—
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—471no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—471no—
259C22⋊C4—471no—
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—21no—
274Q8—21no—
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—471no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4D4×D4711yescharacteristic
296C2×C4C23×D4711yescharacteristic
297C8—21no—
298C8—941no—
299C8—941no—
300C8#1062535212yes—
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—
320C4C2×#1062535211yescharacteristic
321C4#1309407111yescharacteristic
322C2—41no—
323C2—1881no—
324C2#1568977311yescharacteristic
325C2#137×D4711yescharacteristic
326C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3356
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
3. #15689520C2semidirect
4. #15689463C2semidirect
5. #15689461C2semidirect
6. #15689452C2semidirect
7. #15689451C2semidirect
8. #15689416C2semidirect
9. #15689406C2semidirect
10. #15689378C2semidirect
11. Q16×Dic47C2semidirect
13. #15689165C2semidirect
14. #15689162C2semidirect
15. C47×#470C2semidirect
174. #470D47semidirect
179. C47#3356semidirect