Finite Group Databasebeta

← #20255847

Subgroups — #20255847

Order 6016.

344 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#15689831C211yesmaximal, characteristic
2#15689808C211yesmaximal, characteristic
3#15689530C211yesmaximal, characteristic, complemented
4#15689463C211yesmaximal, characteristic, complemented
5#15689459C211yesmaximal, characteristic, complemented
6#15689455C211yesmaximal, characteristic, complemented
7#15689432C211yesmaximal, characteristic, complemented
8#15689407C211yesmaximal, characteristic, complemented
9#15689380C211yesmaximal, characteristic, complemented
10#15689362C211yesmaximal, characteristic, complemented
11#15689227C211yesmaximal, characteristic, complemented
12#15689191C211yesmaximal, characteristic
13#15689162C211yesmaximal, characteristic, complemented
14C2×#13093955C211yesmaximal, characteristic, complemented
15C47×#483C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094019—21no—
21#13094015C2211yescharacteristic
22#13094014—21no—
23#13094014—21no—
24#13094007—21no—
25#13094004—21no—
26#13094004C2211yescharacteristic
27#13094003C2211yescharacteristic
28#13094001—21no—
29#13094000C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31#13093989C2211yescharacteristic
32C4×C22⋊D47C2211yescharacteristic
33(C22⋊D47)⋊C4—21no—
34#13093983—21no—
35#13093982C2211yescharacteristic
36C2×C4⋊Dic47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093955C2211yescharacteristic
44#13093955C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093947C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic
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
63C22×Dic47—21no—
64C2×C4×D47—21no—
65C2×C4×D47C2311yescharacteristic
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⋊Dic47D411yescharacteristic
78#10625337—22no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4D411yescharacteristic
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90Dic47⋊C4—21no—
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×Dic47C2311yescharacteristic
101C2×C47⋊C8—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—42no—
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C22⋊D47—22no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—81no—
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C4×D47—21no—
128C4×D47—21no—
129C4×D47—81no—
130Dic94—21no—
131Dic94—21no—
132Dic94—81no—
133C8×C47—21no—
134C8×C47—21no—
135C47⋊C8—21no—
136C47⋊C8#4112yes—
137C22×C47—21no—
138C22×C47—21no—
139C22×C47#13712yes—
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—21no—
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158#3344—471nomaximal, Sylow
159C2×C47—22no—
160C2×C47#54711yescharacteristic
161C2×C47C2×#13711yescharacteristic
162C2×C47#57711yescharacteristic
163D47—41no—
164#554—471no—
165#552—471no—
166#501—471no—
167#485—471no—
168#484—471no—
169#483—471no—
170#483D4711yescharacteristic, complemented
171#479—471no—
172#475—471no—
173#470—471no—
174#467—471no—
175#441—471no—
176#435—471no—
177#428—471no—
178C2×#106—471no—
179C47#334411yescharacteristic, complemented, Sylow
180C2×Q16—471no—
181C2×M16—471no—
182C22×C8—471no—
183C4⋊Q8—471no—
184#126—941no—
185#125—471no—
186#125—941no—
187#125—941no—
188#123—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×D4—471no—
198C4×D4—941no—
199#117—471no—
200#117—941no—
201C2×C4⋊C4—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
222#97—471no—
223C2×Q8—471no—
224C2×Q8—941no—
225C2×Q8C22×D4711yescharacteristic
226C2×D4—471no—
227C22×C4—21no—
228C22×C4—471no—
229C22×C4—941no—
230C22×C4—941no—
231C22×C4C22×D4711yescharacteristic
232Q16—942no—
233M16—942no—
234C2×C8—471no—
235C2×C8—471no—
236C2×C8—942no—
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⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—471no—
260C22⋊C4—471no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C42—471no—
266C42—941no—
267C42—941no—
268C42—941no—
269C23—471no—
270C23D4×D4711yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—941no—
274Q8—941no—
275Q8—3761no—
276D4—942no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
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—21no—
299C8—472no—
300C8—941no—
301C22—21no—
302C22—21no—
303C22—941no—
304C22—941no—
305C22—941no—
306C22#1309405312yes—
307C22C2×D4×D4711yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—941no—
314C4—941no—
315C4—941no—
316C4—1881no—
317C4—1881no—
318C4—1881no—
319C4—1881no—
320C4#41×D4711yescharacteristic
321C4#1309407111yescharacteristic
322C2—22no—
323C2—1881no—
324C2#1568977111yescharacteristic
325C2C2×#1309405311yescharacteristic
326C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47#3344
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. #15689530C2semidirect
4. #15689463C2semidirect
5. #15689459C2semidirect
6. #15689455C2semidirect
7. #15689432C2semidirect
8. #15689407C2semidirect
9. #15689380C2semidirect
10. #15689362C2semidirect
11. #15689227C2semidirect
13. #15689162C2semidirect
14. C2×#13093955C2semidirect
15. C47×#483C2semidirect
170. #483D47semidirect
179. C47#3344semidirect