Finite Group Databasebeta

← #20255839

Subgroups — #20255839

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#15689828C211yesmaximal, characteristic
2#15689808C211yesmaximal, characteristic
3#15689530C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689458C211yesmaximal, characteristic, complemented
6#15689455C211yesmaximal, characteristic, complemented
7#15689453C211yesmaximal, characteristic, complemented
8#15689433C211yesmaximal, characteristic, complemented
9#15689407C211yesmaximal, characteristic, complemented
10#15689382C211yesmaximal, characteristic, complemented
11#15689364C211yesmaximal, characteristic, complemented
12#15689229C211yesmaximal, characteristic, complemented
13#15689194C211yesmaximal, characteristic
14#15689162C211yesmaximal, characteristic, complemented
15C2×#106×C47C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094019—21no—
20#13094015C2211yescharacteristic
21#13094014—21no—
22#13094014—21no—
23#13094007—21no—
24#13094004C2211yescharacteristic
25#13094004C2211yescharacteristic
26#13094003—21no—
27#13094003C2211yescharacteristic
28#13094003C2211yescharacteristic
29#13094002—21no—
30#13093989C2211yescharacteristic
31#13093989C2211yescharacteristic
32C4×C22⋊D47—21no—
33C4×C22⋊D47C2211yescharacteristic
34#13093983—21no—
35#13093982C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic
52C22×C8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54C2×C4⋊C4×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#106×C47C2211yescharacteristic
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47D411yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47C2311yescharacteristic
65C2×Dic94—21no—
66C2×Dic94C2311yescharacteristic
67C2×Dic94C2311yescharacteristic
68C2×C8×C47—22no—
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊Dic47—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
89Dic47⋊C4—21no—
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⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103Dic188—22no—
104#10625324—22no—
105C23×C47C2×D411yescharacteristic
106C22×D47C2×D411yescharacteristic
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—42no—
114C2×C4×C47—81no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C22⋊D47—22no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124C2×Dic47C2×D411yescharacteristic
125C4×D47—21no—
126C4×D47—21no—
127C4×D47—81no—
128Dic94—21no—
129Dic94—21no—
130Dic94—21no—
131Dic94—21no—
132Dic94—81no—
133C8×C47—21no—
134C8×C47#4112yes—
135C47⋊C8—21no—
136C47⋊C8—21no—
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#483—471no—
171#479—471no—
172#475—471no—
173#470—471no—
174#467—471no—
175#441—471no—
176#435—471no—
177#428—471no—
178C2×#106D4711yescharacteristic, complemented
179C47#334411yescharacteristic, complemented, Sylow
180C2×Q16—471no—
181C2×M16—471no—
182C22×C8C2×D4711yescharacteristic
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—471no—
193C22⋊Q8—941no—
194C22⋊Q8—941no—
195C4×Q8—471no—
196C4×Q8—471no—
197C4×D4—471no—
198C4×D4—941no—
199#117—471no—
200#117—941no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4C2×D4711yescharacteristic
203C2×C4⋊C4C2×D4711yescharacteristic
204#107—471no—
205#107—471no—
206#107—471no—
207#106—471no—
208#106—471no—
209#106C2×D4711yescharacteristic
210#106C2×D4711yescharacteristic
211#106C2×D4711yescharacteristic
212#106C2×D4711yescharacteristic
213C4⋊C8—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220C22⋊C8—471no—
221C22⋊C8—471no—
222#97—471no—
223C2×Q8—471no—
224C2×Q8—471no—
225C2×Q8—941no—
226C2×D4—471no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—471no—
230C22×C4—941no—
231C22×C4C22×D4711yescharacteristic
232Q16—942no—
233M16—942no—
234C2×C8—22no—
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—941no—
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⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C4⋊C4C22×D4711yescharacteristic
258C22⋊C4—471no—
259C22⋊C4—471no—
260C22⋊C4—941no—
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—941no—
272Q8—941no—
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—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—941no—
299C8—941no—
300C8#1062535012yes—
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—
320C4C2×#1062535011yescharacteristic
321C4#1309407211yescharacteristic
322C2—22no—
323C2—1881no—
324C2#1568977411yescharacteristic
325C2C2×#1309405311yescharacteristic
326C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#106×C47C2
socleC22×C47C22×D4
hypercenterC2×#106D47
hypocenterC47#3344
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #15689530C2semidirect
4. #15689467C2semidirect
5. #15689458C2semidirect
6. #15689455C2semidirect
7. #15689453C2semidirect
8. #15689433C2semidirect
9. #15689407C2semidirect
10. #15689382C2semidirect
11. #15689364C2semidirect
12. #15689229C2semidirect
14. #15689162C2semidirect
15. C2×#106×C47C2semidirect
178. C2×#106D47semidirect
179. C47#3344semidirect