Finite Group Databasebeta

← #20255837

Subgroups — #20255837

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#15689813C211yesmaximal, characteristic
2#15689529C211yesmaximal, characteristic, complemented
3#15689461C211yesmaximal, characteristic, complemented
4#15689458C211yesmaximal, characteristic, complemented
5#15689453C211yesmaximal, characteristic, complemented
6#15689451C211yesmaximal, characteristic, complemented
7#15689430C211yesmaximal, characteristic, complemented
8#15689405C211yesmaximal, characteristic, complemented
9#15689379C211yesmaximal, characteristic, complemented
10#15689362C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic
13#15689163C211yesmaximal, characteristic, complemented
14C2×#13093955C211yesmaximal, characteristic, complemented
15C47×#554C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094014—21no—
22#13094005—21no—
23#13094003C2211yescharacteristic
24#13094003C2211yescharacteristic
25C4×Dic94C2211yescharacteristic
26#13093983C2211yescharacteristic
27#13093980—21no—
28C2×C4⋊Dic47C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093955C2211yescharacteristic
37#13093955C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093947C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#125×C47—21no—
50C22⋊Q8×C47—21no—
51C22⋊Q8×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47—21no—
56C4×D4×C47C2211yescharacteristic
57C2×C4⋊C4×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47D411yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×Dic47—21no—
67C2×Dic94C2311yescharacteristic
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47D411yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C22⋊C4×C47D411yescharacteristic
81C22⋊C4×C47D411yescharacteristic
82C42×C47—21no—
83C42×C47C2311yescharacteristic
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87#10625337—22no—
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99#10625329—22no—
100C2×C47⋊C8—22no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47C2×D411yescharacteristic
106C23×C47C2×D411yescharacteristic
107Q8×C47—21no—
108Q8×C47—21no—
109Q8×C47—81no—
110D4×C47—22no—
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×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—81no—
120C2×C4×C47—81no—
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—42no—
131Dic94—21no—
132Dic94—21no—
133C47⋊C8—21no—
134C47⋊C8—21no—
135C47⋊C8—21no—
136C47⋊C8#4112yes—
137C22×C47—21no—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47#13712yes—
143C22×C47C22×D411yescharacteristic
144C4×C47—21no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47C2×#4111yescharacteristic
153C4×C472−1+411yescharacteristic
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158#3344—471nomaximal, Sylow
159C2×C47—22no—
160C2×C47—41no—
161C2×C47#54711yescharacteristic
162C2×C47C2×#13711yescharacteristic
163C2×C47#57711yescharacteristic
164#554D4711yescharacteristic
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×#106—471no—
179C47#334411yescharacteristic, complemented, Sylow
180C2×Q16—471no—
181C2×M16—471no—
182C22×C8—471no—
183C4⋊Q8C2×D4711yescharacteristic
184#126—941no—
185#125—21no—
186#125—471no—
187#125—941no—
188#123—941no—
189C22⋊Q8—21no—
190C22⋊Q8—21no—
191C22⋊Q8—471no—
192C22⋊Q8—471no—
193C22⋊Q8C2×D4711yescharacteristic
194C22⋊Q8C2×D4711yescharacteristic
195C4×Q8—471no—
196C4×Q8C2×D4711yescharacteristic
197C4×D4—21no—
198C4×D4C2×D4711yescharacteristic
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#106—471no—
210#106—471no—
211#106—471no—
212#106—471no—
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—21no—
224C2×Q8—471no—
225C2×Q8C22×D4711yescharacteristic
226C2×D4C22⋊D4711yescharacteristic
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—941no—
230C22×C4C22×D4711yescharacteristic
231C22×C4C22×D4711yescharacteristic
232Q16—942no—
233M16—942no—
234C2×C8—471no—
235C2×C8—471no—
236C2×C8—471no—
237C2×C8—471no—
238C2×C8—942no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
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—21no—
259C22⋊C4—21no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4C22⋊D4711yescharacteristic
264C22⋊C4C22⋊D4711yescharacteristic
265C42—21no—
266C42—941no—
267C42—941no—
268C42C22×D4711yescharacteristic
269C23C2×C22⋊D4711yescharacteristic
270C23C2×C22⋊D4711yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—81no—
274Q8—941no—
275Q8—941no—
276D4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—1882no—
292C2×C4C2×C22⋊D4711yescharacteristic
293C2×C4C2×C22⋊D4711yescharacteristic
294C2×C4C2×C22⋊D4711yescharacteristic
295C2×C4C2×C22⋊D4711yescharacteristic
296C2×C4C23×D4711yescharacteristic
297C8—472no—
298C8—941no—
299C8—941no—
300C8—941no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#1309405512yes—
307C22C22×C22⋊D4711yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—1881no—
317C4—1881no—
318C4—1881no—
319C4—1881no—
320C4#41×D4711yescharacteristic
321C4#1309407111yescharacteristic
322C2—22no—
323C2—41no—
324C2#1568977211yescharacteristic
325C2C2×#1309405511yescharacteristic
326C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#554C2
socleC22×C47C22×D4
hypercenter#554D47
hypocenterC47#3344
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #15689529C2semidirect
3. #15689461C2semidirect
4. #15689458C2semidirect
5. #15689453C2semidirect
6. #15689451C2semidirect
7. #15689430C2semidirect
8. #15689405C2semidirect
9. #15689379C2semidirect
10. #15689362C2semidirect
11. #15689228C2semidirect
13. #15689163C2semidirect
14. C2×#13093955C2semidirect
179. C47#3344semidirect