Finite Group Databasebeta

← #20255796

Subgroups — #20255796

Order 6016.

352 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689844C211yesmaximal, characteristic, complemented
2#15689837C211yesmaximal, characteristic
3#15689520C211yesmaximal, characteristic, complemented
4#15689463C211yesmaximal, characteristic, complemented
5#15689461C211yesmaximal, characteristic, complemented
6#15689445C211yesmaximal, characteristic, complemented
7#15689444C211yesmaximal, characteristic, complemented
8#15689416C211yesmaximal, characteristic, complemented
9#15689401C211yesmaximal, characteristic, complemented
10#15689349C211yesmaximal, characteristic, complemented
11SD16×Dic47C211yesmaximal, characteristic, complemented
12C8×C22⋊D47C211yesmaximal, characteristic, complemented
13#15689161C211yesmaximal, characteristic, complemented
14#15689158C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×C8×D47C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094019—21no—
20#13094017—21no—
21#13094011—21no—
22#13094010—21no—
23#13094010—21no—
24#13094000C2211yescharacteristic
25#13093996—21no—
26#13093995C2211yescharacteristic
27Q8×Dic47C2211yescharacteristic
28#13093989—21no—
29D4×Dic47C2211yescharacteristic
30C4×C22⋊D47C2211yescharacteristic
31#13093983C2211yescharacteristic
32#13093983C2211yescharacteristic
33#13093982C2211yescharacteristic
34#13093982C2211yescharacteristic
35#13093980—21no—
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093955C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47D411yescharacteristic
65C22×Dic47—21no—
66C2×C4×D47C2311yescharacteristic
67C2×Dic94—21no—
68C2×Dic94—21no—
69SD16×C47—22no—
70C2×C8×C47—22no—
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47D411yescharacteristic
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4D411yescharacteristic
87C4⋊Dic47—21no—
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4D411yescharacteristic
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C8×D47—22no—
105C23×C47—21no—
106C23×C47C2×D411yescharacteristic
107C22×D47C2×D411yescharacteristic
108Q8×C47—21no—
109Q8×C47—21no—
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—81no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—22no—
121C22⋊D47—81no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—42no—
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C4×D47—21no—
131C4×D47—21no—
132Dic94—42no—
133Dic94—81no—
134C8×C47—21no—
135C8×C47#4112yes—
136C47⋊C8—21no—
137C47⋊C8—21no—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47—41no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47C22×D411yescharacteristic
145C2×D47—21no—
146C2×D47—21no—
147C2×D47—21no—
148C4×C47—21no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47C2×#4111yescharacteristic
153C4×C472−1+411yescharacteristic
154Dic47—21no—
155Dic47—21no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47#13512yes—
161#3340—471nomaximal, Sylow
162C2×C47—41no—
163C2×C47—81no—
164C2×C47#54711yescharacteristic
165C2×C47C2×#13511yescharacteristic
166C2×C47#57711yescharacteristic
167D47—41no—
168#556—471no—
169#555—471no—
170#498—471no—
171#485—471no—
172#485—471no—
173#482—471no—
174#482—471no—
175#477—471no—
176#474—471no—
177#465—471no—
178#465D4711yescharacteristic, complemented
179C4×SD16—471no—
180C8×D4—471no—
181#427—471no—
182#427—471no—
183C47#334011yescharacteristic, complemented, Sylow
184C2×SD16C2×D4711yescharacteristic
185C22×C8—471no—
186C22×C8C2×D4711yescharacteristic
187C4⋊Q8—471no—
188C4⋊Q8—471no—
189#126—941no—
190#126—941no—
191#124—941no—
192#124—941no—
193#124—941no—
194C22⋊Q8—471no—
195C22⋊Q8C2×D4711yescharacteristic
196#121—471no—
197#121—941no—
198#121C2×D4711yescharacteristic
199C4×Q8—471no—
200C4×Q8—941no—
201C4×D4—471no—
202C4×D4—471no—
203#117—471no—
204#117—471no—
205#117—471no—
206#117—471no—
207#117—941no—
208#107—471no—
209#107—471no—
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214#106—471no—
215#106—471no—
216#106C2×D4711yescharacteristic
217C4⋊C8—471no—
218#103—471no—
219#103—471no—
220#103C2×D4711yescharacteristic
221#102—471no—
222#102—471no—
223#102C2×D4711yescharacteristic
224C22⋊C8—471no—
225C22⋊C8—471no—
226C4×C8—471no—
227C2×Q8—941no—
228C2×Q8—941no—
229C2×Q8C22×D4711yescharacteristic
230C2×D4—21no—
231C2×D4—471no—
232C2×D4—941no—
233C2×D4C22×D4711yescharacteristic
234C22×C4—471no—
235C22×C4—941no—
236C22×C4C22×D4711yescharacteristic
237SD16—22no—
238C2×C8—22no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—942no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
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—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C42—471no—
268C42—941no—
269C42—941no—
270C42—941no—
271C42—941no—
272C42—941no—
273C23—21no—
274C23—471no—
275C23D4×D4711yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—3761no—
279Q8—1882no—
280D4—21no—
281D4—21no—
282D4—81no—
283D4—942no—
284D4—3761no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—471no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—1882no—
300C2×C4D4×D4711yescharacteristic
301C2×C4C23×D4711yescharacteristic
302C8—21no—
303C8—941no—
304C8—941no—
305C8#1062535212yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—941no—
313C22—941no—
314C22—941no—
315C22C2×D4×D4711yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—472no—
321C4—941no—
322C4—941no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4—1881no—
327C4C2×#1062535211yescharacteristic
328C4#1309407111yescharacteristic
329C2—41no—
330C2—81no—
331C2—1881no—
332C2#1568977311yescharacteristic
333C2#135×D4711yescharacteristic
334C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3340
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #15689844C2semidirect
3. #15689520C2semidirect
4. #15689463C2semidirect
5. #15689461C2semidirect
6. #15689445C2semidirect
7. #15689444C2semidirect
8. #15689416C2semidirect
9. #15689401C2semidirect
10. #15689349C2semidirect
11. SD16×Dic47C2semidirect
12. C8×C22⋊D47C2semidirect
13. #15689161C2semidirect
14. #15689158C2semidirect
15. C47×#465C2semidirect
178. #465D47semidirect
183. C47#3340semidirect