Finite Group Databasebeta

← #20256208

Subgroups — #20256208

Order 6016.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689847C211yesmaximal, characteristic, complemented
2#15689832C211yesmaximal, characteristic, complemented
3#15689491C211yesmaximal, characteristic, complemented
4#15689484C211yesmaximal, characteristic, complemented
5#15689479C211yesmaximal, characteristic, complemented
6#15689432C211yesmaximal, characteristic, complemented
7#15689424C211yesmaximal, characteristic, complemented
8#15689406C211yesmaximal, characteristic, complemented
9#15689340C211yesmaximal, characteristic
10#15689340C211yesmaximal, characteristic
11#15689252C211yesmaximal, characteristic, complemented
12#15689233C211yesmaximal, characteristic
13#15689224C211yesmaximal, characteristic, complemented
14SD16×Dic47C211yesmaximal, characteristic, complemented
15C47×#461C211yesmaximal, characteristic, complemented
16C2×#10625334C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094019—21no—
19#13094019—21no—
20#13094016C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094013C2211yescharacteristic
23#13094013C2211yescharacteristic
24#13094004—21no—
25#13094003—21no—
26#13094001—21no—
27#13094001—21no—
28Q8×Dic47C2211yescharacteristic
29Q8×Dic47C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×D188C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34#13093982—21no—
35C2×Dic47⋊C4—21no—
36#13093958C2211yescharacteristic
37#13093956C2211yescharacteristic
38#13093955C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C4⋊Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×Dic94—21no—
68C2×Dic94D411yescharacteristic
69SD16×C47—22no—
70SD16×C47—22no—
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C42×C47C2311yescharacteristic
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80#10625334—22no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47D411yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98Dic47⋊C4D411yescharacteristic
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47—21no—
106C22×D47—21no—
107Q8×C47—21no—
108Q8×C47—21no—
109Q8×C47—21no—
110Q8×C47—21no—
111D4×C47—21no—
112D4×C47#4112yes—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—81no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—42no—
124C2×Dic47—81no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129D188—21no—
130D188—21no—
131C4×D47—42no—
132Dic94—41no—
133Dic94—81no—
134C8×C47—21no—
135C8×C47—21no—
136C47⋊C8—21no—
137C47⋊C8—21no—
138C22×C47—22no—
139C22×C47—41no—
140C22×C47—41no—
141C22×C47C22×D411yescharacteristic
142C2×D47—41no—
143C2×D47—41no—
144C2×D47—41no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47C2×#4111yescharacteristic
151C4×C472−1+411yescharacteristic
152Dic47—21no—
153Dic47—21no—
154Dic47—21no—
155Dic47—21no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159#3376—471nomaximal, Sylow
160C2×C47—42no—
161C2×C47#54811yescharacteristic
162C2×C47#57511yescharacteristic
163C2×C47#57711yescharacteristic
164D47—81no—
165#556—471no—
166#554—471no—
167#491—471no—
168#489—471no—
169#488—471no—
170#479—471no—
171#478—471no—
172#475—471no—
173#463—471no—
174#463—471no—
175#461D4711yescharacteristic, complemented
176#446—471no—
177#442—471no—
178#440—471no—
179C4×SD16—471no—
180C47#337611yescharacteristic, complemented, Sylow
181C2×SD16C2×D4711yescharacteristic
182C2×SD16C2×D4711yescharacteristic
183C2×D8—471no—
184C4⋊Q8—471no—
185C4⋊Q8C2×D4711yescharacteristic
186#126—941no—
187#126—941no—
188#125—471no—
189#125—471no—
190#124—471no—
191#124—471no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194C22⋊Q8—941no—
195C22⋊Q8—941no—
196C4×Q8—471no—
197C4×Q8—471no—
198C4×Q8—471no—
199C4×D4—471no—
200C4×D4—471no—
201C4×D4—471no—
202C4×D4C2×D4711yescharacteristic
203#117—941no—
204C2×C4⋊C4—941no—
205#107—471no—
206#106—471no—
207#106—471no—
208C4⋊C8—471no—
209C4⋊C8—471no—
210C4⋊C8C2×D4711yescharacteristic
211#103—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103C2×D4711yescharacteristic
216#103C2×D4711yescharacteristic
217#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221#97—471no—
222#97—471no—
223C4×C8—471no—
224C2×Q8—471no—
225C2×Q8—941no—
226C2×Q8C22×D4711yescharacteristic
227C2×Q8C22×D4711yescharacteristic
228C2×D4—471no—
229C2×D4C22×D4711yescharacteristic
230C22×C4—21no—
231C22×C4—941no—
232C22×C4—941no—
233C22×C4—941no—
234SD16—22no—
235SD16—22no—
236D8—942no—
237C2×C8—471no—
238C2×C8—471no—
239C2×C8C22×D4711yescharacteristic
240C2×C8C22×D4711yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4C22×D4711yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C42—471no—
266C42—471no—
267C42—941no—
268C42—941no—
269C42C22×D4711yescharacteristic
270C23—21no—
271C23—941no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—3761no—
277Q8—1881no—
278D4—21no—
279D4—941no—
280D4—941no—
281D4#1062535212yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—471no—
289C2×C4—471no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—3761no—
294C2×C4—1882no—
295C2×C4—1882no—
296C2×C4D4×D4711yescharacteristic
297C2×C4D4×D4711yescharacteristic
298C2×C4C23×D4711yescharacteristic
299C8—21no—
300C8—21no—
301C8—941no—
302C8—941no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—1881no—
307C22—1881no—
308C22—1881no—
309C22C2×D4×D4711yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—941no—
316C4—941no—
317C4—941no—
318C4—941no—
319C4—1881no—
320C4—1881no—
321C4—1881no—
322C4C2×#1062535211yescharacteristic
323C4#1309407111yescharacteristic
324C2—42no—
325C2—3761no—
326C2#1568977911yescharacteristic
327C2#1568992211yescharacteristic
328C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3376
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #15689847C2semidirect
2. #15689832C2semidirect
3. #15689491C2semidirect
4. #15689484C2semidirect
5. #15689479C2semidirect
6. #15689432C2semidirect
7. #15689424C2semidirect
8. #15689406C2semidirect
11. #15689252C2semidirect
13. #15689224C2semidirect
14. SD16×Dic47C2semidirect
15. C47×#461C2semidirect
175. #461D47semidirect
180. C47#3376semidirect