Finite Group Databasebeta

← #20256156

Subgroups — #20256156

Order 6016.

344 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#15689858C211yesmaximal, characteristic
2#15689489C211yesmaximal, characteristic
3#15689485C211yesmaximal, characteristic, complemented
4#15689480C211yesmaximal, characteristic, complemented
5#15689427C211yesmaximal, characteristic, complemented
6#15689420C211yesmaximal, characteristic, complemented
7#15689410C211yesmaximal, characteristic, complemented
8#15689345C211yesmaximal, characteristic, complemented
9#15689345C211yesmaximal, characteristic, complemented
10#15689323C211yesmaximal, characteristic
11#15689254C211yesmaximal, characteristic, complemented
12#15689228C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14C4×#10625336C211yesmaximal, characteristic, complemented
15C47×#557C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19#13094021C2211yescharacteristic
20#13094013—21no—
21#13094012C2211yescharacteristic
22#13094012C2211yescharacteristic
23#13094009—21no—
24#13094009—21no—
25C4×Dic94C2211yescharacteristic
26C4×D188C2211yescharacteristic
27C4×D188C2211yescharacteristic
28#13093986—21no—
29#13093957C2211yescharacteristic
30#13093955C2211yescharacteristic
31#13093955C2211yescharacteristic
32C4⋊(C47⋊C8)C2211yescharacteristic
33C4⋊(C47⋊C8)C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093944C2211yescharacteristic
40#13093944C2211yescharacteristic
41#13093944C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45#13093935C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47—21no—
49C4⋊Q8×C47C2211yescharacteristic
50#125×C47—21no—
51#125×C47—21no—
52#125×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54C4×Q8×C47—21no—
55C4×Q8×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×Q8×C47C2211yescharacteristic
58C4×Q8×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47D411yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×D188—21no—
63C2×D188—21no—
64C2×D188C2311yescharacteristic
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×Dic94C2311yescharacteristic
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47D411yescharacteristic
78C4⋊C4×C47D411yescharacteristic
79C4⋊C4×C47D411yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C42×C47—21no—
84C42×C47—21no—
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87C42×C47C2311yescharacteristic
88C42×C47C2311yescharacteristic
89#10625337—22no—
90#10625336—22no—
91#10625336—22no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C22×D47—21no—
106C22×D47—21no—
107Q8×C47—21no—
108Q8×C47—41no—
109Q8×C47—42no—
110Q8×C47#4112yes—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C2×Dic47—21no—
123C2×Dic47—21no—
124D188—21no—
125D188—21no—
126D188—21no—
127D188—21no—
128D188—42no—
129D188—81no—
130C4×D47—81no—
131C4×D47—81no—
132Dic94—21no—
133Dic94—21no—
134C47⋊C8—21no—
135C47⋊C8—21no—
136C47⋊C8—21no—
137C47⋊C8—21no—
138C22×C47C22×D411yescharacteristic
139C2×D47—41no—
140C2×D47—41no—
141C2×D47—41no—
142C2×D47—41no—
143C2×D47—41no—
144C2×D47—41no—
145C4×C47—22no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47C2×#4111yescharacteristic
156C4×C472−1+411yescharacteristic
157Dic47—41no—
158Dic47—41no—
159#3371—471nomaximal, Sylow
160C2×C47#54811yescharacteristic
161C2×C47#57511yescharacteristic
162C2×C47#57711yescharacteristic
163D47—81no—
164D47—81no—
165#559—471no—
166#557D4711yescharacteristic, complemented
167#490—471no—
168#489—471no—
169#488—471no—
170#479—471no—
171#478—471no—
172#476—471no—
173#464—471no—
174#464—471no—
175#460—471no—
176#446—471no—
177#441—471no—
178#440—471no—
179C4×SD16—471no—
180C47#337111yescharacteristic, complemented, Sylow
181C2×Q16—471no—
182C2×SD16—471no—
183C2×SD16—471no—
184C4⋊Q8—21no—
185C4⋊Q8C2×D4711yescharacteristic
186#127—471no—
187#125—21no—
188#125—21no—
189#125C2×D4711yescharacteristic
190#125C2×D4711yescharacteristic
191#124—471no—
192#124—471no—
193#124—941no—
194#123—941no—
195#123—941no—
196C4×Q8—21no—
197C4×Q8—471no—
198C4×Q8C2×D4711yescharacteristic
199C4×Q8C2×D4711yescharacteristic
200C4×Q8C2×D4711yescharacteristic
201C4×Q8C2×D4711yescharacteristic
202C4×D4—471no—
203C4×D4—471no—
204C4×D4—941no—
205#107—471no—
206#106—471no—
207#106—471no—
208C4⋊C8—471no—
209C4⋊C8—471no—
210C4⋊C8—471no—
211#103—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#102—471no—
216#102—471no—
217#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221#97—471no—
222#97—471no—
223C4×C8—471no—
224C2×Q8—21no—
225C2×Q8—471no—
226C2×Q8C22⋊D4711yescharacteristic
227C2×Q8C22×D4711yescharacteristic
228C2×D4—471no—
229C2×D4—471no—
230C2×D4—941no—
231C2×D4—941no—
232C22×C4—941no—
233C22×C4—941no—
234Q16—942no—
235SD16—942no—
236SD16—942no—
237C2×C8—471no—
238C2×C8—471no—
239C2×C8—471no—
240C2×C8—471no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—471no—
250C4⋊C4—941no—
251C4⋊C4C22⋊D4711yescharacteristic
252C4⋊C4C22⋊D4711yescharacteristic
253C4⋊C4C22⋊D4711yescharacteristic
254C4⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C4⋊C4C22×D4711yescharacteristic
257C22⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—941no—
267C42C22×D4711yescharacteristic
268C42C22×D4711yescharacteristic
269C42C22×D4711yescharacteristic
270C23—941no—
271C23—941no—
272Q8—21no—
273Q8—41no—
274Q8—42no—
275Q8—941no—
276Q8—941no—
277Q8#1062535412yes—
278D4—941no—
279D4—941no—
280D4—941no—
281D4—941no—
282D4—3761no—
283D4—1882no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—3761no—
291C2×C4—3761no—
292C2×C4C2×C22⋊D4711yescharacteristic
293C2×C4C2×C22⋊D4711yescharacteristic
294C2×C4C2×C22⋊D4711yescharacteristic
295C2×C4C2×C22⋊D4711yescharacteristic
296C2×C4C2×C22⋊D4711yescharacteristic
297C2×C4C2×C22⋊D4711yescharacteristic
298C2×C4C23×D4711yescharacteristic
299C8—941no—
300C8—941no—
301C8—941no—
302C8—941no—
303C22—1881no—
304C22—1881no—
305C22—1881no—
306C22—1881no—
307C22—1881no—
308C22—1881no—
309C22C22×C22⋊D4711yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—1881no—
321C4—1881no—
322C4C2×#1062535411yescharacteristic
323C4#1309407211yescharacteristic
324C2—3761no—
325C2—3761no—
326C2#1568978411yescharacteristic
327C2#1568992111yescharacteristic
328C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#557C2
socleC22×C47C22×D4
hypercenter#557D47
hypocenterC47#3371
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
3. #15689485C2semidirect
4. #15689480C2semidirect
5. #15689427C2semidirect
6. #15689420C2semidirect
7. #15689410C2semidirect
8. #15689345C2semidirect
9. #15689345C2semidirect
11. #15689254C2semidirect
12. #15689228C2semidirect
13. #15689221C2semidirect
14. C4×#10625336C2semidirect
15. C47×#557C2semidirect
166. #557D47semidirect
180. C47#3371semidirect