Finite Group Databasebeta

← #20255887

Subgroups — #20255887

Order 6016.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689839C211yesmaximal, characteristic, complemented
2#15689826C211yesmaximal, characteristic, complemented
3#15689450C211yesmaximal, characteristic, complemented
4#15689449C211yesmaximal, characteristic, complemented
5#15689449C211yesmaximal, characteristic, complemented
6#15689438C211yesmaximal, characteristic, complemented
7#15689420C211yesmaximal, characteristic, complemented
8#15689400C211yesmaximal, characteristic, complemented
9#15689377C211yesmaximal, characteristic, complemented
10#15689360C211yesmaximal, characteristic, complemented
11#15689236C211yesmaximal, characteristic, complemented
12#15689196C211yesmaximal, characteristic, complemented
13#15689164C211yesmaximal, characteristic, complemented
14#15689158C211yesmaximal, characteristic, complemented
15C47×#501C211yesmaximal, characteristic, complemented
16C2×D376C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19#13094019—21no—
20#13094013—21no—
21#13094013—21no—
22#13094009—21no—
23#13093999—21no—
24#13093999—21no—
25#13093999C2211yescharacteristic
26#13093999C2211yescharacteristic
27#13093999C2211yescharacteristic
28#13093999C2211yescharacteristic
29C4×D188C2211yescharacteristic
30C4×D188C2211yescharacteristic
31C4×D188C2211yescharacteristic
32#13093986—21no—
33#13093982—21no—
34#13093982C2211yescharacteristic
35#13093982C2211yescharacteristic
36#13093982C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D188—21no—
61C2×D188—21no—
62C2×D188—21no—
63C2×D188—21no—
64C2×D188D411yescharacteristic
65C2×D188C2311yescharacteristic
66C2×D188C2311yescharacteristic
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×C4×D47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C2×C8×C47C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C42×C47C2311yescharacteristic
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4D411yescharacteristic
92(C2×D47)⋊C4D411yescharacteristic
93C4⋊Dic47D411yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102D376—22no—
103#10625324—22no—
104C8×D47—22no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47C2×D411yescharacteristic
108C22×D47C2×D411yescharacteristic
109Q8×C47—81no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47C2×D411yescharacteristic
120C2×Dic47C2×D411yescharacteristic
121D188—21no—
122D188—21no—
123D188—21no—
124D188—21no—
125D188—41no—
126D188—42no—
127D188—81no—
128D188—81no—
129D188—81no—
130C4×D47—21no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—42no—
135C4×D47—81no—
136C4×D47—81no—
137C8×C47—21no—
138C8×C47#4112yes—
139C47⋊C8—21no—
140C47⋊C8—21no—
141C22×C47C22×D411yescharacteristic
142C2×D47—21no—
143C2×D47—21no—
144C2×D47—21no—
145C2×D47—21no—
146C2×D47—21no—
147C2×D47—21no—
148C2×D47—41no—
149C2×D47—41no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47C2×#4111yescharacteristic
161C4×C472−1+411yescharacteristic
162Dic47—21no—
163Dic47—21no—
164Dic47—41no—
165Dic47—41no—
166#3347—471nomaximal, Sylow
167C2×C47#54711yescharacteristic
168C2×C47#57511yescharacteristic
169C2×C47#57611yescharacteristic
170D47—41no—
171D47—41no—
172D47—81no—
173D47—81no—
174#555—471no—
175#553—471no—
176#501D4711yescharacteristic, complemented
177#482—471no—
178#482—471no—
179#482—471no—
180#480—471no—
181#478—471no—
182#474—471no—
183#469—471no—
184#466—471no—
185#442—471no—
186#435—471no—
187#428—471no—
188#427—471no—
189C47#334711yescharacteristic, complemented, Sylow
190C2×D8—471no—
191C2×M16—471no—
192C22×C8—471no—
193C4⋊Q8C2×D4711yescharacteristic
194#126—941no—
195#125C2×D4711yescharacteristic
196#124—941no—
197#124—941no—
198#123—941no—
199#121—471no—
200#121—471no—
201#121—471no—
202#121—471no—
203#121—941no—
204#121—941no—
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—941no—
209#117—471no—
210#117—471no—
211#117—471no—
212#117—941no—
213C2×C4⋊C4—471no—
214#107—471no—
215#107—471no—
216#107—471no—
217#107C2×D4711yescharacteristic
218#107C2×D4711yescharacteristic
219#106—471no—
220#106—471no—
221#106C2×D4711yescharacteristic
222#106C2×D4711yescharacteristic
223C4⋊C8—471no—
224#102—471no—
225#102—471no—
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230C22⋊C8—471no—
231C22⋊C8—471no—
232#97C2×D4711yescharacteristic
233C2×Q8—21no—
234C2×D4—471no—
235C2×D4—471no—
236C2×D4—471no—
237C2×D4—941no—
238C2×D4—941no—
239C2×D4—941no—
240C2×D4—941no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246D8—942no—
247M16—942no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8—942no—
251C2×C8C22×D4711yescharacteristic
252C2×C8C22×D4711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—941no—
260C4⋊C4C22×D4711yescharacteristic
261C4⋊C4C22×D4711yescharacteristic
262C4⋊C4C22×D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C22⋊C4—471no—
265C22⋊C4—471no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—941no—
276C42—941no—
277C42—941no—
278C42C22×D4711yescharacteristic
279C23—471no—
280C23—471no—
281C23—941no—
282C23—941no—
283Q8—81no—
284D4—941no—
285D4—941no—
286D4—941no—
287D4—941no—
288D4—3761no—
289D4—3761no—
290D4—3761no—
291D4—1881no—
292D4—1882no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—471no—
298C2×C4—471no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—3761no—
306C2×C4—3761no—
307C2×C4—1882no—
308C2×C4D4×D4711yescharacteristic
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—941no—
313C8—941no—
314C8#1062535412yes—
315C22—941no—
316C22—941no—
317C22—941no—
318C22—941no—
319C22—941no—
320C22—941no—
321C22—1881no—
322C22—1881no—
323C22—1881no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22C2×D4×D4711yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—941no—
335C4—941no—
336C4—1881no—
337C4—1881no—
338C4C2×#1062535411yescharacteristic
339C4#1309407211yescharacteristic
340C2—3761no—
341C2—3761no—
342C2—1881no—
343C2—1881no—
344C2#1568977611yescharacteristic
345C2#1568992211yescharacteristic
346C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3347
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #15689839C2semidirect
2. #15689826C2semidirect
3. #15689450C2semidirect
4. #15689449C2semidirect
5. #15689449C2semidirect
6. #15689438C2semidirect
7. #15689420C2semidirect
8. #15689400C2semidirect
9. #15689377C2semidirect
10. #15689360C2semidirect
11. #15689236C2semidirect
12. #15689196C2semidirect
13. #15689164C2semidirect
14. #15689158C2semidirect
15. C47×#501C2semidirect
176. #501D47semidirect
189. C47#3347semidirect