Finite Group Databasebeta

← #20255740

Subgroups — #20255740

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689831C211yesmaximal, characteristic, complemented
2#15689773C211yesmaximal, characteristic
3#15689520C211yesmaximal, characteristic, complemented
4#15689452C211yesmaximal, characteristic, complemented
5#15689451C211yesmaximal, characteristic, complemented
6#15689440C211yesmaximal, characteristic, complemented
7#15689439C211yesmaximal, characteristic, complemented
8#15689411C211yesmaximal, characteristic, complemented
9#15689406C211yesmaximal, characteristic, complemented
10#15689349C211yesmaximal, characteristic, complemented
11SD16×Dic47C211yesmaximal, characteristic, complemented
12C8×C22⋊D47C211yesmaximal, characteristic, complemented
13C2×#13093956C211yesmaximal, characteristic, complemented
14#106×D47C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×C8×D47C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094014—21no—
21#13094006—21no—
22#13094005—21no—
23#13094004—21no—
24#13094001—21no—
25#13094001—21no—
26#13094000C2211yescharacteristic
27#13093995C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30C4×C22⋊D47C2211yescharacteristic
31(C22⋊D47)⋊C4—21no—
32C2×C4⋊Dic47C2211yescharacteristic
33C2×C4⋊Dic47C2211yescharacteristic
34C4⋊C4×D47C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36#13093956C2211yescharacteristic
37#13093956C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41#13093955C2211yescharacteristic
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—
66C22×Dic47—21no—
67C22×Dic47—21no—
68#10625352—44no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47C2311yescharacteristic
72C2×Dic94—21no—
73C2×Dic94—21no—
74SD16×C47—22no—
75C2×C8×C47—22no—
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47D411yescharacteristic
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4D411yescharacteristic
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C8×D47—22no—
106C23×C47—21no—
107C23×C47C2×D411yescharacteristic
108C22×D47C2×D411yescharacteristic
109Q8×C47—21no—
110Q8×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—42no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—42no—
122C22⋊D47SD1614yescomplemented
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—42no—
128C2×Dic47—42no—
129C2×Dic47—81no—
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—42no—
136C4×D47—81no—
137Dic94—42no—
138Dic94—81no—
139C8×C47—21no—
140C8×C47#4112yescomplemented
141C47⋊C8—21no—
142C47⋊C8—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C2×SD1612yes—
149C22×C47C22×D411yescharacteristic
150C2×D47—21no—
151C2×D47—21no—
152C2×D47C2×SD1612yes—
153C4×C47—21no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47C2×#4111yescharacteristic
158C4×C472−1+411yescharacteristic
159Dic47—21no—
160Dic47—21no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165Dic47C2×SD1612yes—
166#3335—471nomaximal, Sylow
167C2×C47—22no—
168C2×C47—81no—
169C2×C47#54711yescharacteristic
170C2×C47C22×SD1611yescharacteristic
171C2×C47#57711yescharacteristic
172D47—22no—
173#554—471no—
174#547—471no—
175#498—471no—
176#483—471no—
177#483—471no—
178#481—471no—
179#481—471no—
180#476—471no—
181#475—471no—
182#465—471no—
183#465D4711yescharacteristic, complemented
184C4×SD16—471no—
185C8×D4—471no—
186C2×#106—471no—
187C2×#106—471no—
188C47#333511yescharacteristic, complemented, Sylow
189C2×#41—941no—
190C2×SD16C2×D4711yescharacteristic
191C22×C8—471no—
192C22×C8C2×D4711yescharacteristic
193C4⋊Q8—471no—
194C4⋊Q8—471no—
195#125—941no—
196#123—941no—
197#123—941no—
198C22⋊Q8—471no—
199C22⋊Q8—941no—
200C22⋊Q8—941no—
201C22⋊Q8—941no—
202C22⋊Q8C2×D4711yescharacteristic
203#121—471no—
204#121C2×D4711yescharacteristic
205C4×Q8—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—941no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213#106—471no—
214#106—471no—
215#106—471no—
216#106—471no—
217#106—471no—
218#106—471no—
219#106—471no—
220#106—471no—
221#106C2×D4711yescharacteristic
222C4⋊C8—471no—
223#103—471no—
224#103—471no—
225#103C2×D4711yescharacteristic
226#102—471no—
227#102—471no—
228#102C2×D4711yescharacteristic
229C22⋊C8—471no—
230C22⋊C8—471no—
231C4×C8—471no—
232#41—1884no—
233C2×Q8—941no—
234C2×Q8—941no—
235C2×Q8C22×D4711yescharacteristic
236C2×D4—21no—
237C2×D4—471no—
238C2×D4—941no—
239C2×D4C22×D4711yescharacteristic
240C22×C4—471no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4C22×D4711yescharacteristic
247SD16—22no—
248C2×C8—22no—
249C2×C8—471no—
250C2×C8—471no—
251C2×C8—942no—
252C2×C8C22×D4711yescharacteristic
253C2×C8C22×D4711yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4C22×D4711yescharacteristic
269C4⋊C4C22×D4711yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—471no—
273C22⋊C4—471no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C42—471no—
278C42—941no—
279C23—21no—
280C23—471no—
281C23D4×D4711yescharacteristic
282Q8—21no—
283Q8—21no—
284Q8—3761no—
285Q8—1882no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—474no—
290D4—1882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—471no—
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×C4—1882no—
309C2×C4—1882no—
310C2×C4D4×D4711yescharacteristic
311C2×C4C23×D4711yescharacteristic
312C8—21no—
313C8—941no—
314C8—941no—
315C8#1062535212yescomplemented
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—472no—
322C22—941no—
323C22—941no—
324C22SD16×D4712yes—
325C22C2×D4×D4711yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—472no—
331C4—941no—
332C4—941no—
333C4—1881no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4C2×#1062535211yescharacteristic
338C4#1309407111yescharacteristic
339C2—22no—
340C2—81no—
341C2—942no—
342C2#1568977311yescharacteristic
343C2C2×SD16×D4711yescharacteristic
344C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3335
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. #15689831C2semidirect
3. #15689520C2semidirect
4. #15689452C2semidirect
5. #15689451C2semidirect
6. #15689440C2semidirect
7. #15689439C2semidirect
8. #15689411C2semidirect
9. #15689406C2semidirect
10. #15689349C2semidirect
11. SD16×Dic47C2semidirect
12. C8×C22⋊D47C2semidirect
13. C2×#13093956C2semidirect
14. #106×D47C2semidirect
15. C47×#465C2semidirect
122. C22⋊D47SD16semidirect
140. C8×C47#41semidirect
183. #465D47semidirect
188. C47#3335semidirect
315. C8#10625352semidirect