Finite Group Databasebeta

← #20255372

Subgroups — #20255372

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689780C211yesmaximal, characteristic, complemented
2#15689773C211yesmaximal, characteristic, complemented
3#15689481C211yesmaximal, characteristic, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689435C211yesmaximal, characteristic, complemented
6#15689416C211yesmaximal, characteristic, complemented
7#15689367C211yesmaximal, characteristic, complemented
8#15689356C211yesmaximal, characteristic, complemented
9#15689336C211yesmaximal, characteristic, complemented
10#15689260C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12#15689197C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14#103×D47C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×Q8×D47C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094011—21no—
23#13094011C2211yescharacteristic
24#13094006—21no—
25#13094005—21no—
26#13094003—21no—
27#13094003C2211yescharacteristic
28#13094001—21no—
29#13093995—21no—
30#13093995C2211yescharacteristic
31#13093995C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34C4×C22⋊D47—21no—
35C4×C22⋊D47C2211yescharacteristic
36C2×C4⋊Dic47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—41no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47D411yescharacteristic
71C22×Dic47—21no—
72C22×Dic47—21no—
73Q8×D47—22no—
74Q8×D47—41no—
75#10625352—44no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47C2311yescharacteristic
79C2×Dic94—21no—
80C2×Dic94—21no—
81C2×Dic94C2311yescharacteristic
82SD16×C47—22no—
83D8×C47—41no—
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47D411yescharacteristic
95#10625335—41no—
96(C2×D47)⋊C4D411yescharacteristic
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4D411yescharacteristic
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108#10625329—41no—
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C8×D47—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47C2×D411yescharacteristic
115C22×D47C2×D411yescharacteristic
116Q8×C47—21no—
117Q8×C47#4112yescomplemented
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—42no—
123D4×C47—42no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—42no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—22no—
132C22⋊D47—42no—
133C22⋊D47—42no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—42no—
139C2×Dic47—42no—
140C2×Dic47C2×D411yescharacteristic
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143C4×D47—21no—
144C4×D47—21no—
145C4×D47—42no—
146C4×D47—42no—
147Dic94—21no—
148Dic94—21no—
149Dic94—42no—
150Dic94—42no—
151C8×C47—21no—
152C8×C47—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47C22×D411yescharacteristic
165C2×D47—21no—
166C2×D47—21no—
167C2×D47AGL(1,ℤ/8)12yes—
168C4×C47—22no—
169C4×C47—21no—
170C4×C47—41no—
171C4×C47C2×#4111yescharacteristic
172C4×C47H(5,𝔽2)11yescharacteristic
173Dic47—21no—
174Dic47—21no—
175Dic47—21no—
176Dic47—41no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3308—471nomaximal, Sylow
181C2×C47—41no—
182C2×C47—81no—
183C2×C47—81no—
184C2×C47#54611yescharacteristic
185C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C47#57811yescharacteristic
187D47—22no—
188#548—471no—
189#547—471no—
190#489—471no—
191#484—471no—
192#480—471no—
193#477—471no—
194#468—471no—
195#466—471no—
196#463—471no—
197#449D4711yescharacteristic, complemented
198#448—471no—
199#440—471no—
200#435—471no—
201#417—471no—
202C2×#103—471no—
203C47#330811yescharacteristic, complemented, Sylow
204C2×#41—941no—
205C2×#41C2×D4711yescharacteristic
206C22×Q8—471no—
207C2×SD16—471no—
208C2×SD16C2×D4711yescharacteristic
209C2×D8C2×D4711yescharacteristic
210C2×M16—471no—
211C22×C8—471no—
212C4⋊Q8—471no—
213#124—471no—
214#124—941no—
215#123—941no—
216#123—941no—
217C22⋊Q8—471no—
218C22⋊Q8—941no—
219C22⋊Q8—941no—
220#121—471no—
221#121—471no—
222#121—941no—
223#121C2×D4711yescharacteristic
224C4×Q8—471no—
225C4×D4—471no—
226C4×D4—471no—
227C4×D4—941no—
228C2×C4⋊C4—471no—
229C2×C4⋊C4—471no—
230#107—471no—
231#107—471no—
232#107—471no—
233C4⋊C8—471no—
234#103—471no—
235#103—471no—
236#103—471no—
237#103—471no—
238#103—471no—
239#103C2×D4711yescharacteristic
240#102—471no—
241#102—471no—
242#102—471no—
243#102C2×D4711yescharacteristic
244C22⋊C8—471no—
245C22⋊C8C2×D4711yescharacteristic
246#97—471no—
247#41—22no—
248#41—41no—
249#41—1884no—
250C2×Q8—471no—
251C2×Q8—941no—
252C2×Q8—941no—
253C2×Q8—942no—
254C2×Q8—1881no—
255C2×Q8C22×D4711yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—471no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4C22×D4711yescharacteristic
262C2×D4C22×D4711yescharacteristic
263C22×C4—21no—
264C22×C4—471no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4C22×D4711yescharacteristic
270SD16—22no—
271SD16—1881no—
272D8—41no—
273M16—1881no—
274C2×C8—471no—
275C2×C8—471no—
276C2×C8—1881no—
277C2×C8C22×D4711yescharacteristic
278C2×C8C22×D4711yescharacteristic
279C4⋊C4—471no—
280C4⋊C4—471no—
281C4⋊C4—471no—
282C4⋊C4—471no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4—941no—
288C4⋊C4C22×D4711yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—471no—
291C22⋊C4—471no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C42—471no—
299C42—941no—
300C23—21no—
301C23—21no—
302C23—471no—
303C23D4×D4711yescharacteristic
304Q8—21no—
305Q8—941no—
306Q8—941no—
307Q8—1882no—
308Q8—1882no—
309Q8#1062535212yescomplemented
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—42no—
316D4—942no—
317D4—1882no—
318D4—1882no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—471no—
325C2×C4—471no—
326C2×C4—471no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—1882no—
334C2×C4—1882no—
335C2×C4—1882no—
336C2×C4—1882no—
337C2×C4D4×D4711yescharacteristic
338C2×C4C23×D4711yescharacteristic
339C8—21no—
340C8—21no—
341C8—941no—
342C8—941no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—472no—
353C22—941no—
354C22—941no—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—941no—
360C4—941no—
361C4—941no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4C2×#1062535211yescharacteristic
367C4#1309406911yescharacteristic
368C2—41no—
369C2—81no—
370C2—81no—
371C2—942no—
372C2#1568976011yescharacteristic
373C2AGL(1,ℤ/8)×D4711yescharacteristic
374C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#449C2
socleC22×C47C22×D4
hypercenter#449D47
hypocenterC47#3308
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #15689780C2semidirect
2. #15689773C2semidirect
3. #15689481C2semidirect
4. #15689459C2semidirect
5. #15689435C2semidirect
6. #15689416C2semidirect
7. #15689367C2semidirect
8. #15689356C2semidirect
9. #15689336C2semidirect
10. #15689260C2semidirect
11. #15689224C2semidirect
12. #15689197C2semidirect
13. #15689124C2semidirect
14. #103×D47C2semidirect
15. C47×#449C2semidirect
117. Q8×C47#41semidirect
197. #449D47semidirect
203. C47#3308semidirect
309. Q8#10625352semidirect