Finite Group Databasebeta

← #20255686

Subgroups — #20255686

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#15689773C211yesmaximal, characteristic, complemented
2#15689772C211yesmaximal, characteristic, complemented
3#15689472C211yesmaximal, characteristic, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689457C211yesmaximal, characteristic, complemented
6#15689401C211yesmaximal, characteristic, complemented
7#15689367C211yesmaximal, characteristic, complemented
8#15689366C211yesmaximal, characteristic, complemented
9#15689326C211yesmaximal, characteristic, complemented
10#15689265C211yesmaximal, characteristic, complemented
11D8×Dic47C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14#15689121C211yesmaximal, characteristic, complemented
15C47×#449C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625352C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094022C2211yescharacteristic
23#13094007—21no—
24#13094006—21no—
25#13094005—21no—
26#13094005—21no—
27#13094003C2211yescharacteristic
28#13094001—21no—
29#13094000C2211yescharacteristic
30#13093996—21no—
31#13093995C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36C2×Dic47⋊C4—21no—
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
51C8×Dic47C2211yescharacteristic
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—
73C22×Dic47—21no—
74C22×Dic47—21no—
75#10625352—22no—
76#10625352—41no—
77#10625352—44no—
78C2×C4×D47—21no—
79C2×C4×D47C2311yescharacteristic
80C2×Dic94—21no—
81C2×Dic94C2311yescharacteristic
82SD16×C47—41no—
83D8×C47—22no—
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⋊Dic47D411yescharacteristic
93#10625335—41no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4D411yescharacteristic
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4D411yescharacteristic
107C4×Dic47C2311yescharacteristic
108#10625329—41no—
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111#10625324—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47C2×D411yescharacteristic
115C22×D47C2×D411yescharacteristic
116Q8×C47—21no—
117Q8×C47—21no—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—42no—
122D4×C47—42no—
123D4×C47#4112yescomplemented
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×Dic47—42no—
141C2×Dic47—42no—
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—42no—
148Dic94—21no—
149Dic94—21no—
150Dic94—42no—
151C8×C47—21no—
152C8×C47—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—22no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
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×D47—21no—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47C2×#4111yescharacteristic
172C4×C47H(5,𝔽2)11yescharacteristic
173Dic47—21no—
174Dic47—21no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178Dic47—41no—
179Dic47AGL(1,ℤ/8)12yes—
180#3330—471nomaximal, Sylow
181C2×C47—41no—
182C2×C47—42no—
183C2×C47—81no—
184C2×C47#54611yescharacteristic
185C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C47#57811yescharacteristic
187D47—41no—
188#547—471no—
189#547—471no—
190#487—471no—
191#484—471no—
192#484—471no—
193#474—471no—
194#468—471no—
195#468—471no—
196#461—471no—
197#449—471no—
198#449D4711yescharacteristic, complemented
199C4×D8—471no—
200#436—471no—
201#417—471no—
202#417—471no—
203C47#333011yescharacteristic, complemented, Sylow
204C2×#41—471no—
205C2×#41—941no—
206C2×#41C2×D4711yescharacteristic
207C2×SD16—471no—
208C2×SD16C2×D4711yescharacteristic
209C2×D8C2×D4711yescharacteristic
210C2×M16—471no—
211C2×M16—471no—
212C4⋊Q8—471no—
213C4⋊Q8—471no—
214#123—941no—
215#123—941no—
216#123—941no—
217#123—941no—
218C22⋊Q8—471no—
219C22⋊Q8—471no—
220C22⋊Q8—941no—
221#121—471no—
222#121—941no—
223#121C2×D4711yescharacteristic
224C4×D4—471no—
225C4×D4—471no—
226C4×D4—471no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C4⋊C4—941no—
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
246C4×C8—471no—
247#41—22no—
248#41—41no—
249#41—942no—
250#41—1881no—
251#41—1884no—
252C2×Q8—471no—
253C2×Q8—941no—
254C2×Q8C22×D4711yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—471no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4C22×D4711yescharacteristic
261C2×D4C22×D4711yescharacteristic
262C22×C4—21no—
263C22×C4—471no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4C22×D4711yescharacteristic
270SD16—41no—
271SD16—1881no—
272D8—22no—
273M16—1881no—
274M16—1881no—
275C2×C8—471no—
276C2×C8—471no—
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⋊C4—941no—
289C4⋊C4—941no—
290C4⋊C4C22×D4711yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—471no—
293C22⋊C4—471no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C42—471no—
300C23—21no—
301C23—21no—
302C23—471no—
303C23D4×D4711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—941no—
307Q8—941no—
308Q8—1882no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—942no—
315D4—1882no—
316D4—1882no—
317D4#1062535212yescomplemented
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—471no—
324C2×C4—471no—
325C2×C4—471no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—1882no—
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—22no—
345C22—21no—
346C22—21no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—941no—
353C22—941no—
354C22—941no—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—472no—
360C4—941no—
361C4—941no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4C2×#1062535211yescharacteristic
367C4#1309406911yescharacteristic
368C2—41no—
369C2—42no—
370C2—81no—
371C2—1881no—
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#3330
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. #15689773C2semidirect
2. #15689772C2semidirect
3. #15689472C2semidirect
4. #15689459C2semidirect
5. #15689457C2semidirect
6. #15689401C2semidirect
7. #15689367C2semidirect
8. #15689366C2semidirect
9. #15689326C2semidirect
10. #15689265C2semidirect
11. D8×Dic47C2semidirect
12. #15689198C2semidirect
13. #15689124C2semidirect
14. #15689121C2semidirect
15. C47×#449C2semidirect
123. D4×C47#41semidirect
198. #449D47semidirect
203. C47#3330semidirect
317. D4#10625352semidirect