Finite Group Databasebeta

← #20252242

Subgroups — #20252242

Order 6016.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D47C211yesmaximal, characteristic
2#15689599C211yesmaximal, characteristic, complemented
3#15689595C211yesmaximal, characteristic
4#15689226C211yesmaximal, characteristic, complemented
5#15689223C211yesmaximal, characteristic, complemented
6#15689221C211yesmaximal, characteristic, complemented
7#15689220C211yesmaximal, characteristic, complemented
8C4×#10625325C211yesmaximal, characteristic, complemented
9SD16×Dic47C211yesmaximal, characteristic, complemented
10#15689210C211yesmaximal, characteristic, complemented
11#15689158C211yesmaximal, characteristic, complemented
12#15689130C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic
14#15689077C211yesmaximal, characteristic, complemented
15C4×SD16×C47C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21SD16×D47C418yescomplemented
22C2×#10625324C2211yescharacteristic
23C2×C8×D47C2211yescharacteristic
24Q8×Dic47C2211yescharacteristic, complemented
25C4×Dic94—21no—
26C4×Dic94C2211yescharacteristic, complemented
27#13093989—21no—
28#13093989C2211yescharacteristic, complemented
29C4×D188C2211yescharacteristic
30D4×Dic47C2211yescharacteristic
31#13093986C2211yescharacteristic
32C4×C22⋊D47—21no—
33(C22⋊D47)⋊C4—21no—
34#13093982—21no—
35#13093982C2211yescharacteristic
36#13093982C2211yescharacteristic
37#13093981—21no—
38#13093981C2211yescharacteristic
39C2×(C2×D47)⋊C4—21no—
40C22⋊C4×D47—21no—
41#13093957C2211yescharacteristic, complemented
42#13093957C2211yescharacteristic, complemented
43#13093956C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093947C2211yescharacteristic, complemented
47#13093946C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093935C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C8×Dic47C2211yescharacteristic, complemented
53C2×SD16×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic, complemented
55C4×D4×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59C4×C8×C47C2211yescharacteristic, complemented
60C23×D47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66Q8×D47—22no—
67Q8×D47C2×C414yescomplemented
68D4×D47—22no—
69D4×D47C2×C414yes—
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47C2311yescharacteristic
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77SD16×C47C2×C414yescomplemented
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C42×C47—21no—
85C42×C47C2311yescharacteristic
86C22⋊Dic47—21no—
87#10625336C2×C414yescomplemented
88#10625335C2×C414yescomplemented
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4D411yescharacteristic
94(C2×D47)⋊C4D411yescharacteristic
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625325C2×C414yescomplemented
111#10625324—22no—
112C8×D47C2×C414yescomplemented
113C23×C47—21no—
114C22×D47—21no—
115C22×D47—24no—
116C22×D47—81no—
117C22×D47—81no—
118C22×D47C2×D411yescharacteristic
119Q8×C47—21no—
120Q8×C47C22×C412yes—
121D4×C47—21no—
122D4×C47C22×C412yes—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—81no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—24no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—81no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138D188—21no—
139D188C22×C412yes—
140C4×D47—24no—
141C4×D47—81no—
142C4×D47—81no—
143C4×D47C22×C412yes—
144C4×D47#4112yes—
145Dic94—21no—
146Dic94—24no—
147Dic94C22×C412yes—
148C8×C47—21no—
149C8×C47C22×C412yes—
150C47⋊C8—21no—
151C47⋊C8C22×C412yes—
152C22×C47—22no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—22no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—84no—
162C2×D47C4×D412yes—
163C4×C47—22no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47C23×C411yescharacteristic
169C4×C47C2×#4111yescharacteristic
170Dic47—22no—
171Dic47—21no—
172Dic47—21no—
173Dic47—41no—
174Dic47—41no—
175Dic47C4×D412yes—
176#2949—471nomaximal, Sylow
177C2×C47—42no—
178C2×C47C2×C4×D411yescharacteristic
179C2×C47#57711yescharacteristic
180C2×C47#57711yescharacteristic
181D47—22no—
182D47—42no—
183C22×SD16—471no—
184#519—471no—
185#518—471no—
186#440—471no—
187#440—471no—
188#440—471no—
189#440—471no—
190C4×SD16—471no—
191C4×SD16—471no—
192C4×SD16—471no—
193C4×SD16D4711yescharacteristic, complemented
194#427—471no—
195#419—471no—
196#418—471no—
197#405—471no—
198C47#294911yescharacteristic, complemented, Sylow
199C22×Q8—471no—
200C22×D4—471no—
201C2×SD16—471no—
202C2×SD16—471no—
203C2×SD16—478no—
204C2×SD16—471no—
205C2×SD16C2×D4711yescharacteristic
206C2×M16—471no—
207C22×C8—471no—
208C4×Q8—471no—
209C4×Q8—471no—
210C4×Q8—471no—
211C4×Q8—941no—
212C4×Q8—941no—
213C4×Q8C2×D4711yescharacteristic, complemented
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—471no—
217C4×D4—941no—
218C4×D4—941no—
219C4×D4C2×D4711yescharacteristic
220#117—471no—
221#117—471no—
222#117—471no—
223#117—941no—
224#117—941no—
225C2×C22⋊C4—941no—
226C2×C22⋊C4—941no—
227#107—471no—
228#107—471no—
229#106—471no—
230#106C2×D4711yescharacteristic, complemented
231#103—471no—
232#103—471no—
233#103—471no—
234#103C2×D4711yescharacteristic, complemented
235#102—471no—
236#102—471no—
237#102—471no—
238#102C2×D4711yescharacteristic
239#97—471no—
240#97—471no—
241C4×C8—471no—
242C4×C8C2×D4711yescharacteristic, complemented
243C24—941no—
244C2×Q8—474no—
245C2×Q8—471no—
246C2×Q8—941no—
247C2×Q8—942no—
248C2×Q8C22×D4711yescharacteristic
249C2×D4—474no—
250C2×D4—471no—
251C2×D4—942no—
252C2×D4—941no—
253C2×D4C22×D4711yescharacteristic
254C22×C4—21no—
255C22×C4—471no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—941no—
259C22×C4—941no—
260SD16—474no—
261SD16—474no—
262SD16—474no—
263SD16C4×D4714yescomplemented
264M16—942no—
265C2×C8—471no—
266C2×C8—474no—
267C2×C8—471no—
268C2×C8C22×D4711yescharacteristic
269C2×C8C22×D4711yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—471no—
272C4⋊C4—471no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4C22×D4711yescharacteristic
279C4⋊C4C22×D4711yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—471no—
282C22⋊C4—471no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C42—21no—
289C42—471no—
290C42—941no—
291C42—941no—
292C42—941no—
293C42—941no—
294C42—941no—
295C42C22×D4711yescharacteristic
296C23—21no—
297C23—471no—
298C23—944no—
299C23—941no—
300C23—3761no—
301C23—3761no—
302Q8—21no—
303Q8—472no—
304Q8—944no—
305Q8—941no—
306Q8C2×C4×D4712yes—
307D4—21no—
308D4—472no—
309D4—944no—
310D4—941no—
311D4C2×C4×D4712yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—471no—
317C2×C4—472no—
318C2×C4—472no—
319C2×C4—471no—
320C2×C4—471no—
321C2×C4—944no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—3761no—
326C2×C4—3761no—
327C2×C4—3761no—
328C2×C4D4×D4711yescharacteristic
329C2×C4D4×D4711yescharacteristic
330C2×C4C23×D4711yescharacteristic
331C8—21no—
332C8—472no—
333C8—941no—
334C8C2×C4×D4712yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—472no—
339C22—941no—
340C22—941no—
341C22—942no—
342C22—3764no—
343C22—1881no—
344C22—1881no—
345C22C2×D4×D4711yescharacteristic
346C4—22no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—472no—
352C4—942no—
353C4—941no—
354C4—941no—
355C4—1881no—
356C4—1881no—
357C4C22×C4×D4711yescharacteristic
358C4#41×D4711yescharacteristic
359C2—42no—
360C2—942no—
361C2—1882no—
362C2C4×D4×D4711yescharacteristic
363C2#1568992911yescharacteristic
364C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC4×SD16×C47C2
socleC22×C47C22×D4
hypercenterC4×SD16D47
hypocenterC47#2949
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #15689599C2semidirect
4. #15689226C2semidirect
5. #15689223C2semidirect
6. #15689221C2semidirect
7. #15689220C2semidirect
8. C4×#10625325C2semidirect
9. SD16×Dic47C2semidirect
10. #15689210C2semidirect
11. #15689158C2semidirect
12. #15689130C2semidirect
14. #15689077C2semidirect
15. C4×SD16×C47C2semidirect
21. SD16×D47C4semidirect
24. Q8×Dic47C22semidirect
26. C4×Dic94C22semidirect
28. #13093989C22semidirect
41. #13093957C22semidirect
42. #13093957C22semidirect
43. #13093956C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093947C22semidirect
50. #13093935C22semidirect
51. #13093934C22semidirect
52. C8×Dic47C22semidirect
54. C4×Q8×C47C22semidirect
56. #106×C47C22semidirect
57. #103×C47C22semidirect
59. C4×C8×C47C22semidirect
67. Q8×D47C2×C4semidirect
77. SD16×C47C2×C4semidirect
87. #10625336C2×C4semidirect
88. #10625335C2×C4semidirect
110. #10625325C2×C4semidirect
112. C8×D47C2×C4semidirect
193. C4×SD16D47semidirect
198. C47#2949semidirect
213. C4×Q8C2×D47semidirect
230. #106C2×D47semidirect
234. #103C2×D47semidirect
242. C4×C8C2×D47semidirect
263. SD16C4×D47semidirect