Finite Group Databasebeta

← #20255466

Subgroups — #20255466

Order 6016.

410 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#15689834C211yesmaximal, characteristic, complemented
2#15689768C211yesmaximal, characteristic
3#15689485C211yesmaximal, characteristic, complemented
4#15689460C211yesmaximal, characteristic, complemented
5#15689438C211yesmaximal, characteristic, complemented
6#15689370C211yesmaximal, characteristic, complemented
7#15689365C211yesmaximal, characteristic, complemented
8#15689346C211yesmaximal, characteristic, complemented
9#15689286C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12#15689193C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#474C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×Dic188C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625324C2211yescharacteristic, complemented
22C2×C8×D47C2211yescharacteristic
23#13094015—21no—
24#13094012C2211yescharacteristic
25#13094008—21no—
26#13094004C2211yescharacteristic
27#13094004C2211yescharacteristic
28#13094004C2211yescharacteristic, complemented
29#13094000—21no—
30#13094000—21no—
31#13093999C2211yescharacteristic
32#13093998—21no—
33#13093994—21no—
34C4×Dic94C2211yescharacteristic, complemented
35C4×D188C2211yescharacteristic
36#13093986—21no—
37C4⋊C4×D47C2211yescharacteristic
38C4⋊C4×D47C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4—21no—
40#13093957C2211yescharacteristic, complemented
41#13093949C2211yescharacteristic, complemented
42#13093947C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093935C2211yescharacteristic, complemented
52C4⋊Q8×C47C2211yescharacteristic, complemented
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#107×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66#10625352—22no—
67#10625352—41no—
68D4×D47—22no—
69D4×D47—41no—
70C2×D188—21no—
71C2×D188D411yescharacteristic
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47C2311yescharacteristic
76C2×C4×D47C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78C2×Dic94C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C42×C47C2311yescharacteristic
87#10625335—22no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4D411yescharacteristic
95(C2×D47)⋊C4D411yescharacteristic
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47D411yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107Dic188—41no—
108#10625325—41no—
109#10625324—41no—
110C8×D47—41no—
111C23×C47—21no—
112C22×D47—21no—
113C22×D47—42no—
114C22×D47—42no—
115C22×D47—81no—
116C22×D47C2×D411yescharacteristic
117C22×D47C2×D411yescharacteristic
118Q8×C47—81no—
119D4×C47—21no—
120D4×C47#4112yes—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—81no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—42no—
129C22⋊D47—42no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—42no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136D188—22no—
137D188—21no—
138D188—21no—
139D188—81no—
140C4×D47—21no—
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—21no—
144C4×D47—81no—
145C4×D47—81no—
146Dic94—21no—
147Dic94—21no—
148Dic94—21no—
149Dic94—21no—
150C8×C47—21no—
151C8×C47—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—22no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—84no—
167C2×D47#13712yes—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47C2×#4111yescharacteristic
174C4×C47H(5,𝔽2)11yescharacteristic
175Dic47—21no—
176Dic47—21no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3314—471nomaximal, Sylow
181C2×C47—42no—
182C2×C47#54611yescharacteristic
183C2×C47C2×#13711yescharacteristic
184C2×C47#57611yescharacteristic
185D47—22no—
186D47—41no—
187D47—81no—
188#554—471no—
189#546—471no—
190#489—471no—
191#484—471no—
192#480—471no—
193#474D4711yescharacteristic, complemented
194#468—471no—
195#467—471no—
196#464—471no—
197#452—471no—
198#450—471no—
199#440—471no—
200#435—471no—
201#417—471no—
202C2×#102—471no—
203C47#331411yescharacteristic, complemented, Sylow
204C2×#41—471no—
205C22×D4—471no—
206C2×Q16—471no—
207C2×SD16—471no—
208C2×SD16—471no—
209C2×M16—471no—
210C22×C8—471no—
211C4⋊Q8C2×D4711yescharacteristic, complemented
212#125—941no—
213#124—471no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8—471no—
218C22⋊Q8—941no—
219C22⋊Q8—941no—
220#121—471no—
221#121—941no—
222#120—941no—
223C4×Q8—471no—
224C4×D4—471no—
225C4×D4—941no—
226C4×D4C2×D4711yescharacteristic
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C22⋊C4—941no—
230#107—471no—
231#107C2×D4711yescharacteristic, complemented
232#107C2×D4711yescharacteristic, complemented
233C4⋊C8C2×D4711yescharacteristic, complemented
234#103—471no—
235#103—471no—
236#103—471no—
237#103—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241#102—471no—
242#102C2×D4711yescharacteristic
243#102C2×D4711yescharacteristic
244C22⋊C8—471no—
245C22⋊C8—471no—
246#97—471no—
247C24—941no—
248#41—942no—
249#41—1881no—
250C2×Q8—21no—
251C2×Q8—471no—
252C2×Q8—471no—
253C2×D4—471no—
254C2×D4—471no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4—942no—
258C2×D4—941no—
259C2×D4—1881no—
260C2×D4C22×D4711yescharacteristic
261C22×C4—21no—
262C22×C4—471no—
263C22×C4—471no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267Q16—1881no—
268SD16—942no—
269SD16—1881no—
270M16—1881no—
271C2×C8—471no—
272C2×C8—471no—
273C2×C8—1881no—
274C2×C8C22×D4711yescharacteristic
275C2×C8C22×D4711yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—471no—
278C4⋊C4—471no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4C22×D4711yescharacteristic
286C4⋊C4C22×D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—471no—
290C22⋊C4—471no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C42—941no—
298C42C22×D4711yescharacteristic
299C23—21no—
300C23—471no—
301C23—471no—
302C23—941no—
303C23—3761no—
304C23—1882no—
305C23—1882no—
306Q8—81no—
307Q8—941no—
308Q8—941no—
309Q8—941no—
310Q8—941no—
311D4—21no—
312D4—942no—
313D4—941no—
314D4—941no—
315D4—3761no—
316D4—1882no—
317D4—1882no—
318D4#1062535412yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—471no—
324C2×C4—471no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—3761no—
333C2×C4—3761no—
334C2×C4—1882no—
335C2×C4D4×D4711yescharacteristic
336C2×C4D4×D4711yescharacteristic
337C2×C4C23×D4711yescharacteristic
338C8—21no—
339C8—21no—
340C8—941no—
341C8—941no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—472no—
346C22—941no—
347C22—941no—
348C22—941no—
349C22—941no—
350C22—941no—
351C22—3764no—
352C22—1881no—
353C22—1881no—
354C22—1881no—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—941no—
362C4—941no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4C2×#1062535411yescharacteristic
367C4#1309407011yescharacteristic
368C2—42no—
369C2—942no—
370C2—3761no—
371C2—1881no—
372C2#1568976411yescharacteristic
373C2#137×D4711yescharacteristic
374C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#474C2
socleC22×C47C22×D4
hypercenter#474D47
hypocenterC47#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #15689834C2semidirect
3. #15689485C2semidirect
4. #15689460C2semidirect
5. #15689438C2semidirect
6. #15689370C2semidirect
7. #15689365C2semidirect
8. #15689346C2semidirect
9. #15689286C2semidirect
10. #15689275C2semidirect
11. #15689223C2semidirect
12. #15689193C2semidirect
13. #15689121C2semidirect
14. #102×D47C2semidirect
15. C47×#474C2semidirect
18. C2×Dic188C22semidirect
21. C2×#10625324C22semidirect
28. #13094004C22semidirect
34. C4×Dic94C22semidirect
38. C4⋊C4×D47C22semidirect
40. #13093957C22semidirect
41. #13093949C22semidirect
42. #13093947C22semidirect
43. #13093947C22semidirect
44. #13093947C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093935C22semidirect
52. C4⋊Q8×C47C22semidirect
54. #107×C47C22semidirect
55. #107×C47C22semidirect
56. C4⋊C8×C47C22semidirect
193. #474D47semidirect
203. C47#3314semidirect
211. C4⋊Q8C2×D47semidirect
231. #107C2×D47semidirect
232. #107C2×D47semidirect
233. C4⋊C8C2×D47semidirect