Finite Group Databasebeta

← #20255472

Subgroups — #20255472

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#15689828C211yesmaximal, characteristic, complemented
2#15689770C211yesmaximal, characteristic
3#15689481C211yesmaximal, characteristic, complemented
4#15689460C211yesmaximal, characteristic, complemented
5#15689402C211yesmaximal, characteristic, complemented
6#15689367C211yesmaximal, characteristic, complemented
7#15689365C211yesmaximal, characteristic, complemented
8#15689344C211yesmaximal, characteristic, complemented
9#15689287C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11#15689222C211yesmaximal, characteristic, complemented
12#15689197C211yesmaximal, characteristic, complemented
13#15689122C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#480C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×Dic188C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625329C2211yescharacteristic, complemented
22C2×C8×D47C2211yescharacteristic
23#13094023C2211yescharacteristic, complemented
24#13094014—21no—
25#13094011C2211yescharacteristic
26#13094006—21no—
27#13094004C2211yescharacteristic
28#13094004C2211yescharacteristic
29#13094003—21no—
30#13094003C2211yescharacteristic, complemented
31#13094002—21no—
32#13093995—21no—
33#13093992—21no—
34#13093989C2211yescharacteristic, complemented
35#13093986C2211yescharacteristic
36C4×C22⋊D47—21no—
37C4×C22⋊D47C2211yescharacteristic
38C4⋊C4×D47C2211yescharacteristic
39C22⋊C4×D47—21no—
40#13093957C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093947C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic, complemented
52#121×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic, complemented
54#107×C47C2211yescharacteristic, complemented
55#107×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47D411yescharacteristic
67D4×D47—22no—
68D4×D47—41no—
69#10625350—22no—
70#10625350—41no—
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47C2311yescharacteristic
76C2×Dic94—21no—
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—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47D411yescharacteristic
90#10625335—41no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4D411yescharacteristic
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4D411yescharacteristic
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105#10625329—41no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108Dic188—41no—
109#10625325—22no—
110C8×D47—41no—
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47—42no—
115C22×D47—42no—
116C22×D47—81no—
117C22×D47C2×D411yescharacteristic
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—81no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—81no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—22no—
130C22⋊D47—42no—
131C22⋊D47—42no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138D188—21no—
139D188#4112yes—
140C4×D47—21no—
141C4×D47—21no—
142C4×D47—42no—
143C4×D47—81no—
144C4×D47—81no—
145Dic94—21no—
146Dic94—21no—
147Dic94—21no—
148Dic94—21no—
149Dic94—81no—
150C8×C47—21no—
151C8×C47—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47C22×D411yescharacteristic
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—22no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—84no—
167C2×D47#13712yes—
168C4×C47—21no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47C2×#4111yescharacteristic
173C4×C47H(5,𝔽2)11yescharacteristic
174Dic47—21no—
175Dic47—21no—
176Dic47—21no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3314—471nomaximal, Sylow
181C2×C47—41no—
182C2×C47—81no—
183C2×C47#54611yescharacteristic
184C2×C47C2×#13711yescharacteristic
185C2×C47#57611yescharacteristic
186D47—22no—
187D47—42no—
188#554—471no—
189#546—471no—
190#489—471no—
191#484—471no—
192#480D4711yescharacteristic, complemented
193#474—471no—
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⋊Q8—471no—
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—941no—
221#121C2×D4711yescharacteristic
222#120—941no—
223C4×Q8—471no—
224C4×D4—471no—
225C4×D4—471no—
226C4×D4—941no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4C2×D4711yescharacteristic, complemented
229C2×C22⋊C4—941no—
230#107—471no—
231#107C2×D4711yescharacteristic, complemented
232#107C2×D4711yescharacteristic, complemented
233C4⋊C8—471no—
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⋊C8C2×D4711yescharacteristic, complemented
246#97—471no—
247C24—941no—
248#41—942no—
249#41—1881no—
250C2×Q8—471no—
251C2×Q8—471no—
252C2×Q8—941no—
253C2×D4—21no—
254C2×D4—471no—
255C2×D4—471no—
256C2×D4—941no—
257C2×D4—942no—
258C2×D4—941no—
259C2×D4—1881no—
260C2×D4C22×D4711yescharacteristic
261C22×C4—21no—
262C22×C4—471no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4C22×D4711yescharacteristic
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—471no—
298C42—941no—
299C23—21no—
300C23—471no—
301C23—941no—
302C23—3761no—
303C23—1882no—
304C23—1882no—
305C23D4×D4711yescharacteristic
306Q8—941no—
307Q8—941no—
308Q8—941no—
309Q8—941no—
310Q8—3761no—
311D4—21no—
312D4—21no—
313D4—81no—
314D4—472no—
315D4—942no—
316D4—941no—
317D4—1882no—
318D4—1882no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—81no—
325C2×C4—471no—
326C2×C4—471no—
327C2×C4—471no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—3761no—
334C2×C4—3761no—
335C2×C4—1882no—
336C2×C4D4×D4711yescharacteristic
337C2×C4C23×D4711yescharacteristic
338C8—21no—
339C8—21no—
340C8—941no—
341C8—941no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—472no—
349C22—941no—
350C22—941no—
351C22—942no—
352C22—3764no—
353C22—1881no—
354C22—1881no—
355C22C2×D4×D4711yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—941no—
361C4—941no—
362C4—941no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4#41×D4711yescharacteristic
367C4#1309407011yescharacteristic
368C2—41no—
369C2—81no—
370C2—942no—
371C2—1882no—
372C2#1568976511yescharacteristic
373C2#137×D4711yescharacteristic
374C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#480C2
socleC22×C47C22×D4
hypercenter#480D47
hypocenterC47#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #15689828C2semidirect
3. #15689481C2semidirect
4. #15689460C2semidirect
5. #15689402C2semidirect
6. #15689367C2semidirect
7. #15689365C2semidirect
8. #15689344C2semidirect
9. #15689287C2semidirect
10. #15689275C2semidirect
11. #15689222C2semidirect
12. #15689197C2semidirect
13. #15689122C2semidirect
14. #102×D47C2semidirect
15. C47×#480C2semidirect
18. C2×Dic188C22semidirect
21. C2×#10625329C22semidirect
23. #13094023C22semidirect
30. #13094003C22semidirect
34. #13093989C22semidirect
40. #13093957C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093949C22semidirect
43. #13093947C22semidirect
44. #13093947C22semidirect
45. #13093947C22semidirect
51. #13093934C22semidirect
53. C2×C4⋊C4×C47C22semidirect
54. #107×C47C22semidirect
55. #107×C47C22semidirect
58. C22⋊C8×C47C22semidirect
192. #480D47semidirect
203. C47#3314semidirect
228. C2×C4⋊C4C2×D47semidirect
231. #107C2×D47semidirect
232. #107C2×D47semidirect
245. C22⋊C8C2×D47semidirect