Finite Group Databasebeta

← #20255607

Subgroups — #20255607

Order 6016.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689808C211yesmaximal, characteristic, complemented
2#15689770C211yesmaximal, characteristic
3#15689476C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689422C211yesmaximal, characteristic, complemented
6#15689382C211yesmaximal, characteristic, complemented
7#15689367C211yesmaximal, characteristic, complemented
8#15689344C211yesmaximal, characteristic, complemented
9#15689287C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11#15689210C211yesmaximal, characteristic, complemented
12#15689198C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14#15689122C211yesmaximal, characteristic, complemented
15C47×#481C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×Dic188C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625329C2211yescharacteristic, complemented
22C2×#10625324C2211yescharacteristic
23#13094019—21no—
24#13094015C2211yescharacteristic, complemented
25#13094014—21no—
26#13094011C2211yescharacteristic
27#13094007—21no—
28#13094006—21no—
29#13094004C2211yescharacteristic
30#13094004C2211yescharacteristic
31#13094003C2211yescharacteristic, complemented
32#13093995—21no—
33#13093992—21no—
34#13093989C2211yescharacteristic, complemented
35#13093986C2211yescharacteristic
36C4×C22⋊D47C2211yescharacteristic
37#13093983—21no—
38#13093982C2211yescharacteristic
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
51C8×Dic47C2211yescharacteristic, complemented
52#121×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic, complemented
54#106×C47C2211yescharacteristic, complemented
55#106×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×D47C2311yescharacteristic
75C2×Dic94C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88#10625335—41no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4D411yescharacteristic
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105#10625329—41no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108Dic188—41no—
109#10625325—22no—
110#10625324—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—42no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—41no—
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—
144Dic94—21no—
145Dic94—21no—
146Dic94—21no—
147Dic94—21no—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47C22×D411yescharacteristic
159C2×D47—21no—
160C2×D47—22no—
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—84no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47C2×#4111yescharacteristic
171C4×C47H(5,𝔽2)11yescharacteristic
172Dic47—21no—
173Dic47—21no—
174Dic47—21no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178#3323—471nomaximal, Sylow
179C2×C47—41no—
180C2×C47—81no—
181C2×C47#54611yescharacteristic
182C2×C47#57511yescharacteristic
183C2×C47#57711yescharacteristic
184D47—41no—
185D47—42no—
186#552—471no—
187#546—471no—
188#488—471no—
189#485—471no—
190#481D4711yescharacteristic, complemented
191#478—471no—
192#470—471no—
193#468—471no—
194#464—471no—
195#452—471no—
196#450—471no—
197C4×SD16—471no—
198#436—471no—
199#418—471no—
200#417—471no—
201C47#332311yescharacteristic, complemented, Sylow
202C2×#41—471no—
203C22×D4—471no—
204C2×Q16—471no—
205C2×SD16—471no—
206C2×SD16—471no—
207C2×M16—471no—
208C2×M16—471no—
209#126—941no—
210#125—471no—
211#125—941no—
212#124—471no—
213#123—941no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8—471no—
218#121—941no—
219#121C2×D4711yescharacteristic
220#120—941no—
221C4×Q8—471no—
222C4×D4—471no—
223C4×D4—471no—
224#117—471no—
225#117—941no—
226C2×C4⋊C4C2×D4711yescharacteristic, complemented
227C2×C22⋊C4—941no—
228#107—471no—
229#106C2×D4711yescharacteristic, complemented
230#106C2×D4711yescharacteristic, complemented
231C4⋊C8—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102C2×D4711yescharacteristic
241#102C2×D4711yescharacteristic
242C22⋊C8—471no—
243C22⋊C8C2×D4711yescharacteristic, complemented
244C4×C8—471no—
245C24—941no—
246#41—942no—
247#41—1881no—
248C2×Q8—471no—
249C2×Q8—471no—
250C2×D4—21no—
251C2×D4—471no—
252C2×D4—471no—
253C2×D4—941no—
254C2×D4—942no—
255C2×D4—941no—
256C2×D4—1881no—
257C2×D4C22×D4711yescharacteristic
258C22×C4—21no—
259C22×C4—471no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4C22×D4711yescharacteristic
263Q16—1881no—
264SD16—942no—
265SD16—1881no—
266M16—1881no—
267M16—1881no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4C22×D4711yescharacteristic
282C4⋊C4C22×D4711yescharacteristic
283C4⋊C4C22×D4711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—471no—
286C22⋊C4—471no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C42—471no—
295C42—941no—
296C42—941no—
297C23—21no—
298C23—471no—
299C23—941no—
300C23—3761no—
301C23—1882no—
302C23—1882no—
303C23D4×D4711yescharacteristic
304Q8—941no—
305Q8—941no—
306Q8—941no—
307Q8—941no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—472no—
312D4—941no—
313D4—1881no—
314D4—1882no—
315D4—1882no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—471no—
323C2×C4—471no—
324C2×C4—471no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—3761no—
331C2×C4—1882no—
332C2×C4D4×D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—21no—
335C8—21no—
336C8—941no—
337C8—941no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—941no—
345C22—942no—
346C22—941no—
347C22—941no—
348C22—3764no—
349C22—1881no—
350C22—1881no—
351C22C2×D4×D4711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—941no—
357C4—941no—
358C4—941no—
359C4—1881no—
360C4—1881no—
361C4—1881no—
362C4#41×D4711yescharacteristic
363C4#1309407011yescharacteristic
364C2—41no—
365C2—81no—
366C2—1881no—
367C2—1882no—
368C2#1568976511yescharacteristic
369C2#1568991911yescharacteristic
370C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#481C2
socleC22×C47C22×D4
hypercenter#481D47
hypocenterC47#3323
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #15689808C2semidirect
3. #15689476C2semidirect
4. #15689467C2semidirect
5. #15689422C2semidirect
6. #15689382C2semidirect
7. #15689367C2semidirect
8. #15689344C2semidirect
9. #15689287C2semidirect
10. #15689275C2semidirect
11. #15689210C2semidirect
12. #15689198C2semidirect
13. #15689126C2semidirect
14. #15689122C2semidirect
15. C47×#481C2semidirect
18. C2×Dic188C22semidirect
21. C2×#10625329C22semidirect
24. #13094015C22semidirect
31. #13094003C22semidirect
34. #13093989C22semidirect
40. #13093957C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093949C22semidirect
43. #13093947C22semidirect
44. #13093947C22semidirect
45. #13093947C22semidirect
51. C8×Dic47C22semidirect
53. C2×C4⋊C4×C47C22semidirect
54. #106×C47C22semidirect
55. #106×C47C22semidirect
58. C22⋊C8×C47C22semidirect
190. #481D47semidirect
201. C47#3323semidirect
226. C2×C4⋊C4C2×D47semidirect
229. #106C2×D47semidirect
230. #106C2×D47semidirect
243. C22⋊C8C2×D47semidirect