Finite Group Databasebeta

← #20253567

Subgroups — #20253567

Order 6016.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689740C211yesmaximal, characteristic, complemented
2#15689597C211yesmaximal, characteristic, complemented
3#15689464C211yesmaximal, characteristic, complemented
4#15689412C211yesmaximal, characteristic, complemented
5#15689402C211yesmaximal, characteristic, complemented
6#15689337C211yesmaximal, characteristic, complemented
7#15689337C211yesmaximal, characteristic, complemented
8#15689276C211yesmaximal, characteristic, complemented
9#15689256C211yesmaximal, characteristic
10#15689232C211yesmaximal, characteristic, complemented
11#15689222C211yesmaximal, characteristic, complemented
12#15689210C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21#13094023C2211yescharacteristic, complemented
22#13094017—21no—
23#13094011—21no—
24#13094011C2211yescharacteristic, complemented
25#13094005—21no—
26#13094003C2211yescharacteristic
27#13094001—21no—
28#13093989C2211yescharacteristic, complemented
29C4×D188—21no—
30C4×D188—21no—
31D4×Dic47C2211yescharacteristic, complemented
32#13093986C2211yescharacteristic
33#13093986C2211yescharacteristic
34#13093986C2211yescharacteristic
35#13093986C2211yescharacteristic
36#13093983C2211yescharacteristic
37C22⋊C4×D47—21no—
38C22⋊C4×D47—21no—
39#13093957C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C23×D47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×Dic47—21no—
64C2×D188—21no—
65C2×D188—22no—
66C2×D188—22no—
67C2×D188C2311yescharacteristic
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×Dic94—21no—
74C2×Dic94C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C42×C47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88C22⋊Dic47D411yescharacteristic
89#10625334—22no—
90#10625334—22no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47D411yescharacteristic
96C4⋊Dic47D411yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625325—22no—
107#10625325—22no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—24no—
113C22×D47—81no—
114C22×D47—81no—
115D4×C47—21no—
116D4×C47—21no—
117D4×C47—81no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—81no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132D188—24no—
133D188—21no—
134D188—21no—
135D188#4112yes—
136D188#4112yes—
137C4×D47—81no—
138C4×D47—81no—
139C4×D47—81no—
140C4×D47—81no—
141Dic94—21no—
142Dic94—21no—
143Dic94—81no—
144C8×C47—21no—
145C8×C47—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C22×D411yescharacteristic
155C2×D47—22no—
156C2×D47—22no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—84no—
162C4×C47—21no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47C2×#4111yescharacteristic
167C4×C47C2×#4111yescharacteristic
168Dic47—21no—
169Dic47—21no—
170Dic47—21no—
171Dic47—21no—
172Dic47—41no—
173Dic47—41no—
174#3118—471nomaximal, Sylow
175C2×C47—41no—
176C2×C47—81no—
177C2×C47#52511yescharacteristic
178C2×C47#57611yescharacteristic
179C2×C47#57711yescharacteristic
180D47—42no—
181D47—42no—
182#542—471no—
183#518—471no—
184#485—471no—
185#482D4711yescharacteristic, complemented
186#476—471no—
187#474—471no—
188#463—471no—
189#463—471no—
190#450—471no—
191#447—471no—
192#442—471no—
193#440—471no—
194C4×SD16—471no—
195C4×D8—471no—
196#433—471no—
197C47#311811yescharacteristic, complemented, Sylow
198C22×D4—471no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×D8—471no—
202C2×D8—471no—
203C4⋊Q8—471no—
204#126—941no—
205#124—471no—
206#124—941no—
207#123—941no—
208C22⋊Q8—471no—
209C22⋊Q8—941no—
210#121C2×D4711yescharacteristic
211C4×Q8—471no—
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—471no—
217C4×D4—941no—
218C4×D4—941no—
219#117—471no—
220#117C2×D4711yescharacteristic
221C2×C22⋊C4—941no—
222C2×C22⋊C4—941no—
223#107—471no—
224#107C2×D4711yescharacteristic, complemented
225#106—471no—
226#106C2×D4711yescharacteristic, complemented
227C4⋊C8—471no—
228C4⋊C8—471no—
229#103—471no—
230#103—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102C2×D4711yescharacteristic, complemented
236#102C2×D4711yescharacteristic, complemented
237C22⋊C8—471no—
238C22⋊C8C2×D4711yescharacteristic
239#97—471no—
240C4×C8—471no—
241C24—941no—
242C2×Q8—471no—
243C2×Q8—941no—
244C2×D4—21no—
245C2×D4—471no—
246C2×D4—471no—
247C2×D4—942no—
248C2×D4—942no—
249C2×D4—941no—
250C2×D4C22×D4711yescharacteristic
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4C22×D4711yescharacteristic
257SD16—942no—
258SD16—942no—
259D8—942no—
260D8—942no—
261C2×C8—471no—
262C2×C8—471no—
263C2×C8C22×D4711yescharacteristic
264C2×C8C22×D4711yescharacteristic
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4C22×D4711yescharacteristic
272C4⋊C4C22×D4711yescharacteristic
273C4⋊C4C22×D4711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—471no—
277C22⋊C4—471no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—21no—
287C42—471no—
288C42—471no—
289C42—941no—
290C23—21no—
291C23—944no—
292C23—941no—
293C23—941no—
294C23—3761no—
295C23—3761no—
296C23D4×D4711yescharacteristic
297Q8—941no—
298Q8—941no—
299Q8—3761no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—472no—
304D4—472no—
305D4—944no—
306D4—941no—
307D4—941no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—471no—
314C2×C4—471no—
315C2×C4—471no—
316C2×C4—471no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—3761no—
320C2×C4—3761no—
321C2×C4—3761no—
322C2×C4—3761no—
323C2×C4—3761no—
324C2×C4D4×D4711yescharacteristic
325C2×C4C23×D4711yescharacteristic
326C8—21no—
327C8—21no—
328C8—941no—
329C8—941no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—942no—
337C22—942no—
338C22—3764no—
339C22—1881no—
340C22—1881no—
341C22—1881no—
342C22—1881no—
343C22C2×D4×D4711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—941no—
349C4—941no—
350C4—941no—
351C4—941no—
352C4—1881no—
353C4—1881no—
354C4#41×D4711yescharacteristic
355C4#41×D4711yescharacteristic
356C2—41no—
357C2—81no—
358C2—1882no—
359C2—1882no—
360C2#1568963111yescharacteristic
361C2#1568992711yescharacteristic
362C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3118
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #15689740C2semidirect
2. #15689597C2semidirect
3. #15689464C2semidirect
4. #15689412C2semidirect
5. #15689402C2semidirect
6. #15689337C2semidirect
7. #15689337C2semidirect
8. #15689276C2semidirect
10. #15689232C2semidirect
11. #15689222C2semidirect
12. #15689210C2semidirect
13. #15689203C2semidirect
14. #15689181C2semidirect
15. C47×#482C2semidirect
21. #13094023C22semidirect
24. #13094011C22semidirect
28. #13093989C22semidirect
31. D4×Dic47C22semidirect
39. #13093957C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093947C22semidirect
44. #13093947C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. #102×C47C22semidirect
57. #102×C47C22semidirect
185. #482D47semidirect
197. C47#3118semidirect
224. #107C2×D47semidirect
226. #106C2×D47semidirect
235. #102C2×D47semidirect
236. #102C2×D47semidirect