Finite Group Databasebeta

← #20253665

Subgroups — #20253665

Order 6016.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689744C211yesmaximal, characteristic, complemented
2#15689453C211yesmaximal, characteristic, complemented
3#15689441C211yesmaximal, characteristic, complemented
4#15689413C211yesmaximal, characteristic, complemented
5#15689408C211yesmaximal, characteristic, complemented
6#15689345C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689285C211yesmaximal, characteristic, complemented
9#15689268C211yesmaximal, characteristic
10#15689233C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12C4×#10625336C211yesmaximal, characteristic, complemented
13C4×#10625335C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#520C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094019—21no—
22#13094012C2211yescharacteristic
23#13094010—21no—
24#13094006—21no—
25#13094003C2211yescharacteristic
26#13094002—21no—
27#13093998C2211yescharacteristic
28C4×Dic94C2211yescharacteristic
29C4×D188C2211yescharacteristic
30#13093955C2211yescharacteristic
31#13093955C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35C4⋊(C47⋊C8)C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C4×Q8×C47C2211yescharacteristic
50C4×Q8×C47C2211yescharacteristic
51C4×D4×C47—21no—
52C4×D4×C47—21no—
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#117×C47—21no—
56#117×C47C2211yescharacteristic
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—22no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×Dic94—21no—
73C2×Dic94C2311yescharacteristic
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47D411yescharacteristic
78C4⋊C4×C47D411yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊C4×C47D411yescharacteristic
84C22⋊C4×C47D411yescharacteristic
85C42×C47—21no—
86C42×C47—21no—
87C42×C47C2311yescharacteristic
88C42×C47C2311yescharacteristic
89C22⋊Dic47—21no—
90#10625337—22no—
91#10625336—22no—
92#10625335—22no—
93#10625334—22no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—21no—
111Q8×C47—21no—
112Q8×C47#4112yes—
113D4×C47—24no—
114D4×C47—21no—
115D4×C47#4112yes—
116C2×C4×C47—24no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—81no—
123C2×C4×C47—81no—
124C2×C4×C47—81no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—81no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135D188—21no—
136D188—21no—
137C4×D47—81no—
138Dic94—21no—
139Dic94—21no—
140Dic94—81no—
141C47⋊C8—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—21no—
146C22×C47—22no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47C22×D411yescharacteristic
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—21no—
156C4×C47—22no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47C2×#4111yescharacteristic
164C4×C47C2×#4111yescharacteristic
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168#3125—471nomaximal, Sylow
169C2×C47—41no—
170C2×C47—42no—
171C2×C47#52511yescharacteristic
172C2×C47#57711yescharacteristic
173C2×C47#57711yescharacteristic
174D47—81no—
175#542—471no—
176#520D4711yescharacteristic, complemented
177#483—471no—
178#481—471no—
179#476—471no—
180#475—471no—
181#464—471no—
182#463—471no—
183#452—471no—
184#449—471no—
185#442—471no—
186#441—471no—
187C4×SD16—471no—
188C4×SD16—471no—
189#433—471no—
190C47#312511yescharacteristic, complemented, Sylow
191C2×#41C2×D4711yescharacteristic
192C2×Q16—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×D8—471no—
196C4⋊Q8—471no—
197#126—941no—
198#124—471no—
199#124—941no—
200#123—941no—
201C22⋊Q8—471no—
202C22⋊Q8—941no—
203#121—471no—
204C4×Q8—471no—
205C4×Q8C2×D4711yescharacteristic
206C4×Q8C2×D4711yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—471no—
210C4×D4C2×D4711yescharacteristic
211C4×D4C2×D4711yescharacteristic
212#117—21no—
213#117C2×D4711yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D4711yescharacteristic
216#106—471no—
217#106—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221C4⋊C8—471no—
222#103—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230C22⋊C8—471no—
231C22⋊C8—471no—
232#97—471no—
233C4×C8—471no—
234#41—22no—
235#41—22no—
236C2×Q8—471no—
237C2×Q8—941no—
238C2×Q8C22×D4711yescharacteristic
239C2×D4—21no—
240C2×D4—471no—
241C2×D4—941no—
242C2×D4C22×D4711yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—941no—
248C22×C4C22×D4711yescharacteristic
249Q16—942no—
250SD16—942no—
251SD16—942no—
252D8—942no—
253C2×C8—471no—
254C2×C8—471no—
255C2×C8—471no—
256C2×C8—471no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4C22⋊D4711yescharacteristic
266C4⋊C4C22⋊D4711yescharacteristic
267C4⋊C4C22×D4711yescharacteristic
268C4⋊C4C22×D4711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4C22⋊D4711yescharacteristic
277C22⋊C4C22⋊D4711yescharacteristic
278C42—21no—
279C42—21no—
280C42—941no—
281C42C22×D4711yescharacteristic
282C42C22×D4711yescharacteristic
283C23—21no—
284C23—941no—
285C23C2×C22⋊D4711yescharacteristic
286Q8—21no—
287Q8—941no—
288Q8—941no—
289Q8—3761no—
290Q8#1062535012yes—
291D4—24no—
292D4—21no—
293D4—941no—
294D4—941no—
295D4—3761no—
296D4#1062535012yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—3761no—
310C2×C4C2×C22⋊D4711yescharacteristic
311C2×C4C2×C22⋊D4711yescharacteristic
312C2×C4C2×C22⋊D4711yescharacteristic
313C2×C4C2×C22⋊D4711yescharacteristic
314C2×C4C2×C22⋊D4711yescharacteristic
315C2×C4C23×D4711yescharacteristic
316C8—941no—
317C8—941no—
318C8—941no—
319C8—941no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22C22×C22⋊D4711yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C4C2×#1062535011yescharacteristic
342C4C2×#1062535011yescharacteristic
343C2—41no—
344C2—42no—
345C2—3761no—
346C2#1568963411yescharacteristic
347C2#1568993111yescharacteristic
348C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#520C2
socleC22×C47C22×D4
hypercenter#520D47
hypocenterC47#3125
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689453C2semidirect
3. #15689441C2semidirect
4. #15689413C2semidirect
5. #15689408C2semidirect
6. #15689345C2semidirect
7. #15689338C2semidirect
8. #15689285C2semidirect
10. #15689233C2semidirect
11. #15689228C2semidirect
12. C4×#10625336C2semidirect
13. C4×#10625335C2semidirect
14. #15689184C2semidirect
15. C47×#520C2semidirect
176. #520D47semidirect
190. C47#3125semidirect