Finite Group Databasebeta

← #20253659

Subgroups — #20253659

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#15689603C211yesmaximal, characteristic, complemented
2#15689451C211yesmaximal, characteristic, complemented
3#15689439C211yesmaximal, characteristic, complemented
4#15689410C211yesmaximal, characteristic, complemented
5#15689405C211yesmaximal, characteristic, complemented
6#15689342C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689283C211yesmaximal, characteristic, complemented
9#15689266C211yesmaximal, characteristic
10#15689233C211yesmaximal, characteristic, complemented
11#15689228C211yesmaximal, characteristic, complemented
12C4×#10625336C211yesmaximal, characteristic, complemented
13C4×#10625335C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#542C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C4×Dic94C2211yescharacteristic
22C4×Dic94C2211yescharacteristic
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25(C22⋊D47)⋊C4—21no—
26(C22⋊D47)⋊C4—21no—
27#13093982—21no—
28C2×C4⋊Dic47C2211yescharacteristic
29C4⋊C4×D47—21no—
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
48C4⋊Q8×C47C2211yescharacteristic
49#126×C47—21no—
50#124×C47—21no—
51#124×C47C2211yescharacteristic
52#123×C47—21no—
53C22⋊Q8×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C22×Dic47—21no—
67#10625350—22no—
68#10625350—22no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—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×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47D411yescharacteristic
87C22⋊C4×C47D411yescharacteristic
88C42×C47—21no—
89C42×C47C2311yescharacteristic
90C42×C47C2311yescharacteristic
91#10625337—22no—
92#10625336—22no—
93#10625335—22no—
94#10625334—22no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—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—21no—
113Q8×C47—81no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—81no—
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×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—24no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—81no—
134D188—21no—
135D188#4112yes—
136C4×D47—24no—
137C4×D47—81no—
138C4×D47—81no—
139Dic94—21no—
140Dic94#4112yes—
141C47⋊C8—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47C22×D411yescharacteristic
152C2×D47—22no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47C2×#4111yescharacteristic
164C4×C47C2×#4111yescharacteristic
165Dic47—22no—
166Dic47—41no—
167Dic47—41no—
168#3125—471nomaximal, Sylow
169C2×C47—41no—
170C2×C47—81no—
171C2×C47#52511yescharacteristic
172C2×C47#57711yescharacteristic
173C2×C47#57711yescharacteristic
174D47—42no—
175#542D4711yescharacteristic, complemented
176#520—471no—
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×#41—471no—
192C2×Q16—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×D8—471no—
196C4⋊Q8C2×D4711yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D4711yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D4711yescharacteristic
203#121C2×D4711yescharacteristic
204C4×Q8—471no—
205C4×Q8—471no—
206C4×Q8C2×D4711yescharacteristic
207C4×D4—471no—
208C4×D4—471no—
209C4×D4—941no—
210C4×D4—941no—
211C4×D4C2×D4711yescharacteristic
212#117—941no—
213#117C2×D4711yescharacteristic
214C2×C4⋊C4—471no—
215C2×C4⋊C4—941no—
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—942no—
235#41—942no—
236C2×Q8—21no—
237C2×Q8—471no—
238C2×Q8C22×D4711yescharacteristic
239C2×D4—21no—
240C2×D4—471no—
241C2×D4—941no—
242C2×D4C22×D4711yescharacteristic
243C22×C4—21no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4—941no—
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—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4C22⋊D4711yescharacteristic
277C22⋊C4C22⋊D4711yescharacteristic
278C42—21no—
279C42—941no—
280C42—941no—
281C42C22×D4711yescharacteristic
282C42C22×D4711yescharacteristic
283C23—21no—
284C23—941no—
285C23C2×C22⋊D4711yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—472no—
290Q8—941no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—472no—
295D4—944no—
296D4—941no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—944no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—3761no—
308C2×C4—3761no—
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—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—942no—
327C22—1881no—
328C22—1881no—
329C22C22×C22⋊D4711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—942no—
339C4—1881no—
340C4—1881no—
341C4#41×D4711yescharacteristic
342C4#41×D4711yescharacteristic
343C2—41no—
344C2—81no—
345C2—1882no—
346C2#1568963011yescharacteristic
347C2#1568993111yescharacteristic
348C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#542C2
socleC22×C47C22×D4
hypercenter#542D47
hypocenterC47#3125
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #15689603C2semidirect
2. #15689451C2semidirect
3. #15689439C2semidirect
4. #15689410C2semidirect
5. #15689405C2semidirect
6. #15689342C2semidirect
7. #15689335C2semidirect
8. #15689283C2semidirect
10. #15689233C2semidirect
11. #15689228C2semidirect
12. C4×#10625336C2semidirect
13. C4×#10625335C2semidirect
14. #15689184C2semidirect
15. C47×#542C2semidirect
175. #542D47semidirect
190. C47#3125semidirect