Finite Group Databasebeta

← #20254257

Subgroups — #20254257

Order 6016.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689696C211yesmaximal, characteristic, complemented
2#15689690C211yesmaximal, characteristic
3#15689465C211yesmaximal, characteristic, complemented
4#15689461C211yesmaximal, characteristic, complemented
5#15689446C211yesmaximal, characteristic, complemented
6#15689445C211yesmaximal, characteristic, complemented
7#15689368C211yesmaximal, characteristic, complemented
8#15689366C211yesmaximal, characteristic, complemented
9#15689351C211yesmaximal, characteristic, complemented
10#15689349C211yesmaximal, characteristic, complemented
11#15689274C211yesmaximal, characteristic, complemented
12#15689260C211yesmaximal, characteristic, complemented
13#15689260C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic, complemented
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625324C2211yescharacteristic, complemented
21C2×C8×D47C2211yescharacteristic, complemented
22#13094023—21no—
23#13094020—21no—
24#13094011—21no—
25#13094010—21no—
26#13094009—21no—
27#13094006—21no—
28#13094004C2211yescharacteristic, complemented
29#13094003C2211yescharacteristic
30#13094000C2211yescharacteristic, complemented
31#13093995C2211yescharacteristic
32#13093995C2211yescharacteristic
33#13093995C2211yescharacteristic
34#13093995C2211yescharacteristic
35#13093993—21no—
36#13093993—21no—
37#13093983C2211yescharacteristic
38#13093982C2211yescharacteristic, complemented
39#13093958C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093948C2211yescharacteristic, complemented
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C24×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47—41no—
63C2×D4×C47—41no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47D411yescharacteristic
72C2×C22⋊D47D411yescharacteristic
73Q8×D47—41no—
74Q8×D47—41no—
75#10625350—41no—
76#10625350—41no—
77C2×D188D411yescharacteristic
78C2×C4×D47—21no—
79C2×C4×D47C2311yescharacteristic
80C2×C4×D47C2311yescharacteristic
81C2×Dic94—21no—
82C2×Dic94D411yescharacteristic
83C2×Dic94C2311yescharacteristic
84SD16×C47—41no—
85SD16×C47—41no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47—21no—
89C4⋊C4×C47C2311yescharacteristic
90C22⋊C4×C47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97#10625335—41no—
98#10625335—41no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102C4⋊Dic47—21no—
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108C4×Dic47—21no—
109C4×Dic47—21no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112#10625324—41no—
113C8×D47—41no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—42no—
117C23×C47—81no—
118C23×C47—81no—
119C23×C47C2×D411yescharacteristic
120C22×D47C2×D411yescharacteristic
121C22×D47C2×D411yescharacteristic
122Q8×C47—21no—
123Q8×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—42no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—41no—
136C22⋊D47—41no—
137C22⋊D47—81no—
138C22⋊D47—81no—
139C22⋊D47—81no—
140C22⋊D47—81no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47C2×D411yescharacteristic
146C2×Dic47C2×D411yescharacteristic
147D188—41no—
148C4×D47—21no—
149C4×D47—21no—
150C4×D47—21no—
151C4×D47—21no—
152C4×D47—42no—
153Dic94—21no—
154Dic94—21no—
155Dic94—41no—
156Dic94—42no—
157C8×C47—21no—
158C8×C47—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—84no—
171C22×C47C22×D411yescharacteristic
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—21no—
178C4×C47—21no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47H(5,𝔽2)11yescharacteristic
182C4×C47H(5,𝔽2)11yescharacteristic
183Dic47—21no—
184Dic47—21no—
185Dic47—41no—
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189#3200—471nomaximal, Sylow
190C2×C47—41no—
191C2×C47—81no—
192C2×C47—81no—
193C2×C47#53411yescharacteristic
194C2×C47#57711yescharacteristic
195C2×C47#57711yescharacteristic
196D47—41no—
197D47—41no—
198#536—471no—
199#535—471no—
200#485—471no—
201#485—471no—
202#482—471no—
203#482—471no—
204#468—471no—
205#468—471no—
206#465—471no—
207#465—471no—
208#450—471no—
209#450D4711yescharacteristic, complemented
210#448—471no—
211#448—471no—
212#408—471no—
213C47#320011yescharacteristic, complemented, Sylow
214C2×#41—471no—
215C22×Q8—471no—
216C22×D4C2×D4711yescharacteristic
217C2×SD16—471no—
218C2×SD16—471no—
219C2×SD16C2×D4711yescharacteristic
220C2×SD16C2×D4711yescharacteristic
221C2×M16—471no—
222C22×C8—471no—
223C4⋊Q8—941no—
224#127—941no—
225#124—941no—
226#124—941no—
227#123—941no—
228#123—941no—
229C22⋊Q8—471no—
230C22⋊Q8—471no—
231C22⋊Q8—471no—
232C22⋊Q8C2×D4711yescharacteristic
233#121—471no—
234#121—471no—
235#121—471no—
236#121—471no—
237#120—941no—
238#120—941no—
239#117—471no—
240#117—471no—
241#107—471no—
242#107—471no—
243#106—471no—
244#106—471no—
245#103—471no—
246#103—471no—
247#103—471no—
248#103—471no—
249#102—471no—
250#102—471no—
251#102C2×D4711yescharacteristic
252#102C2×D4711yescharacteristic
253C22⋊C8—471no—
254C22⋊C8—471no—
255C22⋊C8—471no—
256C22⋊C8C2×D4711yescharacteristic
257C24—21no—
258#41—1881no—
259#41—1881no—
260C2×Q8—471no—
261C2×Q8—471no—
262C2×Q8—941no—
263C2×Q8—1881no—
264C2×Q8—1881no—
265C2×Q8C22×D4711yescharacteristic
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—471no—
270C2×D4—471no—
271C2×D4—471no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4C22×D4711yescharacteristic
277C2×D4C22×D4711yescharacteristic
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—941no—
281C22×C4C22×D4711yescharacteristic
282SD16—41no—
283SD16—41no—
284SD16—1881no—
285SD16—1881no—
286M16—1881no—
287C2×C8—471no—
288C2×C8—471no—
289C2×C8—1881no—
290C2×C8C22×D4711yescharacteristic
291C2×C8C22×D4711yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—471no—
294C4⋊C4—471no—
295C4⋊C4—471no—
296C4⋊C4—941no—
297C4⋊C4—941no—
298C4⋊C4—941no—
299C4⋊C4C22×D4711yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C42—941no—
311C42—941no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—471no—
318C23—471no—
319C23D4×D4711yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—941no—
323Q8—941no—
324Q8—1881no—
325Q8—1882no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—3761no—
332D4—3761no—
333D4—3761no—
334D4—3761no—
335D4—1881no—
336D4—1881no—
337D4—1881no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—471no—
343C2×C4—471no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—1882no—
353C2×C4D4×D4711yescharacteristic
354C2×C4C23×D4711yescharacteristic
355C8—21no—
356C8—21no—
357C8—941no—
358C8—941no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—941no—
370C22—941no—
371C22—941no—
372C22—941no—
373C22—941no—
374C22—941no—
375C22C2×D4×D4711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—941no—
380C4—941no—
381C4—1881no—
382C4—1881no—
383C4—1881no—
384C4—1881no—
385C4#1309406911yescharacteristic
386C4#1309406911yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—1881no—
391C2—1881no—
392C2#1568968311yescharacteristic
393C2#1568992911yescharacteristic
394C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3200
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #15689696C2semidirect
3. #15689465C2semidirect
4. #15689461C2semidirect
5. #15689446C2semidirect
6. #15689445C2semidirect
7. #15689368C2semidirect
8. #15689366C2semidirect
9. #15689351C2semidirect
10. #15689349C2semidirect
11. #15689274C2semidirect
12. #15689260C2semidirect
13. #15689260C2semidirect
14. #15689088C2semidirect
15. C47×#450C2semidirect
17. C2×Q8×D47C22semidirect
20. C2×#10625324C22semidirect
21. C2×C8×D47C22semidirect
28. #13094004C22semidirect
30. #13094000C22semidirect
38. #13093982C22semidirect
39. #13093958C22semidirect
40. #13093957C22semidirect
41. #13093956C22semidirect
42. #13093955C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093948C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. (C2×D47)⋊C8C22semidirect
209. #450D47semidirect
213. C47#3200semidirect