Finite Group Databasebeta

← #20252431

Subgroups — #20252431

Order 6016.

412 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#15689630C211yesmaximal, characteristic
2#15689199C211yesmaximal, characteristic, complemented
3#15689198C211yesmaximal, characteristic, complemented
4#15689197C211yesmaximal, characteristic, complemented
5#15689194C211yesmaximal, characteristic, complemented
6#15689192C211yesmaximal, characteristic, complemented
7#15689191C211yesmaximal, characteristic, complemented
8C8×C22⋊D47C211yesmaximal, characteristic, complemented
9(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
10#15689181C211yesmaximal, characteristic, complemented
11#15689181C211yesmaximal, characteristic, complemented
12#15689090C211yesmaximal, characteristic, complemented
13#15689085C211yesmaximal, characteristic, complemented
14C22⋊C8×D47C211yesmaximal, characteristic, complemented
15C47×#408C211yesmaximal, characteristic, complemented
16C22×C4×D47C2211yescharacteristic
17C2×#10625329C2211yescharacteristic, complemented
18C2×#10625324C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20C22×C47⋊C8C2211yescharacteristic, complemented
21C2×C8×D47C2211yescharacteristic
22C2×C8×D47C2211yescharacteristic
23#13094005C411yescharacteristic
24#13094005C411yescharacteristic
25#13094000C411yescharacteristic
26#13094000C411yescharacteristic
27#13093995C411yescharacteristic
28#13093995C411yescharacteristic
29#13093992C411yescharacteristic
30#13093992C411yescharacteristic
31C4×C22⋊D47C2211yescharacteristic
32C4×C22⋊D47C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35#13093983C2211yescharacteristic
36Dic47⋊C8C2211yescharacteristic, complemented
37Dic47⋊C8C2211yescharacteristic, complemented
38Dic47⋊C8C2211yescharacteristic, complemented
39Dic47⋊C8C2211yescharacteristic, complemented
40C22⋊(C47⋊C8)C2211yescharacteristic
41C22⋊(C47⋊C8)C2211yescharacteristic
42C22⋊(C47⋊C8)C2211yescharacteristic, complemented
43C22⋊(C47⋊C8)C2211yescharacteristic, complemented
44(C2×D47)⋊C8C2211yescharacteristic
45(C2×D47)⋊C8C2211yescharacteristic
46(C2×D47)⋊C8C2211yescharacteristic
47(C2×D47)⋊C8C2211yescharacteristic
48#13093934C2211yescharacteristic, complemented
49#13093934C2211yescharacteristic, complemented
50C8×Dic47C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×#41×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic, complemented
54C22×C8×C47C2211yescharacteristic, complemented
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C23×D47C2×C411yescharacteristic
60#41×C47—41no—
61#41×C47—41no—
62C2×Q8×C47C2×C411yescharacteristic
63C2×D4×C47C2×C411yescharacteristic
64C2×D4×C47C2×C411yescharacteristic
65C2×D4×C47C2×C411yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47C2×C411yescharacteristic
70C2×C22⋊D47C2×C411yescharacteristic
71C2×C22⋊D47C2×C411yescharacteristic
72C2×C22⋊D47C2×C411yescharacteristic
73C22×Dic47C2×C411yescharacteristic
74C2×C4×D47—41no—
75C2×C4×D47—41no—
76C2×C4×D47C2×C411yescharacteristic
77C2×C4×D47C2×C411yescharacteristic
78C2×C4×D47C2311yescharacteristic
79C2×C4×D47C2311yescharacteristic
80M16×C47—41no—
81C2×C8×C47—41no—
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C22⋊Dic47C2×C411yescharacteristic
87C22⋊Dic47C2×C411yescharacteristic
88C22⋊Dic47C2×C411yescharacteristic
89C22⋊Dic47C2×C411yescharacteristic
90C22⋊Dic47C2×C411yescharacteristic
91C22⋊Dic47C2×C411yescharacteristic
92(C2×D47)⋊C4C2×C411yescharacteristic
93(C2×D47)⋊C4C2×C411yescharacteristic
94(C2×D47)⋊C4C2×C411yescharacteristic
95(C2×D47)⋊C4C2×C411yescharacteristic
96C4⋊Dic47C2×C411yescharacteristic
97C4⋊Dic47C2×C411yescharacteristic
98Dic47⋊C4C2×C411yescharacteristic
99Dic47⋊C4C2×C411yescharacteristic
100Dic47⋊C4C2×C411yescharacteristic
101Dic47⋊C4C2×C411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104#10625329—41no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111#10625324—41no—
112C8×D47—41no—
113C8×D47—41no—
114C23×C47C22×C411yescharacteristic
115C23×C47C22×C411yescharacteristic
116C23×C47C22×C411yescharacteristic
117C22×D47—22no—
118C22×D47—41no—
119C22×D47—41no—
120C22×D47C22×C411yescharacteristic
121C22×D47C22×C411yescharacteristic
122Q8×C47—41no—
123D4×C47—41no—
124D4×C47—41no—
125D4×C47—41no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47C22×C411yescharacteristic
133C2×C4×C47C22×C411yescharacteristic
134C2×C4×C47C22×C411yescharacteristic
135C2×C4×C47C2411yescharacteristic
136C22⋊D47—22no—
137C22⋊D47—22no—
138C22⋊D47—41no—
139C22⋊D47—41no—
140C2×Dic47—41no—
141C2×Dic47C22×C411yescharacteristic
142C2×Dic47C22×C411yescharacteristic
143C2×Dic47C22×C411yescharacteristic
144C2×Dic47C22×C411yescharacteristic
145C2×Dic47C22×C411yescharacteristic
146C2×Dic47C22×C411yescharacteristic
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—21no—
150C4×D47—21no—
151C4×D47—41no—
152C4×D47—41no—
153C8×C47—21no—
154C8×C47—21no—
155C8×C47—21no—
156C8×C47—21no—
157C47⋊C8—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47C23×C411yescharacteristic
171C2×D47—21no—
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—44no—
177C2×D47#13112yes—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47H(5,𝔽2)11yescharacteristic
182C4×C47H(5,𝔽2)11yescharacteristic
183Dic47—21no—
184Dic47—21no—
185Dic47—21no—
186Dic47—21no—
187Dic47—21no—
188Dic47—21no—
189#2976—471nomaximal, Sylow
190C2×C47—41no—
191C2×C47—41no—
192C2×C47—41no—
193C2×C47#51811yescharacteristic
194C2×C47C2×#13111yescharacteristic
195C2×C47#56811yescharacteristic
196D47—22no—
197D47—41no—
198#525—471no—
199#436—471no—
200#436—471no—
201#435—471no—
202#435—471no—
203#435—471no—
204#435—471no—
205C8×D4—471no—
206C8×D4—471no—
207#433—471no—
208#433—471no—
209#408—471no—
210#408D4711yescharacteristic, complemented
211#407—471no—
212C2×C22⋊C8—471no—
213C47#297611yescharacteristic, complemented, Sylow
214C2×#41C2×D4711yescharacteristic
215C23×C4—471no—
216C2×M16—471no—
217C2×M16—471no—
218C2×M16—471no—
219C2×M16C2×D4711yescharacteristic, complemented
220C22×C8—471no—
221C22×C8—471no—
222C22×C8—471no—
223C22×C8C2×D4711yescharacteristic, complemented
224#123—471no—
225#123—471no—
226C22⋊Q8—471no—
227C22⋊Q8—471no—
228#121—471no—
229#121—471no—
230#120—471no—
231#120—471no—
232C4×D4—471no—
233C4×D4—471no—
234C4×D4—471no—
235C4×D4—471no—
236#117—471no—
237C4⋊C8—471no—
238C4⋊C8—471no—
239C4⋊C8—471no—
240C4⋊C8—471no—
241C22⋊C8—471no—
242C22⋊C8—471no—
243C22⋊C8—471no—
244C22⋊C8—471no—
245C22⋊C8—471no—
246C22⋊C8—471no—
247C22⋊C8—471no—
248C22⋊C8—471no—
249C22⋊C8C2×D4711yescharacteristic
250C22⋊C8C2×D4711yescharacteristic
251C22⋊C8C2×D4711yescharacteristic, complemented
252C22⋊C8C2×D4711yescharacteristic, complemented
253#97—471no—
254#97—471no—
255C4×C8—471no—
256C4×C8—471no—
257C24—471no—
258#41—41no—
259#41—41no—
260C2×Q8C4×D4711yescharacteristic
261C2×D4—471no—
262C2×D4—471no—
263C2×D4—471no—
264C2×D4—471no—
265C2×D4C4×D4711yescharacteristic
266C2×D4C4×D4711yescharacteristic
267C2×D4C4×D4711yescharacteristic
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—471no—
273C22×C4—1881no—
274C22×C4—1881no—
275C22×C4C22×D4711yescharacteristic
276C22×C4C22×D4711yescharacteristic
277C22×C4C22×D4711yescharacteristic
278M16—41no—
279M16—1881no—
280M16—1881no—
281M16—1881no—
282C2×C8—41no—
283C2×C8—471no—
284C2×C8—471no—
285C2×C8—471no—
286C2×C8—471no—
287C2×C8—1881no—
288C2×C8—1881no—
289C2×C8—1881no—
290C2×C8C22×D4711yescharacteristic
291C2×C8C22×D4711yescharacteristic
292C2×C8C22×D4711yescharacteristic
293C2×C8C22×D4711yescharacteristic
294C4⋊C4—471no—
295C4⋊C4—471no—
296C4⋊C4—471no—
297C4⋊C4—471no—
298C4⋊C4—471no—
299C4⋊C4—471no—
300C22⋊C4—471no—
301C22⋊C4—471no—
302C22⋊C4—471no—
303C22⋊C4—471no—
304C22⋊C4—471no—
305C22⋊C4—471no—
306C22⋊C4—471no—
307C22⋊C4—471no—
308C22⋊C4—471no—
309C22⋊C4—471no—
310C42—471no—
311C42—471no—
312C23—471no—
313C23—471no—
314C23—942no—
315C23—1881no—
316C23—1881no—
317C23C2×C4×D4711yescharacteristic
318C23C2×C4×D4711yescharacteristic
319C23C2×C4×D4711yescharacteristic
320Q8—41no—
321D4—41no—
322D4—41no—
323D4—41no—
324D4—942no—
325D4—942no—
326D4—1881no—
327D4—1881no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—471no—
335C2×C4—471no—
336C2×C4—471no—
337C2×C4—471no—
338C2×C4—471no—
339C2×C4—471no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—1881no—
345C2×C4—1881no—
346C2×C4—1881no—
347C2×C4C2×C4×D4711yescharacteristic
348C2×C4C2×C4×D4711yescharacteristic
349C2×C4C2×C4×D4711yescharacteristic
350C2×C4C23×D4711yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C8—941no—
356C8—941no—
357C8—941no—
358C8—941no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—472no—
369C22—941no—
370C22—941no—
371C22—941no—
372C22—941no—
373C22—941no—
374C22—1884no—
375C22C22×C4×D4711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—941no—
380C4—941no—
381C4—941no—
382C4—941no—
383C4—941no—
384C4—941no—
385C4#1309406911yescharacteristic
386C4#1309406911yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—942no—
391C2—1881no—
392C2#1568959611yescharacteristic
393C2#131×D4711yescharacteristic
394C2#1568988811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D47
commutator, socleC22×C47C23×C4
FittingC47×#408C2
hypercenter#408D47
hypocenterC47#2976
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #15689199C2semidirect
3. #15689198C2semidirect
4. #15689197C2semidirect
5. #15689194C2semidirect
6. #15689192C2semidirect
7. #15689191C2semidirect
8. C8×C22⋊D47C2semidirect
9. (C22⋊D47)⋊C8C2semidirect
10. #15689181C2semidirect
11. #15689181C2semidirect
12. #15689090C2semidirect
13. #15689085C2semidirect
14. C22⋊C8×D47C2semidirect
15. C47×#408C2semidirect
17. C2×#10625329C22semidirect
20. C22×C47⋊C8C22semidirect
36. Dic47⋊C8C22semidirect
37. Dic47⋊C8C22semidirect
38. Dic47⋊C8C22semidirect
39. Dic47⋊C8C22semidirect
42. C22⋊(C47⋊C8)C22semidirect
43. C22⋊(C47⋊C8)C22semidirect
48. #13093934C22semidirect
49. #13093934C22semidirect
50. C8×Dic47C22semidirect
51. C8×Dic47C22semidirect
53. C2×M16×C47C22semidirect
54. C22×C8×C47C22semidirect
57. C22⋊C8×C47C22semidirect
58. C22⋊C8×C47C22semidirect
210. #408D47semidirect
213. C47#2976semidirect
219. C2×M16C2×D47semidirect
223. C22×C8C2×D47semidirect
251. C22⋊C8C2×D47semidirect
252. C22⋊C8C2×D47semidirect