Finite Group Databasebeta

← #20252434

Subgroups — #20252434

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#15689635C211yesmaximal, characteristic
2#15689202C211yesmaximal, characteristic, complemented
3#15689200C211yesmaximal, characteristic, complemented
4#15689196C211yesmaximal, characteristic, complemented
5#15689196C211yesmaximal, characteristic, complemented
6#15689193C211yesmaximal, characteristic, complemented
7#15689193C211yesmaximal, characteristic, complemented
8C8×D188C211yesmaximal, characteristic, complemented
9#15689188C211yesmaximal, characteristic, complemented
10#15689184C211yesmaximal, characteristic, complemented
11#15689088C211yesmaximal, characteristic, complemented
12#15689088C211yesmaximal, characteristic, complemented
13#15689085C211yesmaximal, characteristic, complemented
14C22⋊C8×D47C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20C2×#10625324C2211yescharacteristic, complemented
21C2×#10625324C2211yescharacteristic, complemented
22C2×C8×D47C2211yescharacteristic
23C2×C8×D47C2211yescharacteristic
24C2×C8×D47C2211yescharacteristic, complemented
25C2×C8×D47C2211yescharacteristic, complemented
26#13094008C411yescharacteristic
27#13094008C411yescharacteristic
28#13094004C411yescharacteristic
29#13094004C411yescharacteristic
30#13093999C411yescharacteristic
31#13093999C411yescharacteristic
32#13093994C411yescharacteristic
33#13093994C411yescharacteristic
34C4×D188C2211yescharacteristic
35C4×D188C2211yescharacteristic
36C4×D188C2211yescharacteristic
37C4×D188C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic, complemented
39C4⋊(C47⋊C8)C2211yescharacteristic, complemented
40C22⋊(C47⋊C8)C2211yescharacteristic
41C22⋊(C47⋊C8)C2211yescharacteristic
42(C2×D47)⋊C8C2211yescharacteristic
43(C2×D47)⋊C8C2211yescharacteristic
44(C2×D47)⋊C8C2211yescharacteristic
45(C2×D47)⋊C8C2211yescharacteristic
46(C2×D47)⋊C8C2211yescharacteristic, complemented
47(C2×D47)⋊C8C2211yescharacteristic, complemented
48(C2×D47)⋊C8C2211yescharacteristic, complemented
49(C2×D47)⋊C8C2211yescharacteristic, complemented
50#13093935C2211yescharacteristic, complemented
51C4×C47⋊C8C2211yescharacteristic, complemented
52#117×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic, complemented
54C4⋊C8×C47C2211yescharacteristic, complemented
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic, complemented
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47C2×C411yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47C2×C411yescharacteristic
62C2×C22⋊D47C2×C411yescharacteristic
63C22×Dic47C2×C411yescharacteristic
64#10625350—41no—
65#10625350—41no—
66C2×D188C2×C411yescharacteristic
67C2×D188C2×C411yescharacteristic
68C2×D188C2×C411yescharacteristic
69C2×D188C2×C411yescharacteristic
70C2×D188C2×C411yescharacteristic
71C2×C4×D47—41no—
72C2×C4×D47—41no—
73C2×C4×D47C2×C411yescharacteristic
74C2×C4×D47C2×C411yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×C4×D47C2311yescharacteristic
77C2×C4×D47C2311yescharacteristic
78C2×C4×D47C2311yescharacteristic
79C2×Dic94C2×C411yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C4⋊C4×C47C2×C411yescharacteristic
85C4⋊C4×C47C2×C411yescharacteristic
86C22⋊C4×C47C2×C411yescharacteristic
87C22⋊C4×C47C2×C411yescharacteristic
88C42×C47C2311yescharacteristic
89C42×C47C2311yescharacteristic
90(C2×D47)⋊C4C2×C411yescharacteristic
91(C2×D47)⋊C4C2×C411yescharacteristic
92(C2×D47)⋊C4C2×C411yescharacteristic
93(C2×D47)⋊C4C2×C411yescharacteristic
94(C2×D47)⋊C4C2×C411yescharacteristic
95(C2×D47)⋊C4C2×C411yescharacteristic
96(C2×D47)⋊C4C2×C411yescharacteristic
97(C2×D47)⋊C4C2×C411yescharacteristic
98C4⋊Dic47C2×C411yescharacteristic
99C4⋊Dic47C2×C411yescharacteristic
100C4⋊Dic47C2×C411yescharacteristic
101C4⋊Dic47C2×C411yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—41no—
107#10625324—41no—
108#10625324—41no—
109#10625324—41no—
110C8×D47—41no—
111C8×D47—41no—
112C8×D47—41no—
113C8×D47—41no—
114C23×C47C22×C411yescharacteristic
115C22×D47—22no—
116C22×D47—41no—
117C22×D47—41no—
118C22×D47C22×C411yescharacteristic
119C22×D47C22×C411yescharacteristic
120C22×D47C22×C411yescharacteristic
121C22×D47C22×C411yescharacteristic
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47C22×C411yescharacteristic
125C2×C4×C47C22×C411yescharacteristic
126C2×C4×C47C22×C411yescharacteristic
127C2×C4×C47C22×C411yescharacteristic
128C2×C4×C47C22×C411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—41no—
131C22⋊D47—41no—
132C2×Dic47—41no—
133C2×Dic47C22×C411yescharacteristic
134C2×Dic47C22×C411yescharacteristic
135C2×Dic47C22×C411yescharacteristic
136C2×Dic47C22×C411yescharacteristic
137D188—22no—
138D188—22no—
139D188—41no—
140D188—41no—
141D188—41no—
142C4×D47—21no—
143C4×D47—21no—
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—21no—
150C4×D47—41no—
151C4×D47—41no—
152Dic94—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×C47C23×C411yescharacteristic
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—21no—
170C2×D47—21no—
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×C47—21no—
182C4×C47—21no—
183C4×C47H(5,𝔽2)11yescharacteristic
184C4×C47H(5,𝔽2)11yescharacteristic
185Dic47—21no—
186Dic47—21no—
187Dic47—21no—
188Dic47—21no—
189#2976—471nomaximal, Sylow
190C2×C47—41no—
191C2×C47#51811yescharacteristic
192C2×C47C2×#13111yescharacteristic
193C2×C47#56811yescharacteristic
194D47—22no—
195D47—41no—
196D47—41no—
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#433D4711yescharacteristic, complemented
209#408—471no—
210#408—471no—
211#407—471no—
212C2×C22⋊C8—471no—
213C47#297611yescharacteristic, complemented, Sylow
214C2×#41—471no—
215C23×C4—471no—
216C2×M16—471no—
217C2×M16—471no—
218C2×M16—471no—
219C2×M16—471no—
220C22×C8—471no—
221C22×C8—471no—
222C22×C8—471no—
223C22×C8—471no—
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#117C2×D4711yescharacteristic
237C4⋊C8—471no—
238C4⋊C8—471no—
239C4⋊C8C2×D4711yescharacteristic, complemented
240C4⋊C8C2×D4711yescharacteristic, complemented
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⋊C8—471no—
250C22⋊C8—471no—
251C22⋊C8C2×D4711yescharacteristic
252C22⋊C8C2×D4711yescharacteristic
253#97—471no—
254#97C2×D4711yescharacteristic, complemented
255C4×C8—471no—
256C4×C8C2×D4711yescharacteristic, complemented
257C24—471no—
258#41—1881no—
259#41—1881no—
260C2×Q8—471no—
261C2×D4—471no—
262C2×D4—471no—
263C2×D4—471no—
264C2×D4—471no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—1881no—
276C22×C4—1881no—
277C22×C4C22×D4711yescharacteristic
278M16—1881no—
279M16—1881no—
280M16—1881no—
281M16—1881no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8—471no—
285C2×C8—471no—
286C2×C8—1881no—
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⋊C4C4×D4711yescharacteristic
299C4⋊C4C4×D4711yescharacteristic
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⋊C4C4×D4711yescharacteristic
309C22⋊C4C4×D4711yescharacteristic
310C42C22×D4711yescharacteristic
311C42C22×D4711yescharacteristic
312C23—471no—
313C23—471no—
314C23—471no—
315C23—471no—
316C23—942no—
317C23—1881no—
318C23—1881no—
319C23C2×C4×D4711yescharacteristic
320Q8—1881no—
321D4—942no—
322D4—942no—
323D4—1881no—
324D4—1881no—
325D4—1881no—
326D4—1881no—
327D4—1881no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—471no—
331C2×C4—471no—
332C2×C4—471no—
333C2×C4—471no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—1881no—
343C2×C4—1881no—
344C2×C4—1881no—
345C2×C4C2×C4×D4711yescharacteristic
346C2×C4C2×C4×D4711yescharacteristic
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—472no—
363C22—941no—
364C22—941no—
365C22—941no—
366C22—941no—
367C22—941no—
368C22—941no—
369C22—941no—
370C22—941no—
371C22—941no—
372C22—941no—
373C22—941no—
374C22—1884no—
375C22C22×C4×D4711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—941no—
382C4—941no—
383C4—941no—
384C4—941no—
385C4#1309407011yescharacteristic
386C4#1309407011yescharacteristic
387C2—41no—
388C2—942no—
389C2—1881no—
390C2—1881no—
391C2—1881no—
392C2#1568959711yescharacteristic
393C2#131×D4711yescharacteristic
394C2#1568988811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D47
commutator, socleC22×C47C23×C4
FittingC47×#433C2
hypercenter#433D47
hypocenterC47#2976
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #15689202C2semidirect
3. #15689200C2semidirect
4. #15689196C2semidirect
5. #15689196C2semidirect
6. #15689193C2semidirect
7. #15689193C2semidirect
8. C8×D188C2semidirect
9. #15689188C2semidirect
10. #15689184C2semidirect
11. #15689088C2semidirect
12. #15689088C2semidirect
13. #15689085C2semidirect
14. C22⋊C8×D47C2semidirect
15. C47×#433C2semidirect
20. C2×#10625324C22semidirect
21. C2×#10625324C22semidirect
24. C2×C8×D47C22semidirect
25. C2×C8×D47C22semidirect
38. C4⋊(C47⋊C8)C22semidirect
39. C4⋊(C47⋊C8)C22semidirect
46. (C2×D47)⋊C8C22semidirect
47. (C2×D47)⋊C8C22semidirect
48. (C2×D47)⋊C8C22semidirect
49. (C2×D47)⋊C8C22semidirect
50. #13093935C22semidirect
51. C4×C47⋊C8C22semidirect
53. C4⋊C8×C47C22semidirect
54. C4⋊C8×C47C22semidirect
57. #97×C47C22semidirect
58. C4×C8×C47C22semidirect
208. #433D47semidirect
213. C47#2976semidirect
239. C4⋊C8C2×D47semidirect
240. C4⋊C8C2×D47semidirect
254. #97C2×D47semidirect
256. C4×C8C2×D47semidirect