Finite Group Databasebeta

← #20255531

Subgroups — #20255531

Order 6016.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689819C211yesmaximal, characteristic, complemented
2D4×D188C211yesmaximal, characteristic, complemented
3#15689488C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689442C211yesmaximal, characteristic, complemented
6#15689424C211yesmaximal, characteristic, complemented
7#15689376C211yesmaximal, characteristic, complemented
8#15689359C211yesmaximal, characteristic, complemented
9#15689319C211yesmaximal, characteristic, complemented
10#15689259C211yesmaximal, characteristic, complemented
11#15689259C211yesmaximal, characteristic, complemented
12#15689236C211yesmaximal, characteristic, complemented
13#15689129C211yesmaximal, characteristic, complemented
14C2×#13093946C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×D4×D47—21no—
19C2×D376C2211yescharacteristic
20C2×D376C2211yescharacteristic, complemented
21C2×D376C2211yescharacteristic, complemented
22#13094021C2211yescharacteristic
23#13094019—21no—
24#13094016C2211yescharacteristic, complemented
25#13094006—21no—
26#13093999—21no—
27#13093998C2211yescharacteristic
28#13093998C2211yescharacteristic
29#13093998C2211yescharacteristic, complemented
30#13093998C2211yescharacteristic, complemented
31#13093996—21no—
32#13093994—21no—
33#13093994—21no—
34C4×D188C2211yescharacteristic
35C4×D188C2211yescharacteristic, complemented
36(C22⋊D47)⋊C4—21no—
37#13093983C2211yescharacteristic, complemented
38C2×C4⋊Dic47C2211yescharacteristic, complemented
39#13093958C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093946C2211yescharacteristic
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic, complemented
47#13093946C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic, complemented
52C2×M16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic, complemented
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic, complemented
56C22⋊C8×C47C2211yescharacteristic, complemented
57C22⋊C8×C47C2211yescharacteristic, complemented
58#97×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
61C2×D4×C47D411yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69D4×D47—44no—
70C2×D188—22no—
71C2×D188—22no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188C2311yescharacteristic
79C2×D188C2311yescharacteristic
80C2×D188C2311yescharacteristic
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84M16×C47—41no—
85C2×C8×C47—41no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C2×C8×C47C2311yescharacteristic
89C2×C8×C47C2311yescharacteristic
90C4⋊C4×C47D411yescharacteristic
91C22⋊C4×C47D411yescharacteristic
92C22⋊C4×C47D411yescharacteristic
93C42×C47C2311yescharacteristic
94C22⋊Dic47—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101C4⋊Dic47—21no—
102C4⋊Dic47C2311yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108C4×Dic47—21no—
109D376—22no—
110D376—41no—
111D376—41no—
112C23×C47C2×D411yescharacteristic
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—42no—
121C22×D47—42no—
122C22×D47—81no—
123C22×D47—81no—
124D4×C47—22no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2411yescharacteristic
134C22⋊D47—42no—
135C22⋊D47—42no—
136C22⋊D47—42no—
137C22⋊D47—81no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—81no—
143D188—21no—
144D188—21no—
145D188—21no—
146D188—21no—
147D188—21no—
148D188—21no—
149D188—21no—
150D188—42no—
151D188—42no—
152D188—42no—
153D188—81no—
154D188#4112yes—
155C4×D47—42no—
156C4×D47—81no—
157C8×C47—21no—
158C8×C47—21no—
159C8×C47—21no—
160C8×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47AGL(1,ℤ/8)12yes—
167C22×C47C22×D411yescharacteristic
168C2×D47—22no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—84no—
181C2×D47—84no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47C2×#4111yescharacteristic
187C4×C47H(5,𝔽2)11yescharacteristic
188Dic47—41no—
189Dic47—41no—
190Dic47—41no—
191Dic47—41no—
192#3318—471nomaximal, Sylow
193C2×C47—22no—
194C2×C47—41no—
195C2×C47#54611yescharacteristic
196C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C47#57611yescharacteristic
198D47—42no—
199D47—81no—
200D47—81no—
201D47—81no—
202#553—471no—
203D42—471no—
204#490—471no—
205#482—471no—
206#481—471no—
207#478—471no—
208#469—471no—
209#466—471no—
210#459—471no—
211#447—471no—
212#447—471no—
213#442—471no—
214#435D4711yescharacteristic, complemented
215#418—471no—
216C2×#102—471no—
217C47#331811yescharacteristic, complemented, Sylow
218C22×D4—471no—
219C22×D4—471no—
220C22×D4—941no—
221C2×D8—471no—
222C2×D8—471no—
223C2×D8—471no—
224C2×M16C2×D4711yescharacteristic, complemented
225C22×C8C2×D4711yescharacteristic, complemented
226#127—471no—
227#126—941no—
228#125—471no—
229#123—941no—
230#121—471no—
231#121—471no—
232#121—471no—
233#121—471no—
234#121—941no—
235#121—941no—
236#120—941no—
237#120—941no—
238C4×D4—471no—
239C4×D4—471no—
240C4×D4—941no—
241C4×D4C2×D4711yescharacteristic
242#117—471no—
243C2×C4⋊C4—471no—
244#107—471no—
245#106—471no—
246#106—471no—
247C4⋊C8C2×D4711yescharacteristic, complemented
248#102—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252#102—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102—471no—
257#102—471no—
258C22⋊C8C2×D4711yescharacteristic, complemented
259C22⋊C8C2×D4711yescharacteristic, complemented
260#97C2×D4711yescharacteristic, complemented
261C24—941no—
262C24—941no—
263C2×D4—471no—
264C2×D4—471no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—942no—
268C2×D4—942no—
269C2×D4—941no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—1881no—
278C2×D4—1881no—
279C2×D4—1884no—
280C2×D4D18811yescharacteristic
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4C22×D4711yescharacteristic
285C22×C4C22×D4711yescharacteristic
286D8—942no—
287D8—1881no—
288D8—1881no—
289M16—41no—
290C2×C8—41no—
291C2×C8C22×D4711yescharacteristic
292C2×C8C22×D4711yescharacteristic
293C2×C8C22×D4711yescharacteristic
294C2×C8C22×D4711yescharacteristic
295C4⋊C4—471no—
296C4⋊C4—471no—
297C4⋊C4—471no—
298C4⋊C4—471no—
299C4⋊C4—941no—
300C4⋊C4—941no—
301C4⋊C4—941no—
302C4⋊C4D18811yescharacteristic
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4D18811yescharacteristic
311C22⋊C4D18811yescharacteristic
312C42—941no—
313C42C22×D4711yescharacteristic
314C23—941no—
315C23—941no—
316C23—941no—
317C23—941no—
318C23—3761no—
319C23—3761no—
320C23—1882no—
321C23—1882no—
322C23—1882no—
323C23—1882no—
324C23C2×D18811yescharacteristic
325C23C2×D18811yescharacteristic
326D4—22no—
327D4—472no—
328D4—941no—
329D4—941no—
330D4—941no—
331D4—941no—
332D4—941no—
333D4—941no—
334D4—941no—
335D4—3761no—
336D4—3761no—
337D4—1882no—
338D4—1882no—
339D4—1882no—
340D4—1882no—
341D4—1882no—
342D4—1882no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—3761no—
352C2×C4—3761no—
353C2×C4—1882no—
354C2×C4C2×D18811yescharacteristic
355C2×C4C2×D18811yescharacteristic
356C2×C4C2×D18811yescharacteristic
357C2×C4C2×D18811yescharacteristic
358C2×C4C23×D4711yescharacteristic
359C8—21no—
360C8—21no—
361C8—21no—
362C8—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—942no—
369C22—3764no—
370C22—3764no—
371C22—1881no—
372C22—1881no—
373C22—1881no—
374C22—1881no—
375C22—1881no—
376C22—1881no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22#1309405212yes—
383C22C22×D18811yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—1881no—
389C4—1881no—
390C4—1881no—
391C4—1881no—
392C4#41×D4711yescharacteristic
393C4#1309406911yescharacteristic
394C2—22no—
395C2—41no—
396C2—3761no—
397C2—3761no—
398C2—3761no—
399C2—1882no—
400C2#1568976811yescharacteristic
401C2C2×#1309405211yescharacteristic
402C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#435C2
socleC22×C47C22×D4
hypercenter#435D47
hypocenterC47#3318
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #15689819C2semidirect
2. D4×D188C2semidirect
3. #15689488C2semidirect
4. #15689448C2semidirect
5. #15689442C2semidirect
6. #15689424C2semidirect
7. #15689376C2semidirect
8. #15689359C2semidirect
9. #15689319C2semidirect
10. #15689259C2semidirect
11. #15689259C2semidirect
12. #15689236C2semidirect
13. #15689129C2semidirect
14. C2×#13093946C2semidirect
15. C47×#435C2semidirect
20. C2×D376C22semidirect
21. C2×D376C22semidirect
24. #13094016C22semidirect
29. #13093998C22semidirect
30. #13093998C22semidirect
35. C4×D188C22semidirect
37. #13093983C22semidirect
38. C2×C4⋊Dic47C22semidirect
39. #13093958C22semidirect
40. #13093956C22semidirect
41. #13093956C22semidirect
45. #13093946C22semidirect
46. #13093946C22semidirect
47. #13093946C22semidirect
48. #13093946C22semidirect
49. #13093946C22semidirect
50. #13093946C22semidirect
51. #13093946C22semidirect
52. C2×M16×C47C22semidirect
53. C22×C8×C47C22semidirect
55. C4⋊C8×C47C22semidirect
56. C22⋊C8×C47C22semidirect
57. C22⋊C8×C47C22semidirect
58. #97×C47C22semidirect
214. #435D47semidirect
217. C47#3318semidirect
224. C2×M16C2×D47semidirect
225. C22×C8C2×D47semidirect
247. C4⋊C8C2×D47semidirect
258. C22⋊C8C2×D47semidirect
259. C22⋊C8C2×D47semidirect
260. #97C2×D47semidirect