Finite Group Databasebeta

← #20255523

Subgroups — #20255523

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
1D4×D188C211yesmaximal, characteristic, complemented
2#15689489C211yesmaximal, characteristic, complemented
3#15689447C211yesmaximal, characteristic, complemented
4#15689441C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689374C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689318C211yesmaximal, characteristic, complemented
9#15689256C211yesmaximal, characteristic, complemented
10#15689256C211yesmaximal, characteristic, complemented
11#15689233C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689127C211yesmaximal, characteristic, complemented
14C2×#13093944C211yesmaximal, characteristic, complemented
15C47×#553C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×D4×D47—21no—
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic, complemented
21C2×#10625334C2211yescharacteristic, complemented
22C2×#10625329C2211yescharacteristic, complemented
23C22×C47⋊C8C2211yescharacteristic, complemented
24#13094021C2211yescharacteristic
25#13093999—21no—
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic
28#13093994—21no—
29#13093994—21no—
30C4×D188C2211yescharacteristic
31#13093957C2211yescharacteristic, complemented
32#13093955C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35#13093945C2211yescharacteristic, complemented
36#13093944C2211yescharacteristic
37#13093944C2211yescharacteristic
38#13093944C2211yescharacteristic
39#13093944C2211yescharacteristic, complemented
40#13093944C2211yescharacteristic, complemented
41#13093944C2211yescharacteristic, complemented
42#13093944C2211yescharacteristic, complemented
43#13093944C2211yescharacteristic, complemented
44#13093944C2211yescharacteristic, complemented
45C22⋊(C47⋊C8)C2211yescharacteristic, complemented
46C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47#13093935C2211yescharacteristic, complemented
48#126×C47—21no—
49#125×C47C2211yescharacteristic, complemented
50#123×C47—21no—
51#121×C47—21no—
52#121×C47C2211yescharacteristic, complemented
53#121×C47C2211yescharacteristic, complemented
54C4×D4×C47—21no—
55C4×D4×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic, complemented
57#117×C47C2211yescharacteristic, complemented
58C2×C4⋊C4×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47D411yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71D4×D47—44no—
72C2×D188—22no—
73C2×D188—22no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—41no—
79C2×D188—41no—
80C2×D188C2311yescharacteristic
81C2×D188C2311yescharacteristic
82C2×D188C2311yescharacteristic
83C2×C4×D47—21no—
84C4⋊C4×C47—21no—
85C4⋊C4×C47—21no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47D411yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2311yescharacteristic
90C4⋊C4×C47C2311yescharacteristic
91C22⋊C4×C47—21no—
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47D411yescharacteristic
96C22⋊C4×C47D411yescharacteristic
97C42×C47—21no—
98C42×C47C2311yescharacteristic
99#10625334—22no—
100#10625334—41no—
101#10625334—41no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105C4⋊Dic47C2311yescharacteristic
106#10625329—41no—
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C23×C47C2×D411yescharacteristic
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—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—42no—
128D4×C47—81no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—81no—
137C2×C4×C47—81no—
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2411yescharacteristic
143C22⋊D47—42no—
144C22⋊D47—42no—
145C2×Dic47—21no—
146D188—21no—
147D188—21no—
148D188—21no—
149D188—21no—
150D188—21no—
151D188—42no—
152D188—42no—
153D188—42no—
154D188—81no—
155D188#4112yes—
156C4×D47—42no—
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—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47AGL(1,ℤ/8)12yes—
170C22×C47C22×D411yescharacteristic
171C2×D47—22no—
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×C47—41no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47C2×#4111yescharacteristic
190C4×C47H(5,𝔽2)11yescharacteristic
191Dic47—41no—
192#3318—471nomaximal, Sylow
193C2×C47—22no—
194C2×C47—41no—
195C2×C47—81no—
196C2×C47#54611yescharacteristic
197C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C47#57611yescharacteristic
199D47—42no—
200D47—81no—
201D47—81no—
202#553D4711yescharacteristic, complemented
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#435—471no—
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×M16—471no—
225C22×C8—471no—
226#127—471no—
227#126—21no—
228#125C2×D4711yescharacteristic, complemented
229#123—21no—
230#121—21no—
231#121—471no—
232#121—471no—
233#121—941no—
234#121C2×D4711yescharacteristic, complemented
235#121C2×D4711yescharacteristic, complemented
236#120—941no—
237#120—941no—
238C4×D4—21no—
239C4×D4—471no—
240C4×D4C2×D4711yescharacteristic
241C4×D4C2×D4711yescharacteristic, complemented
242#117C2×D4711yescharacteristic, complemented
243C2×C4⋊C4C2×D4711yescharacteristic, complemented
244#107—471no—
245#106—471no—
246#106—471no—
247C4⋊C8—471no—
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⋊C8—471no—
259C22⋊C8—471no—
260#97—471no—
261C24—941no—
262C24—941no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—471no—
268C2×D4—942no—
269C2×D4—942no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—1881no—
277C2×D4—1881no—
278C2×D4—1884no—
279C2×D4C22⋊D4711yescharacteristic
280C2×D4C22×D4711yescharacteristic
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—941no—
284C22×C4C22×D4711yescharacteristic
285C22×C4C22×D4711yescharacteristic
286D8—942no—
287D8—1881no—
288D8—1881no—
289M16—1881no—
290C2×C8—471no—
291C2×C8—471no—
292C2×C8—471no—
293C2×C8—471no—
294C2×C8—1881no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—471no—
299C4⋊C4C22⋊D4711yescharacteristic
300C4⋊C4C22×D4711yescharacteristic
301C4⋊C4C22×D4711yescharacteristic
302C4⋊C4C22×D4711yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4C22⋊D4711yescharacteristic
311C22⋊C4C22⋊D4711yescharacteristic
312C42—21no—
313C42C22×D4711yescharacteristic
314C23—21no—
315C23—941no—
316C23—941no—
317C23—941no—
318C23—3761no—
319C23—3761no—
320C23—1882no—
321C23—1882no—
322C23—1882no—
323C23—1882no—
324C23C2×C22⋊D4711yescharacteristic
325C23C2×C22⋊D4711yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—42no—
330D4—81no—
331D4—472no—
332D4—941no—
333D4—941no—
334D4—941no—
335D4—941no—
336D4—941no—
337D4—3761no—
338D4—1882no—
339D4—1882no—
340D4—1882no—
341D4—1882no—
342D4—1882no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—941no—
353C2×C4—1882no—
354C2×C4C2×C22⋊D4711yescharacteristic
355C2×C4C2×C22⋊D4711yescharacteristic
356C2×C4C2×C22⋊D4711yescharacteristic
357C2×C4C2×C22⋊D4711yescharacteristic
358C2×C4C23×D4711yescharacteristic
359C8—941no—
360C8—941no—
361C8—941no—
362C8—941no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—942no—
372C22—3764no—
373C22—3764no—
374C22—1881no—
375C22—1881no—
376C22—1881no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22#1309404912yes—
383C22C22×C22⋊D4711yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—1881no—
392C4#41×D4711yescharacteristic
393C4#1309407011yescharacteristic
394C2—22no—
395C2—41no—
396C2—81no—
397C2—3761no—
398C2—3761no—
399C2—1882no—
400C2#1568976111yescharacteristic
401C2C2×#1309404911yescharacteristic
402C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#553C2
socleC22×C47C22×D4
hypercenter#553D47
hypocenterC47#3318
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×D188C2semidirect
2. #15689489C2semidirect
3. #15689447C2semidirect
4. #15689441C2semidirect
5. #15689420C2semidirect
6. #15689374C2semidirect
7. #15689357C2semidirect
8. #15689318C2semidirect
9. #15689256C2semidirect
10. #15689256C2semidirect
11. #15689233C2semidirect
12. #15689195C2semidirect
13. #15689127C2semidirect
14. C2×#13093944C2semidirect
15. C47×#553C2semidirect
20. C2×#10625334C22semidirect
21. C2×#10625334C22semidirect
22. C2×#10625329C22semidirect
23. C22×C47⋊C8C22semidirect
31. #13093957C22semidirect
32. #13093955C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. #13093945C22semidirect
39. #13093944C22semidirect
40. #13093944C22semidirect
41. #13093944C22semidirect
42. #13093944C22semidirect
43. #13093944C22semidirect
44. #13093944C22semidirect
45. C22⋊(C47⋊C8)C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. #13093935C22semidirect
49. #125×C47C22semidirect
52. #121×C47C22semidirect
53. #121×C47C22semidirect
56. C4×D4×C47C22semidirect
57. #117×C47C22semidirect
58. C2×C4⋊C4×C47C22semidirect
202. #553D47semidirect
217. C47#3318semidirect
228. #125C2×D47semidirect
234. #121C2×D47semidirect
235. #121C2×D47semidirect
241. C4×D4C2×D47semidirect
242. #117C2×D47semidirect
243. C2×C4⋊C4C2×D47semidirect