Finite Group Databasebeta

← #20255403

Subgroups — #20255403

Order 6016.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D188C211yesmaximal, characteristic
2#15689489C211yesmaximal, characteristic, complemented
3#15689447C211yesmaximal, characteristic, complemented
4#15689436C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689323C211yesmaximal, characteristic, complemented
9#15689273C211yesmaximal, characteristic, complemented
10#15689273C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689127C211yesmaximal, characteristic, complemented
14C2×#13093944C211yesmaximal, characteristic, complemented
15C47×#552C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×D4×D47—21no—
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic, complemented
21C2×#10625336C2211yescharacteristic, 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#13093957C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35#13093948C2211yescharacteristic, 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×C47—21no—
50#125×C47C2211yescharacteristic, complemented
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic, complemented
53C22⋊Q8×C47C2211yescharacteristic, complemented
54C4×Q8×C47C2211yescharacteristic, complemented
55C4×D4×C47C2211yescharacteristic
56#117×C47—21no—
57#117×C47C2211yescharacteristic, complemented
58C2×C4⋊C4×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C23×D47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47D411yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68D4×D47—44no—
69C2×D188—22no—
70C2×D188—22no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—41no—
76C2×D188—41no—
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×D188C2311yescharacteristic
80C2×C4×D47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47—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×C47D411yescharacteristic
95C22⋊C4×C47D411yescharacteristic
96C42×C47—21no—
97C42×C47—21no—
98C42×C47C2311yescharacteristic
99#10625336—22no—
100#10625336—41no—
101#10625336—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×C47C2×D411yescharacteristic
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—42no—
121C22×D47—81no—
122C22×D47—81no—
123Q8×C47—21no—
124Q8×C47—21no—
125D4×C47—22no—
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×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—42no—
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2411yescharacteristic
140C22⋊D47—42no—
141C22⋊D47—42no—
142C2×Dic47—21no—
143D188—21no—
144D188—21no—
145D188—21no—
146D188—21no—
147D188—21no—
148D188—42no—
149D188—42no—
150D188—42no—
151D188—81no—
152D188#4112yes—
153C4×D47—42no—
154C47⋊C8—21no—
155C47⋊C8—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47AGL(1,ℤ/8)12yes—
164C22×C47C22×D411yescharacteristic
165C2×D47—22no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—84no—
175C2×D47—84no—
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47—41no—
184C4×C47C2×#4111yescharacteristic
185C4×C47H(5,𝔽2)11yescharacteristic
186Dic47—41no—
187#3310—471nomaximal, Sylow
188C2×C47—22no—
189C2×C47—41no—
190C2×C47#54611yescharacteristic
191C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C47#57711yescharacteristic
193D47—42no—
194D47—81no—
195D47—81no—
196#552D4711yescharacteristic, complemented
197D42—471no—
198#490—471no—
199#482—471no—
200#480—471no—
201#478—471no—
202#468—471no—
203#465—471no—
204#460—471no—
205#450—471no—
206#450—471no—
207#440—471no—
208#435—471no—
209#418—471no—
210C2×#102—471no—
211C47#331011yescharacteristic, complemented, Sylow
212C22×D4—471no—
213C22×D4—471no—
214C22×D4—941no—
215C2×SD16—471no—
216C2×SD16—471no—
217C2×SD16—471no—
218C2×M16—471no—
219C22×C8—471no—
220#127—471no—
221#126—21no—
222#125—21no—
223#125C2×D4711yescharacteristic, complemented
224#123—21no—
225C22⋊Q8C2×D4711yescharacteristic, complemented
226C22⋊Q8C2×D4711yescharacteristic, complemented
227#121—471no—
228#121—471no—
229#121—941no—
230#120—941no—
231#120—941no—
232C4×Q8C2×D4711yescharacteristic, complemented
233C4×D4—471no—
234C4×D4C2×D4711yescharacteristic
235#117—21no—
236#117C2×D4711yescharacteristic, complemented
237C2×C4⋊C4C2×D4711yescharacteristic, complemented
238#107—471no—
239#107—471no—
240#106—471no—
241C4⋊C8—471no—
242#103—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252C22⋊C8—471no—
253C22⋊C8—471no—
254#97—471no—
255C24—941no—
256C24—941no—
257C2×Q8C22×D4711yescharacteristic
258C2×D4—471no—
259C2×D4—471no—
260C2×D4—471no—
261C2×D4—942no—
262C2×D4—942no—
263C2×D4—941no—
264C2×D4—941no—
265C2×D4—941no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—1881no—
270C2×D4—1881no—
271C2×D4—1884no—
272C2×D4C22⋊D4711yescharacteristic
273C22×C4—21no—
274C22×C4—941no—
275C22×C4C22×D4711yescharacteristic
276C22×C4C22×D4711yescharacteristic
277SD16—942no—
278SD16—1881no—
279SD16—1881no—
280M16—1881no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8—471no—
285C2×C8—1881no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—471no—
293C4⋊C4C22⋊D4711yescharacteristic
294C4⋊C4C22×D4711yescharacteristic
295C4⋊C4C22×D4711yescharacteristic
296C4⋊C4C22×D4711yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4C22⋊D4711yescharacteristic
304C22⋊C4C22⋊D4711yescharacteristic
305C42—21no—
306C42—21no—
307C42C22×D4711yescharacteristic
308C23—941no—
309C23—941no—
310C23—941no—
311C23—3761no—
312C23—3761no—
313C23—1882no—
314C23—1882no—
315C23—1882no—
316C23—1882no—
317C23C2×C22⋊D4711yescharacteristic
318C23C2×C22⋊D4711yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—22no—
322D4—472no—
323D4—941no—
324D4—941no—
325D4—941no—
326D4—941no—
327D4—941no—
328D4—3761no—
329D4—1882no—
330D4—1882no—
331D4—1882no—
332D4—1882no—
333D4—1882no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—941no—
344C2×C4—1882no—
345C2×C4C2×C22⋊D4711yescharacteristic
346C2×C4C2×C22⋊D4711yescharacteristic
347C2×C4C2×C22⋊D4711yescharacteristic
348C2×C4C2×C22⋊D4711yescharacteristic
349C2×C4C23×D4711yescharacteristic
350C8—941no—
351C8—941no—
352C8—941no—
353C8—941no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—942no—
360C22—3764no—
361C22—3764no—
362C22—1881no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22#1309404912yes—
371C22C22×C22⋊D4711yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1881no—
381C4#41×D4711yescharacteristic
382C4#1309407011yescharacteristic
383C2—22no—
384C2—41no—
385C2—3761no—
386C2—3761no—
387C2—1882no—
388C2#1568976111yescharacteristic
389C2C2×#1309404911yescharacteristic
390C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#552C2
socleC22×C47C22×D4
hypercenter#552D47
hypocenterC47#3310
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #15689489C2semidirect
3. #15689447C2semidirect
4. #15689436C2semidirect
5. #15689420C2semidirect
6. #15689371C2semidirect
7. #15689354C2semidirect
8. #15689323C2semidirect
9. #15689273C2semidirect
10. #15689273C2semidirect
11. #15689221C2semidirect
12. #15689195C2semidirect
13. #15689127C2semidirect
14. C2×#13093944C2semidirect
15. C47×#552C2semidirect
20. C2×#10625336C22semidirect
21. C2×#10625336C22semidirect
22. C2×#10625329C22semidirect
23. C22×C47⋊C8C22semidirect
31. #13093957C22semidirect
32. #13093957C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. #13093948C22semidirect
39. #13093944C22semidirect
40. #13093944C22semidirect
41. #13093944C22semidirect
42. #13093944C22semidirect
43. #13093944C22semidirect
44. #13093944C22semidirect
45. C22⋊(C47⋊C8)C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. #13093935C22semidirect
50. #125×C47C22semidirect
52. C22⋊Q8×C47C22semidirect
53. C22⋊Q8×C47C22semidirect
54. C4×Q8×C47C22semidirect
57. #117×C47C22semidirect
58. C2×C4⋊C4×C47C22semidirect
196. #552D47semidirect
211. C47#3310semidirect
223. #125C2×D47semidirect
225. C22⋊Q8C2×D47semidirect
226. C22⋊Q8C2×D47semidirect
232. C4×Q8C2×D47semidirect
236. #117C2×D47semidirect
237. C2×C4⋊C4C2×D47semidirect