Finite Group Databasebeta

← #20255529

Subgroups — #20255529

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
2#15689487C211yesmaximal, characteristic, complemented
3#15689444C211yesmaximal, characteristic, complemented
4#15689439C211yesmaximal, characteristic, complemented
5#15689423C211yesmaximal, characteristic, complemented
6#15689374C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689315C211yesmaximal, characteristic, complemented
9#15689257C211yesmaximal, characteristic, complemented
10#15689257C211yesmaximal, characteristic, complemented
11#15689233C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689128C211yesmaximal, characteristic, complemented
14C2×#13093945C211yesmaximal, characteristic, complemented
15D42×C47C211yesmaximal, characteristic, complemented
16C2×#10625334C2211yescharacteristic
17C2×#10625334C2211yescharacteristic, complemented
18C2×#10625334C2211yescharacteristic, complemented
19C2×#10625329C2211yescharacteristic, complemented
20C22×C47⋊C8C2211yescharacteristic, complemented
21#13094019—21no—
22#13094016C2211yescharacteristic, complemented
23#13094006—21no—
24#13093998C2211yescharacteristic, complemented
25#13093998C2211yescharacteristic, complemented
26#13093996—21no—
27C4×D188C2211yescharacteristic, complemented
28(C22⋊D47)⋊C4—21no—
29#13093983C2211yescharacteristic, complemented
30C2×C4⋊Dic47C2211yescharacteristic, complemented
31#13093957C2211yescharacteristic, complemented
32#13093955C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35#13093945C2211yescharacteristic
36#13093945C2211yescharacteristic
37#13093945C2211yescharacteristic
38#13093945C2211yescharacteristic, complemented
39#13093945C2211yescharacteristic, complemented
40#13093945C2211yescharacteristic, complemented
41#13093945C2211yescharacteristic, complemented
42#13093945C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic, complemented
44#13093944C2211yescharacteristic, complemented
45C22⋊(C47⋊C8)C2211yescharacteristic, complemented
46C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47#13093935C2211yescharacteristic, complemented
48C22×D4×C47—21no—
49C22×D4×C47C2211yescharacteristic
50C22×D4×C47C2211yescharacteristic
51#127×C47C2211yescharacteristic
52#121×C47—21no—
53#121×C47C2211yescharacteristic
54#121×C47C2211yescharacteristic
55#120×C47—21no—
56#120×C47—21no—
57C4×D4×C47C2211yescharacteristic
58C4×D4×C47C2211yescharacteristic
59C24×C47—21no—
60C24×C47—21no—
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—41no—
70C2×D4×C47—41no—
71C2×D4×C47—44no—
72C2×D4×C47D411yescharacteristic
73C2×D4×C47C2311yescharacteristic
74C2×D4×C47C2311yescharacteristic
75C2×D4×C47C2311yescharacteristic
76C22×C4×C47—21no—
77C22×C4×C47C2311yescharacteristic
78C22×C4×C47C2311yescharacteristic
79C2×C22⋊D47—21no—
80C2×C22⋊D47—21no—
81C22×Dic47—21no—
82C2×D188C2311yescharacteristic
83C2×C4×D47—21no—
84C4⋊C4×C47D411yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊C4×C47D411yescharacteristic
90C22⋊C4×C47D411yescharacteristic
91C42×C47C2311yescharacteristic
92C22⋊Dic47—21no—
93#10625334—22no—
94#10625334—41no—
95#10625334—41no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105C4×Dic47—21no—
106#10625329—41no—
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—42no—
116C23×C47—42no—
117C23×C47—42no—
118C23×C47—42no—
119C23×C47—81no—
120C23×C47—81no—
121C23×C47C2×D411yescharacteristic
122C23×C47C2×D411yescharacteristic
123C22×D47—21no—
124D4×C47—22no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—21no—
130D4×C47—42no—
131D4×C47—42no—
132D4×C47—42no—
133D4×C47—42no—
134D4×C47—42no—
135D4×C47—81no—
136D4×C47#4112yes—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—42no—
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2411yescharacteristic
148C22⋊D47—42no—
149C22⋊D47—81no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—81no—
154D188—21no—
155D188—21no—
156C4×D47—81no—
157C47⋊C8—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—22no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—84no—
176C22×C47—84no—
177C22×C47AGL(1,ℤ/8)12yes—
178C22×C47C22×D411yescharacteristic
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—41no—
187C4×C47C2×#4111yescharacteristic
188C4×C47H(5,𝔽2)11yescharacteristic
189Dic47—41no—
190Dic47—41no—
191Dic47—41no—
192#3318—471nomaximal, Sylow
193C2×C47—22no—
194C2×C47—41no—
195C2×C47—42no—
196C2×C47—81no—
197C2×C47—81no—
198C2×C47#54611yescharacteristic
199C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
200C2×C47#57611yescharacteristic
201D47—81no—
202#553—471no—
203D42D4711yescharacteristic, complemented
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—21no—
219C22×D4C2×D4711yescharacteristic
220C22×D4C2×D4711yescharacteristic
221C2×D8—471no—
222C2×D8—471no—
223C2×D8—471no—
224C2×M16—471no—
225C22×C8—471no—
226#127C2×D4711yescharacteristic
227#126—941no—
228#125—471no—
229#123—941no—
230#121—21no—
231#121—471no—
232#121—471no—
233#121—941no—
234#121C2×D4711yescharacteristic
235#121C2×D4711yescharacteristic
236#120—21no—
237#120—21no—
238C4×D4—471no—
239C4×D4—941no—
240C4×D4C2×D4711yescharacteristic
241C4×D4C2×D4711yescharacteristic
242#117—471no—
243C2×C4⋊C4—471no—
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—21no—
262C24—21no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—44no—
274C2×D4—471no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4C22⋊D4711yescharacteristic
278C2×D4C22×D4711yescharacteristic
279C2×D4C22×D4711yescharacteristic
280C2×D4C22×D4711yescharacteristic
281C22×C4—21no—
282C22×C4—941no—
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—471no—
296C4⋊C4—471no—
297C4⋊C4—471no—
298C4⋊C4—941no—
299C4⋊C4—941no—
300C4⋊C4—941no—
301C4⋊C4C22⋊D4711yescharacteristic
302C4⋊C4C22×D4711yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4C22⋊D4711yescharacteristic
311C22⋊C4C22⋊D4711yescharacteristic
312C42—941no—
313C42C22×D4711yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—941no—
324C23C2×C22⋊D4711yescharacteristic
325C23C2×C22⋊D4711yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—81no—
338D4—941no—
339D4—941no—
340D4—3761no—
341D4—1882no—
342D4#1062535212yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—3761no—
353C2×C4—3761no—
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—22no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—84no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22#1309405012yes—
383C22C22×C22⋊D4711yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—1881no—
390C4—1881no—
391C4—1881no—
392C4C2×#1062535211yescharacteristic
393C4#1309406911yescharacteristic
394C2—22no—
395C2—41no—
396C2—42no—
397C2—81no—
398C2—81no—
399C2—3761no—
400C2#1568976711yescharacteristic
401C2C2×#1309405011yescharacteristic
402C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD42×C47C2
socleC22×C47C22×D4
hypercenterD42D47
hypocenterC47#3318
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #15689819C2semidirect
2. #15689487C2semidirect
3. #15689444C2semidirect
4. #15689439C2semidirect
5. #15689423C2semidirect
6. #15689374C2semidirect
7. #15689357C2semidirect
8. #15689315C2semidirect
9. #15689257C2semidirect
10. #15689257C2semidirect
11. #15689233C2semidirect
12. #15689195C2semidirect
13. #15689128C2semidirect
14. C2×#13093945C2semidirect
15. D42×C47C2semidirect
17. C2×#10625334C22semidirect
18. C2×#10625334C22semidirect
19. C2×#10625329C22semidirect
20. C22×C47⋊C8C22semidirect
22. #13094016C22semidirect
24. #13093998C22semidirect
25. #13093998C22semidirect
27. C4×D188C22semidirect
29. #13093983C22semidirect
30. C2×C4⋊Dic47C22semidirect
31. #13093957C22semidirect
32. #13093955C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
38. #13093945C22semidirect
39. #13093945C22semidirect
40. #13093945C22semidirect
41. #13093945C22semidirect
42. #13093945C22semidirect
43. #13093945C22semidirect
44. #13093944C22semidirect
45. C22⋊(C47⋊C8)C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. #13093935C22semidirect
203. D42D47semidirect
217. C47#3318semidirect