Finite Group Databasebeta

← #20255409

Subgroups — #20255409

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
1#15689813C211yesmaximal, characteristic, complemented
2#15689487C211yesmaximal, characteristic, complemented
3#15689444C211yesmaximal, characteristic, complemented
4#15689434C211yesmaximal, characteristic, complemented
5#15689423C211yesmaximal, characteristic, complemented
6#15689367C211yesmaximal, characteristic, complemented
7#15689350C211yesmaximal, characteristic, complemented
8#15689320C211yesmaximal, characteristic, complemented
9#15689274C211yesmaximal, characteristic, complemented
10#15689274C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689128C211yesmaximal, characteristic, complemented
14C2×#13093945C211yesmaximal, characteristic, complemented
15D42×C47C211yesmaximal, characteristic
16C2×#10625335C2211yescharacteristic
17C2×#10625335C2211yescharacteristic, complemented
18C2×#10625335C2211yescharacteristic, complemented
19C2×#10625329C2211yescharacteristic, complemented
20C22×C47⋊C8C2211yescharacteristic, complemented
21#13094017—21no—
22#13094016C2211yescharacteristic, complemented
23#13094014—21no—
24#13094005—21no—
25#13094003C2211yescharacteristic, complemented
26#13094003C2211yescharacteristic, complemented
27C4×Dic94C2211yescharacteristic, complemented
28#13093983C2211yescharacteristic, complemented
29#13093980—21no—
30C2×C4⋊Dic47C2211yescharacteristic, complemented
31#13093957C2211yescharacteristic, complemented
32#13093957C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35#13093947C2211yescharacteristic, complemented
36#13093945C2211yescharacteristic
37#13093945C2211yescharacteristic
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic, complemented
40#13093945C2211yescharacteristic, complemented
41#13093945C2211yescharacteristic, complemented
42#13093945C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic, 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
79C22×Dic47—21no—
80C2×Dic94C2311yescharacteristic
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47D411yescharacteristic
87C22⋊C4×C47D411yescharacteristic
88C42×C47C2311yescharacteristic
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92#10625335—22no—
93#10625335—41no—
94#10625335—41no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—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
123D4×C47—22no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—42no—
130D4×C47—42no—
131D4×C47—42no—
132D4×C47—42no—
133D4×C47—42no—
134D4×C47—81no—
135D4×C47#4112yes—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—42no—
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2411yescharacteristic
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—42no—
152Dic94—21no—
153Dic94—21no—
154C47⋊C8—21no—
155C47⋊C8—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—22no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—84no—
173C22×C47—84no—
174C22×C47AGL(1,ℤ/8)12yes—
175C22×C47C22×D411yescharacteristic
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—41no—
181C4×C47C2×#4111yescharacteristic
182C4×C47H(5,𝔽2)11yescharacteristic
183Dic47—41no—
184Dic47—41no—
185Dic47—41no—
186Dic47—41no—
187#3310—471nomaximal, Sylow
188C2×C47—22no—
189C2×C47—41no—
190C2×C47—42no—
191C2×C47—81no—
192C2×C47—81no—
193C2×C47#54611yescharacteristic
194C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C47#57711yescharacteristic
196#552—471no—
197D42D4711yescharacteristic
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—21no—
213C22×D4C2×D4711yescharacteristic
214C22×D4C2×D4711yescharacteristic
215C2×SD16—471no—
216C2×SD16—471no—
217C2×SD16—471no—
218C2×M16—471no—
219C22×C8—471no—
220#127C2×D4711yescharacteristic
221#126—941no—
222#125—471no—
223#125—941no—
224#123—941no—
225C22⋊Q8—471no—
226C22⋊Q8—471no—
227#121—21no—
228#121C2×D4711yescharacteristic
229#121C2×D4711yescharacteristic
230#120—21no—
231#120—21no—
232C4×Q8—471no—
233C4×D4C2×D4711yescharacteristic
234C4×D4C2×D4711yescharacteristic
235#117—471no—
236#117—941no—
237C2×C4⋊C4—471no—
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—21no—
256C24—21no—
257C2×Q8—471no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D4711yescharacteristic
270C2×D4C22×D4711yescharacteristic
271C2×D4C22×D4711yescharacteristic
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—471no—
287C4⋊C4—471no—
288C4⋊C4—471no—
289C4⋊C4—941no—
290C4⋊C4—941no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4—941no—
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—941no—
306C42—941no—
307C42C22×D4711yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D4711yescharacteristic
318C23C2×C22⋊D4711yescharacteristic
319Q8—941no—
320Q8—941no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#1062535212yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
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—22no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#1309405012yes—
371C22C22×C22⋊D4711yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—1881no—
378C4—1881no—
379C4—1881no—
380C4—1881no—
381C4C2×#1062535211yescharacteristic
382C4#1309406911yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#1568976711yescharacteristic
389C2C2×#1309405011yescharacteristic
390C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD42×C47C2
socleC22×C47C22×D4
hypercenterD42D47
hypocenterC47#3310
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. #15689813C2semidirect
2. #15689487C2semidirect
3. #15689444C2semidirect
4. #15689434C2semidirect
5. #15689423C2semidirect
6. #15689367C2semidirect
7. #15689350C2semidirect
8. #15689320C2semidirect
9. #15689274C2semidirect
10. #15689274C2semidirect
11. #15689223C2semidirect
12. #15689195C2semidirect
13. #15689128C2semidirect
14. C2×#13093945C2semidirect
17. C2×#10625335C22semidirect
18. C2×#10625335C22semidirect
19. C2×#10625329C22semidirect
20. C22×C47⋊C8C22semidirect
22. #13094016C22semidirect
25. #13094003C22semidirect
26. #13094003C22semidirect
27. C4×Dic94C22semidirect
28. #13093983C22semidirect
30. C2×C4⋊Dic47C22semidirect
31. #13093957C22semidirect
32. #13093957C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. #13093947C22semidirect
39. #13093945C22semidirect
40. #13093945C22semidirect
41. #13093945C22semidirect
42. #13093945C22semidirect
43. #13093945C22semidirect
44. #13093945C22semidirect
45. C22⋊(C47⋊C8)C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. #13093935C22semidirect
211. C47#3310semidirect