Finite Group Databasebeta

← #20253440

Subgroups — #20253440

Order 6016.

454 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689658C211yesmaximal, characteristic, complemented
2C4×D4×D47C211yesmaximal, characteristic, complemented
3#15689460C211yesmaximal, characteristic, complemented
4#15689443C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689339C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689275C211yesmaximal, characteristic, complemented
9#15689258C211yesmaximal, characteristic
10#15689214C211yesmaximal, characteristic, complemented
11#15689210C211yesmaximal, characteristic, complemented
12#15689205C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689175C211yesmaximal, characteristic, complemented
15C47×#478C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C22×C4×D47—21no—
18C2×#10625325C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×D376C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22#13094019—21no—
23#13094012C2211yescharacteristic, complemented
24#13094009—21no—
25#13094004C2211yescharacteristic
26#13093999C2211yescharacteristic
27#13093989C2211yescharacteristic, complemented
28C4×D188C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30#13093986—21no—
31#13093986C2211yescharacteristic
32#13093986C2211yescharacteristic, complemented
33C4×C22⋊D47—21no—
34(C22⋊D47)⋊C4—21no—
35#13093982—21no—
36C4⋊C4×D47C2211yescharacteristic
37C22⋊C4×D47—21no—
38C42×D47C2211yescharacteristic
39#13093957C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic, complemented
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50C8×Dic47C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52#125×C47C2211yescharacteristic, complemented
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64D4×D47—22no—
65D4×D47—22no—
66C2×D188—21no—
67C2×D188C2311yescharacteristic
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—44no—
74C2×C4×D47D411yescharacteristic
75C2×C4×D47D411yescharacteristic
76C2×C4×D47C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88#10625335—22no—
89#10625334—22no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47D411yescharacteristic
103C4×Dic47D411yescharacteristic
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107D376—22no—
108#10625325—22no—
109C23×C47—21no—
110C22×D47—24no—
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—42no—
114C22×D47—42no—
115C22×D47C2×D411yescharacteristic
116D4×C47—21no—
117D4×C47#4112yes—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—42no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—24no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—42no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132D188—21no—
133D188—21no—
134D188—21no—
135D188—42no—
136D188#4112yes—
137C4×D47—22no—
138C4×D47—21no—
139C4×D47—21no—
140C4×D47—22no—
141C4×D47—42no—
142C4×D47—42no—
143C4×D47—42no—
144C4×D47—42no—
145Dic94—21no—
146Dic94—21no—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—22no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C22×D411yescharacteristic
155C2×D47—21no—
156C2×D47—21no—
157C2×D47—22no—
158C2×D47—48no—
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47#13512yes—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47C2×#4111yescharacteristic
171C4×C47C2×#4111yescharacteristic
172Dic47—21no—
173Dic47—21no—
174Dic47—41no—
175Dic47—41no—
176Dic47AGL(1,ℤ/8)12yes—
177#3105—471nomaximal, Sylow
178C2×C47—42no—
179C2×C47#52511yescharacteristic
180C2×C47C2×#13511yescharacteristic
181C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
182D47—22no—
183D47—42no—
184D47—81no—
185#529—471no—
186C2×C4×D4—471no—
187#484—471no—
188#481—471no—
189#478—471no—
190#478D4711yescharacteristic, complemented
191#463—471no—
192#463—471no—
193#450—471no—
194#447—471no—
195C4×SD16—471no—
196C4×SD16—471no—
197C4×D8—471no—
198C4×D8—471no—
199#431—471no—
200C47#310511yescharacteristic, complemented, Sylow
201C22×D4—471no—
202C23×C4—941no—
203C2×SD16—471no—
204C2×SD16—471no—
205C2×D8—471no—
206C2×D8—471no—
207#126—941no—
208#125C2×D4711yescharacteristic, complemented
209#124—471no—
210#123—941no—
211C22⋊Q8—471no—
212#121—471no—
213C4×Q8—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—471no—
217C4×D4—471no—
218C4×D4—941no—
219C4×D4—941no—
220C4×D4—941no—
221C4×D4C2×D4711yescharacteristic
222#117—941no—
223C2×C4⋊C4—471no—
224C2×C22⋊C4—941no—
225C2×C42—471no—
226#107—471no—
227#107C2×D4711yescharacteristic, complemented
228#106—471no—
229#106C2×D4711yescharacteristic, complemented
230C4⋊C8—471no—
231C4⋊C8C2×D4711yescharacteristic, complemented
232#103—471no—
233#103—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237#102—471no—
238#102C2×D4711yescharacteristic
239#102C2×D4711yescharacteristic
240C22⋊C8—471no—
241C22⋊C8—471no—
242C4×C8—471no—
243C4×C8—471no—
244C24—941no—
245C2×Q8—471no—
246C2×D4—471no—
247C2×D4—471no—
248C2×D4—941no—
249C2×D4—941no—
250C2×D4—942no—
251C2×D4—942no—
252C2×D4C22×D4711yescharacteristic
253C22×C4—21no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—471no—
257C22×C4—941no—
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—1884no—
263SD16—942no—
264SD16—942no—
265D8—942no—
266D8—942no—
267C2×C8—471no—
268C2×C8—471no—
269C2×C8C22×D4711yescharacteristic
270C2×C8C22×D4711yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—471no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4C22×D4711yescharacteristic
278C4⋊C4C22×D4711yescharacteristic
279C4⋊C4C22×D4711yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C42—471no—
290C42—471no—
291C42—471no—
292C42—941no—
293C42C22×D4711yescharacteristic
294C23—21no—
295C23—471no—
296C23—944no—
297C23—941no—
298C23—941no—
299C23—1882no—
300C23—1882no—
301Q8—941no—
302Q8—941no—
303D4—21no—
304D4—472no—
305D4—944no—
306D4—941no—
307D4—941no—
308D4—941no—
309D4—1882no—
310D4#1062535412yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—471no—
316C2×C4—471no—
317C2×C4—471no—
318C2×C4—942no—
319C2×C4—942no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—1882no—
325C2×C4—1882no—
326C2×C4—1882no—
327C2×C4—1882no—
328C2×C4—1882no—
329C2×C4D4×D4711yescharacteristic
330C2×C4D4×D4711yescharacteristic
331C2×C4C23×D4711yescharacteristic
332C8—21no—
333C8—21no—
334C8—941no—
335C8—941no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—472no—
340C22—941no—
341C22—941no—
342C22—942no—
343C22—1888no—
344C22—1881no—
345C22—1881no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22C2×D4×D4711yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—472no—
356C4—941no—
357C4—941no—
358C4—1881no—
359C4—1881no—
360C4#41×D4711yescharacteristic
361C4C2×#1062535411yescharacteristic
362C2—42no—
363C2—942no—
364C2—3761no—
365C2—1882no—
366C2#1568963611yescharacteristic
367C2#135×D4711yescharacteristic
368C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3105
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #15689658C2semidirect
2. C4×D4×D47C2semidirect
3. #15689460C2semidirect
4. #15689443C2semidirect
5. #15689420C2semidirect
6. #15689339C2semidirect
7. #15689338C2semidirect
8. #15689275C2semidirect
10. #15689214C2semidirect
11. #15689210C2semidirect
12. #15689205C2semidirect
13. #15689203C2semidirect
14. #15689175C2semidirect
15. C47×#478C2semidirect
23. #13094012C22semidirect
27. #13093989C22semidirect
32. #13093986C22semidirect
39. #13093957C22semidirect
40. #13093955C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093949C22semidirect
43. #13093947C22semidirect
44. #13093946C22semidirect
47. #13093944C22semidirect
50. C8×Dic47C22semidirect
51. C8×Dic47C22semidirect
52. #125×C47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. C4⋊C8×C47C22semidirect
190. #478D47semidirect
200. C47#3105semidirect
208. #125C2×D47semidirect
227. #107C2×D47semidirect
229. #106C2×D47semidirect
231. C4⋊C8C2×D47semidirect