Finite Group Databasebeta

← #20254407

Subgroups — #20254407

Order 6016.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#127×D47C211yesmaximal, characteristic, complemented
2#15689658C211yesmaximal, characteristic, complemented
3#15689512C211yesmaximal, characteristic, complemented
4#15689510C211yesmaximal, characteristic, complemented
5#15689489C211yesmaximal, characteristic, complemented
6#15689322C212yesmaximal, complemented
7#15689317C212yesmaximal, complemented
8#15689275C212yesmaximal, complemented
9#15689258C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic, complemented
11C47×#490C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47—21no—
14C2×D4×D47C2212yes—
15C2×#10625325C2212yescomplemented
16C2×#10625335C2212yescomplemented
17C2×D376C2212yescomplemented
18C2×#10625334C2212yescomplemented
19#13094021C2211yescharacteristic
20#13094020—21no—
21#13094020—21no—
22#13094020C2212yes—
23#13094019—21no—
24#13094012C2211yescharacteristic, complemented
25#13094009—21no—
26#13094004C2211yescharacteristic
27#13093999C2211yescharacteristic
28#13093989C2211yescharacteristic, complemented
29#13093986—21no—
30#13093986C2211yescharacteristic, complemented
31#13093982—21no—
32C42×D47C2211yescharacteristic
33Dic47⋊C8C2212yescomplemented
34#13093944C2212yescomplemented
35#13093944C2212yescomplemented
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic, complemented
38#127×C47C2211yescharacteristic
39#125×C47C2211yescharacteristic, complemented
40#102×C47C2212yescomplemented
41#102×C47C2212yescomplemented
42#97×C47C2211yescharacteristic, complemented
43C23×D47—22no—
44C2×D4×C47—21no—
45C2×D4×C47—21no—
46C2×D4×C47C2312yes—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—22no—
50D4×D47—42no—
51D4×D47—42no—
52D4×D47—44no—
53D4×D47—44no—
54C2×D188—21no—
55C2×D188—21no—
56C2×D188—21no—
57C2×D188C2312yes—
58C2×D188C2311yescharacteristic
59C2×C4×D47—21no—
60C2×C4×D47D411yescharacteristic
61C2×C4×D47D411yescharacteristic
62C2×C4×D47C2311yescharacteristic
63C2×Dic94C2311yescharacteristic
64C2×C8×C47C2312yes—
65C4⋊C4×C47—21no—
66C4⋊C4×C47—21no—
67C4⋊C4×C47C2311yescharacteristic
68C4⋊C4×C47C2311yescharacteristic
69C42×C47C2311yescharacteristic
70#10625335—42no—
71#10625334—42no—
72(C2×D47)⋊C4—21no—
73(C2×D47)⋊C4—21no—
74(C2×D47)⋊C4—21no—
75(C2×D47)⋊C4—21no—
76(C2×D47)⋊C4—21no—
77C4⋊Dic47—21no—
78Dic47⋊C4—21no—
79C4×Dic47—21no—
80C4×Dic47D411yescharacteristic
81C4×Dic47D411yescharacteristic
82C4×Dic47C2311yescharacteristic
83C2×C47⋊C8C2312yes—
84D376—42no—
85#10625325—42no—
86C23×C47—22no—
87C22×D47—21no—
88C22×D47—22no—
89C22×D47—44no—
90C22×D47—44no—
91C22×D47—44no—
92C22×D47C2×D411yescharacteristic
93D4×C47—22no—
94D4×C47—22no—
95D4×C47—42no—
96D4×C47—42no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2411yescharacteristic
102C22⋊D47—44no—
103C22⋊D47—44no—
104C22⋊D47—44no—
105C2×Dic47—21no—
106C2×Dic47C2×D411yescharacteristic
107C2×Dic47C2×D411yescharacteristic
108C2×Dic47C2×D411yescharacteristic
109D188—22no—
110D188—22no—
111D188—22no—
112D188—42no—
113D188—42no—
114D188—42no—
115C4×D47—22no—
116C4×D47—22no—
117C4×D47—22no—
118C4×D47—42no—
119Dic94—22no—
120C8×C47—22no—
121C47⋊C8—22no—
122C22×C47—42no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47C22×D411yescharacteristic
126C2×D47—21no—
127C2×D47—21no—
128C2×D47—42no—
129C2×D47—41no—
130C2×D47—41no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—41no—
134C2×D47—88no—
135C2×D47AGL(1,ℤ/8)12yes—
136C4×C47—21no—
137C4×C47—21no—
138C4×C47—41no—
139C4×C47—41no—
140C4×C47H(5,𝔽2)12yes—
141Dic47—21no—
142Dic47—21no—
143Dic47—41no—
144Dic47AGL(1,ℤ/8)12yes—
145#3217—471nomaximal, Sylow
146C2×C47—82no—
147C2×C47#53511yescharacteristic
148C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
150D47—22no—
151D47—81no—
152D47—82no—
153C2×#127—471no—
154#529—471no—
155#496—471no—
156#496—471no—
157#490—471no—
158#490D4711yescharacteristic, complemented
159#460—472no—
160#459—472no—
161#450—472no—
162#447—472no—
163#432—471no—
164C47#321711yescharacteristic, complemented, Sylow
165C22×D4—472no—
166C22×D4—941no—
167C22×D4—941no—
168C2×SD16—472no—
169C2×SD16—472no—
170C2×D8—472no—
171C2×D8—472no—
172#127—472no—
173#127—471no—
174#127—941no—
175#127—941no—
176#127C2×D4711yescharacteristic
177#126—941no—
178#125C2×D4711yescharacteristic, complemented
179#124—471no—
180#123—941no—
181C22⋊Q8—471no—
182#121—471no—
183C4×Q8—471no—
184C4×D4—471no—
185C4×D4—941no—
186#117—941no—
187C2×C42—471no—
188C4⋊C8—472no—
189#102—472no—
190#102—472no—
191#102C2×D4712yescomplemented
192#102C2×D4712yescomplemented
193C22⋊C8—472no—
194#97—471no—
195#97C2×D4711yescharacteristic, complemented
196C24—942no—
197C2×Q8—471no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—472no—
201C2×D4—471no—
202C2×D4—941no—
203C2×D4—942no—
204C2×D4—942no—
205C2×D4—942no—
206C2×D4—941no—
207C2×D4—941no—
208C2×D4—1882no—
209C2×D4—1882no—
210C2×D4—1884no—
211C2×D4—1884no—
212C2×D4C22×D4712yes—
213C22×C4—471no—
214C22×C4—471no—
215C22×C4—471no—
216C22×C4—941no—
217SD16—1882no—
218SD16—1882no—
219D8—1882no—
220D8—1882no—
221C2×C8—472no—
222C2×C8C22×D4712yes—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—941no—
226C4⋊C4—941no—
227C4⋊C4C22×D4711yescharacteristic
228C4⋊C4C22×D4711yescharacteristic
229C22⋊C4—941no—
230C22⋊C4—941no—
231C22⋊C4—941no—
232C22⋊C4—941no—
233C22⋊C4—941no—
234C42—471no—
235C42—471no—
236C42—471no—
237C42—941no—
238C42C22×D4711yescharacteristic
239C23—22no—
240C23—471no—
241C23—941no—
242C23—942no—
243C23—1884no—
244C23—1884no—
245C23—1884no—
246Q8—942no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—42no—
251D4—942no—
252D4—942no—
253D4—942no—
254D4—1882no—
255D4—1882no—
256D4—1882no—
257D4—1884no—
258D4—1884no—
259D4—1884no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—471no—
263C2×C4—471no—
264C2×C4—471no—
265C2×C4—942no—
266C2×C4—942no—
267C2×C4—942no—
268C2×C4—941no—
269C2×C4—1882no—
270C2×C4D4×D4711yescharacteristic
271C2×C4D4×D4711yescharacteristic
272C2×C4C23×D4711yescharacteristic
273C8—22no—
274C8—942no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—472no—
279C22—941no—
280C22—941no—
281C22—3768no—
282C22—1881no—
283C22—1882no—
284C22—1882no—
285C22—1881no—
286C22—1882no—
287C22—1881no—
288C22C2×D4×D4711yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—472no—
294C4—941no—
295C4—941no—
296C4—1881no—
297C4#1309407012yes—
298C2—82no—
299C2—942no—
300C2—3762no—
301C2—3761no—
302C2#1568969111yescharacteristic
303C2AGL(1,ℤ/8)×D4711yescharacteristic
304C2AGL(1,ℤ/8)×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#490C2
socleC22×C47C22×D4
hypercenter#490D47
hypocenterC47#3217
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #127×D47C2semidirect
2. #15689658C2semidirect
3. #15689512C2semidirect
4. #15689510C2semidirect
5. #15689489C2semidirect
6. #15689322C2semidirect
7. #15689317C2semidirect
8. #15689275C2semidirect
9. #15689258C2semidirect
10. #15689178C2semidirect
11. C47×#490C2semidirect
15. C2×#10625325C22semidirect
16. C2×#10625335C22semidirect
17. C2×D376C22semidirect
18. C2×#10625334C22semidirect
24. #13094012C22semidirect
28. #13093989C22semidirect
30. #13093986C22semidirect
33. Dic47⋊C8C22semidirect
34. #13093944C22semidirect
35. #13093944C22semidirect
37. #13093935C22semidirect
39. #125×C47C22semidirect
40. #102×C47C22semidirect
41. #102×C47C22semidirect
42. #97×C47C22semidirect
158. #490D47semidirect
164. C47#3217semidirect
178. #125C2×D47semidirect
191. #102C2×D47semidirect
192. #102C2×D47semidirect
195. #97C2×D47semidirect