Finite Group Databasebeta

← #20254370

Subgroups — #20254370

Order 6016.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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#15689671C211yesmaximal, characteristic, complemented
2#124×D47C211yesmaximal, characteristic, complemented
3#15689510C211yesmaximal, characteristic, complemented
4#15689483C211yesmaximal, characteristic, complemented
5#15689482C211yesmaximal, characteristic, complemented
6#15689340C212yesmaximal, complemented
7#15689336C212yesmaximal, complemented
8#15689260C212yesmaximal, complemented
9#15689255C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic, complemented
11C47×#496C211yesmaximal, characteristic, complemented
12C2×#10625352—21no—
13C2×Q8×D47C2211yescharacteristic
14C2×D4×D47C2211yescharacteristic
15C2×#10625335C2212yescomplemented
16C2×#10625334C2212yes—
17#13094024C2211yescharacteristic, complemented
18#13094013C2211yescharacteristic
19#13094012C2211yescharacteristic
20#13094011—21no—
21#13094011C2211yescharacteristic
22#13094010—21no—
23#13094010—21no—
24#13093995—21no—
25#13093995C2212yes—
26D4×Dic47—21no—
27D4×Dic47C2212yescomplemented
28C22⋊C4×D47—21no—
29C22⋊C4×D47—21no—
30C42×D47C2211yescharacteristic
31Dic47⋊C8C2212yescomplemented
32#13093949C2212yescomplemented
33#13093948C2212yescomplemented
34#13093946C2212yes—
35#13093945C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic, complemented
38C2×SD16×C47C2212yescomplemented
39C2×D8×C47C2212yes—
40#127×C47C2211yescharacteristic, complemented
41#124×C47C2211yescharacteristic
42#97×C47C2211yescharacteristic, complemented
43C23×D47—21no—
44C2×Q8×C47C2311yescharacteristic
45C2×D4×C47—21no—
46C2×D4×C47—21no—
47C2×D4×C47C2311yescharacteristic
48C2×D4×C47C2312yes—
49C2×C22⋊D47—22no—
50C2×C22⋊D47—21no—
51C22×Dic47—22no—
52Q8×D47—42no—
53#10625352—44no—
54D4×D47—42no—
55C2×D188C2311yescharacteristic
56C2×C4×D47—21no—
57C2×C4×D47D411yescharacteristic
58C2×C4×D47D411yescharacteristic
59C2×C4×D47C2311yescharacteristic
60C2×Dic94—21no—
61C2×Dic94—21no—
62C2×Dic94C2311yescharacteristic
63SD16×C47—42no—
64D8×C47—42no—
65C2×C8×C47C2312yes—
66C22⋊C4×C47—21no—
67C22⋊C4×C47—21no—
68C42×C47C2311yescharacteristic
69C22⋊Dic47—21no—
70C22⋊Dic47—21no—
71C22⋊Dic47—22no—
72C22⋊Dic47—22no—
73#10625335—42no—
74#10625334—42no—
75(C2×D47)⋊C4—21no—
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4—21no—
79C4⋊Dic47—21no—
80C4⋊Dic47C2312yes—
81C4×Dic47D411yescharacteristic
82C4×Dic47D411yescharacteristic
83C4×Dic47C2311yescharacteristic
84C2×C47⋊C8C2312yes—
85C23×C47—21no—
86C23×C47—22no—
87C22×D47—21no—
88C22×D47—42no—
89C22×D47—42no—
90C22×D47—42no—
91C22×D47C2×D411yescharacteristic
92Q8×C47—22no—
93D4×C47—22no—
94D4×C47—22no—
95D4×C47—22no—
96D4×C47—42no—
97D4×C47—42no—
98C2×C4×C47—21no—
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2411yescharacteristic
102C22⋊D47—42no—
103C22⋊D47—44no—
104C2×Dic47—22no—
105C2×Dic47—21no—
106C2×Dic47—44no—
107C2×Dic47C2×D411yescharacteristic
108C2×Dic47C2×D411yescharacteristic
109C2×Dic47C2×D411yescharacteristic
110D188—22no—
111C4×D47—22no—
112C4×D47—22no—
113C4×D47—41no—
114C4×D47—42no—
115Dic94—22no—
116Dic94—42no—
117Dic94—42no—
118C8×C47—22no—
119C47⋊C8—22no—
120C22×C47—41no—
121C22×C47—42no—
122C22×C47—42no—
123C22×C47—41no—
124C22×C47—42no—
125C22×C47—41no—
126C22×C47C22×D411yescharacteristic
127C2×D47—21no—
128C2×D47—21no—
129C2×D47—41no—
130C2×D47—41no—
131C2×D47—41no—
132C2×D47—84no—
133C2×D47AGL(1,ℤ/8)12yes—
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—41no—
137C4×C47H(5,𝔽2)12yes—
138Dic47—21no—
139Dic47—21no—
140Dic47—21no—
141Dic47—41no—
142Dic47—42no—
143#3213—471nomaximal, Sylow
144C2×C47—81no—
145C2×C47—82no—
146C2×C47#53511yescharacteristic
147C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C47#57511yescharacteristic
149D47—22no—
150D47—81no—
151#532—471no—
152C2×#124—471no—
153#496—471no—
154#496D4711yescharacteristic, complemented
155#489—471no—
156#489—471no—
157#463—472no—
158#463—472no—
159#448—472no—
160#447—472no—
161#432—471no—
162C47#321311yescharacteristic, complemented, Sylow
163C2×#41—941no—
164C22×Q8—471no—
165C22×D4—471no—
166C2×SD16—472no—
167C2×SD16C2×D4712yescomplemented
168C2×D8—472no—
169C2×D8C2×D4712yes—
170C4⋊Q8—471no—
171#127C2×D4711yescharacteristic, complemented
172#124—471no—
173#124—471no—
174#124—471no—
175#124—941no—
176#124—941no—
177#124—941no—
178#124C2×D4711yescharacteristic
179#121—472no—
180#121—941no—
181C4×D4—472no—
182C4×D4—941no—
183C2×C22⋊C4—941no—
184C2×C22⋊C4—941no—
185C2×C42—471no—
186C4⋊C8—472no—
187#103—472no—
188#103—472no—
189#102—472no—
190#102—472no—
191C22⋊C8—472no—
192#97—471no—
193#97C2×D4711yescharacteristic, complemented
194C24—941no—
195#41—1884no—
196C2×Q8—471no—
197C2×Q8—941no—
198C2×Q8—941no—
199C2×Q8—1882no—
200C2×Q8C22×D4711yescharacteristic
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—471no—
204C2×D4—941no—
205C2×D4—942no—
206C2×D4—1882no—
207C2×D4C22×D4711yescharacteristic
208C2×D4C22×D4712yes—
209C22×C4—471no—
210C22×C4—471no—
211C22×C4—471no—
212C22×C4—941no—
213C22×C4—942no—
214SD16—42no—
215SD16—1882no—
216D8—42no—
217D8—1882no—
218C2×C8—472no—
219C2×C8C22×D4712yes—
220C4⋊C4—472no—
221C4⋊C4—941no—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—941no—
225C22⋊C4—941no—
226C22⋊C4—941no—
227C22⋊C4—941no—
228C22⋊C4—942no—
229C22⋊C4—942no—
230C22⋊C4—941no—
231C22⋊C4—941no—
232C42—471no—
233C42—471no—
234C42—471no—
235C42C22×D4711yescharacteristic
236C23—21no—
237C23—22no—
238C23—471no—
239C23—941no—
240C23—1882no—
241C23—1882no—
242C23—1882no—
243Q8—22no—
244Q8—942no—
245Q8—1882no—
246Q8—1882no—
247D4—22no—
248D4—22no—
249D4—22no—
250D4—42no—
251D4—42no—
252D4—942no—
253D4—1882no—
254D4—1884no—
255C2×C4—21no—
256C2×C4—471no—
257C2×C4—471no—
258C2×C4—471no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—941no—
262C2×C4—942no—
263C2×C4—1881no—
264C2×C4—1882no—
265C2×C4—1884no—
266C2×C4D4×D4711yescharacteristic
267C2×C4D4×D4711yescharacteristic
268C2×C4C23×D4711yescharacteristic
269C8—22no—
270C8—942no—
271C22—42no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—472no—
278C22—941no—
279C22—941no—
280C22—3764no—
281C22—1881no—
282C22—1881no—
283C22—1881no—
284C22C2×D4×D4711yescharacteristic
285C4—21no—
286C4—21no—
287C4—41no—
288C4—941no—
289C4—941no—
290C4—941no—
291C4—1882no—
292C4—1881no—
293C4#1309406912yes—
294C2—81no—
295C2—82no—
296C2—942no—
297C2—3761no—
298C2#1568968611yescharacteristic
299C2AGL(1,ℤ/8)×D4711yescharacteristic
300C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#496C2
socleC22×C47C22×D4
hypercenter#496D47
hypocenterC47#3213
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #15689671C2semidirect
2. #124×D47C2semidirect
3. #15689510C2semidirect
4. #15689483C2semidirect
5. #15689482C2semidirect
6. #15689340C2semidirect
7. #15689336C2semidirect
8. #15689260C2semidirect
9. #15689255C2semidirect
10. #15689178C2semidirect
11. C47×#496C2semidirect
15. C2×#10625335C22semidirect
17. #13094024C22semidirect
27. D4×Dic47C22semidirect
31. Dic47⋊C8C22semidirect
32. #13093949C22semidirect
33. #13093948C22semidirect
37. #13093935C22semidirect
38. C2×SD16×C47C22semidirect
40. #127×C47C22semidirect
42. #97×C47C22semidirect
154. #496D47semidirect
162. C47#3213semidirect
167. C2×SD16C2×D47semidirect
171. #127C2×D47semidirect
193. #97C2×D47semidirect