Finite Group Databasebeta

← #20255629

Subgroups — #20255629

Order 6016.

460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689839C211yesmaximal, characteristic, complemented
2#15689758C211yesmaximal, characteristic, complemented
3#15689445C212yesmaximal, complemented
4#15689410C211yesmaximal, characteristic, complemented
5#15689375C212yesmaximal, complemented
6#15689315C211yesmaximal, characteristic, complemented
7#15689258C212yesmaximal, complemented
8C4×D376C211yesmaximal, characteristic, complemented
9#15689202C211yesmaximal, characteristic, complemented
10#15689126C212yesmaximal, complemented
11C47×#486C211yesmaximal, characteristic, complemented
12C2×D4×D47—21no—
13C2×D4×D47C2212yes—
14C2×D376C2211yescharacteristic
15C2×#10625334C2212yescomplemented
16C2×#10625324C2212yescomplemented
17#13094013—22no—
18#13093999—21no—
19#13093999C2212yescomplemented
20#13093995—21no—
21#13093995C2212yes—
22#13093992—22no—
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25C4×D188C2211yescharacteristic, complemented
26#13093982—21no—
27#13093982C2212yescomplemented
28#13093958C2211yescharacteristic, complemented
29#13093955C2212yescomplemented
30C4⋊(C47⋊C8)C2211yescharacteristic, complemented
31#13093946C2211yescharacteristic
32#13093946C2211yescharacteristic, complemented
33#13093945C2212yescomplemented
34#13093944C2212yes—
35(C2×D47)⋊C8C2212yescomplemented
36C4⋊Q8×C47C2211yescharacteristic, complemented
37#127×C47C2211yescharacteristic
38#102×C47C2212yescomplemented
39#102×C47C2212yescomplemented
40C4×C8×C47C2211yescharacteristic, complemented
41C23×D47—22no—
42C2×Q8×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47—21no—
45C2×D4×C47C2312yes—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—22no—
48D4×D47—24no—
49D4×D47—42no—
50D4×D47—44no—
51C2×D188—22no—
52C2×D188D411yescharacteristic
53C2×D188C2311yescharacteristic
54C2×D188C2311yescharacteristic
55C2×C4×D47—21no—
56C2×C4×D47—21no—
57C2×C4×D47C2312yes—
58C2×C8×C47C2311yescharacteristic
59C2×C8×C47C2311yescharacteristic
60C4⋊C4×C47—21no—
61C4⋊C4×C47C2312yes—
62C42×C47C2311yescharacteristic
63C22⋊Dic47—22no—
64#10625334—42no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—21no—
67(C2×D47)⋊C4—21no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4D412yes—
70C4⋊Dic47D411yescharacteristic
71C4⋊Dic47C2311yescharacteristic
72C4⋊Dic47C2311yescharacteristic
73C4×Dic47—22no—
74C2×C47⋊C8C2312yes—
75D376—22no—
76#10625324—42no—
77C23×C47—22no—
78C22×D47—21no—
79C22×D47—21no—
80C22×D47—44no—
81C22×D47—44no—
82C22×D47—82no—
83C22×D47C2×D412yes—
84Q8×C47—81no—
85D4×C47—22no—
86D4×C47—22no—
87D4×C47—42no—
88D4×C47—81no—
89C2×C4×C47—22no—
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2411yescharacteristic
93C22⋊D47—44no—
94C22⋊D47—44no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47C2×D412yes—
98D188—22no—
99D188—21no—
100D188—21no—
101D188—21no—
102D188—82no—
103D188#4112yes—
104C4×D47—22no—
105C4×D47—22no—
106C4×D47—42no—
107C4×D47—42no—
108C8×C47—21no—
109C8×C47—21no—
110C47⋊C8—22no—
111C22×C47—42no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47C22×D411yescharacteristic
115C2×D47—22no—
116C2×D47—22no—
117C2×D47—22no—
118C2×D47—22no—
119C2×D47—41no—
120C2×D47—41no—
121C2×D47—41no—
122C2×D47—41no—
123C2×D47—41no—
124C2×D47—88no—
125C4×C47—21no—
126C4×C47—42no—
127C4×C47AGL(1,ℤ/8)12yes—
128C4×C47C2×#4111yescharacteristic
129C4×C47H(5,𝔽2)11yescharacteristic
130Dic47—22no—
131Dic47—41no—
132Dic47—41no—
133#3325—471nomaximal, Sylow
134C2×C47—82no—
135C2×C47#54611yescharacteristic
136C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C47#57611yescharacteristic
138D47—42no—
139D47—42no—
140D47—81no—
141#555—471no—
142D42—471no—
143#486D4711yescharacteristic, complemented
144#482—472no—
145#476—471no—
146#469—472no—
147#459—471no—
148#447—472no—
149C4×D8—471no—
150#436—471no—
151#418—472no—
152C47#332511yescharacteristic, complemented, Sylow
153C22×D4—472no—
154C22×D4—941no—
155C2×D8—472no—
156C2×D8—471no—
157C2×M16—472no—
158C4⋊Q8C2×D4711yescharacteristic, complemented
159#127C2×D4711yescharacteristic
160#124—942no—
161#121—472no—
162#121—472no—
163#121—941no—
164#121—941no—
165#120—942no—
166C4×D4—471no—
167C4×D4—471no—
168C4×D4—471no—
169#117—472no—
170#117—941no—
171#107—471no—
172#106—472no—
173C4⋊C8—471no—
174#102—472no—
175#102—471no—
176#102—471no—
177#102—472no—
178#102C2×D4712yescomplemented
179#102C2×D4712yescomplemented
180C22⋊C8—472no—
181C4×C8C2×D4711yescharacteristic, complemented
182C24—942no—
183C2×Q8—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—471no—
187C2×D4—471no—
188C2×D4—471no—
189C2×D4—942no—
190C2×D4—942no—
191C2×D4—944no—
192C2×D4—942no—
193C2×D4—1882no—
194C2×D4—1884no—
195C2×D4C22×D4712yes—
196C22×C4—472no—
197C22×C4—941no—
198C22×C4—941no—
199D8—942no—
200D8—1882no—
201M16—1882no—
202C2×C8—472no—
203C2×C8C22×D4711yescharacteristic
204C2×C8C22×D4711yescharacteristic
205C4⋊C4—21no—
206C4⋊C4—471no—
207C4⋊C4—471no—
208C4⋊C4—471no—
209C4⋊C4C22×D4712yes—
210C22⋊C4—472no—
211C22⋊C4—942no—
212C22⋊C4—942no—
213C22⋊C4—942no—
214C22⋊C4—941no—
215C22⋊C4—941no—
216C42—942no—
217C42C22×D4711yescharacteristic
218C23—22no—
219C23—472no—
220C23—941no—
221C23—941no—
222C23—3762no—
223C23—1884no—
224C23—1884no—
225Q8—81no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—81no—
230D4—472no—
231D4—942no—
232D4—941no—
233D4—941no—
234D4—941no—
235D4—3762no—
236D4—1884no—
237D4—1884no—
238C2×C4—22no—
239C2×C4—472no—
240C2×C4—942no—
241C2×C4—942no—
242C2×C4—941no—
243C2×C4—941no—
244C2×C4—1882no—
245C2×C4—1882no—
246C2×C4D4×D4711yescharacteristic
247C2×C4D4×D4711yescharacteristic
248C2×C4C23×D4711yescharacteristic
249C8—21no—
250C8—21no—
251C8—942no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—942no—
256C22—942no—
257C22—942no—
258C22—942no—
259C22—3768no—
260C22—1881no—
261C22—1881no—
262C22—1881no—
263C22—1881no—
264C22—1881no—
265C22C2×D4×D4711yescharacteristic
266C4—21no—
267C4—42no—
268C4—942no—
269C4—1881no—
270C4—1881no—
271C4#1309405112yes—
272C4#41×D4711yescharacteristic
273C4#1309407011yescharacteristic
274C2—82no—
275C2—3761no—
276C2—1882no—
277C2—1882no—
278C2#1568976611yescharacteristic
279C2C2×#1309405111yescharacteristic
280C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3325
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689839C2semidirect
2. #15689758C2semidirect
3. #15689445C2semidirect
4. #15689410C2semidirect
5. #15689375C2semidirect
6. #15689315C2semidirect
7. #15689258C2semidirect
8. C4×D376C2semidirect
9. #15689202C2semidirect
10. #15689126C2semidirect
11. C47×#486C2semidirect
15. C2×#10625334C22semidirect
16. C2×#10625324C22semidirect
19. #13093999C22semidirect
25. C4×D188C22semidirect
27. #13093982C22semidirect
28. #13093958C22semidirect
29. #13093955C22semidirect
30. C4⋊(C47⋊C8)C22semidirect
32. #13093946C22semidirect
33. #13093945C22semidirect
35. (C2×D47)⋊C8C22semidirect
36. C4⋊Q8×C47C22semidirect
38. #102×C47C22semidirect
39. #102×C47C22semidirect
40. C4×C8×C47C22semidirect
143. #486D47semidirect
152. C47#3325semidirect
158. C4⋊Q8C2×D47semidirect
178. #102C2×D47semidirect
179. #102C2×D47semidirect
181. C4×C8C2×D47semidirect