Finite Group Databasebeta

← #20255000

Subgroups — #20255000

Order 6016.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×#13094052C212yesmaximal, complemented
2#15689769C212yesmaximal, complemented
3#15689507C211yesmaximal, characteristic, complemented
4#15689369C212yesmaximal, complemented
5#15689339C212yesmaximal, complemented
6#15689287C212yesmaximal, complemented
7#15689259C212yesmaximal, complemented
8C4×D376C211yesmaximal, characteristic, complemented
9C47×#436C211yesmaximal, characteristic, complemented
10C2×#10625350C2212yes—
11C22×D188C2212yescomplemented
12#13094052—28no—
13C2×Dic188C2211yescharacteristic, complemented
14C2×#10625325C2212yescomplemented
15C2×#10625325C2212yescomplemented
16C2×D376C2212yes—
17C2×D376C2211yescharacteristic
18C2×D376C2211yescharacteristic
19#13094012C2212yescomplemented
20#13094009—22no—
21#13094003C2212yescomplemented
22#13093998C2212yes—
23#13093997—22no—
24#13093992—22no—
25C4×D188C2212yescomplemented
26C22⋊C4×D47—22no—
27#13093958C2211yescharacteristic, complemented
28#13093949C2212yescomplemented
29#13093946C2212yescomplemented
30#13093946C2212yescomplemented
31C2×M16×C47C2212yescomplemented
32C4×D4×C47C2211yescharacteristic
33C4⋊C8×C47C2211yescharacteristic, complemented
34C22⋊C8×C47C2212yescomplemented
35C4×C8×C47C2211yescharacteristic, complemented
36C23×D47—22no—
37C2×D4×C47D411yescharacteristic
38C22×C4×C47C2312yes—
39C2×C22⋊D47—22no—
40C2×C22⋊D47—22no—
41#10625350—24no—
42#10625350—42no—
43C2×D188—24no—
44C2×D188—22no—
45C2×D188—42no—
46C2×D188C2312yes—
47C2×D188C2312yes—
48C2×C4×D47—22no—
49C2×C4×D47—22no—
50C2×Dic94C2312yes—
51M16×C47—24no—
52C2×C8×C47C2312yes—
53C2×C8×C47C2311yescharacteristic
54C2×C8×C47C2311yescharacteristic
55C4⋊C4×C47D411yescharacteristic
56C22⋊C4×C47D412yes—
57C42×C47C2311yescharacteristic
58C22⋊Dic47—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—22no—
63C4⋊Dic47C2312yes—
64Dic47⋊C4—22no—
65Dic188—41no—
66D376—24no—
67D376—41no—
68D376D414yescomplemented
69#10625325—24no—
70#10625325—24no—
71C23×C47C2×D412yes—
72C22×D47—22no—
73C22×D47—22no—
74C22×D47—44no—
75C22×D47—44no—
76C22×D47—82no—
77D4×C47—41no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2411yescharacteristic
84C22⋊D47—44no—
85C22⋊D47—82no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88D188—22no—
89D188—22no—
90D188—22no—
91D188—44no—
92D188C2×D414yes—
93C4×D47—44no—
94C4×D47—82no—
95Dic94—22no—
96Dic94—22no—
97C8×C47—22no—
98C8×C47—21no—
99C8×C47C2×D412yes—
100C22×C47—22no—
101C22×C47—22no—
102C22×C47—22no—
103C22×C47C22×D411yescharacteristic
104C2×D47—24no—
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—88no—
111C4×C47—22no—
112C4×C47—21no—
113C4×C47—21no—
114C4×C47C22×D411yescharacteristic
115C4×C47H(5,𝔽2)11yescharacteristic
116Dic47—42no—
117Dic47—42no—
118#3273—471nomaximal, Sylow
119C2×C47—42no—
120C2×C47D4211yescharacteristic
121C2×C47#57511yescharacteristic
122C2×C47#57611yescharacteristic
123D47—44no—
124D47—82no—
125C2×AGL(1,ℤ/8)—472no—
126#546—472no—
127#495—471no—
128#468—472no—
129#463—472no—
130#452—472no—
131#447—472no—
132C4×D8—471no—
133#436D4711yescharacteristic, complemented
134C47#327311yescharacteristic, complemented, Sylow
135C2×#41—472no—
136C22×D4—472no—
137AGL(1,ℤ/8)—948no—
138C2×Q16—471no—
139C2×SD16—472no—
140C2×SD16—472no—
141C2×D8—471no—
142C2×D8—472no—
143C2×D8—471no—
144C2×M16C2×D4712yescomplemented
145#124—472no—
146#123—942no—
147C22⋊Q8—472no—
148#121—472no—
149#121—942no—
150#120—942no—
151C4×D4—472no—
152C4×D4C2×D4711yescharacteristic
153C2×C22⋊C4—942no—
154#107—471no—
155C4⋊C8C2×D4711yescharacteristic, complemented
156#103—472no—
157#102—472no—
158#102—472no—
159C22⋊C8C2×D4712yescomplemented
160C4×C8C2×D4711yescharacteristic, complemented
161C24—942no—
162#41—944no—
163#41—1882no—
164C2×Q8—472no—
165C2×D4—472no—
166C2×D4—472no—
167C2×D4—944no—
168C2×D4—942no—
169C2×D4—942no—
170C2×D4—942no—
171C2×D4—1882no—
172C2×D4D18811yescharacteristic
173C22×C4—942no—
174C22×C4—942no—
175C22×C4C22×D4712yes—
176Q16—1881no—
177SD16—944no—
178SD16—944no—
179D8—474no—
180D8—944no—
181D8—1881no—
182M16—24no—
183C2×C8C22×D4711yescharacteristic
184C2×C8C22×D4712yes—
185C2×C8C22×D4711yescharacteristic
186C4⋊C4—472no—
187C4⋊C4—942no—
188C4⋊C4D18811yescharacteristic
189C22⋊C4—942no—
190C22⋊C4—942no—
191C22⋊C4—942no—
192C22⋊C4—942no—
193C22⋊C4—942no—
194C22⋊C4D18812yes—
195C42C22×D4711yescharacteristic
196C23—942no—
197C23—942no—
198C23—3762no—
199C23—1884no—
200C23—1884no—
201C23C2×D18812yes—
202Q8—942no—
203Q8—942no—
204D4—41no—
205D4—474no—
206D4—942no—
207D4—942no—
208D4—942no—
209D4—3762no—
210D4—1884no—
211D4—1884no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—3762no—
217C2×C4—1884no—
218C2×C4C2×D18811yescharacteristic
219C2×C4C2×D18811yescharacteristic
220C2×C4C2×D18812yes—
221C2×C4C23×D4711yescharacteristic
222C8—22no—
223C8—21no—
224C8D4×D4712yes—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—944no—
229C22—3768no—
230C22—1882no—
231C22—1882no—
232C22—1882no—
233C22—1882no—
234C22—1882no—
235C22C22×D18811yescharacteristic
236C4—22no—
237C4—21no—
238C4—21no—
239C4—1882no—
240C4—1882no—
241C4C2×D4×D4711yescharacteristic
242C4#1309407011yescharacteristic
243C2—42no—
244C2—3762no—
245C2—1884no—
246C2D4×D18811yescharacteristic
247C2#1568992311yescharacteristic
248C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#436C2
socleC22×C47C22×D4
hypercenter#436D47
hypocenterC47#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#13094052C2semidirect
2. #15689769C2semidirect
3. #15689507C2semidirect
4. #15689369C2semidirect
5. #15689339C2semidirect
6. #15689287C2semidirect
7. #15689259C2semidirect
8. C4×D376C2semidirect
9. C47×#436C2semidirect
11. C22×D188C22semidirect
13. C2×Dic188C22semidirect
14. C2×#10625325C22semidirect
15. C2×#10625325C22semidirect
19. #13094012C22semidirect
21. #13094003C22semidirect
25. C4×D188C22semidirect
27. #13093958C22semidirect
28. #13093949C22semidirect
29. #13093946C22semidirect
30. #13093946C22semidirect
31. C2×M16×C47C22semidirect
33. C4⋊C8×C47C22semidirect
34. C22⋊C8×C47C22semidirect
35. C4×C8×C47C22semidirect
68. D376D4semidirect
133. #436D47semidirect
134. C47#3273semidirect
144. C2×M16C2×D47semidirect
155. C4⋊C8C2×D47semidirect
159. C22⋊C8C2×D47semidirect
160. C4×C8C2×D47semidirect