Finite Group Databasebeta

← #20254377

Subgroups — #20254377

Order 6016.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689673C211yesmaximal, characteristic, complemented
2C2×#13094012C211yesmaximal, characteristic, complemented
3#15689512C212yesmaximal, complemented
4#15689483C212yesmaximal, complemented
5#15689339C214yesmaximal, complemented
6#15689264C212yesmaximal, complemented
7#15689259C212yesmaximal, complemented
8C47×#432C211yesmaximal, characteristic, complemented
9C2×#10625350—21no—
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12C2×#10625325C2214yescomplemented
13C2×D376C2214yes—
14#13094024C2211yescharacteristic, complemented
15#13094021C2211yescharacteristic, complemented
16#13094012—21no—
17#13094012—21no—
18#13094012—21no—
19#13094012C2212yes—
20#13094012C2212yes—
21#13093998—21no—
22#13093998C2212yes—
23C4×D188—21no—
24C4×D188C2212yescomplemented
25C2×(C2×D47)⋊C4—21no—
26C2×(C2×D47)⋊C4—21no—
27#13093949C2214yescomplemented
28#13093946C2214yes—
29C2×C42×C47C2211yescharacteristic
30C4⋊C8×C47C2212yescomplemented
31C22⋊C8×C47C2212yes—
32#97×C47C2212yescomplemented
33C23×D47—21no—
34C22×C4×C47D411yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—22no—
38C22×Dic47—21no—
39#10625350—44no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—42no—
44C2×D188C2312yes—
45C2×D188C2312yes—
46C2×C4×D47—22no—
47C2×Dic94—21no—
48C2×Dic94—21no—
49C2×Dic94—42no—
50C2×Dic94C2312yes—
51C2×C8×C47C2314yes—
52C42×C47D411yescharacteristic
53C42×C47D411yescharacteristic
54C42×C47C2311yescharacteristic
55C42×C47C2311yescharacteristic
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62C4⋊Dic47—21no—
63C4⋊Dic47C2312yes—
64D376—44no—
65#10625325—44no—
66C23×C47C2×D411yescharacteristic
67C22×D47—22no—
68C22×D47—22no—
69C22×D47—42no—
70C22×D47—42no—
71C22×D47—42no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—41no—
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C22⋊D47—44no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—42no—
85D188—24no—
86D188—24no—
87D188—42no—
88D188—42no—
89D188—42no—
90C4×D47—44no—
91Dic94—24no—
92Dic94—42no—
93Dic94—42no—
94C8×C47—24no—
95C22×C47—21no—
96C22×C47—21no—
97C22×C47AGL(1,ℤ/8)12yes—
98C22×C47C22×D411yescharacteristic
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—42no—
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—84no—
106C4×C47—21no—
107C4×C47—21no—
108C4×C47—21no—
109C4×C47—21no—
110C4×C47—21no—
111C4×C47H(5,𝔽2)12yes—
112Dic47—42no—
113Dic47—42no—
114#3213—471nomaximal, Sylow
115C2×C47—22no—
116C2×C47#53511yescharacteristic
117C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
118C2×C47#57511yescharacteristic
119D47—82no—
120D47—82no—
121#532—471no—
122C2×#124—471no—
123#496—472no—
124#489—472no—
125#463—474no—
126#448—472no—
127#447—472no—
128#432D4711yescharacteristic, complemented
129C47#321311yescharacteristic, complemented, Sylow
130C2×#41—941no—
131C22×Q8—471no—
132C22×D4—471no—
133C2×SD16—474no—
134C2×D8—474no—
135C4⋊Q8—471no—
136#127—471no—
137#124—472no—
138#124—472no—
139#124—941no—
140#124—941no—
141#124—941no—
142#121—472no—
143#121—941no—
144C4×D4—472no—
145C4×D4—941no—
146C2×C22⋊C4—941no—
147C2×C22⋊C4—941no—
148C2×C42C2×D4711yescharacteristic
149C4⋊C8C2×D4712yescomplemented
150#103—474no—
151#102—474no—
152C22⋊C8C2×D4712yes—
153#97C2×D4712yescomplemented
154C24—941no—
155#41—1884no—
156C2×Q8—472no—
157C2×Q8—941no—
158C2×Q8—941no—
159C2×Q8—1882no—
160C2×D4—472no—
161C2×D4—472no—
162C2×D4—942no—
163C2×D4—941no—
164C2×D4—941no—
165C2×D4—941no—
166C2×D4—1882no—
167C22×C4—941no—
168C22×C4—942no—
169C22×C4D18811yescharacteristic
170C22×C4D18811yescharacteristic
171C22×C4C22×D4711yescharacteristic
172SD16—1884no—
173D8—1884no—
174C2×C8C22×D4714yes—
175C4⋊C4—472no—
176C4⋊C4—941no—
177C22⋊C4—942no—
178C22⋊C4—942no—
179C22⋊C4—942no—
180C22⋊C4—942no—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C42D18811yescharacteristic
184C42D18811yescharacteristic
185C42C22×D4711yescharacteristic
186C42C22×D4711yescharacteristic
187C23—942no—
188C23—942no—
189C23—1882no—
190C23—1882no—
191C23—1882no—
192C23C2×D18811yescharacteristic
193Q8—944no—
194Q8—1882no—
195Q8—1882no—
196D4—944no—
197D4—944no—
198D4—1882no—
199D4—1882no—
200D4—1882no—
201D4—1884no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—1884no—
208C2×C4—1882no—
209C2×C4C2×D18811yescharacteristic
210C2×C4C2×D18811yescharacteristic
211C2×C4C2×D18811yescharacteristic
212C2×C4C2×D18811yescharacteristic
213C2×C4C2×D18811yescharacteristic
214C2×C4C23×D4711yescharacteristic
215C8—24no—
216C22—21no—
217C22—21no—
218C22—3764no—
219C22—1882no—
220C22—1882no—
221C22—1882no—
222C22—1882no—
223C22—1882no—
224C22—1882no—
225C22#1309405212yes—
226C22C22×D18811yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—1882no—
233C4—1882no—
234C4#1309407012yes—
235C2—22no—
236C2—3762no—
237C2—3762no—
238C2#1568969211yescharacteristic
239C2C2×#1309405211yescharacteristic
240C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3213
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #15689673C2semidirect
2. C2×#13094012C2semidirect
3. #15689512C2semidirect
4. #15689483C2semidirect
5. #15689339C2semidirect
6. #15689264C2semidirect
7. #15689259C2semidirect
8. C47×#432C2semidirect
12. C2×#10625325C22semidirect
14. #13094024C22semidirect
15. #13094021C22semidirect
24. C4×D188C22semidirect
27. #13093949C22semidirect
30. C4⋊C8×C47C22semidirect
32. #97×C47C22semidirect
128. #432D47semidirect
129. C47#3213semidirect
149. C4⋊C8C2×D47semidirect
153. #97C2×D47semidirect