Finite Group Databasebeta

← #20258169

Subgroups — #20258169

Order 6016.

1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.

normal subgroups only

This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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#15689959C211yesmaximal, characteristic, complemented
2C2×#13094070C211yesmaximal, characteristic, complemented
3#15689935C218yesmaximal, complemented
4#15689928C218yesmaximal, complemented
5#15689923C216yesmaximal, complemented
6C2×#13094052C216yesmaximal, complemented
7C47×#568C211yesmaximal, characteristic, complemented
8#13094072—21no—
9#13094071C2214yescomplemented
10#13094070—24no—
11#13094070C2218yescomplemented
12#13094070C2214yescomplemented
13#13094069—23no—
14C2×#10625354—21no—
15C2×#10625350C2213yescomplemented
16C2×#10625350C2216yescomplemented
17#41×D47—24no—
18C22×D188C2213yescomplemented
19C2×D4×D47—23no—
20#13094057C2214yescomplemented
21#13094057C22112yescomplemented
22#13094052C22112yescomplemented
23#13094052C22124yescomplemented
24#13094052C22112yescomplemented
25#13094046C22124yescomplemented
26C2×#10625325C22112yescomplemented
27C2×D376C22112yescomplemented
28C2×#41×C47C2211yescharacteristic
29#131×C47C2218yescomplemented
30C2×M16×C47C2216yescomplemented
31C23×D47—23no—
32#41×C47D414yes—
33#41×C47C2314yes—
34C2×Q8×C47D411yescharacteristic
35C2×D4×C47D413yes—
36C22×C4×C47C2313yes—
37C2×C22⋊D47—23no—
38C2×C22⋊D47—26no—
39#10625354—24no—
40#10625354—28no—
41Q8×D47—24no—
42#10625352—212no—
43D4×D47—224no—
44D4×D47—212no—
45#10625350—26no—
46#10625350—26no—
47#10625350—26no—
48#10625350C23112yes—
49#10625350C2314yes—
50#10625350C23112yescomplemented
51C2×D188—23no—
52C2×D188—26no—
53C2×D188C23112yes—
54C2×D188C2313yes—
55C2×D188C2316yescomplemented
56C2×C4×D47—23no—
57C2×C4×D47—26no—
58C2×Dic94C2311yescharacteristic
59C2×Dic94C2316yescomplemented
60M16×C47C2314yes—
61M16×C47C23112yescomplemented
62C2×C8×C47C23112yescomplemented
63Dic188C2318yescomplemented
64D376C23124yescomplemented
65#10625325C23124yescomplemented
66#10625325C2318yescomplemented
67C23×C47C2×D413yes—
68C22×D47—23no—
69C22×D47—26no—
70C22×D47—212no—
71C22×D47—86no—
72Q8×C47C2×D414yes—
73D4×C47C2×D4112yes—
74C2×C4×C47C2×D413yes—
75C2×C4×C47C2×D416yes—
76C2×C4×C47C2416yes—
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—24no—
79C22⋊D47—212no—
80C22⋊D47—212no—
81C2×Dic47—21no—
82C2×Dic47—26no—
83D188—23no—
84D188—212no—
85D188—26no—
86D188C2416yes—
87D188C2414yes—
88C4×D47—24no—
89C4×D47—212no—
90C4×D47—212no—
91Dic94—21no—
92Dic94—26no—
93Dic94C2414yes—
94Dic94C2412yes—
95C8×C47C2418yes—
96C22×C47—43no—
97C22×C47C22×D411yescharacteristic
98C22×C47C22×D416yes—
99C2×D47—24no—
100C2×D47—26no—
101C2×D47—46no—
102C2×D47—86no—
103C2×D47—812no—
104C4×C47C22×D411yescharacteristic
105C4×C47C22×D416yes—
106C4×C47C2511yescharacteristic
107Dic47—24no—
108Dic47—22no—
109#3585—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—26no—
112C2×C47C23×D411yescharacteristic
113D47—46no—
114D47—44no—
115#585—471no—
116C2×H(5,𝔽2)—471no—
117#577—478no—
118#576—478no—
119#575—476no—
120C2×AGL(1,ℤ/8)—476no—
121#568D4711yescharacteristic, complemented
122C47#358511yescharacteristic, complemented, Sylow
1232−1+4—474no—
1242−1+4—941no—
125H(5,𝔽2)—474no—
126H(5,𝔽2)—478no—
127H(5,𝔽2)—944no—
128H(5,𝔽2)—943no—
129C2×#41—476no—
130C2×#41—473no—
131C2×#41—944no—
132C2×#41—941no—
133C2×#41C2×D4711yescharacteristic
134C22×D4—473no—
135C22×D4—943no—
136#137—474no—
137#137—4712no—
138AGL(1,ℤ/8)—4712no—
139AGL(1,ℤ/8)—4724no—
140AGL(1,ℤ/8)—4712no—
141#135—4724no—
142C2×SD16—4712no—
143C2×D8—4712no—
144#131C2×D4718yescomplemented
145C2×M16C2×D4716yescomplemented
146C24—943no—
147#41—4712no—
148#41—474no—
149#41—4712no—
150#41—948no—
151#41—944no—
152#41—9412no—
153#41—946no—
154#41—946no—
155#41—946no—
156#41D18814yes—
157#41C22×D4714yes—
158C2×Q8—471no—
159C2×Q8—476no—
160C2×Q8—944no—
161C2×Q8D18811yescharacteristic
162C2×D4—4712no—
163C2×D4—473no—
164C2×D4—476no—
165C2×D4—943no—
166C2×D4—946no—
167C2×D4—9424no—
168C2×D4—9412no—
169C2×D4—943no—
170C2×D4—946no—
171C2×D4D18813yes—
172C22×C4—943no—
173C22×C4—946no—
174C22×C4C22×D4713yes—
175Q16—478no—
176SD16—4724no—
177SD16—478no—
178D8—4724no—
179M16C22×D4714yes—
180M16C22×D47112yescomplemented
181C2×C8C22×D47112yescomplemented
182C23—946no—
183C23—9412no—
184C23—943no—
185C23—3766no—
186C23C2×D18813yes—
187Q8—474no—
188Q8—472no—
189Q8—946no—
190Q8—941no—
191Q8C2×D18814yes—
192D4—474no—
193D4—476no—
194D4—9412no—
195D4—944no—
196D4—9412no—
197D4—943no—
198D4—9412no—
199D4—946no—
200D4C2×D188112yes—
201C2×C4—941no—
202C2×C4—946no—
203C2×C4—944no—
204C2×C4—9412no—
205C2×C4—9412no—
206C2×C4C2×D18813yes—
207C2×C4C2×D18816yes—
208C2×C4C23×D4716yes—
209C2×C4C23×D4711yescharacteristic
210C8C23×D4718yes—
211C22—43no—
212C22—944no—
213C22—946no—
214C22—37612no—
215C22—3766no—
216C22—1886no—
217C22C22×D18811yescharacteristic
218C22C22×D18816yes—
219C4—942no—
220C4—944no—
221C4C22×D18811yescharacteristic
222C4C22×D18816yes—
223C4C24×D4711yescharacteristic
224C2—21no—
225C2—26no—
226C2—1886no—
227C2—1884no—
228C2C23×D18811yescharacteristic
subgroupG/H
centerC2C23×D188
commutatorC4×C47C25
FrattiniC4C24×D47
FittingC47×#568C2
socleC2×C47C23×D4
hypercenter#568D47
hypocenterC47#3585
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×#41 ◁ #568

Complements

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

NH ≅ G/Ntype
1. #15689959C2semidirect
2. C2×#13094070C2semidirect
3. #15689935C2semidirect
4. #15689928C2semidirect
5. #15689923C2semidirect
6. C2×#13094052C2semidirect
7. C47×#568C2semidirect
9. #13094071C22semidirect
11. #13094070C22semidirect
12. #13094070C22semidirect
15. C2×#10625350C22semidirect
16. C2×#10625350C22semidirect
18. C22×D188C22semidirect
20. #13094057C22semidirect
21. #13094057C22semidirect
22. #13094052C22semidirect
23. #13094052C22semidirect
24. #13094052C22semidirect
25. #13094046C22semidirect
26. C2×#10625325C22semidirect
27. C2×D376C22semidirect
29. #131×C47C22semidirect
30. C2×M16×C47C22semidirect
50. #10625350C23semidirect
55. C2×D188C23semidirect
59. C2×Dic94C23semidirect
61. M16×C47C23semidirect
62. C2×C8×C47C23semidirect
63. Dic188C23semidirect
64. D376C23semidirect
65. #10625325C23semidirect
66. #10625325C23semidirect
121. #568D47semidirect
122. C47#3585semidirect
144. #131C2×D47semidirect
145. C2×M16C2×D47semidirect
180. M16C22×D47semidirect
181. C2×C8C22×D47semidirect