Finite Group Databasebeta

← #20258167

Subgroups — #20258167

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
1C2×#13094070C211yesmaximal, characteristic, complemented
2#15689931C218yesmaximal, complemented
3#15689926C218yesmaximal, complemented
4#15689921C216yesmaximal, complemented
5C2×#13094049C216yesmaximal, complemented
6#15689890C211yesmaximal, characteristic, complemented
7C47×#585C211yesmaximal, characteristic, complemented
8#13094070—24no—
9#13094070C2218yescomplemented
10C2×#10625354—21no—
11C2×#10625350C2213yescomplemented
12C22×D188C2213yescomplemented
13C2×D4×D47—23no—
14#13094055C22112yescomplemented
15#13094054C2214yescomplemented
16#13094050C22112yescomplemented
17#13094049C22112yescomplemented
18#13094049C22124yescomplemented
19#13094044C22124yescomplemented
20C2×#10625336C22112yescomplemented
21C2×#10625334C22112yescomplemented
22#13094031C2218yescomplemented
23C2×#10625329C2216yescomplemented
242−1+4×C47—21no—
252−1+4×C47C2214yescomplemented
26H(5,𝔽2)×C47—23no—
27H(5,𝔽2)×C47C2214yescomplemented
28C2×#41×C47—24no—
29C2×#41×C47C2211yescharacteristic
30C2×#41×C47C2216yescomplemented
31C23×D47—23no—
32#41×C47—24no—
33#41×C47—212no—
34#41×C47—26no—
35#41×C47—26no—
36#41×C47D414yes—
37#41×C47C2314yes—
38#41×C47C2314yes—
39#41×C47C23112yescomplemented
40C2×Q8×C47—24no—
41C2×Q8×C47D411yescharacteristic
42C2×Q8×C47C2316yescomplemented
43C2×D4×C47—26no—
44C2×D4×C47—212no—
45C2×D4×C47D413yes—
46C2×D4×C47C2316yescomplemented
47C22×C4×C47—26no—
48C22×C4×C47C2313yes—
49C2×C22⋊D47—23no—
50#10625354—28no—
51D4×D47—224no—
52#10625350—26no—
53#10625350C23112yes—
54C2×D188—23no—
55C2×D188—26no—
56C2×D188C23112yes—
57C2×D188C2313yes—
58C2×C4×D47—23no—
59C2×Dic94C2311yescharacteristic
60#10625337C2318yescomplemented
61#10625336C23124yescomplemented
62#10625335C2318yescomplemented
63#10625334C23124yescomplemented
64#10625329C2314yes—
65#10625329C23112yescomplemented
66C2×C47⋊C8C23112yescomplemented
67C23×C47—26no—
68C23×C47C2×D413yes—
69C22×D47—23no—
70C22×D47—212no—
71C22×D47—86no—
72Q8×C47—26no—
73Q8×C47C2×D414yes—
74Q8×C47C2414yes—
75D4×C47—24no—
76D4×C47—212no—
77D4×C47—26no—
78D4×C47C2×D4112yes—
79D4×C47C2414yes—
80C2×C4×C47—26no—
81C2×C4×C47—24no—
82C2×C4×C47—212no—
83C2×C4×C47C2×D413yes—
84C2×C4×C47C2×D416yes—
85C2×C4×C47C2416yes—
86C2×C4×C47C2411yescharacteristic
87C22⋊D47—212no—
88C2×Dic47—21no—
89D188—23no—
90D188—212no—
91D188C2416yes—
92C4×D47—212no—
93Dic94—21no—
94Dic94C2412yes—
95C47⋊C8C2418yes—
96C22×C47—24no—
97C22×C47—43no—
98C22×C47—86no—
99C22×C47C22×D411yescharacteristic
100C22×C47C22×D416yes—
101C2×D47—26no—
102C2×D47—46no—
103C2×D47—812no—
104C4×C47—24no—
105C4×C47C22×D411yescharacteristic
106C4×C47C22×D416yes—
107C4×C47C2511yescharacteristic
108Dic47—22no—
109#3585—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—26no—
112C2×C47—44no—
113C2×C47C23×D411yescharacteristic
114D47—46no—
115#585D4711yescharacteristic, complemented
116C2×H(5,𝔽2)—471no—
117#577—478no—
118#576—478no—
119#575—476no—
120C2×AGL(1,ℤ/8)—476no—
121#568—471no—
122C47#358511yescharacteristic, complemented, Sylow
1232−1+4—21no—
1242−1+4C2×D4714yescomplemented
125H(5,𝔽2)—23no—
126H(5,𝔽2)—478no—
127H(5,𝔽2)—944no—
128H(5,𝔽2)C2×D4714yescomplemented
129C2×#41—24no—
130C2×#41—473no—
131C2×#41—941no—
132C2×#41C2×D4711yescharacteristic
133C2×#41C2×D4716yescomplemented
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#131—478no—
145C2×M16—476no—
146C24—943no—
147#41—24no—
148#41—212no—
149#41—26no—
150#41—26no—
151#41—4712no—
152#41—948no—
153#41—946no—
154#41C22⋊D4714yes—
155#41C22×D4714yes—
156#41C22×D4714yes—
157#41C22×D47112yescomplemented
158C2×Q8—24no—
159C2×Q8—471no—
160C2×Q8C22⋊D4711yescharacteristic
161C2×Q8C22×D4716yescomplemented
162C2×D4—26no—
163C2×D4—212no—
164C2×D4—4712no—
165C2×D4—473no—
166C2×D4—943no—
167C2×D4—9424no—
168C2×D4—943no—
169C2×D4—946no—
170C2×D4C22⋊D4713yes—
171C2×D4C22×D4716yescomplemented
172C22×C4—26no—
173C22×C4—943no—
174C22×C4C22×D4713yes—
175Q16—478no—
176SD16—4724no—
177SD16—478no—
178D8—4724no—
179M16—474no—
180M16—4712no—
181C2×C8—4712no—
182C23—26no—
183C23—9412no—
184C23—943no—
185C23—3766no—
186C23C2×C22⋊D4713yes—
187Q8—26no—
188Q8—472no—
189Q8—941no—
190Q8C2×C22⋊D4714yes—
191Q8C23×D4714yes—
192D4—24no—
193D4—212no—
194D4—26no—
195D4—476no—
196D4—9412no—
197D4—943no—
198D4—9412no—
199D4C2×C22⋊D47112yes—
200D4C23×D4714yes—
201C2×C4—26no—
202C2×C4—24no—
203C2×C4—212no—
204C2×C4—941no—
205C2×C4—9412no—
206C2×C4C2×C22⋊D4716yes—
207C2×C4C2×C22⋊D4713yes—
208C2×C4C23×D4716yes—
209C2×C4C23×D4711yescharacteristic
210C8—478no—
211C22—24no—
212C22—43no—
213C22—86no—
214C22—946no—
215C22—37612no—
216C22—1886no—
217C22C22×C22⋊D4716yes—
218C22C22×C22⋊D4711yescharacteristic
219C4—24no—
220C4—942no—
221C4C22×C22⋊D4711yescharacteristic
222C4C22×C22⋊D4716yes—
223C4C24×D4711yescharacteristic
224C2—21no—
225C2—26no—
226C2—44no—
227C2—1886no—
228C2C23×C22⋊D4711yescharacteristic
subgroupG/H
centerC2C23×C22⋊D47
commutatorC4×C47C25
FrattiniC4C24×D47
FittingC47×#585C2
socleC2×C47C23×D4
hypercenter#585D47
hypocenterC47#3585
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×#41 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. #15689931C2semidirect
3. #15689926C2semidirect
4. #15689921C2semidirect
5. C2×#13094049C2semidirect
6. #15689890C2semidirect
7. C47×#585C2semidirect
9. #13094070C22semidirect
11. C2×#10625350C22semidirect
12. C22×D188C22semidirect
14. #13094055C22semidirect
15. #13094054C22semidirect
16. #13094050C22semidirect
17. #13094049C22semidirect
18. #13094049C22semidirect
19. #13094044C22semidirect
20. C2×#10625336C22semidirect
21. C2×#10625334C22semidirect
22. #13094031C22semidirect
23. C2×#10625329C22semidirect
25. 2−1+4×C47C22semidirect
27. H(5,𝔽2)×C47C22semidirect
30. C2×#41×C47C22semidirect
39. #41×C47C23semidirect
42. C2×Q8×C47C23semidirect
46. C2×D4×C47C23semidirect
60. #10625337C23semidirect
61. #10625336C23semidirect
62. #10625335C23semidirect
63. #10625334C23semidirect
65. #10625329C23semidirect
66. C2×C47⋊C8C23semidirect
115. #585D47semidirect
122. C47#3585semidirect
124. 2−1+4C2×D47semidirect
128. H(5,𝔽2)C2×D47semidirect
133. C2×#41C2×D47semidirect
157. #41C22×D47semidirect
161. C2×Q8C22×D47semidirect
171. C2×D4C22×D47semidirect