Finite Group Databasebeta

← #20255188

Subgroups — #20255188

Order 6016.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689928C212yesmaximal, complemented
2#15689925C212yesmaximal, complemented
3#15689500C211yesmaximal, characteristic, complemented
4#15689394C212yesmaximal, complemented
5#15689393C212yesmaximal, complemented
6#15689292C214yesmaximal, complemented
7#15689241C211yesmaximal, characteristic, complemented
8C47×#443C211yesmaximal, characteristic, complemented
9#13094070C2214yescomplemented
10#13094052—24no—
11#13094052C2214yescomplemented
12#13094051—24no—
13#13094049C2214yescomplemented
14#13094047—22no—
15#13094046—22no—
16#13094046C2211yescharacteristic
17C2×D376—22no—
18C2×D376C2212yescomplemented
19C2×D376C2212yescomplemented
20D8×D47—22no—
21#13094030C2212yescomplemented
22#13094021C2212yescomplemented
23#13093960C2211yescharacteristic, complemented
24#13093952C2212yescomplemented
25#13093940C2214yescomplemented
26#135×C47C2211yescharacteristic
27#131×C47C2212yescomplemented
28#108×C47C2211yescharacteristic, complemented
29#104×C47C2212yescomplemented
30C4×C8×C47C2211yescharacteristic, complemented
31#41×C47C2312yes—
32#10625354—24no—
33D4×D47—24no—
34D4×D47—44no—
35#10625350—24no—
36#10625350C2312yes—
37C2×D188—24no—
38C2×D188—42no—
39C2×D188C2314yes—
40Q16×C47D411yescharacteristic, complemented
41SD16×C47D412yescomplemented
42D8×C47D411yescharacteristic, complemented
43M16×C47—22no—
44M16×C47C2312yes—
45C2×C8×C47—22no—
46C2×C8×C47C2311yescharacteristic
47C2×C8×C47C2311yescharacteristic
48C42×C47C2311yescharacteristic
49#10625336—24no—
50#10625334—24no—
51#10625329C2312yes—
52Dic188D411yescharacteristic, complemented
53D376—24no—
54D376—22no—
55D376—22no—
56D376—22no—
57D376—22no—
58D376D411yescharacteristic, complemented
59#10625325—24no—
60#10625325D412yescomplemented
61#10625324—22no—
62C8×D47—22no—
63C22×D47—24no—
64C22×D47—44no—
65Q8×C47C2×D412yes—
66D4×C47—22no—
67D4×C47C2×D412yes—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47C2411yescharacteristic
71C22⋊D47—22no—
72C22⋊D47—44no—
73D188—24no—
74D188—24no—
75D188—44no—
76D188—84no—
77D188C2×D412yes—
78C4×D47—22no—
79C4×D47—44no—
80Dic94C2×D412yes—
81C8×C47—22no—
82C8×C47C2×D411yescharacteristic
83C8×C47C2×D411yescharacteristic
84C8×C47C2×D411yescharacteristic
85C8×C47C2×D411yescharacteristic
86C47⋊C8—22no—
87C22×C47—22no—
88C22×C47H(5,𝔽2)11yescharacteristic
89C2×D47—22no—
90C2×D47—44no—
91C2×D47—84no—
92C2×D47—164no—
93C4×C47—22no—
94C4×C47—22no—
95C4×C47C22×D411yescharacteristic
96C4×C47C22×D411yescharacteristic
97Dic47—22no—
98#3292—471nomaximal, Sylow
99C2×C47—21no—
100C2×C47—42no—
101C2×C47D4211yescharacteristic
102D47—42no—
103D47—84no—
104#576—472no—
105#576—472no—
106#493—471no—
107#472—472no—
108#472—472no—
109#453—474no—
110#443—471no—
111#443D4711yescharacteristic, complemented
112C47#329211yescharacteristic, complemented, Sylow
113H(5,𝔽2)—474no—
114AGL(1,ℤ/8)—474no—
115AGL(1,ℤ/8)—474no—
116AGL(1,ℤ/8)—944no—
117AGL(1,ℤ/8)—944no—
118#135—471no—
119#135—942no—
120#135—942no—
121#135C2×D4711yescharacteristic
122C2×D8—472no—
123C2×D8—472no—
124C2×D8—942no—
125C2×D8—942no—
126#131—472no—
127#131C2×D4712yescomplemented
128#127—472no—
129#108—471no—
130#108C2×D4711yescharacteristic, complemented
131#104—472no—
132#104C2×D4712yescomplemented
133#100—474no—
134C4×C8C2×D4711yescharacteristic, complemented
135#41—472no—
136#41—944no—
137#41—944no—
138#41C22×D4712yes—
139C2×D4—474no—
140C2×D4—944no—
141C2×D4—944no—
142C2×D4—1882no—
143C2×D4—1884no—
144Q16—471no—
145Q16D18811yescharacteristic, complemented
146SD16—472no—
147SD16—944no—
148SD16—944no—
149SD16D18812yescomplemented
150D8—471no—
151D8—944no—
152D8—944no—
153D8—942no—
154D8—942no—
155D8—942no—
156D8—942no—
157D8D18811yescharacteristic, complemented
158M16—22no—
159M16—472no—
160M16—942no—
161M16C22×D4712yes—
162C2×C8—22no—
163C2×C8—942no—
164C2×C8C22×D4711yescharacteristic
165C2×C8C22×D4711yescharacteristic
166C42C22×D4711yescharacteristic
167C23—944no—
168C23—1884no—
169Q8—472no—
170Q8C2×D18812yes—
171D4—22no—
172D4—472no—
173D4—942no—
174D4—944no—
175D4—944no—
176D4—3764no—
177D4—1884no—
178D4—1884no—
179D4C2×D18812yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—942no—
183C2×C4—1884no—
184C2×C4C23×D4711yescharacteristic
185C8—22no—
186C8—942no—
187C8C2×D18811yescharacteristic
188C8C2×D18811yescharacteristic
189C8D4×D4711yescharacteristic
190C8D4×D4711yescharacteristic
191C22—22no—
192C22—942no—
193C22—3764no—
194C22—1884no—
195C22—7524no—
196C22#1309407011yescharacteristic
197C4—22no—
198C4—22no—
199C4—942no—
200C4C2×D4×D4711yescharacteristic
201C4C22×D18811yescharacteristic
202C2—21no—
203C2—42no—
204C2—3764no—
205C2—1882no—
206C2D4×D18811yescharacteristic
subgroupG/H
centerC2D4×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#443C2
socleC2×C47D42
hypercenter#443D47
hypocenterC47#3292
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #15689928C2semidirect
2. #15689925C2semidirect
3. #15689500C2semidirect
4. #15689394C2semidirect
5. #15689393C2semidirect
6. #15689292C2semidirect
7. #15689241C2semidirect
8. C47×#443C2semidirect
9. #13094070C22semidirect
11. #13094052C22semidirect
13. #13094049C22semidirect
18. C2×D376C22semidirect
19. C2×D376C22semidirect
21. #13094030C22semidirect
22. #13094021C22semidirect
23. #13093960C22semidirect
24. #13093952C22semidirect
25. #13093940C22semidirect
27. #131×C47C22semidirect
28. #108×C47C22semidirect
29. #104×C47C22semidirect
30. C4×C8×C47C22semidirect
40. Q16×C47D4semidirect
41. SD16×C47D4semidirect
42. D8×C47D4semidirect
52. Dic188D4semidirect
58. D376D4semidirect
60. #10625325D4semidirect
111. #443D47semidirect
112. C47#3292semidirect
127. #131C2×D47semidirect
130. #108C2×D47semidirect
132. #104C2×D47semidirect
134. C4×C8C2×D47semidirect
145. Q16D188semidirect
149. SD16D188semidirect
157. D8D188semidirect