Finite Group Databasebeta

← #20252785

Subgroups — #20252785

Order 6016.

800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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#15689682C213yesmaximal, complemented
2#15689313C214yesmaximal, complemented
3#15689310C214yesmaximal, complemented
4C2×#13093939C213yesmaximal, complemented
5C2×H(5,𝔽2)×C47C211yesmaximal, characteristic, complemented
6C22×C22⋊D47C2211yescharacteristic, complemented
7#13094007—23no—
8#13094005C2216yescomplemented
9#13093996—26no—
10#13093993—23no—
11#13093992C2216yescomplemented
12C2×C22⋊Dic47C2213yescomplemented
13#13093939C22112yescomplemented
14H(5,𝔽2)×C47—26no—
15H(5,𝔽2)×C47C2214yes—
16C2×#41×C47—23no—
17C22×D4×C47—23no—
18C22×D4×C47C2213yes—
19C24×C47—21no—
20C24×C47D413yescomplemented
21C24×C47C2311yescharacteristic
22C23×D47C2311yescharacteristic, complemented
23#41×C47—212no—
24#41×C47—212no—
25C2×Q8×C47—21no—
26C2×D4×C47—23no—
27C2×D4×C47—212no—
28C2×D4×C47—26no—
29C2×D4×C47—212no—
30C2×D4×C47—26no—
31C2×D4×C47D416yescomplemented
32C2×D4×C47C2316yes—
33C22×C4×C47—23no—
34C22×C4×C47D413yescomplemented
35C2×C22⋊D47—23no—
36C2×C22⋊D47—23no—
37C2×C22⋊D47—26no—
38C22×Dic47—23no—
39C22×Dic47C2311yescharacteristic, complemented
40C22⋊Dic47—23no—
41C22⋊Dic47—26no—
42C22⋊Dic47C2316yescomplemented
43(C2×D47)⋊C4—26no—
44Dic47⋊C4—26no—
45C23×C47—24no—
46C23×C47—23no—
47C23×C47—23no—
48C23×C47—81no—
49C23×C47—83no—
50C23×C47—82no—
51C23×C47C2×D416yes—
52C23×C47C2×D413yes—
53C23×C47C2×D413yes—
54C23×C47C2411yescharacteristic
55C22×D47—23no—
56C22×D47—81no—
57Q8×C47—24no—
58D4×C47—212no—
59D4×C47—212no—
60D4×C47—212no—
61C2×C4×C47—212no—
62C2×C4×C47—23no—
63C2×C4×C47—23no—
64C2×C4×C47C2×D416yes—
65C22⋊D47—41no—
66C22⋊D47—43no—
67C22⋊D47—86no—
68C2×Dic47—23no—
69C2×Dic47—26no—
70C2×Dic47—83no—
71C22×C47—26no—
72C22×C47—43no—
73C22×C47—41no—
74C22×C47—43no—
75C22×C47—46no—
76C22×C47—46no—
77C22×C47—83no—
78C22×C47—84no—
79C22×C47#12011yescharacteristic
80C22×C47#12013yes—
81C22×C47C22×D413yes—
82C2×D47—46no—
83C2×D47—41no—
84C4×C47—26no—
85Dic47—46no—
86Dic47—41no—
87#3026—471nomaximal, Sylow
88C2×C47—23no—
89C2×C47—21no—
90C2×C47—23no—
91C2×C47—46no—
92C2×C47C2×#12011yescharacteristic
93D47—81no—
94C2×H(5,𝔽2)D4711yescharacteristic, complemented
95#534—473no—
96#458—474no—
97B(4,𝔽2)—474no—
98C2×#99—473no—
99C47#302611yescharacteristic, complemented, Sylow
100H(5,𝔽2)—26no—
101H(5,𝔽2)C2×D4714yes—
102C2×#41—23no—
103C22×D4—23no—
104C22×D4—471no—
105C22×D4C2×D4713yes—
106#123—476no—
107#123—943no—
108#121—946no—
109#120—476no—
110#120—943no—
111C2×C22⋊C4—473no—
112#99—4712no—
113C24—21no—
114C24—471no—
115C24C22⋊D4713yescomplemented
116C24C22×D4711yescharacteristic
117#41—212no—
118#41—212no—
119C2×Q8—21no—
120C2×D4—23no—
121C2×D4—212no—
122C2×D4—26no—
123C2×D4—212no—
124C2×D4—26no—
125C2×D4—946no—
126C2×D4—943no—
127C2×D4—943no—
128C2×D4C22⋊D4716yescomplemented
129C2×D4C22×D4716yes—
130C22×C4—23no—
131C22×C4—471no—
132C22×C4—943no—
133C22×C4C22⋊D4713yescomplemented
134C4⋊C4—946no—
135C22⋊C4—476no—
136C22⋊C4—943no—
137C22⋊C4—946no—
138C22⋊C4—946no—
139C23—24no—
140C23—23no—
141C23—23no—
142C23—81no—
143C23—83no—
144C23—82no—
145C23—943no—
146C23—3761no—
147C23C2×C22⋊D4716yes—
148C23C2×C22⋊D4713yes—
149C23C2×C22⋊D4713yes—
150C23C23×D4711yescharacteristic
151Q8—24no—
152D4—212no—
153D4—212no—
154D4—212no—
155D4—3766no—
156D4—1881no—
157D4—1883no—
158C2×C4—212no—
159C2×C4—23no—
160C2×C4—23no—
161C2×C4—946no—
162C2×C4—943no—
163C2×C4—3763no—
164C2×C4C2×C22⋊D4716yes—
165C22—26no—
166C22—43no—
167C22—43no—
168C22—41no—
169C22—46no—
170C22—46no—
171C22—83no—
172C22—84no—
173C22—1886no—
174C22—1881no—
175C22#1309399311yescharacteristic
176C22#1309399313yes—
177C22C22×C22⋊D4713yes—
178C4—26no—
179C4—1886no—
180C4—1881no—
181C2—23no—
182C2—21no—
183C2—23no—
184C2—46no—
185C2—3761no—
186C2C2×#1309399311yescharacteristic
subgroupG/H
centerC2C2×#13093993
commutatorC23×C47C24
FrattiniC23C23×D47
FittingC2×H(5,𝔽2)×C47C2
socleC2×C47C2×#120
hypercenterC2×H(5,𝔽2)D47
hypocenterC47#3026
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C24 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #15689682C2semidirect
2. #15689313C2semidirect
3. #15689310C2semidirect
4. C2×#13093939C2semidirect
5. C2×H(5,𝔽2)×C47C2semidirect
6. C22×C22⋊D47C22semidirect
8. #13094005C22semidirect
11. #13093992C22semidirect
12. C2×C22⋊Dic47C22semidirect
13. #13093939C22semidirect
20. C24×C47D4semidirect
22. C23×D47C23semidirect
31. C2×D4×C47D4semidirect
34. C22×C4×C47D4semidirect
39. C22×Dic47C23semidirect
42. C22⋊Dic47C23semidirect
94. C2×H(5,𝔽2)D47semidirect
99. C47#3026semidirect
115. C24C22⋊D47semidirect
128. C2×D4C22⋊D47semidirect
133. C22×C4C22⋊D47semidirect