Finite Group Databasebeta

← #20251460

Subgroups — #20251460

Order 6016.

456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094018C211yesmaximal, characteristic, complemented
2#15689056C213yesmaximal, complemented
3#15689046C213yesmaximal, complemented
4#15689045C213yesmaximal, complemented
5#15689039C213yesmaximal
6#15688993C211yesmaximal, characteristic, complemented
7C2×#126×C47C211yesmaximal, characteristic, complemented
8C22×C22⋊D47C2211yescharacteristic
9#13094018—24no—
10C2×C4⋊Dic47C2213yes—
11C2×C4⋊Dic47C2213yes—
12C2×Dic47⋊C4C2213yes—
13C2×Dic47⋊C4C2213yes—
14C2×C22⋊Dic47C2213yes—
15C2×(C2×D47)⋊C4C2213yes—
16C2×(C2×D47)⋊C4C2213yes—
17C47⋊#95C2213yes—
18C47⋊#95C2213yes—
19#126×C47—24no—
20C2×C4⋊C4×C47C2213yes—
21C2×C22⋊C4×C47C2213yes—
22C2×C42×C47C2211yescharacteristic
23C24×C47C2311yescharacteristic
24C23×D47C2311yescharacteristic
25C22×C4×C47C2313yes—
26C22×C4×C47C2313yes—
27C2×C22⋊D47—43no—
28C22×Dic47C2311yescharacteristic
29C22×Dic47C2313yes—
30C22×Dic47C2313yes—
31C4⋊C4×C47—26no—
32C22⋊C4×C47—26no—
33C42×C47D414yescomplemented
34C22⋊Dic47—43no—
35(C2×D47)⋊C4—26no—
36(C2×D47)⋊C4—43no—
37C4⋊Dic47—43no—
38C4⋊Dic47—43no—
39Dic47⋊C4—26no—
40Dic47⋊C4—43no—
41C23×C47—21no—
42C23×C47—23no—
43C23×C47—23no—
44C23×C47C2411yescharacteristic
45C22×D47—21no—
46C22×D47—23no—
47C22×D47—23no—
48C2×C4×C47—23no—
49C2×C4×C47—23no—
50C2×C4×C47—23no—
51C2×C4×C47—23no—
52C2×C4×C47—23no—
53C2×C4×C47C2×D416yes—
54C22⋊D47—44no—
55C2×Dic47—23no—
56C2×Dic47—23no—
57C2×Dic47—23no—
58C2×Dic47—23no—
59C2×Dic47—23no—
60C2×Dic47—23no—
61C2×Dic47—23no—
62C22×C47—43no—
63C22×C47—41no—
64C22×C47—43no—
65C22×C47C22×D411yescharacteristic
66C22×C47H(5,𝔽2)13yes—
67C22×C472−1+413yes—
68C2×D47—43no—
69C2×D47—41no—
70C2×D47—43no—
71C4×C47—26no—
72C4×C47—43no—
73Dic47—43no—
74Dic47—43no—
75Dic47—41no—
76#2823—471nomaximal, Sylow
77C2×C47—81no—
78C2×C47#53713yes—
79C2×C47#56011yescharacteristic
80C2×C47#56313yes—
81D47—81no—
82C2×#126—471no—
83C2×#126D4711yescharacteristic, complemented
84#398—473no—
85#396—473no—
86#396—473no—
87#394—473no—
88#384—471no—
89C47#282311yescharacteristic, complemented, Sylow
90C22×D4—471no—
91#126—24no—
92#126—944no—
93C2×C4⋊C4—473no—
94C2×C4⋊C4—473no—
95C2×C4⋊C4—473no—
96C2×C4⋊C4—473no—
97C2×C4⋊C4C2×D4713yes—
98C2×C22⋊C4—473no—
99C2×C22⋊C4—473no—
100C2×C22⋊C4—473no—
101C2×C22⋊C4C2×D4713yes—
102C2×C42C2×D4711yescharacteristic
103#95—473no—
104#95—473no—
105C24—471no—
106C24C22×D4711yescharacteristic
107C2×D4—1883no—
108C22×C4—471no—
109C22×C4—473no—
110C22×C4—473no—
111C22×C4C22×D4713yes—
112C22×C4C22×D4713yes—
113C4⋊C4—26no—
114C4⋊C4—946no—
115C4⋊C4—1883no—
116C4⋊C4—1883no—
117C4⋊C4—1883no—
118C22⋊C4—26no—
119C22⋊C4—946no—
120C22⋊C4—1883no—
121C22⋊C4—1883no—
122C42C22⋊D4714yescomplemented
123C23—21no—
124C23—23no—
125C23—23no—
126C23—941no—
127C23—943no—
128C23—943no—
129C23C23×D4711yescharacteristic
130D4—1884no—
131C2×C4—23no—
132C2×C4—23no—
133C2×C4—23no—
134C2×C4—23no—
135C2×C4—23no—
136C2×C4—943no—
137C2×C4—943no—
138C2×C4—943no—
139C2×C4—943no—
140C2×C4—943no—
141C2×C4—943no—
142C2×C4—943no—
143C2×C4C2×C22⋊D4716yes—
144C22—41no—
145C22—43no—
146C22—43no—
147C22—1881no—
148C22—1883no—
149C22—1883no—
150C22C22×C22⋊D4711yescharacteristic
151C22#1309407013yes—
152C22#1309407113yes—
153C4—26no—
154C4—43no—
155C4—1881no—
156C4—1883no—
157C4—1883no—
158C2—81no—
159C2—3761no—
160C2#1568970113yes—
161C2#1568986411yescharacteristic
162C2#1568987513yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#126×C47C2
hypercenterC2×#126D47
hypocenterC47#2823
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#13094018C2semidirect
2. #15689056C2semidirect
3. #15689046C2semidirect
4. #15689045C2semidirect
6. #15688993C2semidirect
7. C2×#126×C47C2semidirect
33. C42×C47D4semidirect
83. C2×#126D47semidirect
89. C47#2823semidirect
122. C42C22⋊D47semidirect