Finite Group Databasebeta

← #20242155

Subgroups — #20242155

Order 6016.

166 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 89 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#15689180C211yesmaximal, characteristic
2#15689147C211yesmaximal, characteristic
3#15688876C212yesmaximal, complemented
4#15688874C212yesmaximal, complemented
5C4×M16×C47C211yesmaximal, characteristic
6C2×#10625329—21no—
7C4⋊(C47⋊C8)—21no—
8C4⋊(C47⋊C8)C2211yescharacteristic
9C4⋊(C47⋊C8)C2212yes—
10C4⋊(C47⋊C8)C2211yescharacteristic
11C22⋊(C47⋊C8)—21no—
12#13093935—21no—
13C2×M16×C47C412yes—
14C2×C42×C47C2211yescharacteristic
15#97×C47C411yescharacteristic
16#97×C47C411yescharacteristic
17C4×C8×C47C2212yes—
18C22×C4×C47C2×C411yescharacteristic
19C22×C4×C47D411yescharacteristic
20C22×C4×C47Q811yescharacteristic
21M16×C47—24no—
22C2×C8×C47C2×C412yes—
23C2×C8×C47C2×C412yes—
24C42×C47C2×C411yescharacteristic
25C42×C47D411yescharacteristic
26C42×C47Q811yescharacteristic
27C42×C47C2311yescharacteristic
28#10625329—42no—
29C2×C47⋊C8—21no—
30C2×C47⋊C8—21no—
31C2×C47⋊C8—22no—
32C23×C47C4⋊C411yescharacteristic
33C2×C4×C47—22no—
34C2×C4×C47—21no—
35C2×C4×C47—21no—
36C2×C4×C47—41no—
37C2×C4×C47C4⋊C411yescharacteristic
38C2×C4×C47C4⋊C411yescharacteristic
39C2×C4×C47C4⋊C411yescharacteristic
40C2×C4×C47C22×C411yescharacteristic
41C2×C4×C47C2×D411yescharacteristic
42C2×C4×C47C2×Q811yescharacteristic
43C8×C47—22no—
44C8×C47M1614yescomplemented
45C47⋊C8—41no—
46C47⋊C8—42no—
47C47⋊C8—41no—
48C22×C47—21no—
49C22×C47—21no—
50C22×C47—21no—
51C22×C47C2×C4⋊C411yescharacteristic
52C4×C47—21no—
53C4×C47—21no—
54C4×C47—21no—
55C4×C47—21no—
56C4×C47C2×M1612yes—
57C4×C47AGL(1,ℤ/8)11yescharacteristic
58C4×C47#13711yescharacteristic
59#1569—471nomaximal, Sylow
60C2×C47—41no—
61C2×C47#42311yescharacteristic
62C2×C47#42811yescharacteristic
63C2×C47#43011yescharacteristic
64#432—471no—
65#423—471no—
66C4×M16D4711yescharacteristic
67#335—472no—
68#334—472no—
69C47#156911yescharacteristic, complemented, Sylow
70C2×M16—941no—
71C2×M16Dic4712yes—
72C2×C42C2×D4711yescharacteristic
73C4⋊C8—471no—
74C4⋊C8—472no—
75C4⋊C8—471no—
76C4⋊C8—941no—
77C22⋊C8—941no—
78#97—941no—
79#97Dic4711yescharacteristic
80#97Dic4711yescharacteristic
81C4×C8C2×D4712yes—
82C22×C4Dic9411yescharacteristic
83C22×C4D18811yescharacteristic
84C22×C4C2×Dic4711yescharacteristic
85M16—24no—
86M16—1882no—
87C2×C8—941no—
88C2×C8—941no—
89C2×C8—942no—
90C2×C8C2×Dic4712yes—
91C2×C8C2×Dic4712yes—
92C42Dic9411yescharacteristic
93C42D18811yescharacteristic
94C42C2×Dic4711yescharacteristic
95C42C22×D4711yescharacteristic
96C23C4⋊Dic4711yescharacteristic
97C2×C4—22no—
98C2×C4—21no—
99C2×C4—21no—
100C2×C4—41no—
101C2×C4C4⋊Dic4711yescharacteristic
102C2×C4C4⋊Dic4711yescharacteristic
103C2×C4C4⋊Dic4711yescharacteristic
104C2×C4C2×Dic9411yescharacteristic
105C2×C4C2×D18811yescharacteristic
106C2×C4C22×Dic4711yescharacteristic
107C8—22no—
108C8—1881no—
109C8—1882no—
110C8—1881no—
111C8#1062532914yescomplemented
112C22—21no—
113C22—21no—
114C22—21no—
115C22C2×C4⋊Dic4711yescharacteristic
116C4—21no—
117C4—21no—
118C4—21no—
119C4—21no—
120C4C2×#1062532912yes—
121C4#1309405211yescharacteristic
122C4#1309405711yescharacteristic
123C2—41no—
124C2#1568914711yescharacteristic
125C2#1568916511yescharacteristic
126C2#1568917211yescharacteristic
subgroupG/H
centerC2×C4C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC4×M16×C47C2
socleC22×C47C2×C4⋊C4
hypercenterC4×M16D47
hypocenterC47#1569
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #15688876C2semidirect
4. #15688874C2semidirect
44. C8×C47M16semidirect
69. C47#1569semidirect
111. C8#10625329semidirect