Finite Group Databasebeta

← #20245513

Subgroups — #20245513

Order 6016.

140 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 49 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×Dic376C211yesmaximal, characteristic, complemented
2#15689398C212yesmaximal
3#15688953C211yesmaximal, characteristic, complemented
4#15688940C212yesmaximal, complemented
5C47×#504C211yesmaximal, characteristic
6#13094054—22no—
7C2×Dic188C2212yes—
8Dic376—21no—
9Dic376—21no—
10#13093960C2212yes—
11#13093942—22no—
12#131×C47C2211yescharacteristic
13M32×C47—21no—
14M32×C47C2211yescharacteristic
15C2×C16×C47—21no—
16C2×C16×C47C2211yescharacteristic
17#41×C47D411yescharacteristic
18C2×Dic94—22no—
19M16×C47—21no—
20M16×C47D411yescharacteristic
21C2×C8×C47—21no—
22C2×C8×C47C2311yescharacteristic
23#10625337—42no—
24#10625335—42no—
25#10625329—22no—
26Dic188—22no—
27Dic188—22no—
28C16×C47—21no—
29C16×C47D411yescharacteristic
30C16×C47D411yescharacteristic
31Q8×C47D811yescharacteristic
32D4×C47—21no—
33D4×C47D811yescharacteristic
34C2×C4×C47—21no—
35C2×C4×C47C2×D411yescharacteristic
36C2×Dic47—42no—
37Dic94—42no—
38Dic94—42no—
39C8×C47—21no—
40C8×C47C2×D411yescharacteristic
41C8×C47#4111yescharacteristic
42C47⋊C8—42no—
43C22×C47—21no—
44C22×C47#13511yescharacteristic
45C4×C47—21no—
46C4×C47#12111yescharacteristic
47C4×C47C2×D811yescharacteristic
48Dic47—82no—
49#2222—471nomaximal, Sylow
50C2×C47—21no—
51C2×C47—41no—
52C2×C47#46611yescharacteristic
53C2×Q32—471no—
54#504D4711yescharacteristic
55#473—472no—
56#368—471no—
57#362—472no—
58C47#222211yescharacteristic, complemented, Sylow
59#137—942no—
60C2×Q16—472no—
61#131C2×D4711yescharacteristic
62Q32—941no—
63Q32—941no—
64M32—21no—
65M32C2×D4711yescharacteristic
66C2×C16—21no—
67C2×C16C2×D4711yescharacteristic
68#108—472no—
69#101—942no—
70#41D18811yescharacteristic
71C2×Q8—942no—
72Q16—942no—
73Q16—942no—
74Q16—1882no—
75SD16—1882no—
76M16—21no—
77M16—942no—
78M16D18811yescharacteristic
79C2×C8—21no—
80C2×C8C22×D4711yescharacteristic
81C16—21no—
82C16C22⋊D4711yescharacteristic
83C16C22⋊D4711yescharacteristic
84Q8—1882no—
85Q8—1882no—
86Q8D37611yescharacteristic
87D4—21no—
88D4D37611yescharacteristic
89C2×C4—21no—
90C2×C4—1882no—
91C2×C4C2×D18811yescharacteristic
92C8—21no—
93C8—1882no—
94C8#1062535011yescharacteristic
95C8C2×C22⋊D4711yescharacteristic
96C22—21no—
97C22#1309404611yescharacteristic
98C4—21no—
99C4—3762no—
100C4#1309399811yescharacteristic
101C4C2×D37611yescharacteristic
102C2—21no—
103C2—41no—
104C2#1568935911yescharacteristic
subgroupG/H
centerC2#15689359
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#504C2
socleC2×C47#466
hypercenter#504D47
hypocenterC47#2222
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #504

Complements

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

NH ≅ G/Ntype
1. C2×Dic376C2semidirect
3. #15688953C2semidirect
4. #15688940C2semidirect
58. C47#2222semidirect