Finite Group Databasebeta

← #20245514

Subgroups — #20245514

Order 6016.

140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689539C211yesmaximal, characteristic
3#15689399C212yesmaximal
4#15688938C212yesmaximal, complemented
5C47×#368C211yesmaximal, characteristic, complemented
6#13094057—22no—
7C2×Dic188C2212yes—
8#13094030C2211yescharacteristic
9Dic376—21no—
10Dic376—21no—
11#13093964C2211yescharacteristic
12#13093963—21no—
13C16×D47—21no—
14#13093942—22no—
15C2×C16×C47C2211yescharacteristic
16#108×C47C2212yes—
17#10625350D411yescharacteristic
18C2×Dic94—22no—
19M16×C47—22no—
20C2×C8×C47C2311yescharacteristic
21#10625329D411yescharacteristic
22Dic188—22no—
23Dic188—22no—
24Dic188—42no—
25#10625325—42no—
26#10625324—21no—
27C8×D47—21no—
28C16×C47D411yescharacteristic
29C16×C47D411yescharacteristic
30C47⋊C16—21no—
31C2×C4×C47C2×D411yescharacteristic
32C22⋊D47—21no—
33C2×Dic47—42no—
34D188D811yescharacteristic
35C4×D47—21no—
36Dic94—42no—
37Dic94—42no—
38Dic94D811yescharacteristic
39C8×C47—42no—
40C8×C47C2×D411yescharacteristic
41C8×C47#4111yescharacteristic
42C47⋊C8—21no—
43C22×C47#13511yescharacteristic
44C2×D47—21no—
45C4×C47#12111yescharacteristic
46C4×C47C2×D811yescharacteristic
47Dic47—21no—
48Dic47—82no—
49#2222—471nomaximal, Sylow
50C2×C47—21no—
51C2×C47#46611yescharacteristic
52D47—41no—
53C2×Q32—471no—
54#504—471no—
55#473—472no—
56#368D4711yescharacteristic, complemented
57#362—472no—
58C47#222211yescharacteristic, complemented, Sylow
59#137—942no—
60C2×Q16—472no—
61#131—471no—
62Q32—941no—
63Q32—941no—
64M32—471no—
65M32—941no—
66C2×C16—941no—
67C2×C16C2×D4711yescharacteristic
68#108C2×D4712yes—
69#101—942no—
70#41—471no—
71C2×Q8—942no—
72Q16—942no—
73Q16—942no—
74Q16—1882no—
75SD16—1882no—
76M16—22no—
77M16—471no—
78M16—941no—
79C2×C8—941no—
80C2×C8C22×D4711yescharacteristic
81C16—941no—
82C16D18811yescharacteristic
83C16D18811yescharacteristic
84Q8—471no—
85Q8—1882no—
86Q8—1882no—
87D4—471no—
88D4—941no—
89C2×C4—941no—
90C2×C4—1882no—
91C2×C4D4×D4711yescharacteristic
92C8—42no—
93C8—941no—
94C8C2×D18811yescharacteristic
95C8#1062535411yescharacteristic
96C22—941no—
97C22#1309404711yescharacteristic
98C4—941no—
99C4—3762no—
100C4#1309399911yescharacteristic
101C4D8×D4711yescharacteristic
102C2—21no—
103C2—1881no—
104C2#1568936011yescharacteristic
subgroupG/H
centerC2#15689360
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#368C2
socleC2×C47#466
hypercenter#368D47
hypocenterC47#2222
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #368

Complements

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

NH ≅ G/Ntype
1. C2×Dic376C2semidirect
4. #15688938C2semidirect
5. C47×#368C2semidirect
56. #368D47semidirect
58. C47#2222semidirect