Finite Group Databasebeta

← #19132613

Subgroups — #19132613

Order 5504.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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
1C22⋊(C43⋊C16)C211yesmaximal, characteristic
2#14582664C211yesmaximal, characteristic
3C43×#467C211yesmaximal, characteristic
4C2×#10621877—21no—
5C2×C43⋊C16—21no—
6C2×Q16×C43C411yescharacteristic
7C22×C8×C43C2211yescharacteristic
8C22⋊Q8×C43—21no—
9#107×C43C411yescharacteristic
10#103×C43—21no—
11C2×Q8×C43—21no—
12C22×C4×C43D411yescharacteristic
13Q16×C43—41no—
14C2×C8×C43—41no—
15C2×C8×C43C2×C411yescharacteristic
16C2×C8×C43D411yescharacteristic
17C4⋊C4×C43—21no—
18C4⋊C4×C43—41no—
19C22⋊C4×C43—41no—
20#10621877—22no—
21#10621877—41no—
22C2×C43⋊C8—41no—
23C43⋊C16—41no—
24C23×C43SD1611yescharacteristic
25Q8×C43—41no—
26Q8×C43—41no—
27C2×C4×C43—21no—
28C2×C4×C43—21no—
29C2×C4×C43—41no—
30C2×C4×C43—41no—
31C2×C4×C43C22⋊C411yescharacteristic
32C2×C4×C43D811yescharacteristic
33C8×C43—21no—
34C8×C43—21no—
35C43⋊C8—42no—
36C22×C43—21no—
37C22×C43—21no—
38C22×C43—21no—
39C22×C43#10211yescharacteristic
40C4×C43—21no—
41C4×C43—81no—
42C4×C43—81no—
43C4×C43#9911yescharacteristic
44C4×C43#10411yescharacteristic
45#1350—431nomaximal, Sylow
46C2×C43—41no—
47C2×C43#32711yescharacteristic
48C2×C43#35911yescharacteristic
49C2×C43#36211yescharacteristic
50#467D4311yescharacteristic
51C22⋊C16—431no—
52#341—431no—
53C43#135011yescharacteristic, complemented, Sylow
54C2×Q16Dic4311yescharacteristic
55C2×M16—861no—
56C22×C8C2×D4311yescharacteristic
57C22⋊Q8—21no—
58C2×C16—861no—
59#107Dic4311yescharacteristic
60#103—21no—
61C2×Q8—21no—
62C22×C4C22⋊D4311yescharacteristic
63Q16—41no—
64M16—862no—
65M16—1721no—
66C2×C8—41no—
67C2×C8—1721no—
68C2×C8C2×Dic4311yescharacteristic
69C2×C8C22⋊D4311yescharacteristic
70C4⋊C4—21no—
71C4⋊C4—41no—
72C22⋊C4—41no—
73C16—1721no—
74C23#1062188311yescharacteristic
75Q8—41no—
76Q8—41no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—41no—
80C2×C4—41no—
81C2×C4#1062188211yescharacteristic
82C2×C4C22⋊Dic4311yescharacteristic
83C8—21no—
84C8—21no—
85C8—1722no—
86C22—21no—
87C22—21no—
88C22—21no—
89C22#1306324611yescharacteristic
90C4—21no—
91C4—81no—
92C4—81no—
93C4#1306324011yescharacteristic
94C4#1306325211yescharacteristic
95C2—41no—
96C2#1458263311yescharacteristic
97C2#1458270611yescharacteristic
98C2#1458271511yescharacteristic
subgroupG/H
centerC22#13063246
commutatorC2×C8×C43C2×C4
FrattiniC22×C8C2×D43
FittingC43×#467C2
socleC22×C43#102
hypercenter#467D43
hypocenterC43#1350
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
53. C43#1350semidirect