Finite Group Databasebeta

← #19132625

Subgroups — #19132625

Order 5504.

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

normal subgroups only

This group has 140 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
1#14582668C211yesmaximal, characteristic
2#14582625C211yesmaximal, characteristic
3C43×#395C211yesmaximal, characteristic
4C2×#10621877—21no—
5C22⋊(C43⋊C8)—21no—
6C22×Q8×C43C411yescharacteristic
7C2×C4⋊C4×C43—21no—
8C2×C4⋊C4×C43C2211yescharacteristic
9#95×C43—21no—
10#95×C43C411yescharacteristic
11C2×Q8×C43—42no—
12C2×Q8×C43—41no—
13C22×C4×C43—21no—
14C22×C4×C43—21no—
15C22×C4×C43C2×C411yescharacteristic
16C22×C4×C43D411yescharacteristic
17C22×C4×C43D411yescharacteristic
18C4⋊C4×C43—41no—
19C4⋊C4×C43—42no—
20#10621877—22no—
21#10621877—41no—
22C2×C43⋊C8—41no—
23C2×C43⋊C8—41no—
24C23×C43C22⋊C411yescharacteristic
25Q8×C43—42no—
26Q8×C43—42no—
27C2×C4×C43—21no—
28C2×C4×C43—21no—
29C2×C4×C43—22no—
30C2×C4×C43—22no—
31C2×C4×C43—21no—
32C2×C4×C43—21no—
33C2×C4×C43—41no—
34C2×C4×C43—41no—
35C2×C4×C43—41no—
36C2×C4×C43—41no—
37C2×C4×C43—41no—
38C2×C4×C43—41no—
39C2×C4×C43SD1611yescharacteristic
40C2×C4×C43Q1611yescharacteristic
41C43⋊C8—42no—
42C43⋊C8—81no—
43C22×C43—21no—
44C22×C43—21no—
45C22×C43#9911yescharacteristic
46C22×C43#10311yescharacteristic
47C22×C43#10411yescharacteristic
48C4×C43—21no—
49C4×C43—21no—
50C4×C43—42no—
51C4×C43—41no—
52C4×C43—42no—
53C4×C43—41no—
54#1354—431nomaximal, Sylow
55C2×C43—21no—
56C2×C43—21no—
57C2×C43#32811yescharacteristic
58C2×C43AΣL(1,𝔽16)11yescharacteristic
59C2×C43#35611yescharacteristic
60#395D4311yescharacteristic
61#343—431no—
62#324—431no—
63C43#135411yescharacteristic, complemented, Sylow
64C22×Q8Dic4311yescharacteristic
65C2×M16—861no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4C2×D4311yescharacteristic
68C22⋊C8—861no—
69#95—21no—
70#95Dic4311yescharacteristic
71C2×Q8—42no—
72C2×Q8—41no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4C2×Dic4311yescharacteristic
76C22×C4C22⋊D4311yescharacteristic
77C22×C4C22⋊D4311yescharacteristic
78M16—862no—
79M16—1721no—
80C2×C8—1721no—
81C2×C8—1721no—
82C4⋊C4—41no—
83C4⋊C4—42no—
84C23C22⋊Dic4311yescharacteristic
85Q8—42no—
86Q8—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4#1062188411yescharacteristic
100C2×C4#1062188511yescharacteristic
101C8—3441no—
102C8—1722no—
103C22—21no—
104C22—21no—
105C22#1306324011yescharacteristic
106C22#1306324911yescharacteristic
107C22#1306325211yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—41no—
112C4—42no—
113C4—41no—
114C2—21no—
115C2—21no—
116C2#1458263611yescharacteristic
117C2#1458268611yescharacteristic
118C2#1458269811yescharacteristic
subgroupG/H
centerC22#13063240
commutatorC22×C4×C43C2×C4
FrattiniC2×C4⋊C4C2×D43
FittingC43×#395C2
socleC22×C43#99
hypercenter#395D43
hypocenterC43#1354
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
63. C43#1354semidirect