Finite Group Databasebeta

← #19136267

Subgroups — #19136267

Order 5504.

270 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 73 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#14582873C212yesmaximal, complemented
2#14582692C214yesmaximal, complemented
3C43×#535C211yesmaximal, characteristic
4#13063284—22no—
5#13063240—22no—
6#13063240C2214yescomplemented
7C2×#41×C43C2211yescharacteristic
8C22×D4×C43C411yescharacteristic, complemented
9#127×C43C2212yes—
10#124×C43C412yescomplemented
11#121×C43—22no—
12#120×C43—22no—
13#117×C43C411yescharacteristic, complemented
14C24×C43—21no—
15#41×C43—42no—
16C2×Q8×C43C2×C411yescharacteristic
17C2×D4×C43—21no—
18C2×D4×C43—24no—
19C2×D4×C43—42no—
20C2×D4×C43C2×C412yes—
21C2×D4×C43D412yes—
22C2×D4×C43C2311yescharacteristic
23C22×C4×C43C2×C411yescharacteristic
24C22×C4×C43D412yes—
25C4⋊C4×C43—21no—
26C22⋊C4×C43—24no—
27C22⋊C4×C43—21no—
28C42×C43C2×C412yes—
29C22⋊Dic43—24no—
30C4⋊Dic43—42no—
31C4×Dic43—42no—
32C23×C43—22no—
33C23×C43—42no—
34C23×C43—82no—
35C23×C43C22⋊C411yescharacteristic
36C23×C43C2×D412yes—
37Q8×C43—41no—
38D4×C43—42no—
39D4×C43—41no—
40D4×C43—42no—
41D4×C43—42no—
42D4×C43—84no—
43C2×C4×C43—22no—
44C2×C4×C43—22no—
45C2×C4×C43—22no—
46C2×C4×C43—22no—
47C2×C4×C43C22⋊C412yes—
48C2×C4×C43C22⋊C411yescharacteristic
49C2×C4×C43C22×C411yescharacteristic
50C2×Dic43—44no—
51C22×C43—21no—
52C22×C43—22no—
53C22×C43—41no—
54C22×C43—42no—
55C22×C43—44no—
56C22×C43—42no—
57C22×C43—84no—
58C22×C43C2×C22⋊C411yescharacteristic
59C4×C43—22no—
60C4×C43—21no—
61C4×C43—42no—
62C4×C43#9912yes—
63Dic43—84no—
64#2128—431nomaximal, Sylow
65C2×C43—21no—
66C2×C43—42no—
67C2×C43—41no—
68C2×C43—82no—
69C2×C43C2×#9911yescharacteristic
70#535D4311yescharacteristic
71#410—432no—
72#353—434no—
73C43#212811yescharacteristic, complemented, Sylow
74C2×#41C2×D4311yescharacteristic
75C22×D4Dic4311yescharacteristic, complemented
76#127C2×D4312yes—
77#124Dic4312yescomplemented
78#121—22no—
79#120—22no—
80#117—862no—
81#117Dic4311yescharacteristic, complemented
82#99—434no—
83#99—862no—
84C24—21no—
85#41—42no—
86C2×Q8C2×Dic4311yescharacteristic
87C2×D4—24no—
88C2×D4—21no—
89C2×D4—42no—
90C2×D4C2×Dic4312yes—
91C2×D4C22⋊D4312yes—
92C2×D4C22×D4311yescharacteristic
93C22×C4C2×Dic4311yescharacteristic
94C22×C4C22⋊D4312yes—
95C4⋊C4—21no—
96C4⋊C4—1722no—
97C22⋊C4—21no—
98C22⋊C4—24no—
99C22⋊C4—864no—
100C42—1722no—
101C42C2×Dic4312yes—
102C23—22no—
103C23—42no—
104C23—82no—
105C23C22⋊Dic4311yescharacteristic
106C23C2×C22⋊D4312yes—
107Q8—41no—
108D4—41no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—84no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—1724no—
118C2×C4C22⋊Dic4312yes—
119C2×C4C22⋊Dic4311yescharacteristic
120C2×C4C22×Dic4311yescharacteristic
121C22—22no—
122C22—21no—
123C22—42no—
124C22—41no—
125C22—44no—
126C22—42no—
127C22—84no—
128C22C2×C22⋊Dic4311yescharacteristic
129C4—22no—
130C4—21no—
131C4—42no—
132C4—3444no—
133C4#1306324012yes—
134C2—21no—
135C2—42no—
136C2—41no—
137C2—82no—
138C2C2×#1306324011yescharacteristic
subgroupG/H
centerC2C2×#13063240
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#535C2
socleC2×C43C2×#99
hypercenter#535D43
hypocenterC43#2128
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #14582873C2semidirect
2. #14582692C2semidirect
6. #13063240C22semidirect
8. C22×D4×C43C4semidirect
10. #124×C43C4semidirect
13. #117×C43C4semidirect
73. C43#2128semidirect
75. C22×D4Dic43semidirect
77. #124Dic43semidirect
81. #117Dic43semidirect