Finite Group Databasebeta

← #19136270

Subgroups — #19136270

Order 5504.

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

normal subgroups only

This group has 238 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
2#14582694C214yesmaximal, complemented
3C43×#536C211yesmaximal, characteristic
4#13063284—22no—
5#13063240—22no—
6#13063240C2214yes—
7C2×#41×C43C2211yescharacteristic
8C22×Q8×C43C411yescharacteristic, complemented
9C4⋊Q8×C43C412yescomplemented
10#124×C43C2212yes—
11#123×C43—22no—
12C22⋊Q8×C43—22no—
13#117×C43C411yescharacteristic, complemented
14#41×C43—42no—
15C2×Q8×C43—21no—
16C2×Q8×C43—42no—
17C2×Q8×C43C2×C412yes—
18C2×Q8×C43C2×C411yescharacteristic
19C2×D4×C43D412yes—
20C2×D4×C43C2311yescharacteristic
21C22×C4×C43—21no—
22C22×C4×C43C2×C411yescharacteristic
23C22×C4×C43D412yes—
24C4⋊C4×C43—21no—
25C4⋊C4×C43—24no—
26C22⋊C4×C43—21no—
27C22⋊C4×C43—24no—
28C42×C43C2×C412yes—
29C22⋊Dic43—24no—
30C4⋊Dic43—42no—
31C4×Dic43—42no—
32C23×C43C22⋊C411yescharacteristic
33C23×C43C2×D412yes—
34Q8×C43—41no—
35Q8×C43—42no—
36Q8×C43—42no—
37D4×C43—42no—
38D4×C43—41no—
39C2×C4×C43—22no—
40C2×C4×C43—22no—
41C2×C4×C43—22no—
42C2×C4×C43—22no—
43C2×C4×C43—22no—
44C2×C4×C43—42no—
45C2×C4×C43C22⋊C412yes—
46C2×C4×C43C22⋊C411yescharacteristic
47C2×C4×C43C22×C411yescharacteristic
48C2×Dic43—44no—
49C22×C43—21no—
50C22×C43—22no—
51C22×C43—41no—
52C22×C43—42no—
53C22×C43C2×C22⋊C411yescharacteristic
54C4×C43—22no—
55C4×C43—21no—
56C4×C43—42no—
57C4×C43—42no—
58C4×C43#9912yes—
59Dic43—84no—
60#2129—431nomaximal, Sylow
61C2×C43—21no—
62C2×C43—42no—
63C2×C43—41no—
64C2×C43C2×#9911yescharacteristic
65#536D4311yescharacteristic
66#410—432no—
67#354—434no—
68C43#212911yescharacteristic, complemented, Sylow
69C2×#41C2×D4311yescharacteristic
70C22×Q8Dic4311yescharacteristic, complemented
71C4⋊Q8Dic4312yescomplemented
72#124C2×D4312yes—
73#123—22no—
74C22⋊Q8—22no—
75#117—862no—
76#117Dic4311yescharacteristic, complemented
77#99—434no—
78#99—862no—
79#41—42no—
80C2×Q8—21no—
81C2×Q8—42no—
82C2×Q8C2×Dic4312yes—
83C2×Q8C2×Dic4311yescharacteristic
84C2×D4C22⋊D4312yes—
85C2×D4C22×D4311yescharacteristic
86C22×C4—21no—
87C22×C4C2×Dic4311yescharacteristic
88C22×C4C22⋊D4312yes—
89C4⋊C4—24no—
90C4⋊C4—21no—
91C4⋊C4—1722no—
92C22⋊C4—21no—
93C22⋊C4—24no—
94C22⋊C4—864no—
95C42—1722no—
96C42C2×Dic4312yes—
97C23C22⋊Dic4311yescharacteristic
98C23C2×C22⋊D4312yes—
99Q8—41no—
100Q8—42no—
101Q8—42no—
102D4—41no—
103D4—42no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—1724no—
111C2×C4C22⋊Dic4312yes—
112C2×C4C22⋊Dic4311yescharacteristic
113C2×C4C22×Dic4311yescharacteristic
114C22—21no—
115C22—22no—
116C22—41no—
117C22—42no—
118C22C2×C22⋊Dic4311yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C4—3444no—
124C4#1306324012yes—
125C2—21no—
126C2—42no—
127C2—41no—
128C2C2×#1306324011yescharacteristic
subgroupG/H
centerC2C2×#13063240
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#536C2
socleC2×C43C2×#99
hypercenter#536D43
hypocenterC43#2129
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #14582694C2semidirect
8. C22×Q8×C43C4semidirect
9. C4⋊Q8×C43C4semidirect
13. #117×C43C4semidirect
68. C43#2129semidirect
70. C22×Q8Dic43semidirect
71. C4⋊Q8Dic43semidirect
76. #117Dic43semidirect