Finite Group Databasebeta

← C113×#1820 #28386616

Subgroups — C113×#1820 #28386616

Order 14464.

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

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 104 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×#117×C113C211yesmaximal, characteristic
2#381×C113C212yesmaximal
3#342×C113C214yesmaximal
4C23×C4×C113C2211yescharacteristic
5#117×C113—24no—
6C2×C4⋊C4×C113C412yescomplemented
7C2×C22⋊C4×C113C2214yes—
8C2×C22⋊C4×C113C2212yes—
9C2×C42×C113C412yescomplemented
10#95×C113—24no—
11C24×C113C2311yescharacteristic
12C22×C4×C113—24no—
13C22×C4×C113—24no—
14C22×C4×C113C2×C411yescharacteristic
15C22×C4×C113C2×C411yescharacteristic
16C22×C4×C113C2×C414yes—
17C22×C4×C113D414yes—
18C4⋊C4×C113—24no—
19C22⋊C4×C113—24no—
20C22⋊C4×C113—28no—
21C42×C113—24no—
22C23×C113—42no—
23C23×C113C22×C411yescharacteristic
24C23×C113C2×D412yes—
25C23×C113#4114yes—
26C2×C4×C113—22no—
27C2×C4×C113—22no—
28C2×C4×C113—28no—
29C2×C4×C113—24no—
30C2×C4×C113—44no—
31C2×C4×C113—48no—
32C2×C4×C113—44no—
33C2×C4×C113C22⋊C412yes—
34C2×C4×C113C22⋊C412yes—
35C22×C113—22no—
36C22×C113—24no—
37C22×C113—44no—
38C22×C113C2×C22⋊C411yescharacteristic
39C22×C113#11712yes—
40C22×C113#12314yes—
41C4×C113—22no—
42C4×C113—22no—
43C4×C113—44no—
44C4×C113—84no—
45C2×C113—24no—
46C2×C113—22no—
47C2×C113#38111yescharacteristic
48C2×C113#41012yes—
49#1820C11311yesmaximal, characteristic, direct product factor, Sylow
50C113#182011yescharacteristic, direct product factor, Sylow
51C2×#117C2×C11311yescharacteristic
52#381C2×C11312yes—
53#342C2×C11314yes—
54C23×C4C22×C11311yescharacteristic
55#117—24no—
56C2×C4⋊C4C4×C11312yescomplemented
57C2×C22⋊C4C22×C11314yes—
58C2×C22⋊C4C22×C11312yes—
59C2×C42C4×C11312yescomplemented
60#95—24no—
61C24C23×C11311yescharacteristic
62C22×C4—24no—
63C22×C4—24no—
64C22×C4C2×C4×C11311yescharacteristic
65C22×C4C2×C4×C11311yescharacteristic
66C22×C4C2×C4×C11314yes—
67C22×C4D4×C11314yes—
68C4⋊C4—24no—
69C22⋊C4—24no—
70C22⋊C4—28no—
71C42—24no—
72C23—42no—
73C23C22×C4×C11311yescharacteristic
74C23C2×D4×C11312yes—
75C23#41×C11314yes—
76C2×C4—22no—
77C2×C4—22no—
78C2×C4—28no—
79C2×C4—24no—
80C2×C4—44no—
81C2×C4—48no—
82C2×C4—44no—
83C2×C4C22⋊C4×C11312yes—
84C2×C4C22⋊C4×C11312yes—
85C22—22no—
86C22—24no—
87C22—44no—
88C22C2×C22⋊C4×C11311yescharacteristic
89C22#117×C11312yes—
90C22#123×C11314yes—
91C4—22no—
92C4—22no—
93C4—44no—
94C4—84no—
95C2—24no—
96C2—22no—
97C2#381×C11311yescharacteristic
98C2#410×C11312yes—
subgroupG/H
center, socleC22×C113C2×C22⋊C4
commutatorC23C22×C4×C113
Frattini, cosocleC24C23×C113
prime radicalC24×C113C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C4⋊C4×C113C4semidirect
9. C2×C42×C113C4semidirect
49. #1820C113direct (N × H)
50. C113#1820direct (N × H)
56. C2×C4⋊C4C4×C113semidirect
59. C2×C42C4×C113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117×C1132
#381×C1132
#342×C1132
#1820113