Finite Group Databasebeta

← #28406101

Subgroups — #28406101

Order 14464.

332 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 62 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#20299618C212yesmaximal, complemented
2#20299456C214yesmaximal, complemented
3C2×#16813618C211yesmaximal, characteristic
4#16813689C2214yescomplemented
5C22⋊#11744753—22no—
6#16813677—22no—
7C22×D452C411yescharacteristic
8C22×C22⋊D113—22no—
9#16813618—22no—
10#16813618C412yes—
11#16813618C2212yes—
12C2×C4×Dic113C2211yescharacteristic
13C22×D4×C113C411yescharacteristic
14C2×#11744753—24no—
15C23×D113—21no—
16C2×D452—21no—
17C2×D452—42no—
18C2×D452C2×C412yes—
19C2×C22⋊D113—24no—
20C2×C22⋊D113—24no—
21C2×C22⋊D113—48no—
22C22×Dic113D412yes—
23C4×Dic113C2×C411yescharacteristic
24C4×Dic113D412yes—
25C4×Dic113C2311yescharacteristic
26C24×C113—21no—
27C2×D4×C113—21no—
28C2×D4×C113—42no—
29C2×D4×C113C2×C412yes—
30C22×C4×C113C2×C411yescharacteristic
31C23×C113—22no—
32C23×C113—44no—
33C23×C113—42no—
34C23×C113C22⋊C411yescharacteristic
35C22×D113—22no—
36C22×D113—44no—
37C22×D113—42no—
38D4×C113—42no—
39D4×C113—42no—
40C2×C4×C113—22no—
41C2×C4×C113C22⋊C411yescharacteristic
42C2×C4×C113C22×C411yescharacteristic
43C22⋊D113—48no—
44C22⋊D113—48no—
45C2×Dic113—24no—
46C2×Dic113C22⋊C412yes—
47C2×Dic113C2×D412yes—
48D452—42no—
49D452—42no—
50#11744753—44no—
51C22×C113—22no—
52C22×C113—42no—
53C22×C113—44no—
54C22×C113—84no—
55C22×C113#10012yes—
56C22×C113C2×C22⋊C411yescharacteristic
57C2×D113—42no—
58C2×D113—44no—
59C2×D113—84no—
60C4×C113—21no—
61C4×C113—21no—
62Dic113—22no—
63Dic113AGL(1,ℤ/8)14yes—
64C2×C113—22no—
65C2×C113—82no—
66C2×C113C2×#10011yescharacteristic
67C2×C113#41812yes—
68D113—82no—
69#1555—1131nomaximal, Sylow
70C113#155511yescharacteristic, complemented, Sylow
71C2×#127—1131no—
72#432—1132no—
73#331—1134no—
74C22×D4—1131no—
75C22×D4—2262no—
76C22×D4#9067311yescharacteristic
77#127—1132no—
78#127—1132no—
79#127—2262no—
80C2×C42—1131no—
81C4⋊C8—1134no—
82C22⋊C8—2262no—
83#97—2262no—
84C24—21no—
85C24—2261no—
86C2×D4—21no—
87C2×D4—42no—
88C2×D4—1132no—
89C2×D4—4522no—
90C2×D4—4528no—
91C2×D4—2264no—
92C2×D4—2264no—
93C2×D4—2261no—
94C2×D4C2×#9067312yes—
95C22×C4—1132no—
96C22×C4C2×#9067311yescharacteristic
97C2×C8—2264no—
98C42—1132no—
99C42—1131no—
100C42—1131no—
101C23—22no—
102C23—44no—
103C23—42no—
104C23—4524no—
105C23—4522no—
106C23—2262no—
107C23C22⋊#9067311yescharacteristic
108D4—42no—
109D4—42no—
110D4—4522no—
111D4—4522no—
112D4—4528no—
113D4—4528no—
114C2×C4—22no—
115C2×C4—1132no—
116C2×C4—1132no—
117C2×C4—2264no—
118C2×C4C22⋊#9067311yescharacteristic
119C2×C4C22×#9067311yescharacteristic
120C8—4524no—
121C22—22no—
122C22—42no—
123C22—44no—
124C22—84no—
125C22—9044no—
126C22—4522no—
127C22—4524no—
128C22#1681368212yes—
129C22C2×C22⋊#9067311yescharacteristic
130C4—21no—
131C4—21no—
132C4—1134no—
133C4—2262no—
134C2—22no—
135C2—82no—
136C2—9042no—
137C2C2×#1681368211yescharacteristic
138C2#2029959012yes—
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC22×D4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC2×#16813618C2
cosocleC4×Dic113C23
hypercenterC22×D4#90673
hypocenterC113#1555
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20299618C2semidirect
2. #20299456C2semidirect
4. #16813689C22semidirect
70. C113#1555semidirect

Maximal subgroups

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

subgroupindex
#202996182
#202994562
C2×#168136182
#1555113