Finite Group Databasebeta

← #28389655

Subgroups — #28389655

Order 14464.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299314C211yesmaximal, characteristic, complemented
2#20298790C212yesmaximal, complemented
3#20298347C211yesmaximal, characteristic, complemented
4#20298327C212yesmaximal, complemented
5#492×C113C211yesmaximal, characteristic, complemented
6C2×#14268632—22no—
7#16813611—22no—
8#16813597—22no—
9C4×D452C2212yes—
10#16813580—22no—
11C4⋊#11744751C2212yes—
12#16813543—22no—
13C2×SD16×C113—22no—
14C4⋊Q8×C113C2211yescharacteristic
15#127×C113C2211yescharacteristic
16C4×C8×C113C2211yescharacteristic
17C2×D452—22no—
18C2×D452D412yes—
19C2×C4×D113—22no—
20#14268632—44no—
21C2×#11744751—22no—
22C4⋊Dic113D412yes—
23#14268624—24no—
24#14268624—22no—
25C4×Dic113—22no—
26C2×Q8×C113D412yes—
27C2×D4×C113—22no—
28C2×D4×C113—21no—
29SD16×C113—44no—
30C2×C8×C113—21no—
31C4⋊C4×C113—22no—
32C42×C113C2311yescharacteristic
33C23×C113—41no—
34C22×D113—22no—
35Q8×C113—42no—
36D4×C113—42no—
37D4×C113—42no—
38D4×C113—42no—
39C2×C4×C113—22no—
40C2×C4×C113C2×D412yes—
41C2×C4×C113C2×D411yescharacteristic
42C2×Dic113—22no—
43D452—22no—
44D452—22no—
45D452—82no—
46C4×D113—42no—
47C4×D113—42no—
48C8×C113—22no—
49#11744751—42no—
50C22×C113—82no—
51C22×C113—81no—
52C22×C113#12011yescharacteristic
53C2×D113—42no—
54C2×D113—42no—
55C2×D113—42no—
56C4×C113—21no—
57C4×C113—42no—
58C4×C113#13512yes—
59C4×C113AGL(1,ℤ/8)12yes—
60Dic113—42no—
61C2×C113—161no—
62C2×C113#44912yes—
63C2×C113#45311yescharacteristic
64D113—82no—
65#1624—1131nomaximal, Sylow
66C113#162411yescharacteristic, complemented, Sylow
67#555—1131no—
68#492D11311yescharacteristic, complemented
69#459—1132no—
70#333—1131no—
71D4⋊C8—1132no—
72C2×SD16—22no—
73C2×D8—2262no—
74C4⋊Q8C2×D11311yescharacteristic
75#127C2×D11311yescharacteristic
76#124—2262no—
77#121—2262no—
78C4×D4—1132no—
79#117—2262no—
80C4⋊C8—1132no—
81#102—2262no—
82C4×C8C2×D11311yescharacteristic
83C2×Q8C22⋊D11312yes—
84C2×D4—22no—
85C2×D4—21no—
86C2×D4—1132no—
87C2×D4—2262no—
88C22×C4—2262no—
89SD16—44no—
90D8—4524no—
91C2×C8—21no—
92C2×C8—2262no—
93C4⋊C4—22no—
94C4⋊C4—1132no—
95C22⋊C4—2264no—
96C22⋊C4—2262no—
97C42—2262no—
98C42C22×D11311yescharacteristic
99C23—41no—
100C23—2262no—
101Q8—42no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—9042no—
106D4—2262no—
107D4—2262no—
108C2×C4—22no—
109C2×C4—4522no—
110C2×C4—4522no—
111C2×C4—2262no—
112C2×C4D4×D11312yes—
113C2×C4C2×C22⋊D11311yescharacteristic
114C8—22no—
115C8—4522no—
116C22—81no—
117C22—82no—
118C22—4522no—
119C22—4522no—
120C22—4522no—
121C22#1681359011yescharacteristic
122C4—21no—
123C4—42no—
124C4—4522no—
125C4#1681364312yes—
126C4#1681364912yes—
127C2—161no—
128C2—9042no—
129C2#2029874212yes—
130C2#2029876511yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#492×C113C2
socleC22×C113#120
hypercenter#492D113
hypocenterC113#1624
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #20299314C2semidirect
2. #20298790C2semidirect
3. #20298347C2semidirect
4. #20298327C2semidirect
5. #492×C113C2semidirect
66. C113#1624semidirect
68. #492D113semidirect

Maximal subgroups

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

subgroupindex
#202993142
#202987902
#202983472
#202983272
#492×C1132
#1624113