Finite Group Databasebeta

← #28406488

Subgroups — #28406488

Order 14464.

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

normal subgroups only

This group has 236 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
1C2×#16813683C212yesmaximal
2#20299479C214yesmaximal
3#20299075C211yesmaximal, characteristic
4C2×#14268656C2214yes—
5#16813683—22no—
6#16813683—22no—
7C22×Dic226C2211yescharacteristic
8C4×Dic226—22no—
9#16813587—22no—
10#16813581C411yescharacteristic
11#16813578C412yes—
12#16813578C2212yes—
13#117×C113C411yescharacteristic
14#14268656—24no—
15#14268656—24no—
16C2×#11744753—24no—
17C2×Dic226—24no—
18C2×Dic226D412yes—
19C2×Dic226D412yes—
20C22×Dic113C2×C411yescharacteristic
21C22×Dic113C2311yescharacteristic
22C4⋊Dic113—21no—
23#14268626—22no—
24#14268626—22no—
25C22⋊Dic113C2×C412yes—
26C4×Dic113—21no—
27C4×Dic113—22no—
28C4×Dic113—22no—
29C22×C4×C113C2×C411yescharacteristic
30C4⋊C4×C113—21no—
31C22⋊C4×C113C2×C412yes—
32C42×C113—21no—
33C23×C113C22×C411yescharacteristic
34C2×C4×C113—22no—
35C2×C4×C113—22no—
36C2×C4×C113C22⋊C411yescharacteristic
37C2×C4×C113C22⋊C411yescharacteristic
38C2×Dic113—22no—
39C2×Dic113—22no—
40C2×Dic113C22⋊C412yes—
41C2×Dic113C2×D412yes—
42C2×Dic113#4114yes—
43Dic226—24no—
44Dic226—24no—
45#11744753—44no—
46C22×C113—41no—
47C22×C113C2×C22⋊C411yescharacteristic
48C22×C113#11712yes—
49C4×C113—21no—
50C4×C113—21no—
51C4×C113—42no—
52Dic113—22no—
53Dic113—42no—
54Dic113#12314yes—
55C2×C113—21no—
56C2×C113—22no—
57C2×C113#38111yescharacteristic
58#1830—1131nomaximal, Sylow
59C113#183011yescharacteristic, complemented, Sylow
60#519—1131no—
61C2×#101—1132no—
62#344—1134no—
63C22×Q8—1131no—
64C2×M16—1134no—
65C4×Q8—2262no—
66C4×Q8—2262no—
67#117—1131no—
68#117—1132no—
69#117—1132no—
70#117#9067311yescharacteristic
71#101—2262no—
72#101—2262no—
73C2×Q8—1132no—
74C2×Q8—1132no—
75C2×Q8—2264no—
76C22×C4—1131no—
77C22×C4—1131no—
78C22×C4C2×#9067311yescharacteristic
79M16—2264no—
80M16—2264no—
81C2×C8—2264no—
82C4⋊C4—21no—
83C4⋊C4—2262no—
84C4⋊C4—2262no—
85C4⋊C4—2261no—
86C22⋊C4—1132no—
87C22⋊C4C2×#9067312yes—
88C42—21no—
89C42—2262no—
90C42—2262no—
91C42—2261no—
92C23C22×#9067311yescharacteristic
93Q8—2264no—
94Q8—2264no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—1132no—
98C2×C4—1134no—
99C2×C4—1132no—
100C2×C4—2262no—
101C2×C4—2262no—
102C2×C4C22⋊#9067311yescharacteristic
103C2×C4C22⋊#9067311yescharacteristic
104C8—4524no—
105C22—41no—
106C22C2×C22⋊#9067311yescharacteristic
107C22#1681370112yes—
108C4—21no—
109C4—21no—
110C4—42no—
111C4—1134no—
112C4—4522no—
113C4—2262no—
114C2—21no—
115C2—22no—
116C2#2029954111yescharacteristic
subgroupG/H
centerC2#20299541
commutator, prime radicalC23×C113C22×C4
FrattiniC23C22×#90673
Fitting#117×C113C4
socleC2×C113#381
cosocleC22×Dic113C23
hypercenter#117#90673
hypocenterC113#1830
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C23 ◁ #117

Complements

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

NH ≅ G/Ntype
59. C113#1830semidirect

Maximal subgroups

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

subgroupindex
C2×#168136832
#202994792
#202990752
#1830113