Finite Group Databasebeta

← #16777439

Subgroups — #16777439

Order 3328.

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

normal subgroups only

This group has 184 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#13130398C212yesmaximal
2#13116591C211yesmaximal, characteristic
3#11719130—22no—
4C2×C13×M32C411yescharacteristic
5C2×C8×Dic13C2211yescharacteristic
6C2×#88052C411yescharacteristic
7#11718255C414yes—
8#11718254—22no—
9#11718093—22no—
10C22×C8×C13C2×C411yescharacteristic
11C2×C4×Dic13D411yescharacteristic
12C22×#1055Q811yescharacteristic
13C22⋊#1057—42no—
14#88110—42no—
15C4⋊#1057—24no—
16C13×M32—41no—
17C2×C13×C16—21no—
18C8×Dic13C2×C412yes—
19C8×Dic13D412yes—
20#88052—41no—
21C2×#6090—21no—
22#7246—131nomaximal, Sylow
23C22×C4×C13C4⋊C411yescharacteristic
24C22×Dic13SD1612yes—
25C2×#1057—44no—
26C2×C8×C13—21no—
27C2×C8×C13—21no—
28C2×C8×C13C4211yescharacteristic
29C2×C8×C13C22⋊C411yescharacteristic
30C4×Dic13C22⋊C412yes—
31C4×Dic13D811yescharacteristic
32C4×Dic13Q1611yescharacteristic
33C2×#1055—41no—
34C2×#1055C4⋊C412yes—
35C13×C16—41no—
36#6090—41no—
37#2150—131no—
38#1568—132no—
39C23×C13#10611yescharacteristic
40C2×C4×C13—21no—
41C2×C4×C13—21no—
42C2×C4×C13#9511yescharacteristic
43C2×C4×C13#10711yescharacteristic
44C2×Dic13—42no—
45C2×Dic13#10212yes—
46C2×Dic13#10312yes—
47#1057—84no—
48C8×C13—21no—
49C8×C13#10011yescharacteristic
50C8×C13#10111yescharacteristic
51#1055—22no—
52C2×M32—131no—
53C2×M32#26111yescharacteristic
54#432—262no—
55C2×C4×C8—131no—
56C4⋊C16—262no—
57#335—262no—
58#334—134no—
59C22×C13—21no—
60C22×C13—22no—
61C22×C13#34011yescharacteristic
62C4×C13—21no—
63C4×C13#33811yescharacteristic
64C4×C13#34311yescharacteristic
65Dic13—22no—
66Dic13—22no—
67C22×C8—131no—
68C22×C8C2×#26111yescharacteristic
69C2×C42—131no—
70M32—41no—
71M32—521no—
72C2×C16—21no—
73C2×C16—261no—
74C4⋊C8—264no—
75C22⋊C8—522no—
76#97—522no—
77C4×C8—132no—
78C4×C8—132no—
79C2×C13—41no—
80C2×C13#129211yescharacteristic
81C2×C13#138912yes—
82C22×C4—132no—
83C22×C4C4⋊#26111yescharacteristic
84C2×C8—21no—
85C2×C8—21no—
86C2×C8—132no—
87C2×C8—521no—
88C2×C8—524no—
89C2×C8C4×#26111yescharacteristic
90C2×C8C22⋊#26111yescharacteristic
91C42—131no—
92C42—131no—
93C42—132no—
94C16—41no—
95C16—521no—
96C13#724611yescharacteristic, complemented, Sylow
97C23#8810111yescharacteristic
98C2×C4—21no—
99C2×C4—21no—
100C2×C4—132no—
101C2×C4—132no—
102C2×C4—522no—
103C2×C4#8810211yescharacteristic
104C2×C4(C2×#261)⋊C411yescharacteristic
105C8—21no—
106C8—262no—
107C8—1044no—
108C8#8811311yescharacteristic
109C8#8812111yescharacteristic
110C22—22no—
111C22—21no—
112C22#1171826511yescharacteristic
113C4—21no—
114C4—262no—
115C4—262no—
116C4#1171826911yescharacteristic
117C4#1171829111yescharacteristic
118C2—41no—
119C2#1312970611yescharacteristic
120C2#1312991712yes—
subgroupG/H
centerC22#11718265
commutatorC2×C8×C13C42
FrattiniC22×C8C2×#261
FittingC2×C13×M32C4
socleC22×C13#340
prime radicalC23×C13#106
cosocleC2×C8×Dic13C22
hypercenterC2×M32#261
hypocenterC13#7246
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
96. C13#7246semidirect

Maximal subgroups

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

subgroupindex
#131303982
#131165912
#724613