Finite Group Databasebeta

← #16778008

Subgroups — #16778008

Order 3328.

166 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 66 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×#11718223C212yesmaximal
2C2×D13×C32C211yesmaximal, characteristic
3C2×#88104—22no—
4C2×C16×D13C2211yescharacteristic
5#11718223—22no—
6#11718223C414yes—
7C2×C13×C32C411yescharacteristic
8C2×#88034C411yescharacteristic
9D13×C32—22no—
10C2×#6118—42no—
11C2×C8×D13D411yescharacteristic
12#88104—24no—
13#88104—42no—
14C2×C13×C16C2×C411yescharacteristic
15C2×#6090Q811yescharacteristic
16C16×D13C2×C412yes—
17C16×D13D412yes—
18C13×C32—21no—
19#88034—21no—
20#7472—131nomaximal, Sylow
21C2×C4×D13D811yescharacteristic
22C2×#1057—82no—
23#6118—44no—
24#6118—82no—
25C2×C8×C13C4⋊C411yescharacteristic
26C2×#1055Q1611yescharacteristic
27C8×D13C22⋊C412yes—
28C8×D13SD1612yes—
29C13×C16C4211yescharacteristic
30C13×C16C22⋊C411yescharacteristic
31#6090C4⋊C412yes—
32C22×C32—131no—
33C2×#368—132no—
34C22×D13Q3211yescharacteristic
35C2×C4×C13#10711yescharacteristic
36C2×Dic13D1611yescharacteristic
37C4×D13#10212yes—
38C4×D13SD3212yes—
39#1057—84no—
40C8×C13#9511yescharacteristic
41C8×C13#10611yescharacteristic
42#1055#10312yes—
43C22×C16—131no—
44C2×#108—262no—
45C2×C32—131no—
46C2×C32—262no—
47C2×C32#26111yescharacteristic
48#368—134no—
49#368—262no—
50C22×C13#36611yescharacteristic
51C2×D13—21no—
52C2×D13—21no—
53C2×D13#35812yes—
54C4×C13#34011yescharacteristic
55C4×C13#36711yescharacteristic
56Dic13#35712yes—
57C2×M16—522no—
58C22×C8—131no—
59C2×C16—131no—
60C2×C16—132no—
61C2×C16—132no—
62C2×C16C2×#26111yescharacteristic
63#108—264no—
64#108—522no—
65C32—21no—
66C32—261no—
67C2×C13#138011yescharacteristic
68C2×C13#142511yescharacteristic
69C2×C13#142511yescharacteristic
70D13—22no—
71C22×C4—131no—
72M16—524no—
73M16—1042no—
74C2×C8—131no—
75C2×C8—132no—
76C2×C8—132no—
77C2×C8—1042no—
78C2×C8C4⋊#26111yescharacteristic
79C16—132no—
80C16C4×#26111yescharacteristic
81C16C22⋊#26111yescharacteristic
82C13#747211yescharacteristic, complemented, Sylow
83C23—131no—
84C2×C4—131no—
85C2×C4—132no—
86C2×C4—132no—
87C2×C4#8810211yescharacteristic
88C8—132no—
89C8—1044no—
90C8#8810111yescharacteristic
91C8(C2×#261)⋊C411yescharacteristic
92C22—132no—
93C22—261no—
94C22—261no—
95C22#1171822111yescharacteristic
96C4—132no—
97C4#1171822211yescharacteristic
98C4#1171826511yescharacteristic
99C2—262no—
100C2#1312989411yescharacteristic
101C2#1312999911yescharacteristic
102C2#1313000011yescharacteristic
subgroupG/H
centerC22#11718221
commutatorC13×C16C42
FrattiniC2×C16C2×#261
FittingC2×C13×C32C4
socleC22×C13#366
prime radicalC22×D13Q32
cosocleC2×C16×D13C22
hypercenterC2×C32#261
hypocenterC13#7472
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

Complements

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

NH ≅ G/Ntype
82. C13#7472semidirect

Maximal subgroups

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

subgroupindex
C2×#117182232
C2×D13×C322
#747213