Finite Group Databasebeta

← #7441

Subgroups — #7441

Order 256.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2102C211yesmaximal, characteristic
2#1327C211yesmaximal, characteristic
3#1307C211yesmaximal, characteristic
4#432—21no—
5#430C411yescharacteristic
6#423C2211yescharacteristic
7#349—21no—
8#344—21no—
9#339—21no—
10H(3,ℤ/4)C411yescharacteristic
11C2×M16—21no—
12C2×M16C2×C411yescharacteristic
13C2×M16D411yescharacteristic
14#117—21no—
15C2×C42D411yescharacteristic
16M32—41no—
17#108—41no—
18C4⋊C8—41no—
19C4⋊C8—41no—
20C22⋊C8—22no—
21#97—41no—
22C22×C4—21no—
23C22×C4C22⋊C411yescharacteristic
24M16—41no—
25M16—41no—
26M16—41no—
27M16—41no—
28C2×C8—21no—
29C2×C8—21no—
30C2×C8—42no—
31C2×C8—41no—
32C4⋊C4—41no—
33C22⋊C4—41no—
34C42—21no—
35C42—41no—
36C42SD1611yescharacteristic
37C42Q1611yescharacteristic
38C16—81no—
39C23#10411yescharacteristic
40C2×C4—21no—
41C2×C4—21no—
42C2×C4—21no—
43C2×C4—21no—
44C2×C4—81no—
45C2×C4—81no—
46C2×C4#9911yescharacteristic
47C2×C4#10311yescharacteristic
48C8—41no—
49C8—41no—
50C8—82no—
51C8—81no—
52C22—21no—
53C22—41no—
54C22#32811yescharacteristic
55C4—21no—
56C4—41no—
57C4—41no—
58C4—161no—
59C4#35211yescharacteristic
60C4#35511yescharacteristic
61C2—21no—
62C2—41no—
63C2#135311yescharacteristic
subgroupG/H
center, socleC2#1353
commutatorC2×M16C2×C4
Frattini, cosocle#423C22
prime radicalC23#104
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ G
LECSG ▷ #423 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#21022
#13272
#13072