Finite Group Databasebeta

← #7443

Subgroups — #7443

Order 256.

99 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2060C211yesmaximal, characteristic
2#1325C211yesmaximal, characteristic
3#1296C211yesmaximal, characteristic
4#544C411yescharacteristic
5#428—21no—
6C2×C4⋊C8—21no—
7#384C2211yescharacteristic
8#343C411yescharacteristic
9#339—21no—
10#324—21no—
11C2×M16—21no—
12C22×C8—41no—
13C4⋊Q8—41no—
14#125—41no—
15C22⋊Q8—41no—
16#117—21no—
17C2×C4⋊C4—41no—
18C2×C4⋊C4C2×C411yescharacteristic
19C2×C4⋊C4D411yescharacteristic
20C2×C42D411yescharacteristic
21#107—41no—
22#106—41no—
23C4⋊C8—22no—
24C4⋊C8—41no—
25C22⋊C8—41no—
26C2×Q8—41no—
27C22×C4—21no—
28C22×C4—21no—
29C22×C4—21no—
30C22×C4C22⋊C411yescharacteristic
31M16—22no—
32M16—41no—
33C2×C8—41no—
34C2×C8—42no—
35C2×C8—81no—
36C2×C8—81no—
37C2×C8—81no—
38C4⋊C4—21no—
39C4⋊C4—21no—
40C4⋊C4—41no—
41C4⋊C4—41no—
42C4⋊C4—41no—
43C4⋊C4—42no—
44C4⋊C4—81no—
45C4⋊C4—81no—
46C22⋊C4—41no—
47C42—21no—
48C42—41no—
49C42SD1611yescharacteristic
50C42Q1611yescharacteristic
51C23#9911yescharacteristic
52Q8—161no—
53C2×C4—21no—
54C2×C4—21no—
55C2×C4—21no—
56C2×C4—21no—
57C2×C4—21no—
58C2×C4—21no—
59C2×C4—21no—
60C2×C4—21no—
61C2×C4—41no—
62C2×C4—41no—
63C2×C4—41no—
64C2×C4—41no—
65C2×C4—81no—
66C2×C4—81no—
67C2×C4#10311yescharacteristic
68C2×C4#10411yescharacteristic
69C8—42no—
70C8—82no—
71C8—161no—
72C22—21no—
73C22—21no—
74C22#32811yescharacteristic
75C22AΣL(1,𝔽16)11yescharacteristic
76C22#35611yescharacteristic
77C4—21no—
78C4—21no—
79C4—21no—
80C4—21no—
81C4—21no—
82C4—21no—
83C4—81no—
84C4—81no—
85C4—81no—
86C4—81no—
87C2—21no—
88C2—21no—
89C2#135411yescharacteristic
90C2#140211yescharacteristic
91C2#140511yescharacteristic
subgroupG/H
center, socleC22AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4
Frattini, cosocle#384C22
prime radicalC23#99
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ G
LECSG ▷ #384 ▷ 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
#20602
#13252
#12962