Finite Group Databasebeta

← #7413

Subgroups — #7413

Order 256.

89 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2074C211yesmaximal, characteristic
2#1394C211yesmaximal, characteristic
3#1319C211yesmaximal, characteristic
4C2×#103—21no—
5C2×#101—21no—
6#391C2211yescharacteristic
7#382C411yescharacteristic
8#340—21no—
9#336C411yescharacteristic
10#324—21no—
11C22×Q8D411yescharacteristic
12C2×M16—41no—
13C22×C8—21no—
14C2×C4⋊C4—21no—
15C2×C4⋊C4D411yescharacteristic
16C2×C42C2×C411yescharacteristic
17#103—41no—
18#103—41no—
19#101—22no—
20#101—41no—
21C22⋊C8—41no—
22#95—41no—
23#95—41no—
24C2×Q8—21no—
25C2×Q8—41no—
26C2×Q8—41no—
27C2×Q8D811yescharacteristic
28C2×Q8SD1611yescharacteristic
29C22×C4—21no—
30C22×C4—21no—
31C22×C4—21no—
32C22×C4—41no—
33C22×C4C22⋊C411yescharacteristic
34M16—42no—
35M16—81no—
36C2×C8—41no—
37C2×C8—41no—
38C2×C8—41no—
39C2×C8—81no—
40C2×C8—81no—
41C4⋊C4—41no—
42C4⋊C4—41no—
43C4⋊C4—41no—
44C42—41no—
45C23#9911yescharacteristic
46Q8—41no—
47Q8—41no—
48Q8—81no—
49C2×C4—21no—
50C2×C4—21no—
51C2×C4—21no—
52C2×C4—21no—
53C2×C4—41no—
54C2×C4—41no—
55C2×C4—41no—
56C2×C4—41no—
57C2×C4—41no—
58C2×C4—41no—
59C2×C4—81no—
60C2×C4—81no—
61C2×C4—81no—
62C2×C4—81no—
63C2×C4#10211yescharacteristic
64C2×C4#10411yescharacteristic
65C8—81no—
66C8—82no—
67C8—161no—
68C22—21no—
69C22—21no—
70C22#32711yescharacteristic
71C22#35211yescharacteristic
72C22#35411yescharacteristic
73C4—21no—
74C4—21no—
75C4—41no—
76C4—41no—
77C4—81no—
78C4—81no—
79C4—161no—
80C2—21no—
81C2—21no—
82C2#134411yescharacteristic
83C2#141311yescharacteristic
84C2#141411yescharacteristic
subgroupG/H
center, socleC22#354
commutatorC2×C42C2×C4
Frattini, cosocle#391C22
prime radicalC23#99
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ G
LECSG ▷ #391 ▷ 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
#20742
#13942
#13192