Finite Group Databasebeta

← #7439

Subgroups — #7439

Order 256.

85 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2098C211yesmaximal, characteristic
2#1392C211yesmaximal, characteristic
3#1315C211yesmaximal, characteristic
4#430C411yescharacteristic
5#424—21no—
6#421—21no—
7#413—21no—
8#408C2211yescharacteristic
9C22⋊C16—21no—
10H(3,ℤ/4)C411yescharacteristic
11C2×#41D411yescharacteristic
12C2×M16—21no—
13C2×M16—41no—
14C2×M16C2×C411yescharacteristic
15C22×C8D411yescharacteristic
16#117—21no—
17C2×C16—41no—
18#108—41no—
19C4⋊C8—42no—
20#104—42no—
21#101—41no—
22#100—22no—
23C22⋊C8—41no—
24#41—41no—
25#41—41no—
26C2×Q8SD1611yescharacteristic
27C2×D4—21no—
28C2×D4Q1611yescharacteristic
29C22×C4—21no—
30C22×C4C22⋊C411yescharacteristic
31M16—41no—
32M16—42no—
33M16—41no—
34M16—41no—
35M16—81no—
36C2×C8—21no—
37C2×C8—21no—
38C2×C8—41no—
39C2×C8—41no—
40C2×C8—81no—
41C4⋊C4—41no—
42C22⋊C4—41no—
43C42—22no—
44C16—81no—
45C23—21no—
46C23#10411yescharacteristic
47Q8—41no—
48D4—41no—
49D4—81no—
50C2×C4—21no—
51C2×C4—21no—
52C2×C4—21no—
53C2×C4—41no—
54C2×C4—41no—
55C2×C4—42no—
56C2×C4#9911yescharacteristic
57C2×C4#10311yescharacteristic
58C8—41no—
59C8—41no—
60C8—82no—
61C8—81no—
62C22—21no—
63C22—41no—
64C22—41no—
65C22—81no—
66C22#32811yescharacteristic
67C4—21no—
68C4—41no—
69C4—82no—
70C4#35211yescharacteristic
71C4#35311yescharacteristic
72C2—21no—
73C2—41no—
74C2—81no—
75C2#135211yescharacteristic
subgroupG/H
centerC4#353
commutatorC2×M16C2×C4
Frattini, cosocle#408C22
socleC2#1352
prime radicalC2×#41D4
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ G
LECSG ▷ #408 ▷ 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
#20982
#13922
#13152