Finite Group Databasebeta

← #7438

Subgroups — #7438

Order 256.

87 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2098C211yesmaximal, characteristic
2#1391C211yesmaximal, characteristic
3#1315C211yesmaximal, characteristic
4#430C411yescharacteristic, complemented
5#424—21no—
6#421—21no—
7#410—21no—
8#408C2211yescharacteristic
9C22⋊C16—21no—
10H(3,ℤ/4)C411yescharacteristic, complemented
11C2×#41D411yescharacteristic
12C2×M16—21no—
13C2×M16C2×C411yescharacteristic
14C22×C8D411yescharacteristic
15#117—21no—
16#117—41no—
17C2×C16—41no—
18#108—41no—
19C4⋊C8—42no—
20#104—42no—
21#99—22no—
22#99—41no—
23C22⋊C8—41no—
24#41—41no—
25#41—41no—
26C2×Q8Q1611yescharacteristic
27C2×D4—21no—
28C2×D4SD1611yescharacteristic
29C22×C4—21no—
30C22×C4C22⋊C411yescharacteristic
31M16—41no—
32M16—41no—
33M16—41no—
34C2×C8—21no—
35C2×C8—21no—
36C2×C8—41no—
37C2×C8—41no—
38C4⋊C4—41no—
39C4⋊C4—81no—
40C22⋊C4—41no—
41C22⋊C4—42no—
42C42—22no—
43C42—81no—
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—82no—
57C2×C4#9911yescharacteristic
58C2×C4#10311yescharacteristic
59C8—41no—
60C8—41no—
61C8—81no—
62C22—21no—
63C22—41no—
64C22—41no—
65C22—81no—
66C22#32811yescharacteristic
67C4—21no—
68C4—41no—
69C4—82no—
70C4—162no—
71C4#35211yescharacteristic
72C4#35311yescharacteristic
73C2—21no—
74C2—41no—
75C2—81no—
76C2#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

Complements

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

NH ≅ G/Ntype
4. #430C4semidirect
10. H(3,ℤ/4)C4semidirect

Maximal subgroups

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

subgroupindex
#20982
#13912
#13152