Finite Group Databasebeta

← #7410

Subgroups — #7410

Order 256.

83 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2079C211yesmaximal, characteristic
2#1391C211yesmaximal, characteristic
3#1321C211yesmaximal, characteristic
4C2×#106C411yescharacteristic, complemented
5#417—21no—
6#410—21no—
7#408C2211yescharacteristic
8#349—21no—
9#343—21no—
10#341C411yescharacteristic, complemented
11C2×#41D411yescharacteristic
12C2×M16—21no—
13C2×M16D411yescharacteristic
14C22×C8C2×C411yescharacteristic
15#117—41no—
16C2×C4⋊C4—21no—
17M32—41no—
18#106—41no—
19#103—41no—
20#102—41no—
21#99—22no—
22#99—41no—
23C22⋊C8—41no—
24#41—41no—
25#41—41no—
26C2×Q8SD1611yescharacteristic
27C2×D4—21no—
28C2×D4D811yescharacteristic
29C22×C4—21no—
30C22×C4—41no—
31C22×C4C22⋊C411yescharacteristic
32M16—41no—
33M16—41no—
34M16—41no—
35C2×C8—21no—
36C2×C8—21no—
37C2×C8—41no—
38C2×C8—41no—
39C4⋊C4—41no—
40C4⋊C4—41no—
41C4⋊C4—81no—
42C22⋊C4—42no—
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—82no—
56C2×C4—81no—
57C2×C4—161no—
58C2×C4#9911yescharacteristic
59C2×C4#10211yescharacteristic
60C8—41no—
61C8—41no—
62C8—81no—
63C22—21no—
64C22—41no—
65C22—41no—
66C22—81no—
67C22#32711yescharacteristic
68C4—21no—
69C4—41no—
70C4—161no—
71C4—162no—
72C4#35211yescharacteristic
73C4#35411yescharacteristic
74C2—21no—
75C2—41no—
76C2—81no—
77C2#134411yescharacteristic
subgroupG/H
center, socleC2#1344
commutatorC22×C8C2×C4
Frattini, cosocle#408C22
prime radicalC2×#41D4
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ 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. C2×#106C4semidirect
10. #341C4semidirect

Maximal subgroups

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

subgroupindex
#20792
#13912
#13212