Finite Group Databasebeta

← #9440

Subgroups — #9440

Order 256.

217 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 217 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3166C211yesmaximal, characteristic
2#2371C211yesmaximal, characteristic
3#1534C211yesmaximal, characteristic
4#1506C212yesmaximal
5#1300C212yesmaximal
6#533C2211yescharacteristic
7C2×#125C2211yescharacteristic
8#501C414yescomplemented
9#499—22no—
10#432C2212yes—
11#428—22no—
12C4×M16C2211yescharacteristic
13#387—22no—
14#387—22no—
15C4×C4⋊C4—22no—
16#376C2212yes—
17#330—22no—
18#328—22no—
19#328—22no—
20C2×M16—21no—
21C4⋊Q8C2×C412yes—
22#125—21no—
23#125—22no—
24#125C2×C412yes—
25#125D412yes—
26C22⋊Q8—22no—
27C4×Q8—22no—
28#117—21no—
29C2×C4⋊C4—22no—
30C2×C4⋊C4—22no—
31C2×C4⋊C4D412yes—
32C2×C42—22no—
33C2×C42—22no—
34C2×C42C2311yescharacteristic
35#107—24no—
36#106—24no—
37C4⋊C8—22no—
38C22⋊C8—22no—
39#97—22no—
40#97C2×C412yes—
41C4×C8—21no—
42#95—22no—
43#95—22no—
44#95—22no—
45#95D412yes—
46#95D412yes—
47C2×Q8—22no—
48C22×C4—22no—
49C22×C4—22no—
50C22×C4—22no—
51C22×C4C2×D411yescharacteristic
52C22×C4C2×D412yes—
53M16—24no—
54C2×C8—22no—
55C2×C8—42no—
56C4⋊C4—24no—
57C4⋊C4—24no—
58C4⋊C4—22no—
59C4⋊C4—22no—
60C4⋊C4—22no—
61C4⋊C4—44no—
62C4⋊C4—42no—
63C4⋊C4C22⋊C414yes—
64C22⋊C4—41no—
65C42—44no—
66C42—44no—
67C42—41no—
68C42C22×C411yescharacteristic
69C42C2×D411yescharacteristic
70C42#4112yes—
71C23#12011yescharacteristic
72Q8—82no—
73C2×C4—22no—
74C2×C4—24no—
75C2×C4—24no—
76C2×C4—42no—
77C2×C4—42no—
78C2×C4—42no—
79C2×C4—42no—
80C2×C4—42no—
81C2×C4—42no—
82C2×C4—42no—
83C2×C4—42no—
84C2×C4—42no—
85C2×C4C2×C22⋊C411yescharacteristic
86C2×C4C4×D412yes—
87C2×C4#12112yes—
88C2×C4#12311yescharacteristic
89C8—24no—
90C8—82no—
91C22—22no—
92C22#38611yescharacteristic
93C22#45612yes—
94C4—21no—
95C4—21no—
96C4—22no—
97C4—22no—
98C4—44no—
99C4—44no—
100C4—82no—
101C4—82no—
102C2—22no—
103C2#188611yescharacteristic
104C2#190612yes—
subgroupG/H
center, socleC22#386
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
prime radicalC23#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #501C4semidirect

Maximal subgroups

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

subgroupindex
#31662
#23712
#15342
#15062
#13002