Finite Group Databasebeta

← #9482

Subgroups — #9482

Order 256.

259 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 259 conjugacy classes of subgroups — too many to draw. Only its 61 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#2484C211yesmaximal, characteristic
2#2313C211yesmaximal, characteristic
3#1826C212yesmaximal
4#1463C211yesmaximal, characteristic
5#1284C212yesmaximal
6C2×#117C2211yescharacteristic
7C22×C4⋊C4C2211yescharacteristic
8#407C2212yes—
9#400C412yescomplemented
10#398C412yescomplemented
11#387—22no—
12#387—24no—
13#385—21no—
14#381—21no—
15#381—21no—
16#381C2211yescharacteristic
17#380—21no—
18C4×C22⋊C4C2212yes—
19#339—24no—
20#324—22no—
21C23×C4D411yescharacteristic
22C23×C4D411yescharacteristic
23C23×C4C2311yescharacteristic
24C2×M16—22no—
25#117—22no—
26#117—22no—
27C2×C4⋊C4—22no—
28C2×C4⋊C4—22no—
29C2×C4⋊C4—22no—
30C2×C4⋊C4—22no—
31C2×C4⋊C4C2×C411yescharacteristic
32C2×C4⋊C4C2×C411yescharacteristic
33C2×C4⋊C4C2×C412yes—
34C2×C4⋊C4D412yes—
35C2×C22⋊C4—21no—
36C2×C22⋊C4—22no—
37C2×C22⋊C4—21no—
38C2×C42—21no—
39C2×C42D414yes—
40C22⋊C8—22no—
41C22⋊C8—22no—
42#95—22no—
43#95—24no—
44#95—22no—
45#95—22no—
46#95—22no—
47#95—22no—
48#95—21no—
49#95C2×C412yes—
50C24C2×D411yescharacteristic
51C22×C4—21no—
52C22×C4—21no—
53C22×C4—21no—
54C22×C4—21no—
55C22×C4—22no—
56C22×C4—21no—
57C22×C4—21no—
58C22×C4—24no—
59C22×C4—42no—
60C22×C4—42no—
61C22×C4—42no—
62C22×C4C22⋊C412yes—
63C22×C4C22⋊C412yes—
64C22×C4C22×C411yescharacteristic
65C22×C4C2×D412yes—
66C22×C4C2×D411yescharacteristic
67C22×C4#4112yes—
68M16—44no—
69C2×C8—42no—
70C4⋊C4—24no—
71C4⋊C4—24no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—44no—
75C4⋊C4—82no—
76C22⋊C4—44no—
77C22⋊C4—42no—
78C22⋊C4—41no—
79C22⋊C4—41no—
80C42—44no—
81C42—42no—
82C23—22no—
83C23—22no—
84C23—41no—
85C23C2×C22⋊C411yescharacteristic
86C23#12011yescharacteristic
87C23#12311yescharacteristic
88C2×C4—24no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—22no—
92C2×C4—22no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—42no—
96C2×C4—42no—
97C2×C4—42no—
98C2×C4—42no—
99C2×C4—42no—
100C2×C4—42no—
101C2×C4—44no—
102C2×C4—42no—
103C2×C4—44no—
104C2×C4—42no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—42no—
108C2×C4—42no—
109C2×C4—44no—
110C2×C4—81no—
111C2×C4C4×D412yes—
112C2×C4#12112yes—
113C8—82no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—21no—
120C22—21no—
121C22—44no—
122C22#38611yescharacteristic
123C22#42112yes—
124C22#45812yes—
125C4—22no—
126C4—22no—
127C4—42no—
128C4—42no—
129C4—84no—
130C4—82no—
131C4—81no—
132C4—81no—
133C2—22no—
134C2—22no—
135C2—41no—
136C2#189011yescharacteristic
137C2#189711yescharacteristic
138C2#191211yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
9. #400C4semidirect
10. #398C4semidirect

Maximal subgroups

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

subgroupindex
#24842
#23132
#18262
#14632
#12842