Finite Group Databasebeta

← #9452

Subgroups — #9452

Order 256.

234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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#2983C211yesmaximal, characteristic
2#2546C211yesmaximal, characteristic
3#1558C212yesmaximal
4#1467C211yesmaximal, characteristic
5#1285C212yesmaximal
6C2×C4⋊Q8C412yes—
7C2×C4⋊Q8C2211yescharacteristic
8C2×C4×Q8C2211yescharacteristic
9#446—24no—
10#432—21no—
11#432C2212yes—
12#432C2212yes—
13#431—21no—
14#398—21no—
15#398—21no—
16#391C412yes—
17#389—21no—
18#389—21no—
19C4×C4⋊C4C2211yescharacteristic
20#333—24no—
21#324—21no—
22#324—21no—
23C22×Q8C2×C412yes—
24C22×Q8C2×C411yescharacteristic
25C4⋊Q8—22no—
26C4⋊Q8—22no—
27C4⋊Q8—44no—
28C4×Q8—22no—
29C4×Q8—22no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—22no—
32C2×C4⋊C4—22no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4D411yescharacteristic
37C2×C4⋊C4D411yescharacteristic
38C2×C42C2×C412yes—
39C2×C42D411yescharacteristic
40C2×C42D411yescharacteristic
41C2×C42C2311yescharacteristic
42C4⋊C8—22no—
43C4⋊C8—22no—
44C4⋊C8—22no—
45C4⋊C8D414yes—
46C22⋊C8—22no—
47C22⋊C8—22no—
48#97—22no—
49#97—22no—
50#97—22no—
51C4×C8—22no—
52#95—22no—
53#95—22no—
54#95—21no—
55C2×Q8—22no—
56C2×Q8—22no—
57C2×Q8—24no—
58C2×Q8—41no—
59C2×Q8—42no—
60C2×Q8—42no—
61C22×C4—22no—
62C22×C4—22no—
63C22×C4C22⋊C411yescharacteristic
64C22×C4C22⋊C411yescharacteristic
65C22×C4C22⋊C411yescharacteristic
66C22×C4C22⋊C411yescharacteristic
67C22×C4C22×C411yescharacteristic
68C22×C4C2×D411yescharacteristic
69C22×C4C2×D411yescharacteristic
70C2×C8—24no—
71C2×C8—42no—
72C4⋊C4—24no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—44no—
77C4⋊C4—44no—
78C4⋊C4—41no—
79C4⋊C4—42no—
80C4⋊C4—41no—
81C42—21no—
82C42—21no—
83C42—21no—
84C42—21no—
85C42—42no—
86C42C2×D412yes—
87C42#4112yes—
88C23C2×C22⋊C411yescharacteristic
89Q8—44no—
90Q8—84no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—22no—
96C2×C4—24no—
97C2×C4—21no—
98C2×C4—21no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—42no—
104C2×C4—42no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—42no—
108C2×C4—42no—
109C2×C4—42no—
110C2×C4#10012yes—
111C2×C4C4×D412yes—
112C2×C4#12011yescharacteristic
113C2×C4#12112yes—
114C2×C4#12311yescharacteristic
115C8—44no—
116C8—82no—
117C22—21no—
118C22—21no—
119C22#38611yescharacteristic
120C22C2×#10011yescharacteristic
121C22#41311yescharacteristic
122C4—21no—
123C4—22no—
124C4—22no—
125C4—22no—
126C4—44no—
127C4—41no—
128C4—41no—
129C4—41no—
130C4—82no—
131C4#45612yes—
132C2—21no—
133C2—21no—
134C2#188611yescharacteristic
135C2#190011yescharacteristic
136C2#190911yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC23C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#29832
#25462
#15582
#14672
#12852