Finite Group Databasebeta

← #9456

Subgroups — #9456

Order 256.

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

normal subgroups only

This group has 216 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#2568C211yesmaximal, characteristic
3#1556C212yesmaximal
4#1467C211yesmaximal, characteristic
5#1285C212yesmaximal
6C2×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#446—24no—
9#432—21no—
10#432C2212yes—
11#432C2212yes—
12#431—21no—
13#400—21no—
14#400—21no—
15#391—21no—
16#391—21no—
17#391C412yes—
18#382C412yes—
19C4×C4⋊C4C2211yescharacteristic
20#332—24no—
21#324—21no—
22#324—21no—
23C22×Q8—21no—
24C22×Q8C2×C411yescharacteristic
25C4⋊Q8—22no—
26C4⋊Q8—22no—
27C4×Q8—22no—
28C4×Q8—22no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4C2×C412yes—
32C2×C4⋊C4C2×C411yescharacteristic
33C2×C4⋊C4D411yescharacteristic
34C2×C4⋊C4D411yescharacteristic
35C2×C42C2×C412yes—
36C2×C42D411yescharacteristic
37C2×C42D411yescharacteristic
38C2×C42C2311yescharacteristic
39C4⋊C8—22no—
40C4⋊C8—22no—
41C4⋊C8—22no—
42C4⋊C8D414yes—
43C22⋊C8—22no—
44C22⋊C8—22no—
45#97—22no—
46#97—22no—
47#97—22no—
48C4×C8—22no—
49#95—22no—
50#95—22no—
51#95—22no—
52#95—22no—
53#95—21no—
54C2×Q8—22no—
55C2×Q8—22no—
56C2×Q8—41no—
57C2×Q8—44no—
58C2×Q8—41no—
59C2×Q8—41no—
60C22×C4—22no—
61C22×C4—22no—
62C22×C4C22⋊C411yescharacteristic
63C22×C4C22⋊C411yescharacteristic
64C22×C4C22⋊C411yescharacteristic
65C22×C4C22⋊C411yescharacteristic
66C22×C4C22×C411yescharacteristic
67C22×C4C2×D411yescharacteristic
68C22×C4C2×D411yescharacteristic
69C2×C8—24no—
70C2×C8—42no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—24no—
75C4⋊C4—42no—
76C4⋊C4—42no—
77C42—21no—
78C42—21no—
79C42—21no—
80C42—21no—
81C42—42no—
82C42C2×D412yes—
83C42#4112yes—
84C23C2×C22⋊C411yescharacteristic
85Q8—44no—
86Q8—82no—
87Q8—82no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—22no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—21no—
98C2×C4—41no—
99C2×C4—41no—
100C2×C4—41no—
101C2×C4—42no—
102C2×C4—42no—
103C2×C4—44no—
104C2×C4—42no—
105C2×C4—42no—
106C2×C4#10112yes—
107C2×C4C4×D412yes—
108C2×C4#12011yescharacteristic
109C2×C4#12112yes—
110C2×C4#12311yescharacteristic
111C8—44no—
112C8—82no—
113C22—21no—
114C22—21no—
115C22#38611yescharacteristic
116C22C2×#10111yescharacteristic
117C22#41311yescharacteristic
118C4—21no—
119C4—22no—
120C4—22no—
121C4—22no—
122C4—41no—
123C4—41no—
124C4—41no—
125C4—82no—
126C4—82no—
127C4#45412yes—
128C2—21no—
129C2—21no—
130C2#188811yescharacteristic
131C2#190111yescharacteristic
132C2#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
#25682
#15562
#14672
#12852