Finite Group Databasebeta

← #8962

Subgroups — #8962

Order 256.

255 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 255 conjugacy classes of subgroups — too many to draw. Only its 73 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
2C4×C4⋊Q8C211yesmaximal, characteristic
3#1479C212yesmaximal
4#1461C211yesmaximal, characteristic
5#1276C212yesmaximal
6C2×C4⋊Q8C411yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8C2×C4×Q8C2211yescharacteristic
9#446—24no—
10#432—22no—
11#431C2212yes—
12#431C2212yes—
13#391C411yescharacteristic
14#391C411yescharacteristic
15#389—22no—
16#384C411yescharacteristic
17C4×C4⋊C4—22no—
18C43C2211yescharacteristic
19Q8⋊C8—24no—
20#324—22no—
21C22×Q8C2×C411yescharacteristic
22C22×Q8C2×C411yescharacteristic
23C4⋊Q8—22no—
24C4⋊Q8—22no—
25C4×Q8—22no—
26C4×Q8—22no—
27C4×Q8—22no—
28C4×Q8—22no—
29C2×C4⋊C4—22no—
30C2×C4⋊C4—22no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4C2×C411yescharacteristic
33C2×C4⋊C4C2×C411yescharacteristic
34C2×C4⋊C4D412yes—
35C2×C42—21no—
36C2×C42—21no—
37C2×C42—21no—
38C2×C42C2×C411yescharacteristic
39C2×C42C2×C411yescharacteristic
40C2×C42D412yes—
41C2×C42C2311yescharacteristic
42C4⋊C8—24no—
43C4⋊C8—22no—
44C4⋊C8D414yes—
45C22⋊C8—22no—
46C22⋊C8—22no—
47#97—24no—
48C4×C8—22no—
49C4×C8—22no—
50#95—22no—
51#95—22no—
52C2×Q8—22no—
53C2×Q8—21no—
54C2×Q8—21no—
55C2×Q8—21no—
56C2×Q8—22no—
57C2×Q8—22no—
58C2×Q8—22no—
59C2×Q8M1612yes—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4C22⋊C412yes—
65C22×C4C22⋊C412yes—
66C22×C4C22×C411yescharacteristic
67C22×C4C2×D411yescharacteristic
68C22×C4C2×D411yescharacteristic
69C2×C8—24no—
70C2×C8—42no—
71C4⋊C4—28no—
72C4⋊C4—22no—
73C4⋊C4—24no—
74C4⋊C4—22no—
75C4⋊C4—44no—
76C4⋊C4—42no—
77C42—24no—
78C42—22no—
79C42—22no—
80C42—21no—
81C42—22no—
82C42—42no—
83C42—41no—
84C42—41no—
85C42M1612yes—
86C42C2×D412yes—
87C42#4112yes—
88C23C2×C22⋊C411yescharacteristic
89Q8—24no—
90Q8—42no—
91Q8—42no—
92Q8—42no—
93C2×C4—22no—
94C2×C4—22no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—22no—
98C2×C4—22no—
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—22no—
102C2×C4—22no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—42no—
109C2×C4—42no—
110C2×C4—41no—
111C2×C4C4×D412yes—
112C2×C4#12011yescharacteristic
113C2×C4#12112yes—
114C2×C4#12311yescharacteristic
115C2×C4C2×M1611yescharacteristic
116C2×C4C2×M1611yescharacteristic
117C2×C4#13112yes—
118C8—44no—
119C8—82no—
120C22—21no—
121C22—21no—
122C22#38611yescharacteristic
123C22#40711yescharacteristic
124C22#40811yescharacteristic
125C4—24no—
126C4—22no—
127C4—21no—
128C4—42no—
129C4—42no—
130C4—42no—
131C4—42no—
132C4—81no—
133C4#43512yes—
134C4#43612yes—
135C4#45612yes—
136C2—21no—
137C2—21no—
138C2#187011yescharacteristic
139C2#188411yescharacteristic
140C2#188611yescharacteristic
subgroupG/H
centerC2×C4#120
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
socleC22#386
prime radicalC23C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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
C4×C4⋊Q82
#14792
#14612
#12762