Finite Group Databasebeta

← #11782

Subgroups — #11782

Order 256.

207 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 207 conjugacy classes of subgroups — too many to draw. Only its 53 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#2546C211yesmaximal, characteristic
2C4×#101C211yesmaximal, characteristic
3#1467C211yesmaximal, characteristic
4#1346C214yesmaximal
5C2×C4⋊Q8—21no—
6C2×C4⋊Q8C411yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#432—21no—
9C2×#101—21no—
10C4×M16—21no—
11#398C412yes—
12#398C2212yes—
13#391—21no—
14#389—21no—
15#389—21no—
16C4×C4⋊C4C411yescharacteristic
17#343C2212yes—
18#324—21no—
19#324C2212yes—
20C22×Q8—21no—
21C22×Q8D411yescharacteristic
22C2×M16—22no—
23C4⋊Q8—41no—
24C4⋊Q8—41no—
25C4⋊Q8—44no—
26C4×Q8—41no—
27C4×Q8—41no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4—22no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—22no—
32C2×C4⋊C4C2×C412yes—
33C2×C4⋊C4C2×C411yescharacteristic
34C2×C4⋊C4D411yescharacteristic
35C2×C4⋊C4C2311yescharacteristic
36C2×C42—21no—
37C2×C42C2×C411yescharacteristic
38C2×C42D411yescharacteristic
39C2×C42D411yescharacteristic
40C4⋊C8—41no—
41#101—24no—
42C22⋊C8—22no—
43#97—41no—
44#97—41no—
45C4×C8—41no—
46#95—22no—
47#95—22no—
48#95C2×C412yes—
49C2×Q8—22no—
50C2×Q8—22no—
51C2×Q8—41no—
52C2×Q8—42no—
53C2×Q8—42no—
54C2×Q8—42no—
55C22×C4—22no—
56C22×C4—22no—
57C22×C4C22⋊C411yescharacteristic
58C22×C4C22⋊C411yescharacteristic
59C22×C4C22⋊C411yescharacteristic
60C22×C4C22⋊C411yescharacteristic
61C22×C4C22×C411yescharacteristic
62C22×C4C2×D411yescharacteristic
63C22×C4C2×D411yescharacteristic
64M16—24no—
65M16—42no—
66C2×C8—42no—
67C2×C8—42no—
68C4⋊C4—24no—
69C4⋊C4—41no—
70C4⋊C4—41no—
71C4⋊C4—41no—
72C4⋊C4—42no—
73C4⋊C4—44no—
74C4⋊C4—41no—
75C4⋊C4—41no—
76C4⋊C4—44no—
77C42—21no—
78C42—21no—
79C42—21no—
80C42—21no—
81C42—21no—
82C42—21no—
83C42—42no—
84C23C2×C22⋊C411yescharacteristic
85Q8—44no—
86Q8—84no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—22no—
92C2×C4—24no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—21no—
98C2×C4—21no—
99C2×C4—42no—
100C2×C4—42no—
101C2×C4—41no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—42no—
105C2×C4—42no—
106C2×C4—42no—
107C2×C4#9911yescharacteristic
108C2×C4#9911yescharacteristic
109C2×C4#10412yes—
110C2×C4AGL(1,ℤ/8)12yes—
111C8—44no—
112C8—82no—
113C22—21no—
114C22—21no—
115C22C2×#9911yescharacteristic
116C22#41811yescharacteristic
117C22C2×#10411yescharacteristic
118C4—21no—
119C4—22no—
120C4—22no—
121C4—44no—
122C4—41no—
123C4—41no—
124C4—41no—
125C4—41no—
126C4—82no—
127C4#35612yes—
128C2—21no—
129C2—21no—
130C2#150711yescharacteristic
131C2#212311yescharacteristic
132C2C2×#35611yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radicalC23C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#25462
C4×#1012
#14672
#13462