Finite Group Databasebeta

← #11794

Subgroups — #11794

Order 256.

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

normal subgroups only

This group has 189 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#2568C211yesmaximal, characteristic
2C4×#101C211yesmaximal, characteristic
3#1467C211yesmaximal, characteristic
4#1353C214yesmaximal
5C2×C4⋊Q8C411yescharacteristic
6C2×C4×Q8C2211yescharacteristic
7#432—21no—
8C2×#101—21no—
9C4×M16—21no—
10#400C412yes—
11#400C2212yes—
12#391—21no—
13#391—21no—
14#391—21no—
15#382—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—41no—
26C4×Q8—41no—
27C2×C4⋊C4—21no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4C2×C412yes—
30C2×C4⋊C4C2×C411yescharacteristic
31C2×C4⋊C4D411yescharacteristic
32C2×C4⋊C4C2311yescharacteristic
33C2×C42—21no—
34C2×C42C2×C411yescharacteristic
35C2×C42D411yescharacteristic
36C2×C42D411yescharacteristic
37C4⋊C8—41no—
38#101—24no—
39C22⋊C8—22no—
40#97—41no—
41#97—41no—
42C4×C8—41no—
43#95—22no—
44#95—22no—
45#95—22no—
46#95—22no—
47#95C2×C412yes—
48C2×Q8—22no—
49C2×Q8—22no—
50C2×Q8—41no—
51C2×Q8—44no—
52C2×Q8—41no—
53C2×Q8—41no—
54C22×C4—22no—
55C22×C4—22no—
56C22×C4C22⋊C411yescharacteristic
57C22×C4C22⋊C411yescharacteristic
58C22×C4C22⋊C411yescharacteristic
59C22×C4C22⋊C411yescharacteristic
60C22×C4C22×C411yescharacteristic
61C22×C4C2×D411yescharacteristic
62C22×C4C2×D411yescharacteristic
63M16—24no—
64M16—42no—
65C2×C8—42no—
66C2×C8—42no—
67C4⋊C4—41no—
68C4⋊C4—41no—
69C4⋊C4—41no—
70C4⋊C4—42no—
71C4⋊C4—42no—
72C4⋊C4—42no—
73C42—21no—
74C42—21no—
75C42—21no—
76C42—21no—
77C42—21no—
78C42—21no—
79C42—42no—
80C23C2×C22⋊C411yescharacteristic
81Q8—44no—
82Q8—82no—
83Q8—82no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—22no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—42no—
99C2×C4—42no—
100C2×C4—44no—
101C2×C4—42no—
102C2×C4—42no—
103C2×C4#9911yescharacteristic
104C2×C4#9911yescharacteristic
105C2×C4#10412yes—
106C2×C4#13712yes—
107C8—44no—
108C8—82no—
109C22—21no—
110C22—21no—
111C22C2×#9911yescharacteristic
112C22#41911yescharacteristic
113C22C2×#10411yescharacteristic
114C4—21no—
115C4—22no—
116C4—22no—
117C4—41no—
118C4—41no—
119C4—41no—
120C4—41no—
121C4—82no—
122C4—82no—
123C4#35512yes—
124C2—21no—
125C2—21no—
126C2#150811yescharacteristic
127C2#212311yescharacteristic
128C2C2×#35511yescharacteristic
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
#25682
C4×#1012
#14672
#13532