Finite Group Databasebeta

← #9488

Subgroups — #9488

Order 256.

227 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 227 conjugacy classes of subgroups — too many to draw. Only its 67 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#2581C211yesmaximal, characteristic
3#1801C211yesmaximal, characteristic
4#1487C212yesmaximal
5#1286C212yesmaximal
6C2×C4×Q8C2211yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#446—24no—
9#432—22no—
10#431C2212yes—
11#423C2212yes—
12C2×#101—21no—
13#400C412yes—
14#395C412yes—
15#391—21no—
16#389—21no—
17#387—22no—
18#382C2211yescharacteristic
19#343—21no—
20Q8⋊C8—24no—
21C22×Q8C2×C411yescharacteristic
22C22×Q8D411yescharacteristic
23C2×M16—22no—
24C4×Q8—22no—
25C4×Q8—22no—
26C4×Q8—22no—
27C4×Q8—22no—
28C2×C4⋊C4—22no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4C2×C411yescharacteristic
32C2×C4⋊C4C2×C412yes—
33C2×C4⋊C4D411yescharacteristic
34C2×C42—21no—
35C2×C42D412yes—
36C2×C42C2311yescharacteristic
37C4⋊C8—24no—
38C4⋊C8—22no—
39C4⋊C8—22no—
40C4⋊C8—22no—
41#101—42no—
42C22⋊C8—22no—
43#97—24no—
44C4×C8D414yes—
45#95—22no—
46#95—22no—
47#95—22no—
48#95—21no—
49#95C2×C412yes—
50C2×Q8—22no—
51C2×Q8—21no—
52C2×Q8—21no—
53C2×Q8—22no—
54C2×Q8—22no—
55C2×Q8—42no—
56C22×C4—21no—
57C22×C4—22no—
58C22×C4—21no—
59C22×C4C22⋊C412yes—
60C22×C4C22⋊C412yes—
61C22×C4C22×C411yescharacteristic
62C22×C4C2×D411yescharacteristic
63C22×C4C2×D411yescharacteristic
64M16—42no—
65M16—42no—
66C2×C8—24no—
67C2×C8—42no—
68C4⋊C4—24no—
69C4⋊C4—22no—
70C4⋊C4—22no—
71C4⋊C4—44no—
72C4⋊C4—41no—
73C4⋊C4—41no—
74C4⋊C4—41no—
75C4⋊C4—41no—
76C42—22no—
77C42—22no—
78C42—42no—
79C42C2×D412yes—
80C42#4112yes—
81C23C2×C22⋊C411yescharacteristic
82Q8—24no—
83Q8—42no—
84Q8—42no—
85Q8—42no—
86C2×C4—22no—
87C2×C4—22no—
88C2×C4—22no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—41no—
92C2×C4—41no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—42no—
96C2×C4—42no—
97C2×C4—42no—
98C2×C4—42no—
99C2×C4—41no—
100C2×C4—42no—
101C2×C4C4×D412yes—
102C2×C4#12011yescharacteristic
103C2×C4#12112yes—
104C2×C4#12311yescharacteristic
105C2×C4AGL(1,ℤ/8)11yescharacteristic
106C2×C4#13712yes—
107C2×C4#13711yescharacteristic
108C8—44no—
109C8—82no—
110C22—21no—
111C22—21no—
112C22#38611yescharacteristic
113C22#41711yescharacteristic
114C22#41911yescharacteristic
115C4—22no—
116C4—21no—
117C4—21no—
118C4—42no—
119C4—42no—
120C4—42no—
121C4—82no—
122C4—81no—
123C4#46812yes—
124C4#47012yes—
125C2—21no—
126C2—21no—
127C2#189111yescharacteristic
128C2#189411yescharacteristic
129C2#191211yescharacteristic
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
#25812
#18012
#14872
#12862