Finite Group Databasebeta

← #9450

Subgroups — #9450

Order 256.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#2565C211yesmaximal, characteristic
3#1534C212yesmaximal
4#1467C211yesmaximal, characteristic
5#1285C212yesmaximal
6C2×#125C2211yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#446—24no—
9#432—21no—
10#432C2212yes—
11#432C2212yes—
12#431—21no—
13#398—21no—
14#398—21no—
15#391C411yescharacteristic
16#391C411yescharacteristic
17#387—21no—
18#387—21no—
19#384C411yescharacteristic
20#382C411yescharacteristic
21C4×C4⋊C4C2211yescharacteristic
22#330—24no—
23#324—21no—
24#324—21no—
25C22×Q8C2×C411yescharacteristic
26#125—22no—
27#125—22no—
28C4×Q8—22no—
29C4×Q8—22no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4D411yescharacteristic
39C2×C4⋊C4D411yescharacteristic
40C2×C42C2×C411yescharacteristic
41C2×C42C2×C411yescharacteristic
42C2×C42D411yescharacteristic
43C2×C42D411yescharacteristic
44C2×C42C2311yescharacteristic
45C4⋊C8—22no—
46C4⋊C8—22no—
47C4⋊C8—22no—
48C4⋊C8—22no—
49C22⋊C8—22no—
50C22⋊C8—22no—
51#97—22no—
52#97—22no—
53#97D414yes—
54C4×C8—22no—
55#95—21no—
56#95—21no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95—21no—
62C2×Q8—22no—
63C2×Q8—22no—
64C2×Q8—41no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4C22⋊C411yescharacteristic
70C22×C4C22⋊C411yescharacteristic
71C22×C4C22⋊C411yescharacteristic
72C22×C4C22⋊C411yescharacteristic
73C22×C4C22×C411yescharacteristic
74C22×C4C2×D411yescharacteristic
75C22×C4C2×D411yescharacteristic
76C2×C8—24no—
77C2×C8—42no—
78C4⋊C4—22no—
79C4⋊C4—22no—
80C4⋊C4—22no—
81C4⋊C4—22no—
82C4⋊C4—22no—
83C4⋊C4—42no—
84C4⋊C4—42no—
85C4⋊C4—42no—
86C4⋊C4—41no—
87C4⋊C4—42no—
88C4⋊C4—41no—
89C42—21no—
90C42—21no—
91C42—21no—
92C42—21no—
93C42—41no—
94C42—41no—
95C42C2×D412yes—
96C42#4112yes—
97C23C2×C22⋊C411yescharacteristic
98Q8—44no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—22no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—42no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4#10112yes—
124C2×C4C4×D412yes—
125C2×C4#12011yescharacteristic
126C2×C4#12112yes—
127C2×C4#12311yescharacteristic
128C8—44no—
129C8—82no—
130C22—21no—
131C22—21no—
132C22#38611yescharacteristic
133C22C2×#10111yescharacteristic
134C22#41311yescharacteristic
135C4—22no—
136C4—22no—
137C4—22no—
138C4—21no—
139C4—21no—
140C4—42no—
141C4—41no—
142C4—41no—
143C4—41no—
144C4—81no—
145C4—81no—
146C4—81no—
147C2—21no—
148C2—21no—
149C2#188411yescharacteristic
150C2#190111yescharacteristic
151C2#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
#25652
#15342
#14672
#12852