Finite Group Databasebeta

← #11792

Subgroups — #11792

Order 256.

189 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 189 conjugacy classes of subgroups — too many to draw. Only its 51 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#2581C211yesmaximal, characteristic
2C4×#101C211yesmaximal, characteristic
3#1467C211yesmaximal, characteristic
4#1354C212yesmaximal
5#1353C212yesmaximal
6C2×C4×Q8C411yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#432—21no—
9C2×#101—21no—
10C4×M16—21no—
11#400C411yescharacteristic
12#400C2211yescharacteristic
13#395C411yescharacteristic
14#395C2211yescharacteristic
15#391—21no—
16#389—21no—
17#387—21no—
18#387—21no—
19#382C411yescharacteristic
20#343C2212yes—
21#324—21no—
22#324C2212yes—
23C22×Q8C2×C411yescharacteristic
24C22×Q8D411yescharacteristic
25C2×M16—22no—
26C4×Q8—41no—
27C4×Q8—41no—
28C4×Q8—41no—
29C4×Q8—41no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4C2×C411yescharacteristic
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4D411yescharacteristic
37C2×C4⋊C4C2311yescharacteristic
38C2×C42—21no—
39C2×C42C2×C411yescharacteristic
40C2×C42D411yescharacteristic
41C2×C42D411yescharacteristic
42C4⋊C8—41no—
43#101—24no—
44C22⋊C8—22no—
45#97—41no—
46#97—41no—
47C4×C8—41no—
48#95—21no—
49#95—21no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95C2×C411yescharacteristic
56#95C2×C411yescharacteristic
57C2×Q8—22no—
58C2×Q8—22no—
59C2×Q8—41no—
60C2×Q8—42no—
61C2×Q8—41no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4C22⋊C411yescharacteristic
67C22×C4C22⋊C411yescharacteristic
68C22×C4C22⋊C411yescharacteristic
69C22×C4C22⋊C411yescharacteristic
70C22×C4C22×C411yescharacteristic
71C22×C4C2×D411yescharacteristic
72C22×C4C2×D411yescharacteristic
73M16—24no—
74M16—42no—
75C2×C8—42no—
76C2×C8—42no—
77C4⋊C4—41no—
78C4⋊C4—41no—
79C4⋊C4—41no—
80C4⋊C4—41no—
81C4⋊C4—42no—
82C4⋊C4—42no—
83C4⋊C4—41no—
84C4⋊C4—41no—
85C4⋊C4—42no—
86C42—21no—
87C42—21no—
88C42—21no—
89C42—21no—
90C42—21no—
91C42—21no—
92C42—42no—
93C23C2×C22⋊C411yescharacteristic
94Q8—44no—
95Q8—42no—
96Q8—42no—
97C2×C4—21no—
98C2×C4—21no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—22no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—41no—
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—42no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4#9911yescharacteristic
123C2×C4#9911yescharacteristic
124C2×C4#10412yes—
125C2×C4#13712yes—
126C8—44no—
127C8—82no—
128C22—21no—
129C22—21no—
130C22C2×#9911yescharacteristic
131C22#41911yescharacteristic
132C22C2×#10411yescharacteristic
133C4—21no—
134C4—21no—
135C4—22no—
136C4—22no—
137C4—41no—
138C4—41no—
139C4—42no—
140C4—41no—
141C4—41no—
142C4—81no—
143C4—81no—
144C4—81no—
145C2—21no—
146C2—21no—
147C2#150811yescharacteristic
148C2#212011yescharacteristic
149C2#213311yescharacteristic
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
#25812
C4×#1012
#14672
#13542
#13532