Finite Group Databasebeta

← #8775

Subgroups — #8775

Order 256.

192 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 57 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#2356C211yesmaximal, characteristic
2C4×#101C211yesmaximal, characteristic
3#1467C211yesmaximal, characteristic
4#1300C212yesmaximal
5#1288C212yesmaximal
6C2×C4×Q8C2211yescharacteristic
7#432C2212yes—
8C2×#101—21no—
9C4×M16C2212yes—
10#391—21no—
11#387—21no—
12#387—21no—
13#383C411yescharacteristic
14#383C2211yescharacteristic
15#382C411yescharacteristic
16C4×C4⋊C4—21no—
17C4×C4⋊C4C411yescharacteristic
18#376C411yescharacteristic
19#376C2211yescharacteristic
20#343—21no—
21#324—21no—
22#324—21no—
23C22×Q8D411yescharacteristic
24C2×M16—22no—
25C4×Q8—22no—
26C4×Q8—22no—
27C2×C4⋊C4—21no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4D411yescharacteristic
30C2×C4⋊C4D411yescharacteristic
31C2×C4⋊C4D411yescharacteristic
32C2×C42—21no—
33C2×C42—21no—
34C2×C42—21no—
35C2×C42C2×C411yescharacteristic
36C2×C42C2×C411yescharacteristic
37C2×C42C2311yescharacteristic
38C4⋊C8—22no—
39#101—24no—
40C22⋊C8—22no—
41#97—22no—
42#97—22no—
43C4×C8—22no—
44#95—21no—
45#95—21no—
46#95—21no—
47#95—21no—
48#95—21no—
49#95—21no—
50#95—21no—
51#95C2×C411yescharacteristic
52#95C2×C411yescharacteristic
53#95C2×C411yescharacteristic
54#95C2×C411yescharacteristic
55C2×Q8—22no—
56C2×Q8—22no—
57C2×Q8—41no—
58C22×C4—21no—
59C22×C4—21no—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4C22⋊C411yescharacteristic
63C22×C4C22⋊C411yescharacteristic
64C22×C4C22⋊C411yescharacteristic
65C22×C4C22⋊C411yescharacteristic
66C22×C4C22×C411yescharacteristic
67C22×C4C2×D411yescharacteristic
68C22×C4C2×D411yescharacteristic
69M16—24no—
70M16—42no—
71C2×C8—42no—
72C2×C8—42no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—42no—
77C4⋊C4—42no—
78C42—21no—
79C42—21no—
80C42—21no—
81C42—21no—
82C42—42no—
83C42—42no—
84C42—42no—
85C42#4112yes—
86C42#4112yes—
87C23C2×C22⋊C411yescharacteristic
88Q8—44no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—22no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—21no—
98C2×C4—21no—
99C2×C4—41no—
100C2×C4—41no—
101C2×C4—41no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4#10412yes—
115C2×C4#11711yescharacteristic
116C2×C4#11711yescharacteristic
117C2×C4#12312yes—
118C2×C4#12312yes—
119C8—44no—
120C8—82no—
121C22—21no—
122C22—21no—
123C22#38111yescharacteristic
124C22C2×#10411yescharacteristic
125C22#42111yescharacteristic
126C4—22no—
127C4—22no—
128C4—22no—
129C4—21no—
130C4—21no—
131C4—42no—
132C4—41no—
133C4—41no—
134C4—41no—
135C4—81no—
136C4—81no—
137C4—81no—
138C2—21no—
139C2—21no—
140C2#182611yescharacteristic
141C2#182711yescharacteristic
142C2#183011yescharacteristic
subgroupG/H
center, socleC22#381
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
#23562
C4×#1012
#14672
#13002
#12882