Finite Group Databasebeta

← #9190

Subgroups — #9190

Order 256.

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

normal subgroups only

This group has 218 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#2634C211yesmaximal, characteristic
3C4×#101C211yesmaximal, characteristic
4#1528C212yesmaximal
5#1288C212yesmaximal
6C2×#125C2211yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#446—24no—
9#432—21no—
10#432C2212yes—
11#431—21no—
12C2×#101—21no—
13C4×M16C2212yes—
14#400—21no—
15#400C411yescharacteristic
16#400C411yescharacteristic
17#398C411yescharacteristic
18#398C411yescharacteristic
19#395—21no—
20#387—21no—
21#387—21no—
22#383C2211yescharacteristic
23#343—21no—
24#330—24no—
25C22×Q8D411yescharacteristic
26C2×M16—22no—
27#125—22no—
28#125—22no—
29C4×Q8—22no—
30C4×Q8—22no—
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⋊C4C2×C411yescharacteristic
39C2×C4⋊C4D411yescharacteristic
40C2×C42D411yescharacteristic
41C2×C42D411yescharacteristic
42C2×C42C2311yescharacteristic
43C4⋊C8—22no—
44C4⋊C8—22no—
45C4⋊C8—22no—
46#101—24no—
47C22⋊C8—22no—
48#97—22no—
49#97—22no—
50#97D414yes—
51C4×C8—22no—
52C4×C8—22no—
53#95—21no—
54#95—21no—
55#95—21no—
56#95—21no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95C2×C411yescharacteristic
62#95C2×C411yescharacteristic
63C2×Q8—22no—
64C2×Q8—22no—
65C2×Q8—41no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4C22⋊C411yescharacteristic
71C22×C4C22⋊C411yescharacteristic
72C22×C4C22⋊C411yescharacteristic
73C22×C4C22⋊C411yescharacteristic
74C22×C4C22×C411yescharacteristic
75C22×C4C2×D411yescharacteristic
76C22×C4C2×D411yescharacteristic
77M16—24no—
78M16—42no—
79C2×C8—24no—
80C2×C8—42no—
81C4⋊C4—22no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—22no—
85C4⋊C4—22no—
86C4⋊C4—42no—
87C4⋊C4—42no—
88C4⋊C4—41no—
89C4⋊C4—42no—
90C4⋊C4—41no—
91C42—21no—
92C42—21no—
93C42—21no—
94C42—21no—
95C42C2×D412yes—
96C42#4112yes—
97C23C2×C22⋊C411yescharacteristic
98Q8—44no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
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—42no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4#10412yes—
124C2×C4C4×D412yes—
125C2×C4#12011yescharacteristic
126C2×C4#12112yes—
127C2×C4#12311yescharacteristic
128C8—44no—
129C8—44no—
130C22—21no—
131C22—21no—
132C22#38611yescharacteristic
133C22C2×#10411yescharacteristic
134C22#42111yescharacteristic
135C4—22no—
136C4—22no—
137C4—21no—
138C4—21no—
139C4—22no—
140C4—41no—
141C4—41no—
142C4—41no—
143C4—81no—
144C4—81no—
145C4—81no—
146C4—81no—
147C2—21no—
148C2—21no—
149C2#187111yescharacteristic
150C2#191211yescharacteristic
151C2#191511yescharacteristic
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
#26342
C4×#1012
#15282
#12882