Finite Group Databasebeta

← #9374

Subgroups — #9374

Order 256.

184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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#3237C211yesmaximal, characteristic
2#2985C211yesmaximal, characteristic
3#1552C211yesmaximal, characteristic
4#1537C211yesmaximal, characteristic
5#1481C211yesmaximal, characteristic
6#1290C211yesmaximal, characteristic
7#1287C211yesmaximal, characteristic
8#533C2211yescharacteristic
9#533C2211yescharacteristic
10#501C412yes—
11#491C412yes—
12#485—22no—
13#477—21no—
14#475—21no—
15#446—22no—
16#446—21no—
17C8×Q8—21no—
18#433—22no—
19#432C2211yescharacteristic
20#432C2211yescharacteristic
21#432C2211yescharacteristic
22#431C2211yescharacteristic
23C2×C4⋊C8C2211yescharacteristic
24#332—21no—
25#332—21no—
26#330—22no—
27Q8⋊C8—21no—
28Q8⋊C8—21no—
29C22×C8—21no—
30C4⋊Q8C2×C411yescharacteristic
31C4⋊Q8C2×C411yescharacteristic
32C4⋊Q8D411yescharacteristic
33C4⋊Q8D411yescharacteristic
34#125—21no—
35#125C2×C412yes—
36C22⋊Q8—21no—
37C22⋊Q8—21no—
38C22⋊Q8—21no—
39C22⋊Q8—21no—
40C4×Q8—21no—
41C4×Q8—21no—
42C4×Q8—21no—
43C4×Q8—21no—
44#117—21no—
45#117D412yes—
46C2×C42C2311yescharacteristic
47#107—22no—
48#106—22no—
49C4⋊C8—22no—
50C4⋊C8—22no—
51C4⋊C8—21no—
52C4⋊C8—21no—
53C4⋊C8—21no—
54C4⋊C8—21no—
55C4⋊C8—21no—
56C4⋊C8—21no—
57#103—22no—
58#103—22no—
59C22⋊C8—21no—
60C22⋊C8—21no—
61C22⋊C8—21no—
62C22⋊C8—21no—
63#97—22no—
64#97—21no—
65#97C2×C412yes—
66#97D412yes—
67C4×C8—22no—
68C4×C8D411yescharacteristic
69C4×C8D411yescharacteristic
70C2×Q8—21no—
71C2×Q8—21no—
72C2×Q8—21no—
73C2×Q8—21no—
74C22×C4C2×D411yescharacteristic
75C22×C4#4111yescharacteristic
76C22×C4#4111yescharacteristic
77C2×C8—22no—
78C2×C8—21no—
79C2×C8—22no—
80C2×C8—21no—
81C2×C8—41no—
82C2×C8—41no—
83C2×C8—81no—
84C4⋊C4—22no—
85C4⋊C4—22no—
86C4⋊C4—21no—
87C4⋊C4—21no—
88C4⋊C4—21no—
89C4⋊C4—21no—
90C4⋊C4—21no—
91C4⋊C4—21no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4C22⋊C412yes—
95C4⋊C4C22⋊C412yes—
96C22⋊C4—22no—
97C22⋊C4—41no—
98C42—22no—
99C42—41no—
100C42C22×C411yescharacteristic
101C42C2×D411yescharacteristic
102C42C2×D411yescharacteristic
103C42C2×D411yescharacteristic
104C23#12311yescharacteristic
105Q8—42no—
106Q8—42no—
107Q8—41no—
108Q8—41no—
109Q8—81no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4C2×C22⋊C411yescharacteristic
119C2×C4C4×D411yescharacteristic
120C2×C4C4×D411yescharacteristic
121C2×C4#12011yescharacteristic
122C2×C4#12111yescharacteristic
123C2×C4#12111yescharacteristic
124C8—41no—
125C8—42no—
126C8—41no—
127C8—42no—
128C8—81no—
129C8—81no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22#38611yescharacteristic
134C4—21no—
135C4—21no—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—42no—
140C4—42no—
141C4—81no—
142C4—81no—
143C4#47111yescharacteristic
144C4#47311yescharacteristic
145C2—41no—
146C2#188111yescharacteristic
147C2#190811yescharacteristic
148C2#191211yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
prime radicalC23#123
LCSG ▷ C42 ▷ 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
#32372
#29852
#15522
#15372
#14812
#12902
#12872