Finite Group Databasebeta

← #10493

Subgroups — #10493

Order 256.

186 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 49 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#3209C211yesmaximal, characteristic
2#1966C211yesmaximal, characteristic
3#1574C211yesmaximal, characteristic
4#1561C211yesmaximal, characteristic
5#1548C211yesmaximal, characteristic
6#1485C211yesmaximal, characteristic
7#1299C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×C4⋊Q8C2211yescharacteristic
10#494—21no—
11#487—21no—
12#462—21no—
13#462—21no—
14#451—22no—
15#431C2211yescharacteristic
16#431C2211yescharacteristic
17#423C2211yescharacteristic
18#423C2211yescharacteristic
19C2×#101—22no—
20C4×M16C2211yescharacteristic
21#335—21no—
22#334—21no—
23#333—22no—
24#332—21no—
25#332—21no—
26Q8⋊C8—22no—
27C22×Q8D412yes—
28C2×Q16—22no—
29C2×Q16—22no—
30C2×M16—21no—
31C2×M16—21no—
32C2×M16—21no—
33C4⋊Q8—21no—
34C4⋊Q8—21no—
35C4⋊Q8—21no—
36C4⋊Q8—21no—
37C4⋊Q8D411yescharacteristic
38C4⋊Q8D411yescharacteristic
39#125—21no—
40C22⋊Q8—21no—
41C22⋊Q8—21no—
42C4×Q8—21no—
43C4×Q8—21no—
44#117—21no—
45C2×C4⋊C4—21no—
46C2×C4⋊C4—21no—
47C2×C42C2311yescharacteristic
48C4⋊C8—21no—
49C4⋊C8—21no—
50C4⋊C8—21no—
51C4⋊C8—21no—
52C4⋊C8D412yes—
53C4⋊C8D411yescharacteristic
54C4⋊C8D411yescharacteristic
55#103—22no—
56#103—22no—
57#101—44no—
58C22⋊C8—21no—
59C22⋊C8—21no—
60#97—21no—
61C4×C8—21no—
62C4×C8—21no—
63C4×C8—21no—
64C2×Q8—22no—
65C2×Q8—21no—
66C2×Q8—21no—
67C2×Q8—22no—
68C2×Q8—42no—
69C2×Q8—42no—
70C22×C4—22no—
71C22×C4C2×D411yescharacteristic
72C22×C4#4111yescharacteristic
73C22×C4#4111yescharacteristic
74Q16—82no—
75Q16—82no—
76M16—22no—
77M16—41no—
78M16—42no—
79M16—81no—
80C2×C8—21no—
81C2×C8—21no—
82C2×C8—22no—
83C2×C8—41no—
84C2×C8—41no—
85C2×C8—41no—
86C4⋊C4—21no—
87C4⋊C4—21no—
88C4⋊C4—21no—
89C4⋊C4—21no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C22⋊C4—41no—
97C42—41no—
98C42C2×D411yescharacteristic
99C42C2×D411yescharacteristic
100C42C2×D411yescharacteristic
101C42#4111yescharacteristic
102C23#12311yescharacteristic
103Q8—41no—
104Q8—42no—
105Q8—41no—
106Q8—42no—
107Q8—41no—
108Q8—41no—
109Q8—82no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—44no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—42no—
119C2×C4#12011yescharacteristic
120C2×C4#12111yescharacteristic
121C2×C4#12111yescharacteristic
122C2×C4#12111yescharacteristic
123C2×C4#12311yescharacteristic
124C2×C4#12411yescharacteristic
125C8—42no—
126C8—41no—
127C8—41no—
128C8—42no—
129C8—81no—
130C8—81no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22#39411yescharacteristic
135C4—21no—
136C4—21no—
137C4—21no—
138C4—81no—
139C4—82no—
140C4—81no—
141C4#45311yescharacteristic
142C4#45511yescharacteristic
143C4#47111yescharacteristic
144C4#47311yescharacteristic
145C4#47312yes—
146C2—41no—
147C2#203711yescharacteristic
148C2#204711yescharacteristic
149C2#205211yescharacteristic
subgroupG/H
center, socleC22#394
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#123
LCSG ▷ C2×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
#32092
#19662
#15742
#15612
#15482
#14852
#12992