Finite Group Databasebeta

← #10494

Subgroups — #10494

Order 256.

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

normal subgroups only

This group has 172 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#3229C211yesmaximal, characteristic
2#1997C211yesmaximal, characteristic
3#1574C211yesmaximal, characteristic
4#1561C211yesmaximal, characteristic
5#1549C211yesmaximal, characteristic
6#1485C211yesmaximal, characteristic
7#1299C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×C4⋊Q8C2211yescharacteristic
10#498—21no—
11#487—21no—
12#483—22no—
13#475—21no—
14#475—21no—
15#431C2211yescharacteristic
16#431C2211yescharacteristic
17#423C2211yescharacteristic
18#423C2211yescharacteristic
19C4×M16C2211yescharacteristic
20#343—22no—
21#335—21no—
22#334—21no—
23#332—21no—
24#332—21no—
25#332—22no—
26Q8⋊C8—22no—
27C22×Q8—21no—
28C2×M16—21no—
29C2×M16—21no—
30C2×M16—21no—
31C4⋊Q8—21no—
32C4⋊Q8—21no—
33C4⋊Q8—21no—
34C4⋊Q8—21no—
35C4⋊Q8D411yescharacteristic
36C4⋊Q8D411yescharacteristic
37#125—21no—
38C22⋊Q8—21no—
39C22⋊Q8—21no—
40C4×Q8—21no—
41C4×Q8—21no—
42#117—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4D412yes—
45C2×C42C2311yescharacteristic
46#106—22no—
47#106—22no—
48C4⋊C8—21no—
49C4⋊C8—21no—
50C4⋊C8—21no—
51C4⋊C8—21no—
52C4⋊C8D412yes—
53C4⋊C8D411yescharacteristic
54C4⋊C8D411yescharacteristic
55#103—22no—
56#103—22no—
57C22⋊C8—21no—
58C22⋊C8—21no—
59#97—21no—
60C4×C8—21no—
61C4×C8—21no—
62C4×C8—21no—
63C2×Q8—21no—
64C2×Q8—21no—
65C2×Q8—41no—
66C2×Q8—41no—
67C2×Q8—82no—
68C22×C4—22no—
69C22×C4C2×D411yescharacteristic
70C22×C4#4111yescharacteristic
71C22×C4#4111yescharacteristic
72M16—22no—
73M16—41no—
74M16—42no—
75M16—81no—
76C2×C8—21no—
77C2×C8—21no—
78C2×C8—22no—
79C2×C8—41no—
80C2×C8—41no—
81C2×C8—41no—
82C4⋊C4—22no—
83C4⋊C4—21no—
84C4⋊C4—22no—
85C4⋊C4—21no—
86C4⋊C4—21no—
87C4⋊C4—21no—
88C4⋊C4—41no—
89C4⋊C4—41no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C22⋊C4—41no—
93C42—41no—
94C42C2×D411yescharacteristic
95C42C2×D411yescharacteristic
96C42C2×D411yescharacteristic
97C42#4111yescharacteristic
98C23#12311yescharacteristic
99Q8—41no—
100Q8—41no—
101Q8—41no—
102Q8—41no—
103Q8—82no—
104Q8—82no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—22no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—42no—
113C2×C4—82no—
114C2×C4#12011yescharacteristic
115C2×C4#12111yescharacteristic
116C2×C4#12111yescharacteristic
117C2×C4#12111yescharacteristic
118C2×C4#12311yescharacteristic
119C2×C4#12411yescharacteristic
120C8—42no—
121C8—41no—
122C8—41no—
123C8—42no—
124C8—81no—
125C8—81no—
126C22—21no—
127C22—21no—
128C22—21no—
129C22#39411yescharacteristic
130C4—21no—
131C4—21no—
132C4—21no—
133C4—81no—
134C4—81no—
135C4—82no—
136C4#45411yescharacteristic
137C4#45611yescharacteristic
138C4#47111yescharacteristic
139C4#47112yes—
140C4#47311yescharacteristic
141C2—41no—
142C2#203811yescharacteristic
143C2#204611yescharacteristic
144C2#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
#32292
#19972
#15742
#15612
#15492
#14852
#12992