Finite Group Databasebeta

← #10346

Subgroups — #10346

Order 256.

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

normal subgroups only

This group has 250 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#2646C211yesmaximal, characteristic
2#1823C212yesmaximal
3#1445C211yesmaximal, characteristic
4#1294C212yesmaximal
5#1280C211yesmaximal, characteristic
6C22×C4⋊C4C2211yescharacteristic
7C2×C22⋊C8C2212yes—
8#400—22no—
9#398—22no—
10#385—22no—
11#380C2212yes—
12C2×#95—22no—
13C2×#95C2211yescharacteristic
14C2×#95C2211yescharacteristic
15#340—22no—
16#340—22no—
17C23×C4—21no—
18C23×C4—21no—
19C23×C4D412yes—
20C23×C4C2311yescharacteristic
21C22×C8—22no—
22C2×C4⋊C4—22no—
23C2×C4⋊C4—22no—
24C2×C4⋊C4—21no—
25C2×C4⋊C4—22no—
26C2×C4⋊C4—22no—
27C2×C4⋊C4D412yes—
28C2×C4⋊C4D412yes—
29C2×C4⋊C4Q812yes—
30C2×C22⋊C4—22no—
31C22⋊C8—22no—
32C22⋊C8—22no—
33#95—22no—
34#95—22no—
35#95—22no—
36#95—22no—
37#95—22no—
38#95—44no—
39C24C2×D411yescharacteristic
40C22×C4—22no—
41C22×C4—22no—
42C22×C4—22no—
43C22×C4—22no—
44C22×C4—22no—
45C22×C4—22no—
46C22×C4—22no—
47C22×C4—42no—
48C22×C4—42no—
49C22×C4—42no—
50C22×C4—41no—
51C22×C4—42no—
52C22×C4—41no—
53C22×C4—41no—
54C22×C4—41no—
55C22×C4—42no—
56C22×C4—42no—
57C22×C4—42no—
58C22×C4C2×D412yes—
59C22×C4C2×Q811yescharacteristic
60C22×C4#4112yes—
61C22×C4#4111yescharacteristic
62C2×C8—42no—
63C2×C8—42no—
64C2×C8—42no—
65C4⋊C4—24no—
66C4⋊C4—42no—
67C4⋊C4—42no—
68C4⋊C4—42no—
69C4⋊C4—82no—
70C4⋊C4—82no—
71C22⋊C4—42no—
72C22⋊C4—42no—
73C23—21no—
74C23—21no—
75C23—22no—
76C23#12011yescharacteristic
77C23C22⋊Q811yescharacteristic
78C23#12411yescharacteristic
79C23#13512yes—
80C23AGL(1,ℤ/8)12yes—
81C2×C4—22no—
82C2×C4—22no—
83C2×C4—41no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—44no—
87C2×C4—42no—
88C2×C4—44no—
89C2×C4—42no—
90C2×C4—42no—
91C2×C4—42no—
92C2×C4—42no—
93C2×C4—42no—
94C2×C4—42no—
95C2×C4—42no—
96C2×C4—42no—
97C2×C4—42no—
98C2×C4—42no—
99C2×C4—44no—
100C2×C4—82no—
101C2×C4—81no—
102C2×C4—82no—
103C2×C4—81no—
104C2×C4—81no—
105C2×C4—81no—
106C2×C4—82no—
107C2×C4C22⋊Q812yes—
108C2×C4#12412yes—
109C8—82no—
110C22—22no—
111C22—22no—
112C22—22no—
113C22—22no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22#39311yescharacteristic
119C22#44912yes—
120C22#45511yescharacteristic
121C22#45611yescharacteristic
122C22#45812yes—
123C22#47812yes—
124C22#48811yescharacteristic
125C22#49011yescharacteristic
126C4—22no—
127C4—22no—
128C4—82no—
129C4—82no—
130C4—82no—
131C4—82no—
132C4—82no—
133C2—21no—
134C2—22no—
135C2—21no—
136C2#160912yes—
137C2#161212yes—
138C2#202511yescharacteristic
139C2#202811yescharacteristic
140C2#203011yescharacteristic
subgroupG/H
center, socleC23#120
commutator, Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#26462
#18232
#14452
#12942
#12802