Finite Group Databasebeta

← #10393

Subgroups — #10393

Order 256.

263 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 263 conjugacy classes of subgroups — too many to draw. Only its 45 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#2842C211yesmaximal, characteristic
2#1819C212yesmaximal
3#1819C211yesmaximal, characteristic
4#1304C211yesmaximal, characteristic
5#1304C212yesmaximal
6C22×C22⋊C4C2211yescharacteristic
7#399—22no—
8#396—24no—
9#379C2212yes—
10#379C2211yescharacteristic
11#379C2211yescharacteristic
12#379C2212yes—
13#342—24no—
14#342—22no—
15C25C2311yescharacteristic
16C23×C4Q812yes—
17C2×C4⋊C4—24no—
18C2×C4⋊C4—22no—
19C2×C22⋊C4—22no—
20C2×C22⋊C4—21no—
21C2×C22⋊C4—21no—
22C2×C22⋊C4—22no—
23C2×C22⋊C4—22no—
24C2×C22⋊C4—21no—
25C2×C22⋊C4—22no—
26C2×C22⋊C4—22no—
27C2×C22⋊C4—22no—
28C2×C22⋊C4—22no—
29C2×C22⋊C4—22no—
30C2×C22⋊C4—22no—
31C2×C22⋊C4D414yes—
32C2×C22⋊C4D412yes—
33#95—22no—
34C24—42no—
35C24—82no—
36C24C2×D412yes—
37C24C2×D411yescharacteristic
38C24C2×Q811yescharacteristic
39C24#4112yes—
40C24#4111yescharacteristic
41C22×C4—22no—
42C22×C4—24no—
43C22×C4—22no—
44C22×C4—22no—
45C22×C4—22no—
46C22×C4—42no—
47C22×C4—41no—
48C22×C4—82no—
49C4⋊C4—84no—
50C4⋊C4—82no—
51C22⋊C4—41no—
52C22⋊C4—42no—
53C22⋊C4—41no—
54C22⋊C4—44no—
55C22⋊C4—42no—
56C22⋊C4—44no—
57C22⋊C4—42no—
58C22⋊C4—82no—
59C22⋊C4—82no—
60C22⋊C4—82no—
61C22⋊C4—82no—
62C22⋊C4—82no—
63C22⋊C4—82no—
64C23—24no—
65C23—22no—
66C23—42no—
67C23—41no—
68C23—42no—
69C23—42no—
70C23—42no—
71C23—42no—
72C23—42no—
73C23—42no—
74C23—41no—
75C23—42no—
76C23—88no—
77C23#12011yescharacteristic
78C23C22⋊Q812yes—
79C23C22⋊Q811yescharacteristic
80C23#12412yes—
81C23#12411yescharacteristic
82C2×C4—44no—
83C2×C4—44no—
84C2×C4—44no—
85C2×C4—42no—
86C2×C4—44no—
87C2×C4—42no—
88C2×C4—82no—
89C2×C4—82no—
90C2×C4—82no—
91C2×C4—82no—
92C2×C4—81no—
93C2×C4—82no—
94C2×C4—82no—
95C2×C4—82no—
96C22—22no—
97C22—22no—
98C22—21no—
99C22—22no—
100C22—21no—
101C22—22no—
102C22—22no—
103C22—22no—
104C22—22no—
105C22—22no—
106C22—22no—
107C22—44no—
108C22—84no—
109C22—82no—
110C22—82no—
111C22—84no—
112C22#39311yescharacteristic
113C22#45812yes—
114C4—82no—
115C4—84no—
116C4—82no—
117C4—162no—
118C4—161no—
119C2—22no—
120C2—42no—
121C2—41no—
122C2—42no—
123C2—41no—
124C2#203011yescharacteristic
125C2#203212yes—
subgroupG/H
center, socleC22#393
commutator, Frattini, prime radical, cosocleC25C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#28422
#18192
#13042