Finite Group Databasebeta

← #9502

Subgroups — #9502

Order 256.

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

normal subgroups only

This group has 330 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#2483C211yesmaximal, characteristic
2#2312C211yesmaximal, characteristic
3#1819C212yesmaximal
4#1819C211yesmaximal, characteristic
5#1304C212yesmaximal
6C22×C22⋊C4C2211yescharacteristic
7C22×C22⋊C4C2211yescharacteristic
8#397—22no—
9#388—24no—
10#385—21no—
11#385C412yescomplemented
12#381—21no—
13#381C412yescomplemented
14#380—21no—
15#379C2212yes—
16#379C2211yescharacteristic
17#379C2212yes—
18C4×C22⋊C4—21no—
19#342—24no—
20#342—22no—
21C25C2311yescharacteristic
22C23×C4C2×C411yescharacteristic
23C23×C4C2×C411yescharacteristic
24C23×C4D411yescharacteristic
25C23×C4D411yescharacteristic
26C2×C4⋊C4—22no—
27C2×C4⋊C4—22no—
28C2×C22⋊C4—22no—
29C2×C22⋊C4—22no—
30C2×C22⋊C4—22no—
31C2×C22⋊C4—21no—
32C2×C22⋊C4—21no—
33C2×C22⋊C4—22no—
34C2×C22⋊C4—21no—
35C2×C22⋊C4—22no—
36C2×C22⋊C4—22no—
37C2×C22⋊C4—22no—
38C2×C22⋊C4—22no—
39C2×C22⋊C4—21no—
40C2×C22⋊C4—22no—
41C2×C22⋊C4C2×C412yes—
42C2×C22⋊C4C2×C412yes—
43C2×C22⋊C4D412yes—
44C2×C22⋊C4D414yes—
45C2×C42—22no—
46#95—22no—
47#95—22no—
48#95—22no—
49#95—22no—
50#95—22no—
51C24—42no—
52C24—42no—
53C24—81no—
54C24C22×C411yescharacteristic
55C24C2×D411yescharacteristic
56C24C2×D411yescharacteristic
57C24C2×D412yes—
58C24#4112yes—
59C22×C4—21no—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4—22no—
65C22×C4—21no—
66C22×C4—24no—
67C22×C4—22no—
68C22×C4—22no—
69C22×C4—42no—
70C22×C4—42no—
71C22×C4—42no—
72C22×C4—81no—
73C22×C4—81no—
74C22×C4C22⋊C412yes—
75C22×C4C22⋊C412yes—
76C4⋊C4—82no—
77C4⋊C4—82no—
78C22⋊C4—24no—
79C22⋊C4—24no—
80C22⋊C4—44no—
81C22⋊C4—42no—
82C22⋊C4—41no—
83C22⋊C4—42no—
84C22⋊C4—41no—
85C22⋊C4—42no—
86C22⋊C4—44no—
87C22⋊C4—44no—
88C22⋊C4—44no—
89C22⋊C4—82no—
90C22⋊C4—81no—
91C22⋊C4—82no—
92C42—82no—
93C23—22no—
94C23—22no—
95C23—22no—
96C23—22no—
97C23—24no—
98C23—41no—
99C23—41no—
100C23—41no—
101C23—41no—
102C23—42no—
103C23—42no—
104C23—41no—
105C23—42no—
106C23—42no—
107C23—42no—
108C23—88no—
109C23C2×C22⋊C411yescharacteristic
110C23C4×D412yes—
111C23#12011yescharacteristic
112C23#12112yes—
113C23#12311yescharacteristic
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—42no—
119C2×C4—42no—
120C2×C4—44no—
121C2×C4—42no—
122C2×C4—44no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4—44no—
130C2×C4—81no—
131C2×C4—81no—
132C2×C4—82no—
133C2×C4—82no—
134C2×C4—82no—
135C2×C4—82no—
136C2×C4—82no—
137C22—21no—
138C22—21no—
139C22—21no—
140C22—21no—
141C22—22no—
142C22—21no—
143C22—22no—
144C22—22no—
145C22—22no—
146C22—21no—
147C22—22no—
148C22—22no—
149C22—21no—
150C22—44no—
151C22—44no—
152C22—84no—
153C22—82no—
154C22—84no—
155C22#38611yescharacteristic
156C22#41012yes—
157C22#45812yes—
158C4—42no—
159C4—42no—
160C4—84no—
161C4—82no—
162C4—81no—
163C4—81no—
164C4—162no—
165C2—22no—
166C2—22no—
167C2—42no—
168C2—41no—
169C2—42no—
170C2#189011yescharacteristic
171C2#189911yescharacteristic
172C2#191311yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC24C22×C4
Frattini, prime radical, cosocleC25C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
11. #385C4semidirect
13. #381C4semidirect

Maximal subgroups

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

subgroupindex
#24832
#23122
#18192
#13042