Finite Group Databasebeta

← #9518

Subgroups — #9518

Order 256.

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

normal subgroups only

This group has 259 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#2975C211yesmaximal, characteristic
2#2579C211yesmaximal, characteristic
3#1465C211yesmaximal, characteristic
4#1463C212yesmaximal, complemented
5#1305C212yesmaximal, complemented
6C2×C4×D4C2211yescharacteristic
7C22×C4⋊C4C2211yescharacteristic
8#436—24no—
9#431—21no—
10#407—21no—
11#407C2212yes—
12#407C2212yes—
13#398—21no—
14#396—21no—
15#387—21no—
16#386C411yescharacteristic
17#386C411yescharacteristic
18#385—21no—
19#385C411yescharacteristic
20#385C411yescharacteristic
21#380C2211yescharacteristic
22#324—21no—
23#324—24no—
24#323—21no—
25C22×D4C2×C411yescharacteristic
26C23×C4C2×C411yescharacteristic
27C23×C4C2×C411yescharacteristic
28C23×C4D411yescharacteristic
29C23×C4C2311yescharacteristic
30C2×M16—22no—
31C2×M16—22no—
32C2×M16—22no—
33C4×D4—22no—
34C4×D4—22no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—22no—
37C2×C4⋊C4—21no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4—22no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4D411yescharacteristic
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C22⋊C4C2×C411yescharacteristic
46C2×C22⋊C4C2×C411yescharacteristic
47C2×C22⋊C4C2×C411yescharacteristic
48C2×C22⋊C4D411yescharacteristic
49C2×C42D411yescharacteristic
50C4⋊C8—22no—
51C22⋊C8—22no—
52C22⋊C8—22no—
53C22⋊C8—22no—
54C22⋊C8—22no—
55C22⋊C8D414yes—
56C4×C8—22no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95—21no—
62C24C22⋊C411yescharacteristic
63C24C22×C411yescharacteristic
64C2×D4—22no—
65C2×D4—22no—
66C2×D4—41no—
67C22×C4—21no—
68C22×C4—22no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—22no—
75C22×C4—42no—
76C22×C4—81no—
77C22×C4—81no—
78C22×C4—81no—
79C22×C4C22⋊C411yescharacteristic
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C2×D412yes—
83C22×C4C2×D411yescharacteristic
84C22×C4C2×D411yescharacteristic
85C22×C4#4112yes—
86M16—82no—
87M16—82no—
88M16—82no—
89C2×C8—24no—
90C2×C8—42no—
91C4⋊C4—22no—
92C4⋊C4—42no—
93C4⋊C4—41no—
94C4⋊C4—42no—
95C4⋊C4—41no—
96C4⋊C4—81no—
97C4⋊C4—81no—
98C22⋊C4—22no—
99C22⋊C4—22no—
100C22⋊C4—42no—
101C22⋊C4—41no—
102C22⋊C4—41no—
103C22⋊C4—81no—
104C42—21no—
105C42—21no—
106C23—21no—
107C23—21no—
108C23—21no—
109C23—21no—
110C23—21no—
111C23—41no—
112C23—41no—
113C23—41no—
114C23—41no—
115C23C2×C22⋊C411yescharacteristic
116C23C4×D412yes—
117D4—44no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—22no—
121C2×C4—24no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—41no—
125C2×C4—42no—
126C2×C4—42no—
127C2×C4—41no—
128C2×C4—42no—
129C2×C4—41no—
130C2×C4—42no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—81no—
144C2×C4—82no—
145C2×C4#10112yes—
146C2×C4#12011yescharacteristic
147C2×C4#12112yes—
148C2×C4#12311yescharacteristic
149C8—44no—
150C8—82no—
151C22—21no—
152C22—21no—
153C22—22no—
154C22—22no—
155C22—22no—
156C22—42no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22—81no—
163C22#38611yescharacteristic
164C22C2×#10111yescharacteristic
165C22#41311yescharacteristic
166C4—22no—
167C4—21no—
168C4—22no—
169C4—21no—
170C4—42no—
171C4—41no—
172C4—41no—
173C4—81no—
174C4—81no—
175C4—81no—
176C2—21no—
177C2—21no—
178C2—42no—
179C2—81no—
180C2#189111yescharacteristic
181C2#190111yescharacteristic
182C2#191311yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC24C22×C4
Frattini, cosocleC23×C4C23
prime radicalC22×D4C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1463C2semidirect
5. #1305C2semidirect

Maximal subgroups

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

subgroupindex
#29752
#25792
#14652
#14632
#13052