Finite Group Databasebeta

← #9388

Subgroups — #9388

Order 256.

266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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#2873C211yesmaximal, characteristic
2#2611C211yesmaximal, characteristic
3#1528C212yesmaximal, complemented
4#1464C211yesmaximal, characteristic
5#1300C212yesmaximal, complemented
6C22×M16—21no—
7C2×#125C2211yescharacteristic
8C2×#117C2211yescharacteristic
9#432C2212yes—
10#405—24no—
11C4×M16—21no—
12C4×M16C2212yes—
13#400C411yescharacteristic
14#399C411yescharacteristic
15#398C411yescharacteristic
16#397C411yescharacteristic
17#389—21no—
18#388—21no—
19#387—21no—
20#385—21no—
21#376C2211yescharacteristic
22#330—24no—
23#324—21no—
24#323—21no—
25C23×C4D411yescharacteristic
26C2×M16—24no—
27C2×M16—24no—
28C2×M16—22no—
29C2×M16—22no—
30C22×C8—22no—
31#125—22no—
32#125—22no—
33#117—22no—
34#117—22no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4—21no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4C2×C411yescharacteristic
40C2×C4⋊C4C2×C411yescharacteristic
41C2×C4⋊C4C2×C411yescharacteristic
42C2×C4⋊C4D411yescharacteristic
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C22⋊C4C2×C411yescharacteristic
46C2×C22⋊C4D411yescharacteristic
47C2×C42—21no—
48C2×C42D411yescharacteristic
49C2×C42C2311yescharacteristic
50C4⋊C8—22no—
51C22⋊C8—22no—
52#97—22no—
53#97—22no—
54#97D414yes—
55C4×C8—22no—
56C4×C8—22no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95—21no—
62#95C2×C411yescharacteristic
63#95C2×C411yescharacteristic
64C24C22⋊C411yescharacteristic
65C22×C4—22no—
66C22×C4—22no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4C22⋊C411yescharacteristic
74C22×C4C22⋊C411yescharacteristic
75C22×C4C22⋊C411yescharacteristic
76C22×C4C22×C411yescharacteristic
77C22×C4C2×D411yescharacteristic
78C22×C4C2×D411yescharacteristic
79M16—28no—
80M16—24no—
81M16—24no—
82C2×C8—28no—
83C2×C8—24no—
84C2×C8—42no—
85C4⋊C4—22no—
86C4⋊C4—22no—
87C4⋊C4—22no—
88C4⋊C4—22no—
89C4⋊C4—42no—
90C4⋊C4—42no—
91C4⋊C4—41no—
92C4⋊C4—42no—
93C4⋊C4—41no—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—42no—
97C22⋊C4—42no—
98C42—21no—
99C42—21no—
100C42—42no—
101C42C2×D412yes—
102C42#4112yes—
103C23—21no—
104C23—21no—
105C23—41no—
106C23—41no—
107C23#10412yes—
108C23C2×C22⋊C411yescharacteristic
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—24no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4#10412yes—
135C2×C4C4×D412yes—
136C2×C4#12011yescharacteristic
137C2×C4#12112yes—
138C2×C4#12311yescharacteristic
139C8—28no—
140C8—82no—
141C22—21no—
142C22—21no—
143C22—22no—
144C22—42no—
145C22—41no—
146C22—41no—
147C22—81no—
148C22#38611yescharacteristic
149C22C2×#10411yescharacteristic
150C22C2×#10411yescharacteristic
151C4—22no—
152C4—21no—
153C4—22no—
154C4—21no—
155C4—22no—
156C4—42no—
157C4—41no—
158C4—41no—
159C4—81no—
160C4—81no—
161C4—81no—
162C2—21no—
163C2—21no—
164C2—42no—
165C2#188411yescharacteristic
166C2#189611yescharacteristic
167C2#191511yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC24C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #1528C2semidirect
5. #1300C2semidirect

Maximal subgroups

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

subgroupindex
#28732
#26112
#15282
#14642
#13002