Finite Group Databasebeta

← #9036

Subgroups — #9036

Order 256.

283 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 283 conjugacy classes of subgroups — too many to draw. Only its 67 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#2921C211yesmaximal, characteristic, complemented
2#2392C211yesmaximal, characteristic
3#1486C212yesmaximal, complemented
4#1458C211yesmaximal, characteristic, complemented
5#1303C212yesmaximal, complemented
6C2×C4×D4—21no—
7C2×C4×D4C2211yescharacteristic
8C2×#117C2211yescharacteristic
9#433—24no—
10#431C2212yes—
11#423C2212yes—
12#407—21no—
13C4×M16—21no—
14#398C411yescharacteristic
15#397C411yescharacteristic
16#396—21no—
17#394—21no—
18#394C411yescharacteristic
19#392C411yescharacteristic
20C4×C4⋊C4C2211yescharacteristic
21C4×C22⋊C4—21no—
22D4⋊C8—24no—
23#324—21no—
24#323—21no—
25C22×D4—21no—
26C22×D4C2×C411yescharacteristic
27C23×C4—21no—
28C23×C4D411yescharacteristic
29C2×M16—22no—
30C4×D4—22no—
31C4×D4—22no—
32C4×D4—44no—
33#117—22no—
34#117—22no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4C2×C411yescharacteristic
39C2×C4⋊C4D411yescharacteristic
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C22⋊C4—21no—
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—
51C4⋊C8—22no—
52C4⋊C8D414yescomplemented
53C22⋊C8—24no—
54C22⋊C8—22no—
55#97—22no—
56C4×C8—22no—
57C4×C8—22no—
58#95—21no—
59#95—21no—
60#95C2×C411yescharacteristic
61#95C2×C411yescharacteristic
62C24—21no—
63C24C22⋊C411yescharacteristic
64C2×D4—22no—
65C2×D4—42no—
66C2×D4—42no—
67C2×D4—42no—
68C2×D4—42no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—22no—
73C22×C4—22no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—41no—
77C22×C4—41no—
78C22×C4—42no—
79C22×C4—42no—
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C22⋊C411yescharacteristic
83C22×C4C22×C411yescharacteristic
84C22×C4C2×D411yescharacteristic
85C22×C4C2×D411yescharacteristic
86M16—42no—
87M16—42no—
88C2×C8—24no—
89C2×C8—42no—
90C4⋊C4—22no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4—42no—
94C4⋊C4—42no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C22⋊C4—42no—
98C22⋊C4—42no—
99C22⋊C4—42no—
100C22⋊C4—42no—
101C22⋊C4—42no—
102C42—21no—
103C42—21no—
104C42—42no—
105C42C2×D412yes—
106C42#4112yes—
107C23—22no—
108C23—21no—
109C23—21no—
110C23—21no—
111C23—41no—
112C23—41no—
113C23—41no—
114C23—41no—
115C23—41no—
116C23—41no—
117C23—41no—
118C23—41no—
119C23C2×C22⋊C411yescharacteristic
120D4—24no—
121D4—42no—
122D4—48no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—42no—
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—82no—
144C2×C4—82no—
145C2×C4C4×D412yes—
146C2×C4#12011yescharacteristic
147C2×C4#12112yes—
148C2×C4#12311yescharacteristic
149C2×C4#13512yes—
150C2×C4AGL(1,ℤ/8)12yes—
151C8—44no—
152C8—82no—
153C22—21no—
154C22—21no—
155C22—42no—
156C22—42no—
157C22—42no—
158C22—41no—
159C22—41no—
160C22—42no—
161C22—41no—
162C22—81no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22—81no—
167C22#38611yescharacteristic
168C22#41611yescharacteristic
169C22#41811yescharacteristic
170C4—22no—
171C4—22no—
172C4—42no—
173C4—41no—
174C4—41no—
175C4—41no—
176C4—81no—
177C4—81no—
178C4#44912yes—
179C4#48212yes—
180C2—21no—
181C2—21no—
182C2—81no—
183C2—82no—
184C2#187511yescharacteristic
185C2#188411yescharacteristic
186C2#189111yescharacteristic
subgroupG/H
centerC2×C4#120
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
socleC22#386
prime radical#392C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2921C2semidirect
3. #1486C2semidirect
4. #1458C2semidirect
5. #1303C2semidirect
52. C4⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
#29212
#23922
#14862
#14582
#13032