Finite Group Databasebeta

← #9910

Subgroups — #9910

Order 256.

320 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 81 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#2851C211yesmaximal, characteristic
2#1797C211yesmaximal, characteristic
3C4×#95C211yesmaximal, characteristic
4#1294C212yesmaximal
5#1294C212yesmaximal
6C2×#125C411yescharacteristic, complemented
7C22×C42—21no—
8C22×C42C2211yescharacteristic
9C2×C4⋊C8—21no—
10C2×C22⋊C8C2212yes—
11#389C411yescharacteristic, complemented
12#389C411yescharacteristic, complemented
13#387—21no—
14#387—21no—
15#385—21no—
16#385—21no—
17#382C411yescharacteristic, complemented
18#380C2211yescharacteristic
19#380C2211yescharacteristic
20C2×#95—21no—
21C2×#95C2212yes—
22#336—21no—
23C23×C4—22no—
24C23×C4D411yescharacteristic
25C23×C4D411yescharacteristic
26C23×C4C2311yescharacteristic
27C22×C8—22no—
28#125—42no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4C2×C411yescharacteristic
34C2×C4⋊C4C2×C411yescharacteristic
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C22⋊C4—21no—
38C2×C22⋊C4—21no—
39C2×C42—24no—
40C2×C42—42no—
41C2×C42—42no—
42C2×C42—42no—
43C2×C42C2×C411yescharacteristic
44C2×C42C2×C411yescharacteristic
45C2×C42D411yescharacteristic
46C2×C42D411yescharacteristic
47C4⋊C8—42no—
48C22⋊C8—24no—
49#95—24no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56#95—22no—
57#95Q814yes—
58C24C2×D411yescharacteristic
59C22×C4—21no—
60C22×C4—21no—
61C22×C4—22no—
62C22×C4—22no—
63C22×C4—24no—
64C22×C4—24no—
65C22×C4—24no—
66C22×C4—22no—
67C22×C4—22no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—41no—
73C22×C4—41no—
74C22×C4—41no—
75C22×C4—42no—
76C22×C4—42no—
77C22×C4—42no—
78C22×C4—42no—
79C22×C4C22⋊C411yescharacteristic
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C22⋊C411yescharacteristic
83C22×C4C22×C411yescharacteristic
84C22×C4C2×D411yescharacteristic
85C22×C4C2×Q812yes—
86C22×C4#4112yes—
87C2×C8—42no—
88C2×C8—42no—
89C2×C8—42no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—42no—
95C4⋊C4—42no—
96C4⋊C4—42no—
97C4⋊C4—42no—
98C22⋊C4—42no—
99C22⋊C4—41no—
100C22⋊C4—41no—
101C42—22no—
102C42—22no—
103C42—41no—
104C42—41no—
105C42—48no—
106C23—21no—
107C23—21no—
108C23—21no—
109C23—21no—
110C23C2×C22⋊C411yescharacteristic
111C23C22⋊Q812yes—
112C23#13512yes—
113C23AGL(1,ℤ/8)11yescharacteristic
114C23#13711yescharacteristic
115C2×C4—24no—
116C2×C4—24no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—28no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—44no—
134C2×C4—44no—
135C2×C4—44no—
136C2×C4—44no—
137C2×C4—44no—
138C2×C4—44no—
139C2×C4—44no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4#9912yes—
153C2×C4#10412yes—
154C2×C4#10412yes—
155C2×C4C4×Q812yes—
156C2×C4#12411yescharacteristic
157C2×C4C4⋊Q811yescharacteristic
158C8—82no—
159C22—22no—
160C22—22no—
161C22—22no—
162C22—22no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22#39111yescharacteristic
168C22C2×#9911yescharacteristic
169C22#41011yescharacteristic
170C22#41611yescharacteristic
171C22#41711yescharacteristic
172C22C2×#10411yescharacteristic
173C22C2×#10411yescharacteristic
174C22#47812yes—
175C22#47912yes—
176C4—21no—
177C4—22no—
178C4—21no—
179C4—22no—
180C4—22no—
181C4—22no—
182C4—48no—
183C4—41no—
184C4—81no—
185C4—81no—
186C4—81no—
187C4—81no—
188C2—22no—
189C2—22no—
190C2#150011yescharacteristic
191C2#150111yescharacteristic
192C2#150411yescharacteristic
193C2#150911yescharacteristic
194C2#198911yescharacteristic
195C2#199411yescharacteristic
196C2#199611yescharacteristic
subgroupG/H
center, socleC23C2×C22⋊C4
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
6. C2×#125C4semidirect
11. #389C4semidirect
12. #389C4semidirect
17. #382C4semidirect

Maximal subgroups

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

subgroupindex
#28512
#17972
C4×#952
#12942