Finite Group Databasebeta

← #9883

Subgroups — #9883

Order 256.

300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#389C211yesmaximal, characteristic
2#1797C211yesmaximal, characteristic
3#1749C211yesmaximal, characteristic
4#1280C214yesmaximal
5C22×C4⋊C4C411yescharacteristic
6C22×C4⋊C4C411yescharacteristic
7C22×C4⋊C4C412yes—
8C22×C42C2211yescharacteristic
9C2×C4⋊C8—21no—
10C2×C22⋊C8C2212yes—
11C2×C22⋊C8C2212yes—
12C2×#97—21no—
13#389—21no—
14#389—21no—
15#389—21no—
16#389—21no—
17C2×#95C2212yes—
18#336—21no—
19#336—21no—
20C23×C4C2×C411yescharacteristic
21C23×C4C2×C411yescharacteristic
22C23×C4C2×C412yes—
23C23×C4C2×C412yes—
24C23×C4C2311yescharacteristic
25C22×C8—22no—
26C22×C8—22no—
27C2×C4⋊C4—21no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4—24no—
30C2×C4⋊C4—22no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—22no—
34C2×C4⋊C4—42no—
35C2×C4⋊C4—44no—
36C2×C42—42no—
37C2×C42D411yescharacteristic
38C2×C42D411yescharacteristic
39C2×C42D411yescharacteristic
40C2×C42D411yescharacteristic
41C4⋊C8—42no—
42C22⋊C8—22no—
43C22⋊C8—24no—
44C22⋊C8Q814yes—
45#97—42no—
46#95—22no—
47#95—22no—
48C24C22×C411yescharacteristic
49C22×C4—22no—
50C22×C4—22no—
51C22×C4—22no—
52C22×C4—22no—
53C22×C4—22no—
54C22×C4—22no—
55C22×C4—22no—
56C22×C4—22no—
57C22×C4—24no—
58C22×C4—41no—
59C22×C4—41no—
60C22×C4—41no—
61C22×C4—42no—
62C22×C4—42no—
63C22×C4—42no—
64C22×C4—42no—
65C22×C4C22⋊C411yescharacteristic
66C22×C4C22⋊C411yescharacteristic
67C22×C4C22⋊C411yescharacteristic
68C22×C4C22⋊C411yescharacteristic
69C22×C4M1614yes—
70C22×C4C2×D411yescharacteristic
71C22×C4C2×D411yescharacteristic
72C22×C4C2×Q812yes—
73C22×C4#4112yes—
74C2×C8—24no—
75C2×C8—42no—
76C2×C8—42no—
77C2×C8—42no—
78C2×C8—42no—
79C2×C8—42no—
80C4⋊C4—24no—
81C4⋊C4—24no—
82C4⋊C4—42no—
83C4⋊C4—44no—
84C4⋊C4—42no—
85C4⋊C4—44no—
86C42—22no—
87C42—22no—
88C42—41no—
89C42—41no—
90C23—21no—
91C23—21no—
92C23—21no—
93C23—21no—
94C23C2×C22⋊C411yescharacteristic
95C23C4×Q812yes—
96C23C2×M1612yes—
97C23#13112yes—
98C2×C4—28no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—24no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—42no—
114C2×C4—42no—
115C2×C4—44no—
116C2×C4—44no—
117C2×C4—42no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—42no—
123C2×C4—84no—
124C2×C4#9912yes—
125C2×C4#10012yes—
126C2×C4#10112yes—
127C2×C4C22⋊Q812yes—
128C2×C4#12411yescharacteristic
129C2×C4C4⋊Q811yescharacteristic
130C8—44no—
131C8—82no—
132C22—22no—
133C22—22no—
134C22—22no—
135C22—22no—
136C22—22no—
137C22—22no—
138C22#39111yescharacteristic
139C22#40711yescharacteristic
140C22#40811yescharacteristic
141C22C2×#9911yescharacteristic
142C22#41011yescharacteristic
143C22C2×#10011yescharacteristic
144C22C2×#10111yescharacteristic
145C22#44614yes—
146C4—22no—
147C4—22no—
148C4—22no—
149C4—22no—
150C4—21no—
151C4—21no—
152C4—44no—
153C4—41no—
154C4—82no—
155C2—24no—
156C2#146311yescharacteristic
157C2#146611yescharacteristic
158C2#147011yescharacteristic
159C2#147111yescharacteristic
160C2#198511yescharacteristic
161C2#199611yescharacteristic
162C2#199711yescharacteristic
subgroupG/H
center, socleC23C2×C22⋊C4
commutator, prime radicalC24C22×C4
Frattini, cosocleC23×C4C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#3892
#17972
#17492
#12802