Finite Group Databasebeta

← #11548

Subgroups — #11548

Order 256.

190 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 49 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#2484C211yesmaximal, characteristic
2#1464C211yesmaximal, characteristic
3#1458C211yesmaximal, characteristic
4#1326C212yesmaximal
5#1317C212yesmaximal
6C2×#117C2211yescharacteristic
7C22×C4⋊C4C411yescharacteristic
8#432—21no—
9#431—21no—
10#400—21no—
11#398—21no—
12#387—21no—
13#387—21no—
14#385C411yescharacteristic
15#385C2211yescharacteristic
16#381C411yescharacteristic
17#381C411yescharacteristic
18#381C2211yescharacteristic
19#324—21no—
20#324—21no—
21#323C2212yes—
22#323C2212yes—
23C23×C4C2×C411yescharacteristic
24C23×C4C2×C411yescharacteristic
25C23×C4C2×C411yescharacteristic
26#117—41no—
27#117—41no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—41no—
33C2×C4⋊C4—41no—
34C2×C4⋊C4D411yescharacteristic
35C2×C4⋊C4D411yescharacteristic
36C2×C22⋊C4C2×C411yescharacteristic
37C2×C22⋊C4C2×C411yescharacteristic
38C2×C22⋊C4C2×C411yescharacteristic
39C2×C22⋊C4C2311yescharacteristic
40C2×C42D411yescharacteristic
41C2×C42D411yescharacteristic
42C4⋊C8—41no—
43C4⋊C8—41no—
44C22⋊C8—22no—
45C22⋊C8—22no—
46#97—41no—
47C4×C8—41no—
48#95—21no—
49#95—21no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56C24C22×C411yescharacteristic
57C22×C4—21no—
58C22×C4—22no—
59C22×C4—21no—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4—22no—
65C22×C4—41no—
66C22×C4—42no—
67C22×C4—41no—
68C22×C4—41no—
69C22×C4—41no—
70C22×C4C22⋊C411yescharacteristic
71C22×C4C22⋊C411yescharacteristic
72C22×C4C22⋊C411yescharacteristic
73C22×C4C22⋊C411yescharacteristic
74C22×C4C2×D411yescharacteristic
75C22×C4C2×D411yescharacteristic
76C2×C8—42no—
77C2×C8—42no—
78C4⋊C4—41no—
79C4⋊C4—41no—
80C4⋊C4—42no—
81C4⋊C4—42no—
82C4⋊C4—42no—
83C4⋊C4—41no—
84C4⋊C4—41no—
85C22⋊C4—22no—
86C22⋊C4—41no—
87C22⋊C4—41no—
88C22⋊C4—41no—
89C42—21no—
90C42—21no—
91C42—21no—
92C42—21no—
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23C2×C22⋊C411yescharacteristic
98C23#13112yes—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—22no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—42no—
110C2×C4—42no—
111C2×C4—41no—
112C2×C4—42no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—42no—
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—82no—
129C2×C4#9911yescharacteristic
130C2×C4#9911yescharacteristic
131C8—82no—
132C8—82no—
133C22—21no—
134C22—21no—
135C22—22no—
136C22—42no—
137C22—42no—
138C22—41no—
139C22—41no—
140C22#40811yescharacteristic
141C22C2×#9911yescharacteristic
142C22#41311yescharacteristic
143C4—21no—
144C4—21no—
145C4—41no—
146C4—41no—
147C4—42no—
148C4—41no—
149C4—41no—
150C4—41no—
151C4—81no—
152C4—81no—
153C4—81no—
154C2—21no—
155C2—21no—
156C2—42no—
157C2#146811yescharacteristic
158C2#212011yescharacteristic
159C2#212311yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutator, prime radicalC24C22×C4
Frattini, cosocleC2×C22⋊C4C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#24842
#14642
#14582
#13262
#13172