Finite Group Databasebeta

← #7803

Subgroups — #7803

Order 256.

169 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 169 conjugacy classes of subgroups — too many to draw. Only its 47 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#2810C211yesmaximal, characteristic
2#2099C211yesmaximal, characteristic
3#2084C211yesmaximal, characteristic
4#2083C211yesmaximal, characteristic
5#1271C211yesmaximal, characteristic
6#1271C211yesmaximal, characteristic
7#1271C211yesmaximal, characteristic
8C2×#107—21no—
9C2×#106—21no—
10#400—21no—
11#400—21no—
12#400—21no—
13#389C2211yescharacteristic
14#389C2211yescharacteristic
15#389C2211yescharacteristic
16#387—21no—
17#387—21no—
18#387—21no—
19#384C2211yescharacteristic
20#340—21no—
21#340—21no—
22#340—21no—
23#340—21no—
24#336C2211yescharacteristic
25#336C2211yescharacteristic
26#336C2211yescharacteristic
27C22×C8—21no—
28C22×C8—21no—
29C22×C8—21no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4D411yescharacteristic
37C2×C4⋊C4D411yescharacteristic
38C2×C4⋊C4D411yescharacteristic
39C2×C4⋊C4D411yescharacteristic
40C2×C4⋊C4D411yescharacteristic
41C2×C4⋊C4D411yescharacteristic
42C2×C42—21no—
43C2×C42C2311yescharacteristic
44#107—42no—
45#106—42no—
46#95—21no—
47#95—21no—
48#95—21no—
49#95—21no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95—21no—
56C22×C4—21no—
57C22×C4—21no—
58C22×C4—21no—
59C22×C4—21no—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4—41no—
63C22×C4C2×D411yescharacteristic
64C22×C4C2×D411yescharacteristic
65C22×C4C2×D411yescharacteristic
66C2×C8—22no—
67C2×C8—22no—
68C2×C8—41no—
69C2×C8—41no—
70C2×C8—41no—
71C2×C8—41no—
72C2×C8—41no—
73C2×C8—41no—
74C2×C8—41no—
75C4⋊C4—21no—
76C4⋊C4—21no—
77C4⋊C4—21no—
78C4⋊C4—21no—
79C4⋊C4—21no—
80C4⋊C4—21no—
81C4⋊C4—41no—
82C4⋊C4—41no—
83C4⋊C4—41no—
84C4⋊C4—42no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—41no—
89C4⋊C4—41no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C42—41no—
96C42—81no—
97C23#12011yescharacteristic
98C2×C4—21no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—81no—
123C2×C4—81no—
124C2×C4—81no—
125C2×C4#13511yescharacteristic
126C2×C4#13511yescharacteristic
127C2×C4#13511yescharacteristic
128C2×C4AGL(1,ℤ/8)11yescharacteristic
129C2×C4AGL(1,ℤ/8)11yescharacteristic
130C2×C4#13711yescharacteristic
131C8—42no—
132C8—42no—
133C8—81no—
134C22#44911yescharacteristic
135C22#44911yescharacteristic
136C22#45211yescharacteristic
137C22#45411yescharacteristic
138C22#45611yescharacteristic
139C22#45611yescharacteristic
140C22#45811yescharacteristic
141C4—21no—
142C4—21no—
143C4—21no—
144C4—21no—
145C4—21no—
146C4—21no—
147C4—81no—
148C4—81no—
149C4—81no—
150C4—81no—
151C4—81no—
152C4—81no—
153C4—161no—
154C2#160911yescharacteristic
155C2#160911yescharacteristic
156C2#161511yescharacteristic
157C2#162811yescharacteristic
158C2#165011yescharacteristic
159C2#165211yescharacteristic
160C2#166311yescharacteristic
subgroupG/H
center, socle, prime radicalC23#120
commutator, Frattini, cosocleC2×C42C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#28102
#20992
#20842
#20832
#12712