Finite Group Databasebeta

← #10470

Subgroups — #10470

Order 256.

183 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 183 conjugacy classes of subgroups — too many to draw. Only its 55 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#3078C211yesmaximal, characteristic
2#1805C211yesmaximal, characteristic
3#1570C211yesmaximal, characteristic
4#1542C211yesmaximal, characteristic
5#1518C211yesmaximal, characteristic
6#1461C211yesmaximal, characteristic
7#1286C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×C4×Q8C2211yescharacteristic
10#479—22no—
11#477—21no—
12#475—21no—
13#431C2211yescharacteristic
14#431C2211yescharacteristic
15#428—21no—
16#423C2211yescharacteristic
17C2×C4⋊C8C2211yescharacteristic
18#419—21no—
19C2×#103—21no—
20#382C2211yescharacteristic
21#340—21no—
22#334—22no—
23#333—21no—
24#332—21no—
25#328—22no—
26#324—22no—
27C22×Q8D411yescharacteristic
28C2×M16—21no—
29C22×C8—21no—
30C4⋊Q8D411yescharacteristic
31C4⋊Q8D411yescharacteristic
32#125—21no—
33C22⋊Q8—21no—
34C22⋊Q8—21no—
35C4×Q8—21no—
36C4×Q8—21no—
37C4×Q8—21no—
38C4×Q8—21no—
39C4×Q8—21no—
40C4×Q8—21no—
41#117—21no—
42C2×C4⋊C4—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4D411yescharacteristic
45C2×C42—21no—
46C2×C42C2311yescharacteristic
47#107—22no—
48#106—22no—
49C4⋊C8—21no—
50C4⋊C8—21no—
51C4⋊C8—21no—
52C4⋊C8—21no—
53C4⋊C8—21no—
54C4⋊C8D412yes—
55#103—22no—
56#103—22no—
57#103—42no—
58C22⋊C8—21no—
59C22⋊C8D412yes—
60C4×C8—21no—
61C4×C8—21no—
62#95—21no—
63#95—21no—
64C2×Q8—21no—
65C2×Q8—21no—
66C2×Q8—21no—
67C2×Q8—21no—
68C2×Q8—21no—
69C2×Q8—21no—
70C2×Q8—21no—
71C2×Q8SD1612yes—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—41no—
75C22×C4C2×D411yescharacteristic
76C22×C4C2×D411yescharacteristic
77C22×C4#4111yescharacteristic
78M16—41no—
79M16—41no—
80C2×C8—22no—
81C2×C8—22no—
82C2×C8—41no—
83C2×C8—41no—
84C2×C8—41no—
85C2×C8—41no—
86C4⋊C4—21no—
87C4⋊C4—21no—
88C4⋊C4—21no—
89C4⋊C4—21no—
90C4⋊C4—21no—
91C4⋊C4—21no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C22⋊C4—41no—
99C42—41no—
100C42—41no—
101C42—41no—
102C42C2×D411yescharacteristic
103C42C2×D411yescharacteristic
104C42#4111yescharacteristic
105C42#4111yescharacteristic
106C23#12111yescharacteristic
107Q8—22no—
108Q8—22no—
109Q8—41no—
110Q8—41no—
111Q8—81no—
112Q8—81no—
113C2×C4—22no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—81no—
122C2×C4—81no—
123C2×C4—81no—
124C2×C4—81no—
125C2×C4#12011yescharacteristic
126C2×C4#12111yescharacteristic
127C2×C4#12111yescharacteristic
128C2×C4#12311yescharacteristic
129C2×C4#12311yescharacteristic
130C2×C4#12411yescharacteristic
131C2×C4C2×SD1611yescharacteristic
132C2×C4#13511yescharacteristic
133C2×C4#13711yescharacteristic
134C2×C4#13711yescharacteristic
135C8—42no—
136C8—42no—
137C8—81no—
138C8—81no—
139C22—21no—
140C22—21no—
141C22#39411yescharacteristic
142C22#46511yescharacteristic
143C22#47011yescharacteristic
144C4—21no—
145C4—21no—
146C4—21no—
147C4—21no—
148C4—42no—
149C4—81no—
150C4—81no—
151C4—81no—
152C4—161no—
153C4#44811yescharacteristic
154C4#45211yescharacteristic
155C4#48311yescharacteristic
156C4#48511yescharacteristic
157C2—21no—
158C2—21no—
159C2#203511yescharacteristic
160C2#204911yescharacteristic
161C2#205311yescharacteristic
subgroupG/H
center, socleC22#394
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#30782
#18052
#15702
#15422
#15182
#14612
#12862