Finite Group Databasebeta

← #10463

Subgroups — #10463

Order 256.

187 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 187 conjugacy classes of subgroups — too many to draw. Only its 57 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#1801C211yesmaximal, characteristic
3#1567C211yesmaximal, characteristic
4#1550C211yesmaximal, characteristic
5#1493C211yesmaximal, characteristic
6C2×Q8⋊C8C211yesmaximal, characteristic
7#1292C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×C4×Q8C2211yescharacteristic
10#479—22no—
11#477—21no—
12#475—21no—
13#428—21no—
14#423C2211yescharacteristic
15#423C2211yescharacteristic
16#423C2211yescharacteristic
17C2×C4⋊C8C2211yescharacteristic
18#419—21no—
19C2×#101—21no—
20C2×C4×C8C2211yescharacteristic
21#343—21no—
22#335—22no—
23#333—21no—
24#332—21no—
25Q8⋊C8—21no—
26Q8⋊C8—21no—
27Q8⋊C8—21no—
28Q8⋊C8—21no—
29C22×Q8D411yescharacteristic
30C2×M16—21no—
31C2×M16—21no—
32C2×M16—21no—
33C22×C8—21no—
34C22×C8—21no—
35C4⋊Q8D411yescharacteristic
36C4⋊Q8D411yescharacteristic
37#125—21no—
38C22⋊Q8—21no—
39C22⋊Q8—21no—
40C4×Q8—21no—
41C4×Q8—21no—
42C4×Q8—21no—
43C4×Q8—21no—
44C4×Q8—21no—
45C4×Q8—21no—
46#117—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4D411yescharacteristic
49C2×C42—21no—
50C2×C42C2311yescharacteristic
51#107—22no—
52#106—22no—
53C4⋊C8—21no—
54C4⋊C8—21no—
55C4⋊C8—21no—
56C4⋊C8—21no—
57C4⋊C8—21no—
58C4⋊C8—21no—
59C4⋊C8—21no—
60C4⋊C8D412yes—
61#103—22no—
62#103—22no—
63#101—42no—
64C4×C8—21no—
65C4×C8D411yescharacteristic
66C4×C8D411yescharacteristic
67C2×Q8—21no—
68C2×Q8—21no—
69C2×Q8—21no—
70C2×Q8—21no—
71C2×Q8—21no—
72C2×Q8—21no—
73C2×Q8—21no—
74C2×Q8Q1612yes—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4C2×D411yescharacteristic
78C22×C4#4111yescharacteristic
79C22×C4#4111yescharacteristic
80M16—41no—
81M16—41no—
82M16—41no—
83M16—41no—
84M16—41no—
85M16—41no—
86C2×C8—21no—
87C2×C8—22no—
88C2×C8—21no—
89C2×C8—42no—
90C2×C8—41no—
91C2×C8—41no—
92C2×C8—41no—
93C2×C8—81no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—21no—
98C4⋊C4—21no—
99C4⋊C4—21no—
100C4⋊C4—41no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—41no—
104C22⋊C4—41no—
105C42—41no—
106C42—41no—
107C42—41no—
108C42C2×D411yescharacteristic
109C42C2×D411yescharacteristic
110C42C2×D411yescharacteristic
111C42#4111yescharacteristic
112C23#12311yescharacteristic
113Q8—22no—
114Q8—22no—
115Q8—41no—
116Q8—41no—
117Q8—41no—
118Q8—41no—
119Q8—81no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—22no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—81no—
130C2×C4#12011yescharacteristic
131C2×C4#12111yescharacteristic
132C2×C4#12111yescharacteristic
133C2×C4#12111yescharacteristic
134C2×C4#12311yescharacteristic
135C2×C4#12411yescharacteristic
136C2×C4C2×Q1611yescharacteristic
137C2×C4#13511yescharacteristic
138C2×C4AGL(1,ℤ/8)11yescharacteristic
139C2×C4#13711yescharacteristic
140C8—22no—
141C8—41no—
142C8—42no—
143C8—81no—
144C8—81no—
145C8—81no—
146C22—21no—
147C22—21no—
148C22#39411yescharacteristic
149C22#48411yescharacteristic
150C22#48511yescharacteristic
151C4—21no—
152C4—21no—
153C4—21no—
154C4—42no—
155C4—81no—
156C4—81no—
157C4—81no—
158C4#44911yescharacteristic
159C4#45111yescharacteristic
160C4#46711yescharacteristic
161C4#46811yescharacteristic
162C4#47111yescharacteristic
163C4#47311yescharacteristic
164C2—21no—
165C2—21no—
166C2#203611yescharacteristic
167C2#205011yescharacteristic
168C2#205211yescharacteristic
subgroupG/H
center, socleC22#394
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#123
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
#18012
#15672
#15502
#14932
C2×Q8⋊C82
#12922