Finite Group Databasebeta

← #9945

Subgroups — #9945

Order 256.

287 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 287 conjugacy classes of subgroups — too many to draw. Only its 51 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#3095C211yesmaximal, characteristic
2#2583C211yesmaximal, characteristic
3#2484C211yesmaximal, characteristic
4#1826C211yesmaximal, characteristic
5#1511C211yesmaximal, characteristic
6#1463C211yesmaximal, characteristic
7#1284C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C2×#117C2211yescharacteristic
10C22×C4⋊C4C2211yescharacteristic
11#485—22no—
12#484—21no—
13#483—21no—
14#428—21no—
15#419—21no—
16#407C2211yescharacteristic
17#407C2211yescharacteristic
18#400—21no—
19#398—21no—
20#398—21no—
21#395—21no—
22#389—22no—
23#387—22no—
24#385—21no—
25#385—21no—
26#385—21no—
27#381—21no—
28#381C2211yescharacteristic
29C4×C22⋊C4C2211yescharacteristic
30#339—22no—
31#328—22no—
32#324—22no—
33C22×Q8D411yescharacteristic
34C23×C4D411yescharacteristic
35C23×C4D411yescharacteristic
36C23×C4C2311yescharacteristic
37C2×M16—21no—
38C2×M16—21no—
39C22⋊Q8—21no—
40C22⋊Q8—21no—
41C22⋊Q8—21no—
42C22⋊Q8—21no—
43#117—21no—
44#117—21no—
45#117—21no—
46#117—21no—
47C2×C4⋊C4—22no—
48C2×C4⋊C4—22no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4—22no—
57C2×C4⋊C4D411yescharacteristic
58C2×C4⋊C4D411yescharacteristic
59C2×C4⋊C4D411yescharacteristic
60C2×C22⋊C4—21no—
61C2×C22⋊C4—21no—
62C2×C22⋊C4—21no—
63C2×C22⋊C4—21no—
64C2×C42—21no—
65C2×C42D412yes—
66#107—22no—
67#106—22no—
68#103—22no—
69#103—22no—
70C22⋊C8—21no—
71C22⋊C8—21no—
72C22⋊C8—21no—
73C22⋊C8D412yes—
74#95—22no—
75#95—22no—
76#95—22no—
77#95—22no—
78#95—22no—
79#95—21no—
80#95—21no—
81#95D412yes—
82C24C2×D411yescharacteristic
83C2×Q8—21no—
84C2×Q8—21no—
85C2×Q8—42no—
86C22×C4—22no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—22no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—42no—
99C22×C4—42no—
100C22×C4—42no—
101C22×C4C2×D411yescharacteristic
102C22×C4C2×D411yescharacteristic
103C22×C4C2×D411yescharacteristic
104C22×C4C2×D411yescharacteristic
105C22×C4C2×D411yescharacteristic
106C22×C4#4111yescharacteristic
107M16—42no—
108M16—42no—
109C2×C8—22no—
110C2×C8—41no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—44no—
118C4⋊C4—44no—
119C4⋊C4—41no—
120C4⋊C4—41no—
121C4⋊C4—41no—
122C4⋊C4—41no—
123C4⋊C4—41no—
124C4⋊C4—41no—
125C4⋊C4—82no—
126C22⋊C4—24no—
127C22⋊C4—42no—
128C22⋊C4—41no—
129C22⋊C4—41no—
130C22⋊C4—41no—
131C22⋊C4—41no—
132C42—42no—
133C42—41no—
134C42—41no—
135C23—22no—
136C23—22no—
137C23—41no—
138C23#12011yescharacteristic
139C23#12011yescharacteristic
140C23#12111yescharacteristic
141Q8—42no—
142Q8—81no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—24no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—81no—
174C2×C4#12011yescharacteristic
175C2×C4#12111yescharacteristic
176C2×C4#12111yescharacteristic
177C2×C4#12711yescharacteristic
178C8—42no—
179C8—81no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—44no—
188C22#39211yescharacteristic
189C22#45612yes—
190C22#45812yes—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—44no—
196C4—42no—
197C4—82no—
198C4—81no—
199C4—81no—
200C4—81no—
201C4—81no—
202C4—81no—
203C2—22no—
204C2—22no—
205C2—41no—
206C2#200511yescharacteristic
207C2#201011yescharacteristic
208C2#202211yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ 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
#30952
#25832
#24842
#18262
#15112
#14632
#12842