Finite Group Databasebeta

← #10572

Subgroups — #10572

Order 256.

280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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#2646C211yesmaximal, characteristic
2#1853C211yesmaximal, characteristic
3#1852C211yesmaximal, characteristic
4#1444C211yesmaximal, characteristic
5#1294C211yesmaximal, characteristic
6#1294C211yesmaximal, characteristic
7#1280C211yesmaximal, characteristic
8C22×C4⋊C4—21no—
9C22×C4⋊C4C2211yescharacteristic
10C2×#107—21no—
11C2×#106—21no—
12C2×C22⋊C8C2211yescharacteristic
13C2×C22⋊C8C2211yescharacteristic
14#400—21no—
15#400—21no—
16#398—21no—
17#398—21no—
18#385—21no—
19#385—21no—
20#380C2211yescharacteristic
21#380C2211yescharacteristic
22C2×#95—21no—
23C2×#95C2211yescharacteristic
24C2×#95C2211yescharacteristic
25#340—21no—
26#340—21no—
27C23×C4—21no—
28C23×C4—21no—
29C23×C4D411yescharacteristic
30C23×C4D411yescharacteristic
31C23×C4C2311yescharacteristic
32C22×C8—21no—
33C22×C8—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4—21no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—42no—
41C2×C4⋊C4—42no—
42C2×C4⋊C4—42no—
43C2×C4⋊C4—42no—
44C2×C4⋊C4D411yescharacteristic
45C2×C4⋊C4D411yescharacteristic
46C2×C4⋊C4D411yescharacteristic
47C2×C4⋊C4D411yescharacteristic
48C2×C22⋊C4—21no—
49C2×C22⋊C4—21no—
50#107—42no—
51#106—42no—
52C22⋊C8—21no—
53C22⋊C8—21no—
54C22⋊C8Q812yes—
55C22⋊C8Q812yes—
56#95—21no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95—21no—
62#95—21no—
63#95—21no—
64#95—21no—
65#95—42no—
66#95Q812yes—
67C24C2×D411yescharacteristic
68C22×C4—22no—
69C22×C4—22no—
70C22×C4—22no—
71C22×C4—22no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—41no—
83C22×C4—41no—
84C22×C4—41no—
85C22×C4—41no—
86C22×C4—41no—
87C22×C4—41no—
88C22×C4—41no—
89C22×C4—41no—
90C22×C4—41no—
91C22×C4—41no—
92C22×C4—41no—
93C22×C4—41no—
94C22×C4—41no—
95C22×C4—41no—
96C22×C4—41no—
97C22×C4—41no—
98C22×C4C2×D411yescharacteristic
99C22×C4C2×D411yescharacteristic
100C22×C4C2×Q811yescharacteristic
101C22×C4C2×Q811yescharacteristic
102C22×C4C2×Q811yescharacteristic
103C22×C4#4111yescharacteristic
104C2×C8—22no—
105C2×C8—22no—
106C2×C8—41no—
107C2×C8—41no—
108C2×C8—41no—
109C2×C8—41no—
110C4⋊C4—22no—
111C4⋊C4—22no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C4⋊C4—41no—
118C4⋊C4—48no—
119C4⋊C4—81no—
120C4⋊C4—81no—
121C4⋊C4—81no—
122C4⋊C4—81no—
123C22⋊C4—41no—
124C22⋊C4—41no—
125C22⋊C4—41no—
126C22⋊C4—41no—
127C23—21no—
128C23—21no—
129C23—21no—
130C23—21no—
131C23#12011yescharacteristic
132C23C22⋊Q811yescharacteristic
133C23C4⋊Q811yescharacteristic
134C23#13511yescharacteristic
135C23#13511yescharacteristic
136C23AGL(1,ℤ/8)11yescharacteristic
137C23#13711yescharacteristic
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—24no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4C22⋊Q811yescharacteristic
183C2×C4C22⋊Q811yescharacteristic
184C2×C4C4⋊Q811yescharacteristic
185C2×C4C4⋊Q811yescharacteristic
186C8—42no—
187C8—42no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22#39511yescharacteristic
201C22#44911yescharacteristic
202C22#45211yescharacteristic
203C22#45311yescharacteristic
204C22#45611yescharacteristic
205C22B(4,𝔽2)11yescharacteristic
206C22#45811yescharacteristic
207C22#47811yescharacteristic
208C22#47911yescharacteristic
209C22#49911yescharacteristic
210C22#50111yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—44no—
216C4—81no—
217C4—81no—
218C4—82no—
219C4—81no—
220C4—81no—
221C4—81no—
222C4—81no—
223C2—21no—
224C2—21no—
225C2—21no—
226C2—21no—
227C2#160011yescharacteristic
228C2#160311yescharacteristic
229C2#160911yescharacteristic
230C2#161811yescharacteristic
231C2#205911yescharacteristic
232C2#206011yescharacteristic
233C2#206211yescharacteristic
subgroupG/H
center, socleC23#120
commutator, Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ 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
#26462
#18532
#18522
#14442
#12942
#12802