Finite Group Databasebeta

← #10400

Subgroups — #10400

Order 256.

285 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 63 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#2627C211yesmaximal, characteristic
2#1872C211yesmaximal, characteristic
3#1852C211yesmaximal, characteristic
4C2×#328C211yesmaximal, characteristic
5C2×#324C211yesmaximal, characteristic
6#1441C211yesmaximal, characteristic
7#1294C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4C2211yescharacteristic
10C22×C4⋊C4C2211yescharacteristic
11C2×#107—21no—
12C2×#103—21no—
13C2×C22⋊C8C2211yescharacteristic
14C2×C22⋊C8C2211yescharacteristic
15#400—21no—
16#398—21no—
17#398—21no—
18#395—21no—
19#385—21no—
20#381—21no—
21#380C2211yescharacteristic
22C2×#95—21no—
23C2×#95—21no—
24C2×#95C2211yescharacteristic
25#340—21no—
26#340—21no—
27#328—22no—
28#324—22no—
29C22×Q8D411yescharacteristic
30C23×C4—21no—
31C23×C4—21no—
32C23×C4D411yescharacteristic
33C23×C4D411yescharacteristic
34C23×C4C2311yescharacteristic
35C22×C8—21no—
36C22×C8—21no—
37C22⋊Q8—21no—
38C22⋊Q8—21no—
39C22⋊Q8—21no—
40C22⋊Q8—21no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—42no—
53C2×C4⋊C4D411yescharacteristic
54C2×C4⋊C4D411yescharacteristic
55C2×C4⋊C4D411yescharacteristic
56C2×C22⋊C4—21no—
57C2×C22⋊C4—21no—
58#107—42no—
59#103—42no—
60C22⋊C8—21no—
61C22⋊C8—21no—
62C22⋊C8—21no—
63C22⋊C8D412yes—
64#95—21no—
65#95—21no—
66#95—21no—
67#95—21no—
68#95—21no—
69#95—21no—
70#95—21no—
71#95—21no—
72#95—21no—
73#95—42no—
74#95—42no—
75C24C2×D411yescharacteristic
76C2×Q8—21no—
77C2×Q8—21no—
78C2×Q8—41no—
79C2×Q8—41no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—22no—
87C22×C4—22no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—21no—
95C22×C4—41no—
96C22×C4—41no—
97C22×C4—41no—
98C22×C4—41no—
99C22×C4—41no—
100C22×C4—41no—
101C22×C4—41no—
102C22×C4—41no—
103C22×C4—41no—
104C22×C4—41no—
105C22×C4—41no—
106C22×C4—41no—
107C22×C4—41no—
108C22×C4—41no—
109C22×C4—41no—
110C22×C4—41no—
111C22×C4Q1612yes—
112C22×C4C2×D411yescharacteristic
113C22×C4C2×D411yescharacteristic
114C22×C4C2×D411yescharacteristic
115C22×C4#4111yescharacteristic
116C22×C4#4111yescharacteristic
117C22×C4#4111yescharacteristic
118C2×C8—22no—
119C2×C8—41no—
120C2×C8—41no—
121C2×C8—41no—
122C2×C8—41no—
123C2×C8—41no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—41no—
129C4⋊C4—41no—
130C4⋊C4—41no—
131C4⋊C4—41no—
132C4⋊C4—41no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—41no—
136C4⋊C4—41no—
137C4⋊C4—41no—
138C4⋊C4—81no—
139C4⋊C4—81no—
140C22⋊C4—41no—
141C22⋊C4—41no—
142C22⋊C4—41no—
143C22⋊C4—41no—
144C23—21no—
145C23—21no—
146C23—21no—
147C23—21no—
148C23#12011yescharacteristic
149C23#12111yescharacteristic
150C23#12311yescharacteristic
151C23C2×Q1611yescharacteristic
152C23#13511yescharacteristic
153C23AGL(1,ℤ/8)11yescharacteristic
154C23#13711yescharacteristic
155Q8—42no—
156Q8—81no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4#12111yescharacteristic
204C2×C4#12111yescharacteristic
205C2×C4#12311yescharacteristic
206C2×C4#12411yescharacteristic
207C8—42no—
208C8—81no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22#39411yescharacteristic
222C22#44911yescharacteristic
223C22#45111yescharacteristic
224C22#45411yescharacteristic
225C22#45611yescharacteristic
226C22B(4,𝔽2)11yescharacteristic
227C22#45811yescharacteristic
228C22#46711yescharacteristic
229C22#46811yescharacteristic
230C22#48411yescharacteristic
231C22#48511yescharacteristic
232C4—21no—
233C4—21no—
234C4—21no—
235C4—21no—
236C4—42no—
237C4—82no—
238C4—81no—
239C4—82no—
240C4—81no—
241C4—81no—
242C4—81no—
243C4—81no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—21no—
248C2#159711yescharacteristic
249C2#160511yescharacteristic
250C2#160911yescharacteristic
251C2#161711yescharacteristic
252C2#203611yescharacteristic
253C2#203811yescharacteristic
254C2#204411yescharacteristic
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
#26272
#18722
#18522
C2×#3282
C2×#3242
#14412
#12942