Finite Group Databasebeta

← #16111

Subgroups — #16111

Order 256.

567 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 567 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C2×#387C212yesmaximal
2#1445C212yesmaximal
3#1445C211yesmaximal, characteristic
4#1445C211yesmaximal, characteristic
5#1444C211yesmaximal, characteristic
6#1442C212yesmaximal
7#1441C212yesmaximal
8#1436C212yesmaximal
9#1436C212yesmaximal
10C22×C4⋊C4C2212yes—
11C22×C4⋊C4C2211yescharacteristic
12C22×C4⋊C4C2212yes—
13C22×C4⋊C4C2211yescharacteristic
14C22×C4⋊C4C2211yescharacteristic
15C22×C42C2212yes—
16#387—28no—
17C2×#95C2212yes—
18C2×#95C2212yes—
19C2×#95C2212yes—
20C2×#95C2212yes—
21C2×#95C2212yes—
22C2×#95C2212yes—
23C2×#95C2212yes—
24C2×#95C2212yes—
25C2×#95C2212yes—
26C2×#95C2211yescharacteristic
27C2×#95C2212yes—
28C2×#95C2212yes—
29C2×#95C2211yescharacteristic
30C2×#95C2211yescharacteristic
31C2×#95C2211yescharacteristic
32C23×C4C2312yes—
33C23×C4C2311yescharacteristic
34C23×C4C2312yes—
35C23×C4C2311yescharacteristic
36C23×C4C2312yes—
37C23×C4C2312yes—
38C23×C4C2312yes—
39C23×C4C2311yescharacteristic
40C23×C4C2312yes—
41C2×C4⋊C4—24no—
42C2×C4⋊C4—24no—
43C2×C4⋊C4—24no—
44C2×C4⋊C4—24no—
45C2×C4⋊C4—24no—
46C2×C4⋊C4—24no—
47C2×C4⋊C4—41no—
48C2×C4⋊C4—41no—
49C2×C4⋊C4—41no—
50C2×C4⋊C4—41no—
51C2×C4⋊C4—42no—
52C2×C4⋊C4—41no—
53C2×C4⋊C4D414yes—
54C2×C4⋊C4Q814yes—
55C2×C42—24no—
56C2×C42—42no—
57C2×C42—42no—
58#95—24no—
59#95—24no—
60#95—24no—
61#95—24no—
62#95—22no—
63#95—24no—
64#95—24no—
65#95—24no—
66#95—24no—
67#95—24no—
68#95—41no—
69#95—42no—
70#95—42no—
71#95—41no—
72#95—41no—
73C24C2411yescharacteristic
74C22×C4—22no—
75C22×C4—22no—
76C22×C4—22no—
77C22×C4—22no—
78C22×C4—22no—
79C22×C4—22no—
80C22×C4—22no—
81C22×C4—22no—
82C22×C4—22no—
83C22×C4—22no—
84C22×C4—22no—
85C22×C4—22no—
86C22×C4—22no—
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—22no—
90C22×C4—22no—
91C22×C4—22no—
92C22×C4—22no—
93C22×C4—22no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—22no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4—21no—
100C22×C4—22no—
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—22no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—22no—
107C22×C4—22no—
108C22×C4—22no—
109C22×C4—22no—
110C22×C4—21no—
111C22×C4—22no—
112C22×C4—22no—
113C22×C4—22no—
114C22×C4—22no—
115C22×C4—22no—
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4C2×D414yes—
124C22×C4C2×D412yes—
125C22×C4C2×Q812yes—
126C22×C4C2×Q814yes—
127C22×C4#4112yes—
128C22×C4#4114yes—
129C22×C4#4114yes—
130C22×C4#4114yes—
131C4⋊C4—216no—
132C4⋊C4—44no—
133C4⋊C4—44no—
134C4⋊C4—44no—
135C4⋊C4—48no—
136C42—48no—
137C23C22×D411yescharacteristic
138C23C22×Q811yescharacteristic
139C23C2×#4112yes—
140C23C2×#4112yes—
141C23C2×#4111yescharacteristic
142C23C2×#4112yes—
143C23H(5,𝔽2)11yescharacteristic
144C23H(5,𝔽2)11yescharacteristic
145C23H(5,𝔽2)11yescharacteristic
146C232−1+411yescharacteristic
147C232−1+412yes—
148C2×C4—24no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—24no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C22#52512yes—
206C22#52912yes—
207C22#53312yes—
208C22#53411yescharacteristic
209C22#53912yes—
210C22#53911yescharacteristic
211C22#54112yes—
212C22#54212yes—
213C22#54311yescharacteristic
214C22#54712yes—
215C22D4×Q811yescharacteristic
216C22#55011yescharacteristic
217C22#55111yescharacteristic
218C22#55112yes—
219C22#55212yes—
220C22#55212yes—
221C22#55312yes—
222C22#55411yescharacteristic
223C22#55712yes—
224C22#55911yescharacteristic
225C22#55911yescharacteristic
226C22#56211yescharacteristic
227C22#56311yescharacteristic
228C4—42no—
229C4—44no—
230C4—42no—
231C4—44no—
232C4—44no—
233C4—44no—
234C4—44no—
235C4—42no—
236C4—82no—
237C2#246212yes—
238C2#247912yes—
239C2#251711yescharacteristic
240C2#258512yes—
241C2#260011yescharacteristic
242C2#260711yescharacteristic
243C2#272411yescharacteristic
244C2#273211yescharacteristic
245C2#273912yes—
246C2#279411yescharacteristic
247C2#279911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#3872
#14452
#14442
#14422
#14412
#14362