Finite Group Databasebeta

← #15965

Subgroups — #15965

Order 256.

649 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 649 conjugacy classes of subgroups — too many to draw. Only its 183 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×#391C212yesmaximal
2C2×#387C212yesmaximal
3#1446C211yesmaximal, characteristic
4#1444C211yesmaximal, characteristic
5#1443C212yesmaximal
6#1442C212yesmaximal
7#1442C211yesmaximal, characteristic
8#1441C212yesmaximal
9#1436C212yesmaximal
10C23×Q8C2211yescharacteristic
11C22×C4⋊C4C2212yes—
12C22×C4⋊C4C2211yescharacteristic
13C22×C4⋊C4C2212yes—
14C22×C4⋊C4C2211yescharacteristic
15C22×C42C2212yes—
16#391—28no—
17#387—28no—
18C2×#95C2212yes—
19C2×#95C2212yes—
20C2×#95C2212yes—
21C2×#95C2212yes—
22C2×#95C2212yes—
23C2×#95C2211yescharacteristic
24C2×#95C2212yes—
25C2×#95C2211yescharacteristic
26C2×#95C2212yes—
27C2×#95C2212yes—
28C2×#95C2212yes—
29C2×#95C2212yes—
30C2×#95C2211yescharacteristic
31C2×#95C2211yescharacteristic
32C2×#95C2212yes—
33C22×Q8—24no—
34C22×Q8—24no—
35C22×Q8—41no—
36C22×Q8—41no—
37C22×Q8Q814yes—
38C23×C4C2312yes—
39C23×C4C2312yes—
40C23×C4C2312yes—
41C23×C4C2312yes—
42C23×C4C2311yescharacteristic
43C23×C4C2311yescharacteristic
44C23×C4C2312yes—
45C23×C4C2311yescharacteristic
46C23×C4C2312yes—
47C2×C4⋊C4—24no—
48C2×C4⋊C4—24no—
49C2×C4⋊C4—24no—
50C2×C4⋊C4—24no—
51C2×C4⋊C4—24no—
52C2×C4⋊C4—24no—
53C2×C4⋊C4—24no—
54C2×C4⋊C4—42no—
55C2×C4⋊C4—41no—
56C2×C4⋊C4—41no—
57C2×C42—24no—
58C2×C42—24no—
59C2×C42—42no—
60#95—24no—
61#95—24no—
62#95—24no—
63#95—24no—
64#95—24no—
65#95—24no—
66#95—22no—
67#95—24no—
68#95—24no—
69#95—24no—
70#95—22no—
71#95—41no—
72#95—42no—
73#95—41no—
74#95D418yes—
75C24C2411yescharacteristic
76C2×Q8—216no—
77C2×Q8—44no—
78C2×Q8—44no—
79C2×Q8—48no—
80C2×Q8—44no—
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—22no—
98C22×C4—22no—
99C22×C4—22no—
100C22×C4—22no—
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—22no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—22no—
107C22×C4—22no—
108C22×C4—22no—
109C22×C4—22no—
110C22×C4—21no—
111C22×C4—21no—
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×C4—22no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4C2×D414yes—
130C22×C4C2×D414yes—
131C22×C4C2×D414yes—
132C22×C4C2×Q812yes—
133C22×C4C2×Q814yes—
134C22×C4#4112yes—
135C22×C4#4112yes—
136C22×C4#4114yes—
137C22×C4#4114yes—
138C4⋊C4—216no—
139C4⋊C4—48no—
140C4⋊C4—44no—
141C4⋊C4—44no—
142C42—48no—
143C23C22×D412yes—
144C23C22×Q811yescharacteristic
145C23C2×#4112yes—
146C23C2×#4111yescharacteristic
147C23C2×#4112yes—
148C23C2×#4111yescharacteristic
149C23H(5,𝔽2)11yescharacteristic
150C23H(5,𝔽2)11yescharacteristic
151C232−1+411yescharacteristic
152C232−1+412yes—
153C232−1+411yescharacteristic
154Q8—416no—
155C2×C4—24no—
156C2×C4—24no—
157C2×C4—24no—
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—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
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—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4C22⋊Q818yes—
212C22C2×C22⋊Q812yes—
213C22#52512yes—
214C22#52912yes—
215C22#53612yes—
216C22#53911yescharacteristic
217C22#53911yescharacteristic
218C22#54112yes—
219C22#54212yes—
220C22#54311yescharacteristic
221C22D4211yescharacteristic
222C22#54612yes—
223C22#54712yes—
224C22#54812yes—
225C22#55111yescharacteristic
226C22#55111yescharacteristic
227C22#55511yescharacteristic
228C22#55612yes—
229C22#55612yes—
230C22#55711yescharacteristic
231C22#55712yes—
232C22#55711yescharacteristic
233C22#56311yescharacteristic
234C22#56311yescharacteristic
235C4—28no—
236C4—44no—
237C4—42no—
238C4—42no—
239C4—44no—
240C4—44no—
241C4—42no—
242C4—82no—
243C4—82no—
244C2#243711yescharacteristic
245C2#245312yes—
246C2#246311yescharacteristic
247C2#247412yes—
248C2#252311yescharacteristic
249C2#258112yes—
250C2#268011yescharacteristic
251C2#271612yes—
252C2#278911yescharacteristic
253C2#279911yescharacteristic
254C2#280911yescharacteristic
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×#3912
C2×#3872
#14462
#14442
#14432
#14422
#14412
#14362