Finite Group Databasebeta

← #17300

Subgroups — #17300

Order 256.

463 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 463 conjugacy classes of subgroups — too many to draw. Only its 143 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#1444C211yesmaximal, characteristic
2#1443C212yesmaximal
3#1443C212yesmaximal
4#1442C212yesmaximal
5#1442C211yesmaximal, characteristic
6#1442C212yesmaximal
7#1442C211yesmaximal, characteristic
8#1442C212yesmaximal
9#1441C212yesmaximal
10C22×C4⋊C4C2212yes—
11C22×C4⋊C4C2211yescharacteristic
12C22×C4⋊C4C2211yescharacteristic
13C22×C4⋊C4C2211yescharacteristic
14C2×#95C2212yes—
15C2×#95C2212yes—
16C2×#95C2211yescharacteristic
17C2×#95C2212yes—
18C2×#95C2212yes—
19C2×#95C2212yes—
20C2×#95C2211yescharacteristic
21C2×#95C2211yescharacteristic
22C2×#95C2212yes—
23C2×#95C2212yes—
24C2×#95C2212yes—
25C2×#95C2212yes—
26C2×#95C2212yes—
27C2×#95C2212yes—
28C2×#95C2211yescharacteristic
29C2×#95C2212yes—
30C2×#95C2212yes—
31C23×C4C2312yes—
32C23×C4C2312yes—
33C23×C4C2312yes—
34C23×C4C2312yes—
35C23×C4C2312yes—
36C23×C4C2311yescharacteristic
37C23×C4C2312yes—
38C23×C4C2311yescharacteristic
39C23×C4C2311yescharacteristic
40C2×C4⋊C4—24no—
41C2×C4⋊C4—42no—
42C2×C4⋊C4—42no—
43C2×C4⋊C4—41no—
44C2×C4⋊C4—42no—
45C2×C4⋊C4—41no—
46C2×C4⋊C4—41no—
47C2×C4⋊C4—42no—
48C2×C4⋊C4—42no—
49#95—22no—
50#95—24no—
51#95—24no—
52#95—24no—
53#95—24no—
54#95—24no—
55#95—22no—
56#95—22no—
57#95—41no—
58#95—42no—
59#95—42no—
60#95—42no—
61#95—42no—
62#95—42no—
63#95—42no—
64#95—42no—
65#95—42no—
66C24C2411yescharacteristic
67C22×C4—22no—
68C22×C4—22no—
69C22×C4—22no—
70C22×C4—22no—
71C22×C4—22no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—22no—
75C22×C4—21no—
76C22×C4—22no—
77C22×C4—22no—
78C22×C4—22no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—22no—
82C22×C4—22no—
83C22×C4—21no—
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—22no—
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—22no—
107C22×C4—22no—
108C22×C4—22no—
109C22×C4—22no—
110C22×C4—22no—
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#4112yes—
121C22×C4#4112yes—
122C22×C4#4114yes—
123C22×C4#4112yes—
124C4⋊C4—48no—
125C4⋊C4—44no—
126C4⋊C4—44no—
127C4⋊C4—44no—
128C23C2×#4111yescharacteristic
129C23C2×#4111yescharacteristic
130C23C2×#4111yescharacteristic
131C23C2×#4112yes—
132C23H(5,𝔽2)12yes—
133C23H(5,𝔽2)12yes—
134C23H(5,𝔽2)11yescharacteristic
135C232−1+411yescharacteristic
136C232−1+412yes—
137C232−1+411yescharacteristic
138C232−1+411yescharacteristic
139C2×C4—24no—
140C2×C4—22no—
141C2×C4—24no—
142C2×C4—22no—
143C2×C4—24no—
144C2×C4—22no—
145C2×C4—24no—
146C2×C4—24no—
147C2×C4—24no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
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—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C22#53812yes—
197C22#53911yescharacteristic
198C22#53912yes—
199C22#53911yescharacteristic
200C22#53912yes—
201C22#53911yescharacteristic
202C22#53912yes—
203C22#54112yes—
204C22#54212yes—
205C22#55212yes—
206C22#55312yes—
207C22#55511yescharacteristic
208C22#55512yes—
209C22#55611yescharacteristic
210C22#55611yescharacteristic
211C22#55611yescharacteristic
212C22#56011yescharacteristic
213C22H(3,𝔽4)11yescharacteristic
214C22#56212yes—
215C22#56311yescharacteristic
216C22#56312yes—
217C22#56312yes—
218C22#56411yescharacteristic
219C4—42no—
220C4—42no—
221C4—42no—
222C4—44no—
223C4—82no—
224C4—82no—
225C4—82no—
226C4—82no—
227C4—82no—
228C2#276911yescharacteristic
229C2#277512yes—
230C2#278312yes—
231C2#278511yescharacteristic
232C2#278712yes—
233C2#279511yescharacteristic
234C2#281011yescharacteristic
235C2#282411yescharacteristic
236C2#283411yescharacteristic
237C2#283511yescharacteristic
238C2#283912yes—
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
#14442
#14432
#14422
#14412