Finite Group Databasebeta

← #17304

Subgroups — #17304

Order 256.

485 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 485 conjugacy classes of subgroups — too many to draw. Only its 151 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#1445C211yesmaximal, characteristic
2#1444C211yesmaximal, characteristic
3#1443C212yesmaximal
4#1442C212yesmaximal
5#1442C211yesmaximal, characteristic
6#1442C212yesmaximal
7#1441C212yesmaximal
8#1441C212yesmaximal
9#1441C212yesmaximal
10C22×C4⋊C4C2212yes—
11C22×C4⋊C4C2212yes—
12C22×C4⋊C4C2211yescharacteristic
13C22×C4⋊C4C2211yescharacteristic
14C22×C4⋊C4C2211yescharacteristic
15C2×#95C2211yescharacteristic
16C2×#95C2212yes—
17C2×#95C2212yes—
18C2×#95C2212yes—
19C2×#95C2211yescharacteristic
20C2×#95C2212yes—
21C2×#95C2212yes—
22C2×#95C2212yes—
23C2×#95C2212yes—
24C2×#95C2212yes—
25C2×#95C2212yes—
26C2×#95C2212yes—
27C2×#95C2212yes—
28C2×#95C2212yes—
29C2×#95C2211yescharacteristic
30C2×#95C2211yescharacteristic
31C23×C4C2312yes—
32C23×C4C2312yes—
33C23×C4C2312yes—
34C23×C4C2312yes—
35C23×C4C2312yes—
36C23×C4C2311yescharacteristic
37C23×C4C2311yescharacteristic
38C23×C4C2312yes—
39C23×C4C2311yescharacteristic
40C2×C4⋊C4—24no—
41C2×C4⋊C4—24no—
42C2×C4⋊C4—41no—
43C2×C4⋊C4—41no—
44C2×C4⋊C4—42no—
45C2×C4⋊C4—42no—
46C2×C4⋊C4—42no—
47C2×C4⋊C4—42no—
48C2×C4⋊C4—41no—
49C2×C4⋊C4—41no—
50C2×C4⋊C4—42no—
51C2×C4⋊C4—42no—
52C2×C4⋊C4Q814yes—
53#95—22no—
54#95—24no—
55#95—24no—
56#95—24no—
57#95—22no—
58#95—42no—
59#95—42no—
60#95—42no—
61#95—42no—
62#95—41no—
63#95—42no—
64#95—41no—
65#95—42no—
66#95—42no—
67#95—42no—
68#95—42no—
69C24C2411yescharacteristic
70C22×C4—22no—
71C22×C4—22no—
72C22×C4—22no—
73C22×C4—22no—
74C22×C4—22no—
75C22×C4—22no—
76C22×C4—22no—
77C22×C4—22no—
78C22×C4—21no—
79C22×C4—22no—
80C22×C4—21no—
81C22×C4—22no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—22no—
85C22×C4—22no—
86C22×C4—22no—
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—21no—
90C22×C4—22no—
91C22×C4—21no—
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—22no—
121C22×C4—22no—
122C22×C4C2×Q812yes—
123C22×C4C2×Q814yes—
124C22×C4#4112yes—
125C22×C4#4114yes—
126C22×C4#4112yes—
127C4⋊C4—44no—
128C4⋊C4—48no—
129C4⋊C4—48no—
130C4⋊C4—44no—
131C4⋊C4—44no—
132C23C22×Q811yescharacteristic
133C23C2×#4111yescharacteristic
134C23C2×#4112yes—
135C23C2×#4111yescharacteristic
136C23H(5,𝔽2)12yes—
137C23H(5,𝔽2)11yescharacteristic
138C23H(5,𝔽2)12yes—
139C23H(5,𝔽2)11yescharacteristic
140C232−1+411yescharacteristic
141C232−1+412yes—
142C232−1+411yescharacteristic
143C2×C4—24no—
144C2×C4—24no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
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—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—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C22#53812yes—
201C22#53812yes—
202C22#53911yescharacteristic
203C22#53912yes—
204C22#53911yescharacteristic
205C22#54112yes—
206C22#54212yes—
207C22#54311yescharacteristic
208C22#54412yes—
209C22#55212yes—
210C22#55312yes—
211C22#55412yes—
212C22#55511yescharacteristic
213C22#55511yescharacteristic
214C22#55711yescharacteristic
215C22#55711yescharacteristic
216C22#56011yescharacteristic
217C22#56011yescharacteristic
218C22#56212yes—
219C22#56212yes—
220C22#56311yescharacteristic
221C22#56312yes—
222C22#56311yescharacteristic
223C4—42no—
224C4—42no—
225C4—42no—
226C4—44no—
227C4—44no—
228C4—82no—
229C4—82no—
230C4—82no—
231C4—82no—
232C2#276911yescharacteristic
233C2#277412yes—
234C2#278112yes—
235C2#278411yescharacteristic
236C2#279511yescharacteristic
237C2#280212yes—
238C2#280911yescharacteristic
239C2#282611yescharacteristic
240C2#283112yes—
241C2#283411yescharacteristic
242C2#284111yescharacteristic
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
#14452
#14442
#14432
#14422
#14412