Finite Group Databasebeta

← #17003

Subgroups — #17003

Order 256.

545 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 545 conjugacy classes of subgroups — too many to draw. Only its 175 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#1445C212yesmaximal
2#1444C212yesmaximal
3#1444C212yesmaximal
4#1441C212yesmaximal
5#1441C211yesmaximal, characteristic
6#1441C211yesmaximal, characteristic
7#1441C212yesmaximal
8#1436C212yesmaximal
9C4⋊#95C211yesmaximal, characteristic
10C22×C4⋊C4C2211yescharacteristic
11C22×C4⋊C4C2211yescharacteristic
12C22×C4⋊C4C2211yescharacteristic
13C22×C4⋊C4C2212yes—
14C22×C4⋊C4C2212yes—
15C22×C4⋊C4C2211yescharacteristic
16C22×C4⋊C4C2212yes—
17C22×C42C2211yescharacteristic
18C2×#95C2212yes—
19C2×#95C2212yes—
20C2×#95C2212yes—
21C2×#95C2212yes—
22C2×#95C2212yes—
23C2×#95C2212yes—
24C2×#95C2212yes—
25C2×#95C2212yes—
26C2×#95C2212yes—
27C2×#95C2211yescharacteristic
28C2×#95C2212yes—
29C2×#95C2212yes—
30C2×#95C2211yescharacteristic
31C23×C4C2312yes—
32C23×C4C2312yes—
33C23×C4C2311yescharacteristic
34C23×C4C2312yes—
35C23×C4C2311yescharacteristic
36C23×C4C2312yes—
37C23×C4C2312yes—
38C23×C4C2312yes—
39C23×C4C2311yescharacteristic
40C2×C4⋊C4—24no—
41C2×C4⋊C4—22no—
42C2×C4⋊C4—41no—
43C2×C4⋊C4—41no—
44C2×C4⋊C4—42no—
45C2×C4⋊C4—42no—
46C2×C4⋊C4—41no—
47C2×C4⋊C4—41no—
48C2×C4⋊C4—41no—
49C2×C4⋊C4—42no—
50C2×C4⋊C4—42no—
51C2×C4⋊C4—42no—
52C2×C4⋊C4—42no—
53C2×C4⋊C4—42no—
54C2×C4⋊C4—41no—
55C2×C4⋊C4—42no—
56C2×C4⋊C4—42no—
57C2×C4⋊C4Q818yes—
58C2×C4⋊C4Q814yes—
59C2×C42—22no—
60C2×C42—41no—
61C2×C42—41no—
62#95—24no—
63#95—24no—
64#95—24no—
65#95—24no—
66#95—42no—
67#95—42no—
68#95—42no—
69#95—42no—
70#95—42no—
71#95—41no—
72#95—41no—
73#95—42no—
74#95—42no—
75C24C2411yescharacteristic
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
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—22no—
98C22×C4—21no—
99C22×C4—21no—
100C22×C4—22no—
101C22×C4—22no—
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—21no—
107C22×C4—21no—
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×C4—22no—
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4C2×Q814yes—
127C22×C4C2×Q812yes—
128C22×C4C2×Q812yes—
129C22×C4C2×Q814yes—
130C22×C4C2×Q814yes—
131C22×C4C2×Q812yes—
132C22×C4#4114yes—
133C22×C4#4112yes—
134C22×C4#4112yes—
135C4⋊C4—44no—
136C4⋊C4—48no—
137C4⋊C4—44no—
138C4⋊C4—44no—
139C4⋊C4—44no—
140C4⋊C4—48no—
141C4⋊C4—48no—
142C42—44no—
143C23C22×Q811yescharacteristic
144C23C22×Q812yes—
145C23C2×#4111yescharacteristic
146C23C2×#4111yescharacteristic
147C23C2×#4112yes—
148C23H(5,𝔽2)11yescharacteristic
149C23H(5,𝔽2)11yescharacteristic
150C23H(5,𝔽2)11yescharacteristic
151C23H(5,𝔽2)12yes—
152C23H(5,𝔽2)12yes—
153C232−1+411yescharacteristic
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—24no—
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—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—41no—
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×C4—42no—
212C2×C4#12514yes—
213C22C2×#12511yescharacteristic
214C22#53312yes—
215C22#53811yescharacteristic
216C22#53811yescharacteristic
217C22#53911yescharacteristic
218C22#53911yescharacteristic
219C22#53912yes—
220C22#54012yes—
221C22#54012yes—
222C22#54311yescharacteristic
223C22#54312yes—
224C22#54411yescharacteristic
225C22#54412yes—
226C22#55111yescharacteristic
227C22#55312yes—
228C22#55412yes—
229C22#55412yes—
230C22#55412yes—
231C22Q8211yescharacteristic
232C22Q8212yes—
233C22#56011yescharacteristic
234C22#56012yes—
235C22H(3,𝔽4)11yescharacteristic
236C4—24no—
237C4—44no—
238C4—42no—
239C4—42no—
240C4—44no—
241C4—44no—
242C4—44no—
243C4—82no—
244C4—82no—
245C2#250712yes—
246C2#258611yescharacteristic
247C2#264611yescharacteristic
248C2#266712yes—
249C2#274811yescharacteristic
250C2#278012yes—
251C2#278211yescharacteristic
252C2#279211yescharacteristic
253C2#279212yes—
254C2#281111yescharacteristic
255C2#282811yescharacteristic
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
#14412
#14362
C4⋊#952