Finite Group Databasebeta

← #16963

Subgroups — #16963

Order 256.

529 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 529 conjugacy classes of subgroups — too many to draw. Only its 163 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×#389C211yesmaximal, characteristic
2C2×#382C211yesmaximal, characteristic
3#1445C212yesmaximal
4#1443C214yesmaximal
5#1442C212yesmaximal
6#1441C212yesmaximal
7#1441C212yesmaximal
8#1434C211yesmaximal, characteristic
9C22×C4⋊C4C2212yes—
10C22×C4⋊C4C2211yescharacteristic
11C22×C4⋊C4C2211yescharacteristic
12C22×C4⋊C4C2211yescharacteristic
13C22×C4⋊C4C2211yescharacteristic
14C22×C42C2211yescharacteristic
15#389—24no—
16#382—24no—
17C2×#95C2212yes—
18C2×#95C2212yes—
19C2×#95C2214yes—
20C2×#95C2212yes—
21C2×#95C2212yes—
22C2×#95C2212yes—
23C2×#95C2212yes—
24C2×#95C2214yes—
25C2×#95C2214yes—
26C2×#95C2214yes—
27C23×C4C2312yes—
28C23×C4C2312yes—
29C23×C4C2312yes—
30C23×C4C2314yes—
31C23×C4C2311yescharacteristic
32C23×C4C2312yes—
33C23×C4C2311yescharacteristic
34C23×C4C2311yescharacteristic
35C2×C4⋊C4—22no—
36C2×C4⋊C4—24no—
37C2×C4⋊C4—22no—
38C2×C4⋊C4—22no—
39C2×C4⋊C4—22no—
40C2×C4⋊C4—24no—
41C2×C4⋊C4—24no—
42C2×C4⋊C4—24no—
43C2×C4⋊C4—24no—
44C2×C4⋊C4—42no—
45C2×C4⋊C4—42no—
46C2×C42—24no—
47C2×C42D414yes—
48#95—24no—
49#95—24no—
50#95—24no—
51#95—28no—
52#95—24no—
53#95—24no—
54#95—42no—
55#95—44no—
56#95—44no—
57#95—44no—
58C24C2411yescharacteristic
59C22×C4—22no—
60C22×C4—22no—
61C22×C4—22no—
62C22×C4—22no—
63C22×C4—22no—
64C22×C4—22no—
65C22×C4—22no—
66C22×C4—22no—
67C22×C4—22no—
68C22×C4—21no—
69C22×C4—22no—
70C22×C4—22no—
71C22×C4—21no—
72C22×C4—22no—
73C22×C4—22no—
74C22×C4—22no—
75C22×C4—22no—
76C22×C4—24no—
77C22×C4—24no—
78C22×C4—24no—
79C22×C4—24no—
80C22×C4—24no—
81C22×C4—22no—
82C22×C4—22no—
83C22×C4—24no—
84C22×C4—22no—
85C22×C4—24no—
86C22×C4—24no—
87C22×C4—24no—
88C22×C4—24no—
89C22×C4—24no—
90C22×C4—24no—
91C22×C4—22no—
92C22×C4—24no—
93C22×C4—24no—
94C22×C4C2×D412yes—
95C22×C4C2×D412yes—
96C22×C4C2×D412yes—
97C22×C4#4114yes—
98C22×C4#4114yes—
99C22×C4#4114yes—
100C4⋊C4—28no—
101C4⋊C4—44no—
102C4⋊C4—44no—
103C4⋊C4—44no—
104C4⋊C4—48no—
105C42—28no—
106C23C22×D411yescharacteristic
107C23C2×#4112yes—
108C23C2×#4112yes—
109C23C2×#4112yes—
110C23H(5,𝔽2)12yes—
111C23H(5,𝔽2)11yescharacteristic
112C232−1+412yes—
113C232−1+412yes—
114C232−1+411yescharacteristic
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—28no—
120C2×C4—28no—
121C2×C4—22no—
122C2×C4—24no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—24no—
126C2×C4—24no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4—42no—
130C2×C4—42no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—42no—
134C2×C4—42no—
135C2×C4—42no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—44no—
143C2×C4—48no—
144C2×C4—44no—
145C2×C4—44no—
146C2×C4—44no—
147C2×C4—44no—
148C2×C4—44no—
149C2×C4—44no—
150C2×C4—44no—
151C2×C4—44no—
152C2×C4—44no—
153C2×C4—44no—
154C2×C4#12314yes—
155C2×C4#12414yes—
156C22C2×#12311yescharacteristic
157C22#52511yescharacteristic
158C22C2×#12411yescharacteristic
159C22#53511yescharacteristic
160C22#53611yescharacteristic
161C22#53611yescharacteristic
162C22#53711yescharacteristic
163C22#54112yes—
164C22#54114yes—
165C22#54212yes—
166C22#54214yes—
167C22#55212yes—
168C22#55214yes—
169C22#55312yes—
170C22#55314yes—
171C22#56212yes—
172C22#56312yes—
173C4—24no—
174C4—24no—
175C4—44no—
176C4—42no—
177C4—82no—
178C4—82no—
179C4—82no—
180C4—84no—
181C2#248411yescharacteristic
182C2#250411yescharacteristic
183C2#256211yescharacteristic
184C2#262511yescharacteristic
185C2#263211yescharacteristic
186C2#264211yescharacteristic
187C2#276614yes—
188C2#277214yes—
189C2#282011yescharacteristic
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×#3892
C2×#3822
#14452
#14432
#14422
#14412
#14342