Finite Group Databasebeta

← #16607

Subgroups — #16607

Order 256.

713 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 713 conjugacy classes of subgroups — too many to draw. Only its 195 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
1C22×#125C211yesmaximal, characteristic
2C2×#398C212yesmaximal
3C2×#389C211yesmaximal, characteristic
4#1444C212yesmaximal
5#1444C214yesmaximal
6#1442C212yesmaximal
7#1441C212yesmaximal
8#1434C211yesmaximal, characteristic
9C2×#125—28no—
10C2×#125—24no—
11C22×C4⋊C4C2211yescharacteristic
12C22×C4⋊C4C2211yescharacteristic
13C22×C4⋊C4C2211yescharacteristic
14C22×C4⋊C4C2212yes—
15C22×C4⋊C4C2211yescharacteristic
16C22×C4⋊C4C2212yes—
17C22×C4⋊C4C2214yes—
18C22×C4⋊C4C2212yes—
19C22×C42C2211yescharacteristic
20#398—28no—
21#389—24no—
22C2×#95C2212yes—
23C2×#95C2214yes—
24C2×#95C2214yes—
25C2×#95C2212yes—
26C2×#95C2212yes—
27C2×#95C2214yes—
28C2×#95C2212yes—
29C23×C4C2312yes—
30C23×C4C2312yes—
31C23×C4C2311yescharacteristic
32C23×C4C2312yes—
33C23×C4C2314yes—
34C23×C4C2312yes—
35C23×C4C2311yescharacteristic
36C23×C4C2311yescharacteristic
37#125—232no—
38C2×C4⋊C4—24no—
39C2×C4⋊C4—24no—
40C2×C4⋊C4—24no—
41C2×C4⋊C4—24no—
42C2×C4⋊C4—24no—
43C2×C4⋊C4—22no—
44C2×C4⋊C4—22no—
45C2×C4⋊C4—24no—
46C2×C4⋊C4—24no—
47C2×C4⋊C4—22no—
48C2×C4⋊C4—24no—
49C2×C4⋊C4—24no—
50C2×C4⋊C4—22no—
51C2×C4⋊C4—28no—
52C2×C4⋊C4—24no—
53C2×C4⋊C4—44no—
54C2×C4⋊C4—44no—
55C2×C4⋊C4—44no—
56C2×C4⋊C4D418yes—
57C2×C42—24no—
58C2×C42D414yes—
59#95—24no—
60#95—24no—
61#95—28no—
62#95—28no—
63#95—42no—
64#95—44no—
65#95Q818yes—
66C24C2411yescharacteristic
67C22×C4—22no—
68C22×C4—22no—
69C22×C4—22no—
70C22×C4—22no—
71C22×C4—24no—
72C22×C4—22no—
73C22×C4—22no—
74C22×C4—22no—
75C22×C4—22no—
76C22×C4—22no—
77C22×C4—22no—
78C22×C4—24no—
79C22×C4—24no—
80C22×C4—22no—
81C22×C4—22no—
82C22×C4—21no—
83C22×C4—24no—
84C22×C4—24no—
85C22×C4—24no—
86C22×C4—22no—
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—22no—
90C22×C4—21no—
91C22×C4—24no—
92C22×C4—24no—
93C22×C4—24no—
94C22×C4—24no—
95C22×C4—22no—
96C22×C4—24no—
97C22×C4—24no—
98C22×C4—22no—
99C22×C4—22no—
100C22×C4C2×D414yes—
101C22×C4C2×D412yes—
102C22×C4C2×D414yes—
103C22×C4C2×D414yes—
104C22×C4C2×D412yes—
105C22×C4C2×D412yes—
106C22×C4C2×Q818yes—
107C22×C4C2×Q814yes—
108C22×C4#4114yes—
109C4⋊C4—28no—
110C4⋊C4—28no—
111C4⋊C4—28no—
112C4⋊C4—216no—
113C4⋊C4—216no—
114C4⋊C4—48no—
115C4⋊C4—416no—
116C4⋊C4—44no—
117C42—28no—
118C23C22×D411yescharacteristic
119C23C22×D412yes—
120C23C22×Q812yes—
121C23C2×#4112yes—
122C23H(5,𝔽2)12yes—
123C23H(5,𝔽2)11yescharacteristic
124C232−1+412yes—
125C232−1+412yes—
126C232−1+411yescharacteristic
127C2×C4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—28no—
132C2×C4—28no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—24no—
136C2×C4—24no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—28no—
142C2×C4—28no—
143C2×C4—28no—
144C2×C4—28no—
145C2×C4—28no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—44no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—44no—
161C2×C4—44no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—44no—
167C2×C4#12014yes—
168C2×C4C4⋊Q814yes—
169C22C2×#12011yescharacteristic
170C22#52511yescharacteristic
171C22C2×C4⋊Q811yescharacteristic
172C22#53511yescharacteristic
173C22#53512yes—
174C22#53611yescharacteristic
175C22#53611yescharacteristic
176C22#53711yescharacteristic
177C22#53712yes—
178C22#53914yes—
179C22#54414yes—
180C22#54714yes—
181C22D4×Q814yes—
182C22#55412yes—
183C22#55712yes—
184C22#56312yes—
185C22#56412yes—
186C4—24no—
187C4—24no—
188C4—42no—
189C4—44no—
190C4—44no—
191C4—44no—
192C4—48no—
193C4—82no—
194C2#240611yescharacteristic
195C2#243411yescharacteristic
196C2#258411yescharacteristic
197C2#261511yescharacteristic
198C2#263311yescharacteristic
199C2#266011yescharacteristic
200C2#272014yes—
201C2#272614yes—
202C2#282211yescharacteristic
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
C22×#1252
C2×#3982
C2×#3892
#14442
#14422
#14412
#14342