Finite Group Databasebeta

← #16992

Subgroups — #16992

Order 256.

615 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 615 conjugacy classes of subgroups — too many to draw. Only its 187 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×#398C212yesmaximal
2C2×#389C211yesmaximal, characteristic
3C2×#389C211yesmaximal, characteristic
4#1444C212yesmaximal
5#1442C212yesmaximal
6#1441C212yesmaximal
7#1441C214yesmaximal
8#1434C211yesmaximal, characteristic
9C22×C4⋊C4C2212yes—
10C22×C4⋊C4C2211yescharacteristic
11C22×C4⋊C4C2214yes—
12C22×C4⋊C4C2211yescharacteristic
13C22×C4⋊C4C2211yescharacteristic
14C22×C4⋊C4C2212yes—
15C22×C4⋊C4C2211yescharacteristic
16C22×C42C2211yescharacteristic
17#398—28no—
18#389—24no—
19#389—24no—
20C2×#95C2212yes—
21C2×#95C2214yes—
22C2×#95C2212yes—
23C2×#95C2212yes—
24C2×#95C2212yes—
25C2×#95C2214yes—
26C2×#95C2214yes—
27C2×#95C2212yes—
28C23×C4C2312yes—
29C23×C4C2312yes—
30C23×C4C2312yes—
31C23×C4C2311yescharacteristic
32C23×C4C2314yes—
33C23×C4C2312yes—
34C23×C4C2311yescharacteristic
35C23×C4C2311yescharacteristic
36C2×C4⋊C4—22no—
37C2×C4⋊C4—22no—
38C2×C4⋊C4—24no—
39C2×C4⋊C4—22no—
40C2×C4⋊C4—24no—
41C2×C4⋊C4—22no—
42C2×C4⋊C4—22no—
43C2×C4⋊C4—24no—
44C2×C4⋊C4—28no—
45C2×C4⋊C4—24no—
46C2×C4⋊C4—28no—
47C2×C4⋊C4—24no—
48C2×C4⋊C4—44no—
49C2×C4⋊C4—42no—
50C2×C4⋊C4—42no—
51C2×C4⋊C4—44no—
52C2×C4⋊C4D414yes—
53C2×C42—42no—
54C2×C42D414yes—
55#95—24no—
56#95—24no—
57#95—24no—
58#95—28no—
59#95—42no—
60#95—44no—
61#95—44no—
62#95Q818yes—
63C24C2411yescharacteristic
64C22×C4—22no—
65C22×C4—22no—
66C22×C4—22no—
67C22×C4—22no—
68C22×C4—24no—
69C22×C4—22no—
70C22×C4—22no—
71C22×C4—22no—
72C22×C4—22no—
73C22×C4—22no—
74C22×C4—24no—
75C22×C4—22no—
76C22×C4—24no—
77C22×C4—22no—
78C22×C4—24no—
79C22×C4—22no—
80C22×C4—24no—
81C22×C4—22no—
82C22×C4—22no—
83C22×C4—24no—
84C22×C4—22no—
85C22×C4—24no—
86C22×C4—24no—
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—22no—
90C22×C4—22no—
91C22×C4—24no—
92C22×C4—24no—
93C22×C4—24no—
94C22×C4—24no—
95C22×C4—24no—
96C22×C4C2×D412yes—
97C22×C4C2×D414yes—
98C22×C4C2×D412yes—
99C22×C4C2×D412yes—
100C22×C4C2×D412yes—
101C22×C4C2×Q818yes—
102C22×C4C2×Q814yes—
103C22×C4#4114yes—
104C22×C4#4112yes—
105C4⋊C4—28no—
106C4⋊C4—28no—
107C4⋊C4—416no—
108C4⋊C4—44no—
109C4⋊C4—44no—
110C4⋊C4—48no—
111C4⋊C4—48no—
112C42—44no—
113C23C22×D411yescharacteristic
114C23C22×D411yescharacteristic
115C23C22×Q812yes—
116C23C2×#4111yescharacteristic
117C23C2×#4112yes—
118C23H(5,𝔽2)12yes—
119C23H(5,𝔽2)12yes—
120C232−1+412yes—
121C232−1+412yes—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—24no—
127C2×C4—24no—
128C2×C4—28no—
129C2×C4—24no—
130C2×C4—24no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—28no—
135C2×C4—24no—
136C2×C4—28no—
137C2×C4—28no—
138C2×C4—24no—
139C2×C4—28no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—44no—
145C2×C4—44no—
146C2×C4—44no—
147C2×C4—42no—
148C2×C4—44no—
149C2×C4—42no—
150C2×C4—44no—
151C2×C4—44no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—48no—
161C2×C4#12114yes—
162C2×C4C4⋊Q814yes—
163C22C2×#12111yescharacteristic
164C22#52511yescharacteristic
165C22C2×C4⋊Q811yescharacteristic
166C22#53411yescharacteristic
167C22#53511yescharacteristic
168C22#53611yescharacteristic
169C22#53611yescharacteristic
170C22#53712yes—
171C22#53912yes—
172C22#54114yes—
173C22#54414yes—
174C22#54612yes—
175C22D4×Q812yes—
176C22#55312yes—
177C22#55414yes—
178C22#55712yes—
179C22#56214yes—
180C4—24no—
181C4—24no—
182C4—42no—
183C4—48no—
184C4—44no—
185C4—44no—
186C4—82no—
187C4—82no—
188C2#253511yescharacteristic
189C2#254611yescharacteristic
190C2#258311yescharacteristic
191C2#261811yescharacteristic
192C2#263411yescharacteristic
193C2#266011yescharacteristic
194C2#270414yes—
195C2#280214yes—
196C2#281611yescharacteristic
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×#3982
C2×#3892
#14442
#14422
#14412
#14342