Finite Group Databasebeta

← #17061

Subgroups — #17061

Order 256.

615 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 615 conjugacy classes of subgroups — too many to draw. Only its 191 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×#387C211yesmaximal, characteristic
3C2×#384C211yesmaximal, characteristic
4#1445C212yesmaximal
5#1444C212yesmaximal
6#1444C212yesmaximal
7#1442C212yesmaximal
8#1441C212yesmaximal
9#1434C211yesmaximal, characteristic
10C22×C4⋊C4C2212yes—
11C22×C4⋊C4C2211yescharacteristic
12C22×C4⋊C4C2211yescharacteristic
13C22×C4⋊C4C2214yes—
14C22×C4⋊C4C2212yes—
15C22×C4⋊C4C2212yes—
16C22×C42C2211yescharacteristic
17#398—28no—
18#387—24no—
19#384—24no—
20C2×#95C2212yes—
21C2×#95C2214yes—
22C2×#95C2212yes—
23C2×#95C2211yescharacteristic
24C2×#95C2211yescharacteristic
25C2×#95C2211yescharacteristic
26C2×#95C2211yescharacteristic
27C2×#95C2214yes—
28C2×#95C2214yes—
29C2×#95C2212yes—
30C23×C4C2314yes—
31C23×C4C2311yescharacteristic
32C23×C4C2311yescharacteristic
33C23×C4C2311yescharacteristic
34C23×C4C2311yescharacteristic
35C23×C4C2314yes—
36C23×C4C2311yescharacteristic
37C23×C4C2311yescharacteristic
38C23×C4C2311yescharacteristic
39C2×C4⋊C4—22no—
40C2×C4⋊C4—22no—
41C2×C4⋊C4—24no—
42C2×C4⋊C4—24no—
43C2×C4⋊C4—24no—
44C2×C4⋊C4—22no—
45C2×C4⋊C4—28no—
46C2×C4⋊C4—24no—
47C2×C4⋊C4—24no—
48C2×C4⋊C4—24no—
49C2×C4⋊C4—44no—
50C2×C4⋊C4—44no—
51C2×C4⋊C4—44no—
52C2×C4⋊C4—44no—
53C2×C4⋊C4D414yes—
54C2×C42—24no—
55C2×C42D414yes—
56#95—22no—
57#95—22no—
58#95—22no—
59#95—22no—
60#95—24no—
61#95—28no—
62#95—24no—
63#95—44no—
64#95—44no—
65#95Q818yes—
66C24C2411yescharacteristic
67C22×C4—22no—
68C22×C4—22no—
69C22×C4—22no—
70C22×C4—22no—
71C22×C4—22no—
72C22×C4—22no—
73C22×C4—21no—
74C22×C4—24no—
75C22×C4—21no—
76C22×C4—24no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—22no—
80C22×C4—24no—
81C22×C4—24no—
82C22×C4—22no—
83C22×C4—22no—
84C22×C4—24no—
85C22×C4—22no—
86C22×C4—24no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—24no—
90C22×C4—24no—
91C22×C4—24no—
92C22×C4—22no—
93C22×C4—22no—
94C22×C4—22no—
95C22×C4—24no—
96C22×C4—24no—
97C22×C4—24no—
98C22×C4—24no—
99C22×C4—22no—
100C22×C4—22no—
101C22×C4—22no—
102C22×C4C2×D412yes—
103C22×C4C2×D412yes—
104C22×C4C2×D412yes—
105C22×C4C2×D412yes—
106C22×C4C2×D412yes—
107C22×C4C2×D412yes—
108C22×C4C2×Q818yes—
109C22×C4C2×Q814yes—
110C22×C4#4112yes—
111C22×C4#4114yes—
112C4⋊C4—28no—
113C4⋊C4—48no—
114C4⋊C4—48no—
115C4⋊C4—416no—
116C4⋊C4—48no—
117C4⋊C4—44no—
118C42—28no—
119C23C22×D411yescharacteristic
120C23C22×D411yescharacteristic
121C23C22×Q812yes—
122C23C2×#4111yescharacteristic
123C23C2×#4112yes—
124C23H(5,𝔽2)12yes—
125C23H(5,𝔽2)12yes—
126C232−1+412yes—
127C232−1+412yes—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—28no—
135C2×C4—24no—
136C2×C4—24no—
137C2×C4—28no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—28no—
142C2×C4—24no—
143C2×C4—28no—
144C2×C4—28no—
145C2×C4—41no—
146C2×C4—44no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—44no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—44no—
155C2×C4—44no—
156C2×C4—41no—
157C2×C4—44no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—41no—
161C2×C4—44no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4—44no—
169C2×C4—44no—
170C2×C4#12114yes—
171C2×C4#12314yes—
172C2×C4C4⋊Q814yes—
173C22C2×#12111yescharacteristic
174C22C2×#12311yescharacteristic
175C22C2×C4⋊Q811yescharacteristic
176C22#53511yescharacteristic
177C22#53511yescharacteristic
178C22#53512yes—
179C22#53611yescharacteristic
180C22#53611yescharacteristic
181C22#53914yes—
182C22#54012yes—
183C22#54414yes—
184C22#54712yes—
185C22D4×Q812yes—
186C22#55212yes—
187C22#55414yes—
188C22#55712yes—
189C22#56314yes—
190C4—24no—
191C4—24no—
192C4—24no—
193C4—42no—
194C4—48no—
195C4—42no—
196C4—81no—
197C4—84no—
198C4—81no—
199C2#248611yescharacteristic
200C2#250211yescharacteristic
201C2#254611yescharacteristic
202C2#261911yescharacteristic
203C2#262311yescharacteristic
204C2#266011yescharacteristic
205C2#272014yes—
206C2#279114yes—
207C2#282111yescharacteristic
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×#3872
C2×#3842
#14452
#14442
#14422
#14412
#14342