Finite Group Databasebeta

← #17067

Subgroups — #17067

Order 256.

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

normal subgroups only

This group has 595 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×#387C211yesmaximal, characteristic
2C2×#384C211yesmaximal, characteristic
3#1444C212yesmaximal
4#1444C212yesmaximal
5#1444C212yesmaximal
6#1442C212yesmaximal
7#1441C212yesmaximal
8#1441C212yesmaximal
9#1434C211yesmaximal, characteristic
10C22×C4⋊C4C2211yescharacteristic
11C22×C4⋊C4C2211yescharacteristic
12C22×C4⋊C4C2212yes—
13C22×C4⋊C4C2212yes—
14C22×C4⋊C4C2212yes—
15C22×C4⋊C4C2214yes—
16C22×C42C2211yescharacteristic
17#387—24no—
18#384—24no—
19C2×#95C2212yes—
20C2×#95C2212yes—
21C2×#95C2211yescharacteristic
22C2×#95C2211yescharacteristic
23C2×#95C2211yescharacteristic
24C2×#95C2211yescharacteristic
25C2×#95C2214yes—
26C2×#95C2214yes—
27C2×#95C2214yes—
28C2×#95C2212yes—
29C23×C4C2311yescharacteristic
30C23×C4C2314yes—
31C23×C4C2311yescharacteristic
32C23×C4C2311yescharacteristic
33C23×C4C2311yescharacteristic
34C23×C4C2314yes—
35C23×C4C2311yescharacteristic
36C23×C4C2311yescharacteristic
37C23×C4C2311yescharacteristic
38C2×C4⋊C4—22no—
39C2×C4⋊C4—22no—
40C2×C4⋊C4—24no—
41C2×C4⋊C4—24no—
42C2×C4⋊C4—24no—
43C2×C4⋊C4—22no—
44C2×C4⋊C4—24no—
45C2×C4⋊C4—44no—
46C2×C4⋊C4—44no—
47C2×C4⋊C4—44no—
48C2×C4⋊C4—44no—
49C2×C4⋊C4—44no—
50C2×C4⋊C4—44no—
51C2×C4⋊C4Q814yes—
52C2×C42—24no—
53C2×C42D414yes—
54#95—22no—
55#95—22no—
56#95—22no—
57#95—22no—
58#95—24no—
59#95—24no—
60#95—44no—
61#95—44no—
62#95—44no—
63#95Q818yes—
64C24C2411yescharacteristic
65C22×C4—22no—
66C22×C4—22no—
67C22×C4—22no—
68C22×C4—22no—
69C22×C4—22no—
70C22×C4—22no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—24no—
74C22×C4—24no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—22no—
78C22×C4—22no—
79C22×C4—22no—
80C22×C4—24no—
81C22×C4—24no—
82C22×C4—24no—
83C22×C4—22no—
84C22×C4—24no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—24no—
88C22×C4—22no—
89C22×C4—22no—
90C22×C4—24no—
91C22×C4—24no—
92C22×C4—24no—
93C22×C4—24no—
94C22×C4—24no—
95C22×C4—24no—
96C22×C4—22no—
97C22×C4—22no—
98C22×C4—22no—
99C22×C4—22no—
100C22×C4C2×D412yes—
101C22×C4C2×D412yes—
102C22×C4C2×D412yes—
103C22×C4C2×Q818yes—
104C22×C4C2×Q812yes—
105C22×C4C2×Q812yes—
106C22×C4C2×Q812yes—
107C22×C4C2×Q814yes—
108C22×C4#4112yes—
109C22×C4#4114yes—
110C4⋊C4—28no—
111C4⋊C4—48no—
112C4⋊C4—48no—
113C4⋊C4—48no—
114C4⋊C4—416no—
115C4⋊C4—44no—
116C42—28no—
117C23C22×D411yescharacteristic
118C23C22×Q811yescharacteristic
119C23C22×Q812yes—
120C23C2×#4111yescharacteristic
121C23C2×#4112yes—
122C23H(5,𝔽2)12yes—
123C23H(5,𝔽2)12yes—
124C23H(5,𝔽2)12yes—
125C232−1+412yes—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—28no—
133C2×C4—24no—
134C2×C4—24no—
135C2×C4—28no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4—28no—
140C2×C4—24no—
141C2×C4—28no—
142C2×C4—28no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—44no—
148C2×C4—42no—
149C2×C4—44no—
150C2×C4—42no—
151C2×C4—44no—
152C2×C4—44no—
153C2×C4—41no—
154C2×C4—44no—
155C2×C4—44no—
156C2×C4—44no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—44no—
163C2×C4—44no—
164C2×C4—44no—
165C2×C4—44no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4C22⋊Q814yes—
169C2×C4#12314yes—
170C2×C4C4⋊Q814yes—
171C22C2×C22⋊Q811yescharacteristic
172C22C2×#12311yescharacteristic
173C22C2×C4⋊Q811yescharacteristic
174C22#53511yescharacteristic
175C22#53511yescharacteristic
176C22#53511yescharacteristic
177C22#53611yescharacteristic
178C22#53914yes—
179C22#54212yes—
180C22#54412yes—
181C22#54414yes—
182C22#55312yes—
183C22#55412yes—
184C22#55412yes—
185C22#55414yes—
186C22Q8212yes—
187C22#56014yes—
188C4—24no—
189C4—24no—
190C4—24no—
191C4—42no—
192C4—42no—
193C4—48no—
194C4—84no—
195C4—81no—
196C4—81no—
197C2#248711yescharacteristic
198C2#250211yescharacteristic
199C2#256711yescharacteristic
200C2#262311yescharacteristic
201C2#262811yescharacteristic
202C2#266011yescharacteristic
203C2#279014yes—
204C2#279214yes—
205C2#281811yescharacteristic
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×#3872
C2×#3842
#14442
#14422
#14412
#14342