Finite Group Databasebeta

← #10251

Subgroups — #10251

Order 256.

262 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 61 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
1#3229C211yesmaximal, characteristic
2#3078C211yesmaximal, characteristic
3#2546C211yesmaximal, characteristic
4#1546C211yesmaximal, characteristic
5#1503C211yesmaximal, characteristic
6#1479C211yesmaximal, characteristic
7#1303C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×C4⋊Q8—21no—
10C2×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8C2211yescharacteristic
12#498—21no—
13#487—21no—
14#483—22no—
15#479—22no—
16#477—21no—
17#475—21no—
18#475—22no—
19#431C2211yescharacteristic
20#431C2211yescharacteristic
21#428—21no—
22#423C2211yescharacteristic
23#419—21no—
24#398—22no—
25#391—21no—
26#389—22no—
27C4×C4⋊C4C2211yescharacteristic
28#332—22no—
29#328—22no—
30Q8⋊C8—22no—
31C22×Q8—21no—
32C22×Q8D411yescharacteristic
33C2×M16—21no—
34C4⋊Q8—21no—
35C4⋊Q8—21no—
36C4⋊Q8—21no—
37C4⋊Q8—21no—
38C4⋊Q8—42no—
39C4⋊Q8—42no—
40C4⋊Q8D411yescharacteristic
41C4⋊Q8D411yescharacteristic
42#125—21no—
43C22⋊Q8—21no—
44C22⋊Q8—21no—
45C4×Q8—21no—
46C4×Q8—21no—
47C4×Q8—21no—
48C4×Q8—21no—
49C4×Q8—21no—
50C4×Q8—21no—
51#117—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—24no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4D411yescharacteristic
57C2×C4⋊C4D412yes—
58C2×C42—21no—
59C2×C42—21no—
60C2×C42C2311yescharacteristic
61#107—22no—
62#106—22no—
63#106—24no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66C4⋊C8D412yes—
67C4⋊C8D412yes—
68#103—22no—
69#103—22no—
70#103—24no—
71C22⋊C8—21no—
72C22⋊C8—21no—
73C4×C8—21no—
74C4×C8—21no—
75#95—24no—
76#95D412yes—
77C2×Q8—21no—
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—21no—
81C2×Q8—21no—
82C2×Q8—21no—
83C2×Q8—21no—
84C2×Q8—41no—
85C2×Q8—41no—
86C2×Q8—41no—
87C2×Q8—41no—
88C2×Q8—41no—
89C2×Q8—41no—
90C2×Q8SD1612yes—
91C22×C4—22no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—22no—
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4C2×D411yescharacteristic
98M16—41no—
99M16—41no—
100C2×C8—22no—
101C2×C8—22no—
102C2×C8—41no—
103C4⋊C4—24no—
104C4⋊C4—22no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—22no—
111C4⋊C4—21no—
112C4⋊C4—48no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C4⋊C4—41no—
118C4⋊C4—41no—
119C22⋊C4—41no—
120C42—41no—
121C42—41no—
122C42—41no—
123C42—41no—
124C42—41no—
125C42C2×D411yescharacteristic
126C42C2×D411yescharacteristic
127C42C2×D411yescharacteristic
128C42#4111yescharacteristic
129C23#12011yescharacteristic
130Q8—22no—
131Q8—22no—
132Q8—41no—
133Q8—41no—
134Q8—42no—
135Q8—81no—
136Q8—81no—
137Q8—81no—
138Q8—81no—
139Q8—81no—
140C2×C4—22no—
141C2×C4—24no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—42no—
145C2×C4—41no—
146C2×C4—42no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4#12011yescharacteristic
156C2×C4#12011yescharacteristic
157C2×C4#12111yescharacteristic
158C2×C4#12111yescharacteristic
159C2×C4#12111yescharacteristic
160C2×C4#12711yescharacteristic
161C2×C4C2×SD1611yescharacteristic
162C2×C4#13511yescharacteristic
163C2×C4AGL(1,ℤ/8)11yescharacteristic
164C2×C4#13711yescharacteristic
165C8—42no—
166C8—42no—
167C8—81no—
168C22—21no—
169C22—21no—
170C22#39211yescharacteristic
171C22#45011yescharacteristic
172C22#45211yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—44no—
177C4—42no—
178C4—82no—
179C4—81no—
180C4—81no—
181C4—81no—
182C4#44811yescharacteristic
183C4#44911yescharacteristic
184C4#45612yes—
185C4#46511yescharacteristic
186C4#46811yescharacteristic
187C2—21no—
188C2—21no—
189C2#200011yescharacteristic
190C2#200511yescharacteristic
191C2#200911yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#32292
#30782
#25462
#15462
#15032
#14792
#13032