Finite Group Databasebeta

← #10187

Subgroups — #10187

Order 256.

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

normal subgroups only

This group has 248 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
3C2×#462C211yesmaximal, characteristic
4#1546C211yesmaximal, characteristic
5#1481C211yesmaximal, characteristic
6#1461C211yesmaximal, characteristic
7#1301C211yesmaximal, characteristic
8C22×Q16—21no—
9#533C2211yescharacteristic
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#462—22no—
20#462—22no—
21#431C2211yescharacteristic
22#431C2211yescharacteristic
23#428—21no—
24#423C2211yescharacteristic
25C2×C4⋊C8C2211yescharacteristic
26#419—21no—
27C2×#103—21no—
28#332—22no—
29Q8⋊C8—22no—
30#324—22no—
31C22×Q8—21no—
32C22×Q8D411yescharacteristic
33C2×Q16—24no—
34C2×Q16—42no—
35C2×Q16—42no—
36C2×M16—21no—
37C22×C8—21no—
38C4⋊Q8—21no—
39C4⋊Q8—21no—
40C4⋊Q8—21no—
41C4⋊Q8D412yes—
42C4⋊Q8D411yescharacteristic
43C4⋊Q8D411yescharacteristic
44#125—21no—
45C22⋊Q8—21no—
46C22⋊Q8—21no—
47C4×Q8—21no—
48C4×Q8—21no—
49C4×Q8—21no—
50C4×Q8—21no—
51C4×Q8—21no—
52C4×Q8—21no—
53#117—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4—21no—
57C2×C4⋊C4D411yescharacteristic
58C2×C42—21no—
59C2×C42C2311yescharacteristic
60#107—22no—
61#106—22no—
62#106—24no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66C4⋊C8—21no—
67C4⋊C8D412yes—
68C4⋊C8D412yes—
69#103—24no—
70#103—22no—
71#103—22no—
72#103—24no—
73C22⋊C8—21no—
74C22⋊C8D412yes—
75C4×C8—21no—
76C4×C8—21no—
77C2×Q8—21no—
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—21no—
81C2×Q8—22no—
82C2×Q8—21no—
83C2×Q8—21no—
84C2×Q8—21no—
85C2×Q8—41no—
86C2×Q8—41no—
87C2×Q8—41no—
88C2×Q8—41no—
89C2×Q8—41no—
90C2×Q8SD1612yes—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—41no—
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4#4111yescharacteristic
97Q16—48no—
98M16—41no—
99M16—41no—
100C2×C8—22no—
101C2×C8—22no—
102C2×C8—22no—
103C2×C8—41no—
104C2×C8—41no—
105C2×C8—41no—
106C4⋊C4—21no—
107C4⋊C4—22no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—22no—
113C4⋊C4—21no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C4⋊C4—41no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C22⋊C4—41no—
121C42—41no—
122C42—41no—
123C42—41no—
124C42C2×D411yescharacteristic
125C42C2×D411yescharacteristic
126C42C2×D411yescharacteristic
127C42C2×D411yescharacteristic
128C23#12111yescharacteristic
129Q8—22no—
130Q8—22no—
131Q8—42no—
132Q8—41no—
133Q8—41no—
134Q8—42no—
135Q8—42no—
136Q8—42no—
137Q8—81no—
138Q8—81no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4#12011yescharacteristic
152C2×C4#12011yescharacteristic
153C2×C4#12011yescharacteristic
154C2×C4#12111yescharacteristic
155C2×C4#12111yescharacteristic
156C2×C4#12711yescharacteristic
157C2×C4C2×SD1611yescharacteristic
158C2×C4#13511yescharacteristic
159C2×C4AGL(1,ℤ/8)11yescharacteristic
160C2×C4#13711yescharacteristic
161C8—42no—
162C8—42no—
163C8—42no—
164C8—81no—
165C22—21no—
166C22—21no—
167C22#39211yescharacteristic
168C22#46511yescharacteristic
169C22#46811yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—42no—
174C4—82no—
175C4—81no—
176C4—81no—
177C4—81no—
178C4#44811yescharacteristic
179C4#44911yescharacteristic
180C4#45011yescharacteristic
181C4#45211yescharacteristic
182C4#47312yes—
183C2—21no—
184C2—21no—
185C2#200011yescharacteristic
186C2#200911yescharacteristic
187C2#202011yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#121
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
C2×#4622
#15462
#14812
#14612
#13012