Finite Group Databasebeta

← #9892

Subgroups — #9892

Order 256.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#2864C211yesmaximal, characteristic
2#1767C211yesmaximal, characteristic
3C4×#97C211yesmaximal, characteristic
4#1295C212yesmaximal
5#1295C212yesmaximal
6C2×C4⋊C8—21no—
7C2×#97—21no—
8C2×#97C2212yes—
9C2×#97C2212yes—
10C2×C4×C8—21no—
11#389C411yescharacteristic
12#389C411yescharacteristic
13#389C411yescharacteristic
14#389C411yescharacteristic
15#387—21no—
16#387—21no—
17#387—21no—
18#387—21no—
19#382C2211yescharacteristic
20#382C2211yescharacteristic
21C43C2211yescharacteristic
22#336—21no—
23C22×C8—22no—
24C22×C8—22no—
25C2×C4⋊C4—21no—
26C2×C4⋊C4—21no—
27C2×C4⋊C4—21no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4C2×C411yescharacteristic
30C2×C4⋊C4C2×C411yescharacteristic
31C2×C4⋊C4C2×C411yescharacteristic
32C2×C4⋊C4C2×C411yescharacteristic
33C2×C42C2×C411yescharacteristic
34C2×C42C2×C411yescharacteristic
35C2×C42D411yescharacteristic
36C2×C42D411yescharacteristic
37C2×C42D411yescharacteristic
38C2×C42D411yescharacteristic
39C2×C42C2311yescharacteristic
40C4⋊C8—24no—
41#97—24no—
42#97—22no—
43#97—24no—
44#97Q814yes—
45C4×C8—24no—
46#95—21no—
47#95—21no—
48#95—21no—
49#95—21no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54C22×C4—21no—
55C22×C4—21no—
56C22×C4—21no—
57C22×C4—21no—
58C22×C4C22⋊C411yescharacteristic
59C22×C4C22⋊C411yescharacteristic
60C22×C4C22⋊C411yescharacteristic
61C22×C4C22⋊C411yescharacteristic
62C22×C4C22×C411yescharacteristic
63C22×C4C2×D411yescharacteristic
64C22×C4C2×D411yescharacteristic
65C2×C8—24no—
66C2×C8—24no—
67C2×C8—24no—
68C2×C8—24no—
69C2×C8—42no—
70C2×C8—42no—
71C4⋊C4—41no—
72C4⋊C4—41no—
73C4⋊C4—41no—
74C4⋊C4—41no—
75C4⋊C4—42no—
76C4⋊C4—42no—
77C4⋊C4—42no—
78C4⋊C4—42no—
79C42—22no—
80C42—22no—
81C42—22no—
82C42—41no—
83C42—41no—
84C42—41no—
85C42C2×Q812yes—
86C42#4112yes—
87C23C2×C22⋊C411yescharacteristic
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—21no—
98C2×C4—21no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4#10412yes—
116C2×C4#10412yes—
117C2×C4#10412yes—
118C2×C4C4×Q812yes—
119C2×C4C22⋊Q812yes—
120C2×C4#12411yescharacteristic
121C2×C4C4⋊Q811yescharacteristic
122C8—28no—
123C8—44no—
124C22#39111yescharacteristic
125C22#41311yescharacteristic
126C22#41311yescharacteristic
127C22C2×#10411yescharacteristic
128C22C2×#10411yescharacteristic
129C22C2×#10411yescharacteristic
130C22#42111yescharacteristic
131C4—21no—
132C4—21no—
133C4—22no—
134C4—22no—
135C4—22no—
136C4—22no—
137C4—22no—
138C4—41no—
139C4—81no—
140C4—81no—
141C4—81no—
142C4—81no—
143C2#152411yescharacteristic
144C2#152411yescharacteristic
145C2#152911yescharacteristic
146C2#153211yescharacteristic
147C2#198611yescharacteristic
148C2#199411yescharacteristic
149C2#199811yescharacteristic
subgroupG/H
center, socle, prime radicalC23C2×C22⋊C4
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ 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
#28642
#17672
C4×#972
#12952