Finite Group Databasebeta

← #9893

Subgroups — #9893

Order 256.

194 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 69 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
3#1745C211yesmaximal, characteristic
4#1295C212yesmaximal
5#1295C212yesmaximal
6C2×C4⋊C8—21no—
7C2×#97C2212yes—
8C2×#97C2212yes—
9#389C411yescharacteristic
10#389C411yescharacteristic
11#389C411yescharacteristic
12#389C411yescharacteristic
13#387—21no—
14#387—21no—
15#387—21no—
16#387—21no—
17#382C2211yescharacteristic
18#382C2211yescharacteristic
19C43C2211yescharacteristic
20#336—21no—
21#336—21no—
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—22no—
42#97—24no—
43#97Q814yes—
44#95—21no—
45#95—21no—
46#95—21no—
47#95—21no—
48#95—21no—
49#95—21no—
50#95—21no—
51#95—21no—
52C22×C4—21no—
53C22×C4—21no—
54C22×C4—21no—
55C22×C4—21no—
56C22×C4C22⋊C411yescharacteristic
57C22×C4C22⋊C411yescharacteristic
58C22×C4C22⋊C411yescharacteristic
59C22×C4C22⋊C411yescharacteristic
60C22×C4C22×C411yescharacteristic
61C22×C4C2×D411yescharacteristic
62C22×C4C2×D411yescharacteristic
63C2×C8—24no—
64C2×C8—24no—
65C2×C8—42no—
66C2×C8—42no—
67C2×C8—42no—
68C2×C8—42no—
69C4⋊C4—41no—
70C4⋊C4—41no—
71C4⋊C4—41no—
72C4⋊C4—41no—
73C4⋊C4—42no—
74C4⋊C4—42no—
75C4⋊C4—42no—
76C4⋊C4—42no—
77C42—22no—
78C42—41no—
79C42—41no—
80C42—41no—
81C42—41no—
82C42—41no—
83C42C2×Q812yes—
84C42#4112yes—
85C23C2×C22⋊C411yescharacteristic
86C2×C4—21no—
87C2×C4—21no—
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×C4C4×Q812yes—
117C2×C4C22⋊Q812yes—
118C2×C4#12411yescharacteristic
119C2×C4C4⋊Q811yescharacteristic
120C8—44no—
121C8—44no—
122C22#39111yescharacteristic
123C22#41311yescharacteristic
124C22#41311yescharacteristic
125C22C2×#10411yescharacteristic
126C22#42111yescharacteristic
127C22#42111yescharacteristic
128C22#42111yescharacteristic
129C4—21no—
130C4—21no—
131C4—22no—
132C4—22no—
133C4—22no—
134C4—41no—
135C4—41no—
136C4—41no—
137C4—81no—
138C4—81no—
139C4—81no—
140C4—81no—
141C2#152911yescharacteristic
142C2#153211yescharacteristic
143C2#153511yescharacteristic
144C2#153511yescharacteristic
145C2#198611yescharacteristic
146C2#199511yescharacteristic
147C2#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
#17452
#12952