Finite Group Databasebeta

← #11831

Subgroups — #11831

Order 256.

192 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 51 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#2399C211yesmaximal, characteristic
2#1801C211yesmaximal, characteristic
3#1467C211yesmaximal, characteristic
4#1354C212yesmaximal
5#1346C212yesmaximal
6C2×C4×Q8C411yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#432—21no—
9#423—21no—
10C2×#101—21no—
11#398—21no—
12#398C411yescharacteristic
13#398C2211yescharacteristic
14#395—21no—
15#395C411yescharacteristic
16#395C2211yescharacteristic
17C4×C4⋊C4—21no—
18C4×C4⋊C4—21no—
19#376C411yescharacteristic
20#343C2212yes—
21#324—21no—
22#324C2212yes—
23C22×Q8C2×C411yescharacteristic
24C22×Q8D411yescharacteristic
25C2×M16—22no—
26C4×Q8—41no—
27C4×Q8—41no—
28C4×Q8—41no—
29C4×Q8—41no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C4⋊C4D411yescharacteristic
38C2×C4⋊C4C2311yescharacteristic
39C2×C42—21no—
40C2×C42—21no—
41C2×C42C2×C411yescharacteristic
42C2×C42D411yescharacteristic
43C2×C42D411yescharacteristic
44C4⋊C8—41no—
45C4⋊C8—41no—
46C4⋊C8—41no—
47#101—42no—
48C22⋊C8—22no—
49#97—41no—
50#95—21no—
51#95—21no—
52#95—21no—
53#95—21no—
54#95—21no—
55#95C2×C411yescharacteristic
56#95C2×C411yescharacteristic
57C2×Q8—21no—
58C2×Q8—21no—
59C2×Q8—41no—
60C2×Q8—41no—
61C2×Q8—42no—
62C2×Q8—41no—
63C22×C4—21no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4C22⋊C411yescharacteristic
68C22×C4C22⋊C411yescharacteristic
69C22×C4C22⋊C411yescharacteristic
70C22×C4C22⋊C411yescharacteristic
71C22×C4C22×C411yescharacteristic
72C22×C4C2×D411yescharacteristic
73C22×C4C2×D411yescharacteristic
74M16—42no—
75M16—42no—
76C2×C8—42no—
77C2×C8—42no—
78C4⋊C4—41no—
79C4⋊C4—41no—
80C4⋊C4—41no—
81C4⋊C4—41no—
82C4⋊C4—42no—
83C4⋊C4—42no—
84C4⋊C4—42no—
85C4⋊C4—42no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C42—24no—
89C42—21no—
90C42—21no—
91C42—21no—
92C42—21no—
93C42—21no—
94C42—21no—
95C42—41no—
96C42—41no—
97C23C2×C22⋊C411yescharacteristic
98Q8—42no—
99Q8—42no—
100Q8—42no—
101Q8—42no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4#9911yescharacteristic
130C2×C4#9911yescharacteristic
131C2×C4AGL(1,ℤ/8)11yescharacteristic
132C2×C4#13711yescharacteristic
133C8—82no—
134C8—82no—
135C22—21no—
136C22—21no—
137C22C2×#9911yescharacteristic
138C22#41711yescharacteristic
139C22#42111yescharacteristic
140C4—21no—
141C4—21no—
142C4—21no—
143C4—42no—
144C4—42no—
145C4—41no—
146C4—41no—
147C4—42no—
148C4—41no—
149C4—41no—
150C4—41no—
151C4—81no—
152C4#35612yes—
153C2—21no—
154C2—21no—
155C2#151311yescharacteristic
156C2#212011yescharacteristic
157C2C2×#35611yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC2×C4⋊C4C23
prime radicalC23C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#23992
#18012
#14672
#13542
#13462