Finite Group Databasebeta

← #11883

Subgroups — #11883

Order 256.

204 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 59 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#2546C211yesmaximal, characteristic
2#1801C211yesmaximal, characteristic
3#1461C211yesmaximal, characteristic
4#1346C214yesmaximal
5C2×C4⋊Q8—21no—
6C2×C4⋊Q8C411yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#431—21no—
9#423—21no—
10C2×#101—21no—
11#398C412yes—
12#398C2212yes—
13#391—21no—
14#389—21no—
15#389—21no—
16C4×C4⋊C4C411yescharacteristic
17#343C2212yes—
18#324—21no—
19#324C2212yes—
20C22×Q8—21no—
21C22×Q8D411yescharacteristic
22C2×M16—22no—
23C4⋊Q8—41no—
24C4⋊Q8—41no—
25C4⋊Q8—42no—
26C4⋊Q8—42no—
27C4×Q8—41no—
28C4×Q8—41no—
29C2×C4⋊C4—21no—
30C2×C4⋊C4—22no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—22no—
33C2×C4⋊C4C2×C412yes—
34C2×C4⋊C4C2×C411yescharacteristic
35C2×C4⋊C4D411yescharacteristic
36C2×C4⋊C4C2311yescharacteristic
37C2×C42—21no—
38C2×C42C2×C411yescharacteristic
39C2×C42D411yescharacteristic
40C2×C42D411yescharacteristic
41C4⋊C8—41no—
42C4⋊C8—41no—
43C4⋊C8—41no—
44#101—42no—
45C22⋊C8—22no—
46C4×C8—41no—
47#95—22no—
48#95—22no—
49#95C2×C412yes—
50C2×Q8—41no—
51C2×Q8—41no—
52C2×Q8—42no—
53C2×Q8—42no—
54C2×Q8—42no—
55C2×Q8D812yes—
56C2×Q8SD1612yes—
57C22×C4—22no—
58C22×C4—22no—
59C22×C4C22⋊C411yescharacteristic
60C22×C4C22⋊C411yescharacteristic
61C22×C4C22⋊C411yescharacteristic
62C22×C4C22⋊C411yescharacteristic
63C22×C4C22×C411yescharacteristic
64C22×C4C2×D411yescharacteristic
65C22×C4C2×D411yescharacteristic
66M16—42no—
67M16—42no—
68C2×C8—42no—
69C2×C8—42no—
70C4⋊C4—24no—
71C4⋊C4—41no—
72C4⋊C4—41no—
73C4⋊C4—41no—
74C4⋊C4—42no—
75C4⋊C4—41no—
76C4⋊C4—41no—
77C4⋊C4—44no—
78C4⋊C4—42no—
79C4⋊C4—42no—
80C42—21no—
81C42—21no—
82C42—21no—
83C42—21no—
84C42—21no—
85C42—21no—
86C42—42no—
87C23C2×C22⋊C411yescharacteristic
88Q8—42no—
89Q8—42no—
90Q8—84no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—22no—
98C2×C4—24no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—42no—
103C2×C4—42no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—42no—
108C2×C4—42no—
109C2×C4—42no—
110C2×C4#9911yescharacteristic
111C2×C4#9911yescharacteristic
112C2×C4#10212yes—
113C2×C4#10212yes—
114C2×C4C2×D811yescharacteristic
115C2×C4C2×SD1611yescharacteristic
116C8—82no—
117C8—82no—
118C22—21no—
119C22—21no—
120C22C2×#9911yescharacteristic
121C22C2×#10211yescharacteristic
122C22#42111yescharacteristic
123C4—21no—
124C4—21no—
125C4—22no—
126C4—22no—
127C4—21no—
128C4—44no—
129C4—41no—
130C4—41no—
131C4—41no—
132C4—82no—
133C4#35612yes—
134C2—21no—
135C2—21no—
136C2#151911yescharacteristic
137C2#212311yescharacteristic
138C2C2×#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
#25462
#18012
#14612
#13462