Finite Group Databasebeta

← #9100

Subgroups — #9100

Order 256.

249 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 249 conjugacy classes of subgroups — too many to draw. Only its 83 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#2982C211yesmaximal, characteristic
2#2327C211yesmaximal, characteristic
3#1479C212yesmaximal
4#1461C211yesmaximal, characteristic
5#1274C212yesmaximal
6C2×C4⋊Q8C411yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8C2×C4×Q8C2211yescharacteristic
9C8×Q8—24no—
10#431—22no—
11#431C2212yes—
12#431C2212yes—
13#391C411yescharacteristic
14#391C411yescharacteristic
15#387—22no—
16#387—22no—
17#382C411yescharacteristic
18#376C2211yescharacteristic
19Q8⋊C8—24no—
20#324—22no—
21C22×Q8C2×C411yescharacteristic
22C22×Q8C2×C411yescharacteristic
23C4⋊Q8—22no—
24C4⋊Q8C814yescomplemented
25C4×Q8—22no—
26C4×Q8—22no—
27C4×Q8—22no—
28C4×Q8—22no—
29C2×C4⋊C4—22no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4C2×C411yescharacteristic
32C2×C4⋊C4C2×C411yescharacteristic
33C2×C4⋊C4D412yes—
34C2×C42—21no—
35C2×C42C2×C411yescharacteristic
36C2×C42C2×C411yescharacteristic
37C2×C42D412yes—
38C2×C42C2311yescharacteristic
39C4⋊C8—24no—
40C4⋊C8—22no—
41C4⋊C8—22no—
42C22⋊C8—22no—
43C22⋊C8—22no—
44C4×C8—24no—
45C4×C8—22no—
46C4×C8D414yes—
47#95—22no—
48#95—22no—
49#95—22no—
50#95—21no—
51#95—21no—
52C2×Q8—22no—
53C2×Q8—21no—
54C2×Q8—22no—
55C2×Q8—22no—
56C2×Q8—22no—
57C2×Q8C2×C812yes—
58C2×Q8C2×C812yes—
59C2×Q8M1612yes—
60C22×C4—21no—
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—21no—
64C22×C4C22⋊C412yes—
65C22×C4C22⋊C412yes—
66C22×C4C22×C411yescharacteristic
67C22×C4C2×D411yescharacteristic
68C22×C4C2×D411yescharacteristic
69C2×C8—24no—
70C2×C8—42no—
71C4⋊C4—28no—
72C4⋊C4—22no—
73C4⋊C4—24no—
74C4⋊C4—22no—
75C4⋊C4—41no—
76C4⋊C4—41no—
77C42—22no—
78C42—22no—
79C42—21no—
80C42—22no—
81C42—42no—
82C42C2×C812yes—
83C42C2×D412yes—
84C42#4112yes—
85C23C2×C22⋊C411yescharacteristic
86Q8—24no—
87Q8—24no—
88Q8—24no—
89Q8—42no—
90C2×C4—22no—
91C2×C4—22no—
92C2×C4—22no—
93C2×C4—22no—
94C2×C4—22no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4—41no—
100C2×C4—41no—
101C2×C4—42no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—42no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4C22⋊C814yes—
108C2×C4C4×D412yes—
109C2×C4#12011yescharacteristic
110C2×C4#12112yes—
111C2×C4#12311yescharacteristic
112C2×C4C22×C811yescharacteristic
113C2×C4C2×M1611yescharacteristic
114C2×C4#13112yes—
115C8—44no—
116C8—82no—
117C22—21no—
118C22—21no—
119C22#38611yescharacteristic
120C22C2×C22⋊C811yescharacteristic
121C22#40811yescharacteristic
122C4—24no—
123C4—22no—
124C4—21no—
125C4—21no—
126C4—42no—
127C4—42no—
128C4—42no—
129C4—81no—
130C4—81no—
131C4C8×D412yes—
132C4#43512yes—
133C2—21no—
134C2—21no—
135C2#186911yescharacteristic
136C2#190911yescharacteristic
137C2#191211yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC2×C4C22×C8
Frattini, cosocleC2×C42C23
prime radicalC23C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
24. C4⋊Q8C8semidirect

Maximal subgroups

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

subgroupindex
#29822
#23272
#14792
#14612
#12742