Finite Group Databasebeta

← #11482

Subgroups — #11482

Order 256.

196 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 65 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#2327C211yesmaximal, characteristic
2#1461C212yesmaximal
3#1324C212yesmaximal
4#1319C212yesmaximal
5C2×C4⋊Q8C411yescharacteristic
6C2×C4×Q8C411yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#431—22no—
9#391C411yescharacteristic
10#391C2211yescharacteristic
11#387—22no—
12#387—22no—
13#382C2211yescharacteristic
14#376C411yescharacteristic
15#324—22no—
16#324C2214yes—
17C22×Q8C2×C411yescharacteristic
18C22×Q8C2×C411yescharacteristic
19C4⋊Q8—22no—
20C4⋊Q8C814yescomplemented
21C4×Q8—42no—
22C4×Q8—42no—
23C2×C4⋊C4—22no—
24C2×C4⋊C4—21no—
25C2×C4⋊C4C2×C411yescharacteristic
26C2×C4⋊C4D412yes—
27C2×C4⋊C4C2311yescharacteristic
28C2×C42—21no—
29C2×C42C2×C411yescharacteristic
30C2×C42C2×C411yescharacteristic
31C2×C42C2×C411yescharacteristic
32C2×C42D412yes—
33C4⋊C8—42no—
34C22⋊C8—24no—
35C4×C8—42no—
36#95—21no—
37#95—22no—
38#95—21no—
39#95—22no—
40#95—22no—
41C2×Q8—21no—
42C2×Q8—41no—
43C2×Q8—41no—
44C2×Q8—41no—
45C2×Q8—41no—
46C2×Q8C2×C812yes—
47C2×Q8C2×C812yes—
48C2×Q8M1612yes—
49C22×C4—21no—
50C22×C4—21no—
51C22×C4—21no—
52C22×C4—21no—
53C22×C4C22⋊C412yes—
54C22×C4C22⋊C411yescharacteristic
55C22×C4C22⋊C411yescharacteristic
56C22×C4C22×C411yescharacteristic
57C22×C4C2×D412yes—
58C2×C8—44no—
59C4⋊C4—28no—
60C4⋊C4—42no—
61C4⋊C4—41no—
62C4⋊C4—41no—
63C4⋊C4—42no—
64C42—22no—
65C42—22no—
66C42—22no—
67C42—21no—
68C42—41no—
69C42—42no—
70C42C2×C812yes—
71C23C2×C22⋊C411yescharacteristic
72Q8—42no—
73Q8—42no—
74Q8—42no—
75Q8—42no—
76C2×C4—21no—
77C2×C4—22no—
78C2×C4—21no—
79C2×C4—22no—
80C2×C4—22no—
81C2×C4—22no—
82C2×C4—21no—
83C2×C4—22no—
84C2×C4—41no—
85C2×C4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—41no—
90C2×C4—42no—
91C2×C4—41no—
92C2×C4—41no—
93C2×C4—42no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4C22⋊C814yes—
97C2×C4#9912yes—
98C2×C4C22×C811yescharacteristic
99C2×C4C2×M1611yescharacteristic
100C8—84no—
101C22—21no—
102C22—21no—
103C22C2×C22⋊C811yescharacteristic
104C22C2×#9911yescharacteristic
105C22#41311yescharacteristic
106C4—22no—
107C4—24no—
108C4—21no—
109C4—21no—
110C4—42no—
111C4—42no—
112C4—41no—
113C4—42no—
114C4—81no—
115C4—81no—
116C2—21no—
117C2—21no—
118C2#145911yescharacteristic
119C2#212911yescharacteristic
120C2#213311yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC2×C4C22×C8
Frattini, cosocleC2×C4⋊C4C23
prime radicalC23C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
20. C4⋊Q8C8semidirect

Maximal subgroups

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

subgroupindex
#23272
#14612
#13242
#13192