Finite Group Databasebeta

← #11478

Subgroups — #11478

Order 256.

214 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C4×C4⋊Q8C211yesmaximal, characteristic
2#1461C212yesmaximal
3#1325C212yesmaximal
4#1319C212yesmaximal
5C2×C4⋊Q8C411yescharacteristic
6C2×C4×Q8C411yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8#431—22no—
9#391C411yescharacteristic
10#391C2211yescharacteristic
11#389—22no—
12#384C2211yescharacteristic
13C4×C4⋊C4—22no—
14C43C411yescharacteristic
15#324—22no—
16#324C2214yes—
17C22×Q8C2×C411yescharacteristic
18C22×Q8C2×C411yescharacteristic
19C4⋊Q8—22no—
20C4⋊Q8C814yescomplemented
21C4×Q8—41no—
22C4×Q8—41no—
23C4×Q8—41no—
24C4×Q8—41no—
25C2×C4⋊C4—22no—
26C2×C4⋊C4—21no—
27C2×C4⋊C4—22no—
28C2×C4⋊C4C2×C411yescharacteristic
29C2×C4⋊C4D412yes—
30C2×C4⋊C4C2311yescharacteristic
31C2×C42—21no—
32C2×C42—21no—
33C2×C42—21no—
34C2×C42C2×C411yescharacteristic
35C2×C42C2×C411yescharacteristic
36C2×C42C2×C411yescharacteristic
37C2×C42D412yes—
38C4⋊C8—42no—
39C22⋊C8—24no—
40C4×C8—42no—
41#95—22no—
42#95—22no—
43C2×Q8—21no—
44C2×Q8—41no—
45C2×Q8—41no—
46C2×Q8—41no—
47C2×Q8—41no—
48C2×Q8C2×C812yes—
49C2×Q8C2×C812yes—
50C2×Q8M1612yes—
51C22×C4—21no—
52C22×C4—21no—
53C22×C4—21no—
54C22×C4—21no—
55C22×C4C22⋊C412yes—
56C22×C4C22⋊C411yescharacteristic
57C22×C4C22⋊C411yescharacteristic
58C22×C4C22×C411yescharacteristic
59C22×C4C2×D412yes—
60C2×C8—44no—
61C4⋊C4—28no—
62C4⋊C4—42no—
63C4⋊C4—41no—
64C4⋊C4—41no—
65C4⋊C4—44no—
66C4⋊C4—42no—
67C42—24no—
68C42—22no—
69C42—21no—
70C42—22no—
71C42—21no—
72C42—21no—
73C42—41no—
74C42—42no—
75C42—41no—
76C42—41no—
77C42C2×C812yes—
78C23C2×C22⋊C411yescharacteristic
79Q8—42no—
80Q8—42no—
81Q8—42no—
82Q8—42no—
83C2×C4—22no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—22no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—22no—
92C2×C4—22no—
93C2×C4—21no—
94C2×C4—22no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4—41no—
100C2×C4—42no—
101C2×C4—42no—
102C2×C4—41no—
103C2×C4C22⋊C814yes—
104C2×C4#9911yescharacteristic
105C2×C4#9911yescharacteristic
106C2×C4C22×C811yescharacteristic
107C2×C4C2×M1611yescharacteristic
108C8—84no—
109C22—21no—
110C22—21no—
111C22C2×C22⋊C811yescharacteristic
112C22C2×#9911yescharacteristic
113C22#41311yescharacteristic
114C4—24no—
115C4—21no—
116C4—24no—
117C4—21no—
118C4—21no—
119C4—42no—
120C4—42no—
121C4—41no—
122C4—42no—
123C4—81no—
124C4#35612yes—
125C2—21no—
126C2—21no—
127C2#145911yescharacteristic
128C2#212611yescharacteristic
129C2C2×#35611yescharacteristic
subgroupG/H
centerC2×C4#99
commutatorC2×C4C22×C8
Frattini, cosocleC2×C4⋊C4C23
socleC22C2×#99
prime radicalC23C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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
C4×C4⋊Q82
#14612
#13252
#13192