Finite Group Databasebeta

← C2×#1325 #11446

Subgroups — C2×#1325 #11446

Order 256.

299 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 299 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#384C211yesmaximal, characteristic
2C2×#324C212yesmaximal
3#1325C214yesmaximal, direct product factor
4C22×C4⋊C4—22no—
5C22×C4⋊C4C411yescharacteristic
6C22×C4⋊C4C2211yescharacteristic
7C22×C42C411yescharacteristic
8C2×C22⋊C8—22no—
9#384—22no—
10#384C412yes—
11#384C2212yes—
12#324—22no—
13#324C2214yes—
14C23×C4—21no—
15C23×C4—21no—
16C23×C4C2×C411yescharacteristic
17C23×C4D412yes—
18C22×C8—42no—
19C2×C4⋊C4—24no—
20C2×C4⋊C4—21no—
21C2×C4⋊C4—24no—
22C2×C4⋊C4—41no—
23C2×C4⋊C4—41no—
24C2×C4⋊C4—41no—
25C2×C4⋊C4—41no—
26C2×C4⋊C4—48no—
27C2×C4⋊C4C2×C412yes—
28C2×C4⋊C4C2×C411yescharacteristic
29C2×C4⋊C4D412yes—
30C2×C4⋊C4C2311yescharacteristic
31C2×C42—21no—
32C2×C42—22no—
33C2×C42C814yescomplemented
34C2×C42C2×C412yes—
35C22⋊C8—24no—
36C22⋊C8—42no—
37C24C22⋊C411yescharacteristic
38C22×C4—24no—
39C22×C4—24no—
40C22×C4—24no—
41C22×C4—21no—
42C22×C4—21no—
43C22×C4—22no—
44C22×C4—22no—
45C22×C4—22no—
46C22×C4—22no—
47C22×C4—22no—
48C22×C4—44no—
49C22×C4—44no—
50C22×C4—41no—
51C22×C4—41no—
52C22×C4C22⋊C411yescharacteristic
53C22×C4C22⋊C412yes—
54C22×C4C2×C812yes—
55C22×C4M1612yes—
56C22×C4C22×C411yescharacteristic
57C22×C4C2×D412yes—
58C2×C8—44no—
59C2×C8—84no—
60C4⋊C4—41no—
61C4⋊C4—42no—
62C4⋊C4—41no—
63C4⋊C4—42no—
64C4⋊C4—48no—
65C4⋊C4—48no—
66C4⋊C4—42no—
67C42—24no—
68C42—22no—
69C42C2×C814yescomplemented
70C23—22no—
71C23—22no—
72C23C22⋊C812yes—
73C23#9911yescharacteristic
74C23#9911yescharacteristic
75C23#10112yes—
76C23C2×C22⋊C411yescharacteristic
77C2×C4—24no—
78C2×C4—216no—
79C2×C4—24no—
80C2×C4—22no—
81C2×C4—22no—
82C2×C4—22no—
83C2×C4—22no—
84C2×C4—24no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—44no—
92C2×C4—42no—
93C2×C4—42no—
94C2×C4—44no—
95C2×C4—42no—
96C2×C4—82no—
97C2×C4—82no—
98C2×C4—82no—
99C2×C4C22⋊C812yes—
100C2×C4C22×C811yescharacteristic
101C2×C4C2×M1611yescharacteristic
102C8—84no—
103C22—24no—
104C22—24no—
105C22—21no—
106C22—21no—
107C22—21no—
108C22—21no—
109C22#32412yes—
110C22#32412yes—
111C22#35312yes—
112C22#35612yes—
113C22C2×C22⋊C811yescharacteristic
114C22C2×#9911yescharacteristic
115C22C2×#10111yescharacteristic
116C4—28no—
117C4—22no—
118C4—21no—
119C4—21no—
120C4—42no—
121C4—42no—
122C4—82no—
123C2—21no—
124C2—22no—
125C2—21no—
126C2#132514yesdirect product factor
127C2C2×#32411yescharacteristic
128C2C2×#35311yescharacteristic
129C2C2×#35611yescharacteristic
subgroupG/H
center, socleC23#99
commutatorC2×C4C22×C8
Frattini, cosocleC2×C4⋊C4C23
prime radicalC24C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #1325C2direct (N × H)
33. C2×C42C8semidirect
69. C42C2×C8semidirect
126. C2#1325direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#3842
C2×#3242
#13252