Finite Group Databasebeta

← C4×#356 #12630

Subgroups — C4×#356 #12630

Order 256.

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

normal subgroups only

This group has 250 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
1C4×C4⋊Q8C211yesmaximal, characteristic
2C2×#356C212yesmaximal
3C4×#101C212yesmaximal
4#1394C212yesmaximal
5C2×C4⋊Q8C2211yescharacteristic
6C2×C4×Q8C411yescharacteristic
7C2×C4×Q8C2211yescharacteristic
8C2×#101C2214yes—
9C4×M16—22no—
10#391C411yescharacteristic
11#391C2211yescharacteristic
12#389—22no—
13#384C411yescharacteristic
14C4×C4⋊C4—22no—
15C43C411yescharacteristic
16#356C418yesdirect product factor
17#343—22no—
18C22×Q8C2×C411yescharacteristic
19C22×Q8C2311yescharacteristic
20C2×M16—24no—
21C4⋊Q8—22no—
22C4⋊Q8C2×C414yes—
23C4×Q8—41no—
24C4×Q8—41no—
25C4×Q8—41no—
26C4×Q8—41no—
27C2×C4⋊C4—22no—
28C2×C4⋊C4—21no—
29C2×C4⋊C4—22no—
30C2×C4⋊C4C2×C411yescharacteristic
31C2×C4⋊C4C2×C411yescharacteristic
32C2×C4⋊C4D412yes—
33C2×C42—21no—
34C2×C42—21no—
35C2×C42—21no—
36C2×C42C2×C411yescharacteristic
37C2×C42C2×C411yescharacteristic
38C2×C42C2×C411yescharacteristic
39C2×C42D412yes—
40#101—24no—
41#101C2×C418yes—
42#97—42no—
43C4×C8—42no—
44#95—22no—
45#95—22no—
46C2×Q8—21no—
47C2×Q8—41no—
48C2×Q8—41no—
49C2×Q8—41no—
50C2×Q8—41no—
51C2×Q8C4212yes—
52C2×Q8C22×C412yes—
53C2×Q8#4112yes—
54C22×C4—21no—
55C22×C4—21no—
56C22×C4—21no—
57C22×C4—21no—
58C22×C4C22⋊C412yes—
59C22×C4C22⋊C411yescharacteristic
60C22×C4C22⋊C411yescharacteristic
61C22×C4C22×C411yescharacteristic
62C22×C4C2×D412yes—
63M16—28no—
64M16—44no—
65C2×C8—44no—
66C4⋊C4—28no—
67C4⋊C4—41no—
68C4⋊C4—42no—
69C4⋊C4—41no—
70C4⋊C4—44no—
71C4⋊C4—42no—
72C42—24no—
73C42—22no—
74C42—21no—
75C42—22no—
76C42—21no—
77C42—21no—
78C42—41no—
79C42—42no—
80C42—41no—
81C42—41no—
82C42C4212yes—
83C23C2×C22⋊C411yescharacteristic
84Q8—42no—
85Q8—42no—
86Q8—42no—
87Q8—42no—
88C2×C4—22no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—22no—
93C2×C4—21no—
94C2×C4—22no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—22no—
98C2×C4—21no—
99C2×C4—22no—
100C2×C4—41no—
101C2×C4—41no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—42no—
106C2×C4—42no—
107C2×C4—41no—
108C2×C4#9911yescharacteristic
109C2×C4#9911yescharacteristic
110C2×C4C2×C4211yescharacteristic
111C2×C4#11711yescharacteristic
112C2×C4C4×D414yes—
113C8—48no—
114C22—21no—
115C22—21no—
116C22C4×C22⋊C411yescharacteristic
117C22C2×#9911yescharacteristic
118C22#41011yescharacteristic
119C4—24no—
120C4—21no—
121C4—24no—
122C4—21no—
123C4—21no—
124C4—42no—
125C4—41no—
126C4—42no—
127C4—42no—
128C4—81no—
129C4#35612yesdirect product factor
130C2—21no—
131C2—21no—
132C2C4×#9911yescharacteristic
133C2C2×#35611yescharacteristic
134C2#213211yescharacteristic
subgroupG/H
centerC2×C4#99
commutatorC2×C4C2×C42
Frattini, cosocleC22×Q8C23
socleC22C2×#99
prime radicalC23C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ G
LECSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
16. #356C4direct (N × H)
129. C4#356direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C4⋊Q82
C2×#3562
C4×#1012
#13942