Finite Group Databasebeta

← C2×C4×C42⋊C3 #73158

Subgroups — C2×C4×C42⋊C3 #73158

Order 384.

252 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 32 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
1C22×C42⋊C3C211yesmaximal, characteristic
2C4×C42⋊C3C212yesmaximal, direct product factor
3C2×C43C311yesmaximal, characteristic, complemented, Sylow
4C2×C4×A4—41nomaximal
5C2×C42⋊C3C412yesdirect product factor
6C2×C42⋊C3C2211yescharacteristic
7C22×C42—31no—
8C22×C42—31no—
9C22×C42C2×C311yescharacteristic
10C43—32no—
11C43C2×C312yescomplemented
12C22×A4—41no—
13C4×A4—42no—
14C42⋊C3C2×C411yescharacteristic, direct product factor
15C23×C4—31no—
16C23×C4—31no—
17C23×C4A411yescharacteristic
18C2×C42—31no—
19C2×C42—32no—
20C2×C42—32no—
21C2×C42—32no—
22C2×C42—38no—
23C2×C42—32no—
24C2×C42—34no—
25C2×C42—32no—
26C2×C42—32no—
27C2×C42—32no—
28C2×C42C3×C412yescomplemented
29C2×C42C22×C311yescharacteristic
30C2×A4—42no—
31C2×A4—41no—
32C2×C3×C4—161no—
33C24C2×A411yescharacteristic
34C22×C4—38no—
35C22×C4—32no—
36C22×C4—34no—
37C22×C4—32no—
38C22×C4—32no—
39C22×C4—32no—
40C22×C4—32no—
41C22×C4—32no—
42C22×C4—31no—
43C22×C4—32no—
44C22×C4—31no—
45C22×C4—31no—
46C22×C4—31no—
47C22×C4—32no—
48C22×C4C2×A412yes—
49C42—32no—
50C42—31no—
51C42—38no—
52C42—38no—
53C42—34no—
54C42—34no—
55C42—34no—
56C42—34no—
57C42—32no—
58C42C2×C3×C411yescharacteristic, complemented
59C22×C3—161no—
60A4—41no—
61C3×C4—162no—
62C23—32no—
63C23—31no—
64C23—31no—
65C23C4×A412yes—
66C23C22×A411yescharacteristic
67C2×C4—32no—
68C2×C4—38no—
69C2×C4—32no—
70C2×C4—32no—
71C2×C4—34no—
72C2×C4—32no—
73C2×C4—34no—
74C2×C4—34no—
75C2×C4—38no—
76C2×C4—38no—
77C2×C4—34no—
78C2×C4—34no—
79C2×C4—32no—
80C2×C4—31no—
81C2×C4—31no—
82C2×C4—32no—
83C2×C4—31no—
84C2×C4—32no—
85C2×C4—32no—
86C2×C4—32no—
87C2×C4C42⋊C311yescharacteristic, direct product factor
88C2×C3—162no—
89C2×C3—161no—
90C22—31no—
91C22—32no—
92C22—32no—
93C22—32no—
94C22—32no—
95C22—31no—
96C22—31no—
97C22C2×C42⋊C311yescharacteristic
98C22C2×C4×A411yescharacteristic
99C4—38no—
100C4—32no—
101C4—32no—
102C4—34no—
103C4—32no—
104C4C2×C42⋊C312yesdirect product factor
105C3—161noSylow
106C2—31no—
107C2—31no—
108C2—32no—
109C2C4×C42⋊C312yesdirect product factor
110C2C22×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C4C42⋊C3
commutator, hypocenterC42C2×C3×C4
FrattiniC23C22×A4
FittingC2×C43C3
socleC24C2×A4
prime radicalC22×C42⋊C3C2
cosocleC2×C42C22×C3
LCSG ▷ C42
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C4×C42⋊C3C2direct (N × H)
3. C2×C43C3semidirect
5. C2×C42⋊C3C4direct (N × H)
11. C43C2×C3semidirect
14. C42⋊C3C2×C4direct (N × H)
28. C2×C42C3×C4semidirect
58. C42C2×C3×C4semidirect
87. C2×C4C42⋊C3direct (N × H)
104. C4C2×C42⋊C3direct (N × H)
109. C2C4×C42⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C42⋊C32
C4×C42⋊C32
C2×C433
C2×C4×A44