Finite Group Databasebeta

← D4×C42⋊C3 #73162

Subgroups — D4×C42⋊C3 #73162

Order 384.

194 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 24 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⋊C3C212yesmaximal, complemented
2C4×C42⋊C3C211yesmaximal, characteristic, complemented
3C42×D4C311yesmaximal, characteristic, complemented, Sylow
4D4×A4—41nomaximal
5C2×C42⋊C3—22no—
6C2×C42⋊C3C2211yescharacteristic
7C2×C4×D4—31no—
8C22×C42C2×C312yescomplemented
9C4×C4⋊C4—31no—
10C4×C22⋊C4—32no—
11C43C2×C311yescharacteristic, complemented
12C22×A4—42no—
13C4×A4—41no—
14C42⋊C3D411yescharacteristic, direct product factor
15C22×D4A411yescharacteristic
16C23×C4—32no—
17C4×D4—32no—
18C4×D4—32no—
19C4×D4—34no—
20C2×C4⋊C4—31no—
21C2×C22⋊C4—32no—
22C2×C42—22no—
23C2×C42—31no—
24C2×C42—31no—
25C2×C42—32no—
26C2×C42—62no—
27C2×C42C22×C311yescharacteristic
28#95—32no—
29C2×A4—41no—
30C2×A4—82no—
31C3×D4—161no—
32C24C2×A412yes—
33C2×D4—31no—
34C2×D4—31no—
35C2×D4—32no—
36C22×C4—31no—
37C22×C4—34no—
38C22×C4—34no—
39C22×C4—31no—
40C22×C4—32no—
41C22×C4—62no—
42C22×C4—62no—
43C22×C4—64no—
44C22×C4C2×A411yescharacteristic
45C4⋊C4—32no—
46C4⋊C4—32no—
47C22⋊C4—34no—
48C22⋊C4—34no—
49C42—31no—
50C42—32no—
51C42—32no—
52C42—62no—
53C42—62no—
54C42—62no—
55C42C3×D411yescharacteristic, complemented
56C22×C3—162no—
57A4—41no—
58C3×C4—161no—
59C23—22no—
60C23—32no—
61C23—32no—
62C23—62no—
63C23C22×A411yescharacteristic
64D4—32no—
65D4—32no—
66D4—31no—
67D4C42⋊C311yescharacteristic, direct product factor
68C2×C4—32no—
69C2×C4—32no—
70C2×C4—31no—
71C2×C4—31no—
72C2×C4—31no—
73C2×C4—31no—
74C2×C4—32no—
75C2×C4—34no—
76C2×C4—64no—
77C2×C4—64no—
78C2×C4—64no—
79C2×C4—64no—
80C2×C4—62no—
81C2×C4—62no—
82C2×C4—62no—
83C2×C3—161no—
84C2×C3—322no—
85C22—31no—
86C22—31no—
87C22—32no—
88C22—62no—
89C22—62no—
90C22—62no—
91C22—62no—
92C22C2×C42⋊C312yescomplemented
93C22D4×A411yescharacteristic
94C4—32no—
95C4—32no—
96C4—31no—
97C4—62no—
98C4—64no—
99C4C2×C42⋊C311yescharacteristic, complemented
100C3—161noSylow
101C2—22no—
102C2—31no—
103C2—31no—
104C2—62no—
105C2C22×C42⋊C311yescharacteristic
subgroupG/H
centerC2C22×C42⋊C3
commutator, cosocleC2×C42C22×C3
Frattini, socleC23C22×A4
FittingC42×D4C3
hypercenterD4C42⋊C3
hypocenterC42C3×D4
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×C42⋊C3C2semidirect
2. C4×C42⋊C3C2semidirect
3. C42×D4C3semidirect
8. C22×C42C2×C3semidirect
11. C43C2×C3semidirect
14. C42⋊C3D4direct (N × H)
55. C42C3×D4semidirect
67. D4C42⋊C3direct (N × H)
92. C22C2×C42⋊C3semidirect
99. C4C2×C42⋊C3semidirect

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
C42×D43
D4×A44