Finite Group Databasebeta

← C4×D13⋊A4 #11929157

Subgroups — C4×D13⋊A4 #11929157

Order 1248.

132 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 30 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×D13⋊A4C211yesmaximal, characteristic
2C4×C22⋊(C13⋊C3)C211yesmaximal, characteristic, complemented
3Dic13⋊A4C211yesmaximal, characteristic, complemented
4C22×C4×D13C311yesmaximal, characteristic, complemented, Hall
5C2×C22⋊(C13⋊C3)C2211yescharacteristic
6D13⋊A4C412yesdirect product factor
7C4×D13⋊C3—41nomaximal
8C23×D13C2×C311yescharacteristic
9C22×C4×C13C2×C311yescharacteristic, complemented
10C22×Dic13C2×C311yescharacteristic, complemented
11C2×C4×D13—31no—
12C2×C4×D13—31no—
13C2×C4×D13—31no—
14C2×C4×D13—31no—
15C22⋊(C13⋊C3)C2×C411yescharacteristic, complemented
16C2×D13⋊C3—41no—
17C4×C13⋊C3—41no—
18Dic13⋊C3—41no—
19C23×C13C22×C311yescharacteristic
20C22×D13—31no—
21C22×D13—31no—
22C22×D13—32no—
23C22×D13C3×C412yescomplemented
24C2×C4×C13—31no—
25C2×C4×C13—31no—
26C2×Dic13—31no—
27C2×Dic13—31no—
28C4×D13—32no—
29C4×D13—31no—
30C4×D13—31no—
31C4×D13—31no—
32C4×D13A411yescharacteristic, complemented
33C2×C4×A4—131nomaximal, Hall
34C2×C13⋊C3—41no—
35D13⋊C3—42no—
36C22×C13—31no—
37C22×C13—31no—
38C22×C13C2×C3×C411yescharacteristic, complemented
39C2×D13—32no—
40C2×D13—31no—
41C2×D13—32no—
42C2×D13—32no—
43C2×D13—32no—
44C2×D13C2×A411yescharacteristic
45C4×C13—31no—
46C4×C13C2×A411yescharacteristic, complemented
47Dic13—31no—
48Dic13C2×A411yescharacteristic, complemented
49C22×A4—131no—
50C4×A4—131no—
51C4×A4—131no—
52C13⋊C3—41noHall
53C23×C4—131noSylow
54C2×C13—31no—
55C2×C13—31no—
56C2×C13C22×A411yescharacteristic
57D13—32no—
58D13C4×A412yescomplemented
59C2×A4—132no—
60C2×A4—131no—
61C2×C3×C4—521no—
62C24—131no—
63C22×C4—131no—
64C22×C4—391no—
65C22×C4—391no—
66C22×C4—391no—
67C22×C4—391no—
68C22×C4D13⋊C311yescharacteristic, complemented
69C13C2×C4×A411yescharacteristic, complemented, Sylow
70C22×C3—521no—
71A4—131no—
72C3×C4—521no—
73C3×C4—521no—
74C23—132no—
75C23—391no—
76C23—391no—
77C23—392no—
78C23C2×D13⋊C311yescharacteristic
79C2×C4—31no—
80C2×C4—31no—
81C2×C4—131no—
82C2×C4—391no—
83C2×C4—391no—
84C2×C4—392no—
85C2×C4—391no—
86C2×C4—391no—
87C2×C4—391no—
88C2×C3—522no—
89C2×C3—521no—
90C22—31no—
91C22—31no—
92C22—131no—
93C22—392no—
94C22—392no—
95C22—392no—
96C22—392no—
97C22—391no—
98C22C4×D13⋊C311yescharacteristic, complemented
99C4—31no—
100C4—131no—
101C4—391no—
102C4D13⋊A411yescharacteristic, direct product factor
103C3—521noSylow
104C2—31no—
105C2—31no—
106C2—132no—
107C2—392no—
108C2C2×D13⋊A411yescharacteristic
subgroupG/H
center, hypercenterC4D13⋊A4
commutator, hypocenterC22×C13C2×C3×C4
FrattiniC2C2×D13⋊A4
FittingC22×C4×C13C2×C3
socle, cosocleC23×C13C22×C3
prime radicalC2×D13⋊A4C2
LCSG ▷ C22×C13
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊(C13⋊C3)C2semidirect
3. Dic13⋊A4C2semidirect
4. C22×C4×D13C3semidirect
6. D13⋊A4C4direct (N × H)
9. C22×C4×C13C2×C3semidirect
10. C22×Dic13C2×C3semidirect
15. C22⋊(C13⋊C3)C2×C4semidirect
23. C22×D13C3×C4semidirect
32. C4×D13A4semidirect
38. C22×C13C2×C3×C4semidirect
46. C4×C13C2×A4semidirect
48. Dic13C2×A4semidirect
58. D13C4×A4semidirect
68. C22×C4D13⋊C3semidirect
69. C13C2×C4×A4semidirect
98. C22C4×D13⋊C3semidirect
102. C4D13⋊A4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13⋊A42
C4×C22⋊(C13⋊C3)2
Dic13⋊A42
C22×C4×D133
C4×D13⋊C34
C2×C4×A413