Finite Group Databasebeta

← (C22⋊D13)⋊A4 #11929166

Subgroups — (C22⋊D13)⋊A4 #11929166

Order 1248.

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

normal subgroups only

This group has 132 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×C22⋊(C13⋊C3)C211yesmaximal, characteristic, complemented
2C2×D13⋊A4C211yesmaximal, characteristic, complemented
3Dic13⋊A4C211yesmaximal, characteristic, complemented
4C22×C22⋊D13C311yesmaximal, characteristic, complemented, Hall
5C2×C22⋊(C13⋊C3)—21no—
6C2×C22⋊(C13⋊C3)C2211yescharacteristic
7D13⋊A4—21no—
8(C22⋊D13)⋊C3—41nomaximal
9C24×C13C2×C311yescharacteristic, complemented
10C23×D13C2×C311yescharacteristic, complemented
11C2×C22⋊D13—31no—
12C2×C22⋊D13—31no—
13C2×C22⋊D13—31no—
14C2×C22⋊D13—31no—
15C22×Dic13C2×C311yescharacteristic, complemented
16C22⋊(C13⋊C3)D411yescharacteristic, complemented
17C22×C13⋊C3—41no—
18C2×D13⋊C3—41no—
19Dic13⋊C3—41no—
20C23×C13—21no—
21C23×C13—31no—
22C23×C13—31no—
23C23×C13—61no—
24C23×C13C22×C311yescharacteristic
25C22×D13—21no—
26C22×D13—31no—
27C22×D13—31no—
28C22×D13—61no—
29C22⋊D13—32no—
30C22⋊D13—31no—
31C22⋊D13—31no—
32C22⋊D13—31no—
33C22⋊D13A411yescharacteristic, complemented
34C2×Dic13—31no—
35C2×Dic13—31no—
36D4×A4—131nomaximal, Hall
37C2×C13⋊C3—41no—
38C2×C13⋊C3—81no—
39D13⋊C3—81no—
40C22×C13—31no—
41C22×C13—31no—
42C22×C13—31no—
43C22×C13—61no—
44C22×C13—61no—
45C22×C13—61no—
46C22×C13—61no—
47C22×C13C3×D411yescharacteristic, complemented
48C22×C13C2×A411yescharacteristic, complemented
49C2×D13—31no—
50C2×D13—61no—
51C2×D13—61no—
52C2×D13—61no—
53C2×D13—61no—
54C2×D13C2×A411yescharacteristic, complemented
55Dic13—31no—
56Dic13C2×A411yescharacteristic, complemented
57C22×A4—131no—
58C22×A4—131no—
59C4×A4—131no—
60C13⋊C3—41noHall
61C22×D4—131noSylow
62C2×C13—21no—
63C2×C13—31no—
64C2×C13—31no—
65C2×C13—61no—
66C2×C13C22×A411yescharacteristic
67D13—21no—
68D13—61no—
69C2×A4—131no—
70C2×A4—261no—
71C2×A4—261no—
72C3×D4—521no—
73C24—131no—
74C24D13⋊C311yescharacteristic, complemented
75C2×D4—391no—
76C2×D4—391no—
77C2×D4—391no—
78C2×D4—391no—
79C22×C4—131no—
80C13D4×A411yescharacteristic, complemented, Sylow
81C22×C3—521no—
82C22×C3—521no—
83A4—131no—
84C3×C4—521no—
85C23—21no—
86C23—31no—
87C23—31no—
88C23—61no—
89C23—261no—
90C23—391no—
91C23—391no—
92C23—781no—
93C23C2×D13⋊C311yescharacteristic
94D4—131no—
95D4—391no—
96D4—391no—
97D4—392no—
98D4—391no—
99C2×C4—391no—
100C2×C4—391no—
101C2×C3—521no—
102C2×C3—1041no—
103C2×C3—1041no—
104C22—31no—
105C22—31no—
106C22—31no—
107C22—61no—
108C22—61no—
109C22—61no—
110C22—61no—
111C22—131no—
112C22—391no—
113C22—781no—
114C22—781no—
115C22—781no—
116C22—781no—
117C22(C22⋊D13)⋊C311yescharacteristic, complemented
118C22D13⋊A411yescharacteristic, complemented
119C4—131no—
120C4—391no—
121C3—521noSylow
122C2—21no—
123C2—31no—
124C2—31no—
125C2—61no—
126C2—261no—
127C2—781no—
128C2C2×D13⋊A411yescharacteristic
subgroupG/H
center, FrattiniC2C2×D13⋊A4
commutator, socle, cosocleC23×C13C22×C3
FittingC24×C13C2×C3
hypercenterC22D13⋊A4
hypocenterC22×C13C3×D4
LCSG ▷ C23×C13 ▷ C22×C13
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊(C13⋊C3)C2semidirect
2. C2×D13⋊A4C2semidirect
3. Dic13⋊A4C2semidirect
4. C22×C22⋊D13C3semidirect
9. C24×C13C2×C3semidirect
10. C23×D13C2×C3semidirect
15. C22×Dic13C2×C3semidirect
16. C22⋊(C13⋊C3)D4semidirect
33. C22⋊D13A4semidirect
47. C22×C13C3×D4semidirect
48. C22×C13C2×A4semidirect
54. C2×D13C2×A4semidirect
56. Dic13C2×A4semidirect
74. C24D13⋊C3semidirect
80. C13D4×A4semidirect
117. C22(C22⋊D13)⋊C3semidirect
118. C22D13⋊A4semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊(C13⋊C3)2
C2×D13⋊A42
Dic13⋊A42
C22×C22⋊D133
(C22⋊D13)⋊C34
D4×A413