Finite Group Databasebeta

← #11929129

Subgroups — #11929129

Order 1248.

124 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 21 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×A4×C13C211yesmaximal, characteristic, complemented
2C2×A4⋊D13C211yesmaximal, characteristic, complemented
3A4⋊Dic13C211yesmaximal, characteristic, complemented
4#88207—31nomaximal, Hall
5C2×A4×C13—21no—
6C2×A4×C13C2211yescharacteristic
7A4⋊D13—21no—
8#64625—41nomaximal
9C24×C13D311yescharacteristic, complemented
10C2×C22⋊D13—31no—
11C2×C22⋊D13—31no—
12C2×C22⋊D13—31no—
13C22⋊Dic13—31no—
14C22⋊Dic13—31no—
15C22⋊Dic13—31no—
16C22×C3×C13—41no—
17C2×D39—41no—
18A4×C13D411yescharacteristic, complemented
19Dic39—41no—
20C23×C13—21no—
21C23×C13—31no—
22C23×C13—31no—
23C23×C13—61no—
24C23×C13C2×D311yescharacteristic
25C22×D13—31no—
26C22⋊D13—61no—
27C22⋊D13—62no—
28C22⋊D13—61no—
29C22⋊D13—61no—
30C22⋊D13—61no—
31C2×Dic13—31no—
32C2×Dic13—31no—
33C2×Dic13—31no—
34GL(2,ℤ/4)—131nomaximal, Hall
35C2×C3×C13—41no—
36C2×C3×C13—81no—
37D39—81no—
38C22×C13—31no—
39C22×C13—31no—
40C22×C13—32no—
41C22×C13—31no—
42C22×C13—61no—
43C22×C13—61no—
44C22×C13—61no—
45C22×C13#6711yescharacteristic, complemented
46C22×C13S411yescharacteristic, complemented
47C2×D13—61no—
48C2×D13—61no—
49C2×D13—61no—
50Dic13—61no—
51Dic13—61no—
52Dic13—61no—
53C22×A4D1311yescharacteristic, complemented
54C2×S4—131no—
55SL(2,ℤ/4)—131no—
56C3×C13—41noHall
57#120—391noSylow
58C2×C13—21no—
59C2×C13—31no—
60C2×C13—31no—
61C2×C13—61no—
62C2×C13C2×S411yescharacteristic
63D13—121no—
64C2×A4—21no—
65C2×A4C2×D1311yescharacteristic
66S4—261no—
67#67—521no—
68C24D3911yescharacteristic, complemented
69C2×D4—391no—
70C2×D4—391no—
71C2×D4—391no—
72C22⋊C4—391no—
73C22⋊C4—391no—
74C22⋊C4—391no—
75C13GL(2,ℤ/4)11yescharacteristic, complemented, Sylow
76C22×C3—41no—
77C2×D3—521no—
78A4C22⋊D1311yescharacteristic, complemented
79Dic3—521no—
80C23—21no—
81C23—31no—
82C23—31no—
83C23—61no—
84C23—391no—
85C23C2×D3911yescharacteristic
86D4—781no—
87D4—782no—
88D4—781no—
89D4—781no—
90D4—781no—
91C2×C4—391no—
92C2×C4—391no—
93C2×C4—391no—
94C2×C3—41no—
95C2×C3—81no—
96D3—1041no—
97C22—31no—
98C22—31no—
99C22—32no—
100C22—31no—
101C22—61no—
102C22—61no—
103C22—61no—
104C22—781no—
105C22—781no—
106C22—781no—
107C22#6462511yescharacteristic, complemented
108C22A4⋊D1311yescharacteristic, complemented
109C4—781no—
110C4—781no—
111C4—781no—
112C3—41noSylow
113C2—21no—
114C2—31no—
115C2—31no—
116C2—61no—
117C2—1561no—
118C2C2×A4⋊D1311yescharacteristic
subgroupG/H
center, FrattiniC2C2×A4⋊D13
commutator, cosocleC2×A4×C13C22
FittingC24×C13D3
socleC23×C13C2×D3
hypercenterC22A4⋊D13
hypocenterA4×C13D4
LCSG ▷ C2×A4×C13 ▷ A4×C13
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×A4×C13C2semidirect
2. C2×A4⋊D13C2semidirect
3. A4⋊Dic13C2semidirect
9. C24×C13D3semidirect
18. A4×C13D4semidirect
45. C22×C13#67semidirect
46. C22×C13S4semidirect
53. C22×A4D13semidirect
68. C24D39semidirect
75. C13GL(2,ℤ/4)semidirect
78. A4C22⋊D13semidirect
107. C22#64625semidirect
108. C22A4⋊D13semidirect

Maximal subgroups

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

subgroupindex
C22×A4×C132
C2×A4⋊D132
A4⋊Dic132
#882073
#646254
GL(2,ℤ/4)13