Finite Group Databasebeta

← #11928632

Subgroups — #11928632

Order 1248.

136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C3×D4×D13C211yesmaximal, characteristic, complemented
2#10597739C211yesmaximal, characteristic, complemented
3#10597667C211yesmaximal, characteristic, complemented
4C13×#214C211yesmaximal, characteristic, complemented
5#10597598C211yesmaximal, characteristic, complemented
6#10597596C211yesmaximal, characteristic, complemented
7#10597592C211yesmaximal, characteristic, complemented
8#88168—31nomaximal, Hall
9C22×C3×D13—21no—
10C3×D4×C13C2211yescharacteristic
11D156C2211yescharacteristic, complemented
12C13×Dic6C2211yescharacteristic, complemented
13C3×C22⋊D13—21no—
14C3×D52C2211yescharacteristic
15C3×C4×D13C2211yescharacteristic
16#64603—21no—
17#64601—21no—
18C3⋊#1055C2211yescharacteristic, complemented
19C13×C3⋊C8C2211yescharacteristic, complemented
20#6131—31no—
21D4×D13D311yescharacteristic, complemented
22C13×SD16—31no—
23#6106—31no—
24#6104—31no—
25D104—31no—
26#6094—31no—
27C22×C3×C13—21no—
28C2×D39—21no—
29C2×C3×D13—21no—
30C2×C3×D13—42no—
31C2×C3×D13D411yescharacteristic
32C3×C4×C13C2311yescharacteristic
33C3×Dic13D411yescharacteristic
34Dic3×C13—21no—
35C22×D13—21no—
36Q8×C13—31no—
37D4×C13C2×D311yescharacteristic
38C22⋊D13—21no—
39D52—31no—
40D52—61no—
41D52C2×D311yescharacteristic
42C4×D13—61no—
43C4×D13C2×D311yescharacteristic
44C8×C13—31no—
45#1055—31no—
46#932—131nomaximal, Hall
47C2×C3×C13—41no—
48C2×C3×C13C2×D411yescharacteristic
49D39—41no—
50C3×D13—21no—
51C3×D13—41no—
52C22×C13—21no—
53C2×D13—21no—
54C2×D13—42no—
55C2×D13—61no—
56C2×D13#6711yescharacteristic
57C4×C13—61no—
58C4×C13C22×D311yescharacteristic
59Dic13#6711yescharacteristic
60C2×C3×D4—131no—
61#235—131no—
62#214—131no—
63#214D1311yescharacteristic, complemented
64#213—131no—
65#213—131no—
66#208—131no—
67C3×C13AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
68AGL(1,ℤ/8)—391noSylow
69C2×C13—41no—
70C2×C13C2×#6711yescharacteristic
71D13—21no—
72D13—41no—
73D13—121no—
74C23×C3—261no—
75C3×D4—131no—
76C3×D4—261no—
77C3×D4C2×D1311yescharacteristic
78C2×C3×C4—131no—
79#67—261no—
80D12—131no—
81C4×D3—261no—
82Dic6C2×D1311yescharacteristic, complemented
83C3⋊C8—131no—
84C3⋊C8C2×D1311yescharacteristic, complemented
85#41—391no—
86C2×D4—131no—
87SD16—31no—
88SD16—391no—
89D8—391no—
90D8—391no—
91M16—391no—
92C13#93211yescharacteristic, complemented, Sylow
93C22×C3—21no—
94C22×C3—131no—
95C22×C3—261no—
96C22×C3—522no—
97C2×D3—261no—
98C3×C4—131no—
99C3×C4C22×D1311yescharacteristic
100Dic3—21no—
101C23—261no—
102Q8—31no—
103D4—131no—
104D4—261no—
105D4—391no—
106D4—781no—
107D4D3×D1311yescharacteristic
108C2×C4—131no—
109C2×C4—781no—
110C8—31no—
111C8—391no—
112C2×C3—41no—
113C2×C3—261no—
114C2×C3—521no—
115C2×C3D4×D1311yescharacteristic
116D3—521no—
117C22—21no—
118C22—131no—
119C22—261no—
120C22—522no—
121C22—781no—
122C4—61no—
123C4—131no—
124C4C2×D3×D1311yescharacteristic
125C3#8816811yescharacteristic, complemented, Sylow
126C2—41no—
127C2—261no—
128C2—521no—
129C2—1561no—
130C2#67×D1311yescharacteristic
subgroupG/H
centerC2#67×D13
commutator, cosocleC3×C4×C13C23
FrattiniC4C2×D3×D13
FittingC3×D4×C13C22
socleC2×C3×C13C2×D4
hypercenterD4D3×D13
hypocenterC3×C13AGL(1,ℤ/8)
LCSG ▷ C3×C4×C13 ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×D13C2semidirect
2. #10597739C2semidirect
3. #10597667C2semidirect
4. C13×#214C2semidirect
5. #10597598C2semidirect
6. #10597596C2semidirect
7. #10597592C2semidirect
11. D156C22semidirect
12. C13×Dic6C22semidirect
18. C3⋊#1055C22semidirect
19. C13×C3⋊C8C22semidirect
21. D4×D13D3semidirect
63. #214D13semidirect
67. C3×C13AGL(1,ℤ/8)semidirect
82. Dic6C2×D13semidirect
84. C3⋊C8C2×D13semidirect
92. C13#932semidirect
125. C3#88168semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D132
#105977392
#105976672
C13×#2142
#105975982
#105975962
#105975922
#881683
#93213