Finite Group Databasebeta

← #11928973

Subgroups — #11928973

Order 1248.

136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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
1#10597792C211yesmaximal, characteristic, complemented
2D4×D39C211yesmaximal, characteristic, complemented
3C3×C13×D8C211yesmaximal, characteristic, complemented
4#10597668C211yesmaximal, characteristic, complemented
5#10597667C211yesmaximal, characteristic, complemented
6#10597658C211yesmaximal, characteristic, complemented
7#10597657C211yesmaximal, characteristic, complemented
8#88165—31nomaximal, Hall
9C22×D39—21no—
10C3×D4×C13C2211yescharacteristic
11C3×D4×C13C2211yescharacteristic, complemented
12#64625—21no—
13#64625—21no—
14C2×Dic39—21no—
15D156C2211yescharacteristic
16C4×D39C2211yescharacteristic
17Dic78C2211yescharacteristic, complemented
18C3×C8×C13C2211yescharacteristic, complemented
19C3⋊#1055C2211yescharacteristic, complemented
20#6129—31no—
21D4×D13—31no—
22C13×D8D311yescharacteristic, complemented
23#6105—31no—
24#6104—31no—
25#6095—31no—
26#6094—31no—
27C22×C3×C13—21no—
28C22×C3×C13—21no—
29C2×D39—21no—
30C2×D39—42no—
31C2×D39D411yescharacteristic
32C3×C4×C13C2311yescharacteristic
33Dic39—21no—
34Dic39D411yescharacteristic
35C22×D13—61no—
36D4×C13C2×D311yescharacteristic
37D4×C13C2×D311yescharacteristic, complemented
38C22⋊D13—61no—
39C22⋊D13—61no—
40C2×Dic13—61no—
41D52—31no—
42C4×D13—31no—
43Dic26—31no—
44C8×C13C2×D311yescharacteristic, complemented
45#1055—31no—
46#911—131nomaximal, Hall
47C2×C3×C13—41no—
48C2×C3×C13—41no—
49C2×C3×C13C2×D411yescharacteristic
50D39—21no—
51D39—41no—
52C22×C13—21no—
53C22×C13—21no—
54C2×D13—31no—
55C2×D13—61no—
56C2×D13—122no—
57C4×C13C22×D311yescharacteristic
58Dic13—31no—
59Dic13—61no—
60#237—131no—
61D3×D4—131no—
62C3×D8D1311yescharacteristic, complemented
63#214—131no—
64#213—131no—
65#204—131no—
66ΓL(1,𝔽25)—131no—
67C3×C13AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
68AGL(1,ℤ/8)—391noSylow
69C2×C13—41no—
70C2×C13—41no—
71C2×C13D3×D411yescharacteristic
72D13—61no—
73D13—121no—
74C22×D3—261no—
75C3×D4C2×D1311yescharacteristic
76C3×D4C2×D1311yescharacteristic, complemented
77#67—261no—
78#67—261no—
79C2×Dic3—261no—
80D12—131no—
81C4×D3—131no—
82Dic6—131no—
83C3×C8C2×D1311yescharacteristic, complemented
84C3⋊C8—131no—
85#41—391no—
86C2×D4—391no—
87SD16—391no—
88SD16—391no—
89D8—391no—
90D8D3911yescharacteristic, complemented
91M16—391no—
92C13#91111yescharacteristic, complemented, Sylow
93C22×C3—21no—
94C22×C3—21no—
95C2×D3—131no—
96C2×D3—261no—
97C2×D3—522no—
98C3×C4C22×D1311yescharacteristic
99Dic3—131no—
100Dic3—261no—
101C23—781no—
102Q8—391no—
103D4—391no—
104D4—781no—
105D4—781no—
106D4C2×D3911yescharacteristic
107D4C2×D3911yescharacteristic, complemented
108C2×C4—391no—
109C2×C4—781no—
110C8—391no—
111C8C2×D3911yescharacteristic, complemented
112C2×C3—41no—
113C2×C3—41no—
114C2×C3D4×D1311yescharacteristic
115D3—261no—
116D3—521no—
117C22—21no—
118C22—21no—
119C22—391no—
120C22—781no—
121C22—1562no—
122C4—391no—
123C4—781no—
124C4C22×D3911yescharacteristic
125C3#8816511yescharacteristic, complemented, Sylow
126C2—41no—
127C2—41no—
128C2—781no—
129C2—1561no—
130C2D4×D3911yescharacteristic
subgroupG/H
centerC2D4×D39
commutator, cosocleC3×C4×C13C23
FrattiniC4C22×D39
FittingC3×C13×D8C2
socleC2×C3×C13C2×D4
hypercenterD8D39
hypocenterC3×C13AGL(1,ℤ/8)
LCSG ▷ C3×C4×C13 ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. #10597792C2semidirect
2. D4×D39C2semidirect
3. C3×C13×D8C2semidirect
4. #10597668C2semidirect
5. #10597667C2semidirect
6. #10597658C2semidirect
7. #10597657C2semidirect
11. C3×D4×C13C22semidirect
17. Dic78C22semidirect
18. C3×C8×C13C22semidirect
19. C3⋊#1055C22semidirect
22. C13×D8D3semidirect
37. D4×C13C2×D3semidirect
44. C8×C13C2×D3semidirect
62. C3×D8D13semidirect
67. C3×C13AGL(1,ℤ/8)semidirect
76. C3×D4C2×D13semidirect
83. C3×C8C2×D13semidirect
90. D8D39semidirect
92. C13#911semidirect
107. D4C2×D39semidirect
111. C8C2×D39semidirect
125. C3#88165semidirect

Maximal subgroups

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

subgroupindex
#105977922
D4×D392
C3×C13×D82
#105976682
#105976672
#105976582
#105976572
#881653
#91113