Finite Group Databasebeta

← #11928639

Subgroups — #11928639

Order 1248.

136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 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
1D4×D39C211yesmaximal, characteristic, complemented
2#10597732C211yesmaximal, characteristic, complemented
3C13×#214C211yesmaximal, characteristic, complemented
4C3×#6104C211yesmaximal, characteristic, complemented
5#10597603C211yesmaximal, characteristic, complemented
6#10597596C211yesmaximal, characteristic, complemented
7#10597594C211yesmaximal, characteristic, complemented
8#88168—31nomaximal, Hall
9C22×D39—21no—
10C3×D4×C13C2211yescharacteristic
11#64625—21no—
12D156C2211yescharacteristic
13C4×D39C2211yescharacteristic
14C13×Dic6C2211yescharacteristic, complemented
15C3×D52C2211yescharacteristic, complemented
16#64603—21no—
17Dic3×D13—21no—
18C3×#1055C2211yescharacteristic, complemented
19C13×C3⋊C8C2211yescharacteristic, complemented
20#6131—31no—
21D4×D13—31no—
22C13×SD16—31no—
23#6106—31no—
24#6104D311yescharacteristic, complemented
25D104—31no—
26#6094—31no—
27C22×C3×C13—21no—
28C2×D39—21no—
29C2×D39—42no—
30C2×D39D411yescharacteristic
31C2×C3×D13—21no—
32C3×C4×C13C2311yescharacteristic
33Dic39D411yescharacteristic
34Dic3×C13—21no—
35C22×D13—61no—
36Q8×C13—31no—
37D4×C13C2×D311yescharacteristic
38C22⋊D13—61no—
39D52—31no—
40D52—61no—
41D52C2×D311yescharacteristic, complemented
42C4×D13—31no—
43C4×D13—61no—
44C8×C13—31no—
45#1055C2×D311yescharacteristic, complemented
46#911—131nomaximal, Hall
47C2×C3×C13—41no—
48C2×C3×C13C2×D411yescharacteristic
49D39—21no—
50D39—41no—
51C3×D13—41no—
52C22×C13—21no—
53C2×D13—21no—
54C2×D13—31no—
55C2×D13—61no—
56C2×D13—122no—
57C4×C13—61no—
58C4×C13C22×D311yescharacteristic
59Dic13—31no—
60#237—131no—
61D3×D4—131no—
62C3×D8—131no—
63#214D1311yescharacteristic, complemented
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×C13D3×D411yescharacteristic
71D13—41no—
72D13—61no—
73D13—121no—
74C22×D3—261no—
75C3×D4—131no—
76C3×D4C2×D1311yescharacteristic
77#67—261no—
78#67—261no—
79C2×Dic3—261no—
80D12—131no—
81C4×D3—131no—
82Dic6C2×D1311yescharacteristic, complemented
83C3×C8—131no—
84C3⋊C8C2×D1311yescharacteristic, complemented
85#41—391no—
86C2×D4—391no—
87SD16—31no—
88SD16—391no—
89D8—131no—
90D8—391no—
91M16—391no—
92C13#91111yescharacteristic, complemented, Sylow
93C22×C3—21no—
94C22×C3—261no—
95C2×D3—131no—
96C2×D3—261no—
97C2×D3—522no—
98C3×C4C22×D1311yescharacteristic
99Dic3—21no—
100Dic3—131no—
101C23—781no—
102Q8—31no—
103D4—131no—
104D4—391no—
105D4—781no—
106D4—781no—
107D4D3×D1311yescharacteristic
108C2×C4—391no—
109C2×C4—781no—
110C8—31no—
111C8—131no—
112C2×C3—41no—
113C2×C3—521no—
114C2×C3D4×D1311yescharacteristic
115D3—261no—
116D3—521no—
117C22—21no—
118C22—261no—
119C22—391no—
120C22—781no—
121C22—1562no—
122C4—61no—
123C4—391no—
124C4C2×D3×D1311yescharacteristic
125C3#8816811yescharacteristic, complemented, Sylow
126C2—41no—
127C2—521no—
128C2—781no—
129C2—1561no—
130C2#1059775611yescharacteristic
subgroupG/H
centerC2#10597756
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. D4×D39C2semidirect
2. #10597732C2semidirect
3. C13×#214C2semidirect
4. C3×#6104C2semidirect
5. #10597603C2semidirect
6. #10597596C2semidirect
7. #10597594C2semidirect
14. C13×Dic6C22semidirect
15. C3×D52C22semidirect
18. C3×#1055C22semidirect
19. C13×C3⋊C8C22semidirect
24. #6104D3semidirect
41. D52C2×D3semidirect
45. #1055C2×D3semidirect
63. #214D13semidirect
67. C3×C13AGL(1,ℤ/8)semidirect
82. Dic6C2×D13semidirect
84. C3⋊C8C2×D13semidirect
92. C13#911semidirect
125. C3#88168semidirect

Maximal subgroups

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

subgroupindex
D4×D392
#105977322
C13×#2142
C3×#61042
#105976032
#105975962
#105975942
#881683
#91113