Finite Group Databasebeta

← #11928493

Subgroups — #11928493

Order 1248.

136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C2×D156C211yesmaximal, characteristic, complemented
2C3×#6127C211yesmaximal, characteristic, complemented
3C13×#208C211yesmaximal, characteristic, complemented
4#10597601C212yesmaximal, complemented
5#10597596C212yesmaximal, complemented
6#88162—31nomaximal, Hall
7C22×D39—21no—
8C2×C3×C4×C13C2211yescharacteristic
9D156—21no—
10D156C2212yes—
11C3×C22⋊D13—21no—
12C3×D52C2211yescharacteristic, complemented
13C3×C4×D13—21no—
14C3×Dic26C2211yescharacteristic, complemented
15C13×C3⋊C8C2212yescomplemented
16#6127D311yescharacteristic, complemented
17C2×D52—31no—
18C13×M16—31no—
19D104—32no—
20#6095—32no—
21C22×C3×C13D411yescharacteristic
22C2×D39—22no—
23C2×D39—42no—
24C2×C3×D13—21no—
25C3×C4×C13D411yescharacteristic
26C3×C4×C13C2311yescharacteristic
27C3×Dic13—21no—
28C22×D13—61no—
29C2×C4×C13C2×D311yescharacteristic
30C22⋊D13—21no—
31D52—32no—
32D52—61no—
33D52C2×D311yescharacteristic, complemented
34C4×D13—21no—
35Dic26C2×D311yescharacteristic, complemented
36C8×C13—32no—
37#949—131nomaximal, Hall
38C2×C3×C13—21no—
39C2×C3×C13C2×D411yescharacteristic
40D39—42no—
41C3×D13—41no—
42C22×C13#6711yescharacteristic
43C2×D13—21no—
44C2×D13—62no—
45C2×D13—122no—
46C4×C13#6711yescharacteristic
47C4×C13C22×D311yescharacteristic
48Dic13—21no—
49C3×#41—131no—
50C2×D12—131no—
51#215—132no—
52#213—132no—
53#208D1311yescharacteristic, complemented
54C3×C13AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
55AGL(1,ℤ/8)—391noSylow
56C2×C13—21no—
57C2×C13C2×#6711yescharacteristic
58D13—41no—
59D13—122no—
60C22×D3—261no—
61C3×Q8—131no—
62C3×D4—131no—
63C3×D4—261no—
64C2×C3×C4—261no—
65C2×C3×C4C2×D1311yescharacteristic
66D12—132no—
67D12—261no—
68C3⋊C8C2×D1312yescomplemented
69#41—131no—
70C2×D4—391no—
71SD16—392no—
72D8—392no—
73M16—31no—
74C13#94911yescharacteristic, complemented, Sylow
75C22×C3—261no—
76C22×C3D5211yescharacteristic
77C2×D3—262no—
78C2×D3—522no—
79C3×C4—261no—
80C3×C4D5211yescharacteristic
81C3×C4C22×D1311yescharacteristic
82C23—781no—
83Q8—131no—
84D4—131no—
85D4—261no—
86D4—392no—
87D4—781no—
88C2×C4—261no—
89C2×C4D3×D1311yescharacteristic
90C8—32no—
91C2×C3—21no—
92C2×C3—521no—
93C2×C3C2×D5211yescharacteristic
94D3—522no—
95C22—261no—
96C22—782no—
97C22—1562no—
98C22#6460311yescharacteristic
99C4—261no—
100C4#6460311yescharacteristic
101C4C2×D3×D1311yescharacteristic
102C3#8816211yescharacteristic, complemented, Sylow
103C2—21no—
104C2—521no—
105C2—1562no—
106C2C2×#6460311yescharacteristic
subgroupG/H
centerC2C2×#64603
commutator, cosocleC3×C4×C13C23
FrattiniC4C2×D3×D13
FittingC2×C3×C4×C13C22
socleC2×C3×C13C2×D4
hypercenterC2×C4D3×D13
hypocenterC3×C13AGL(1,ℤ/8)
LCSG ▷ C3×C4×C13 ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×D156C2semidirect
2. C3×#6127C2semidirect
3. C13×#208C2semidirect
4. #10597601C2semidirect
5. #10597596C2semidirect
12. C3×D52C22semidirect
14. C3×Dic26C22semidirect
15. C13×C3⋊C8C22semidirect
16. #6127D3semidirect
33. D52C2×D3semidirect
35. Dic26C2×D3semidirect
53. #208D13semidirect
54. C3×C13AGL(1,ℤ/8)semidirect
68. C3⋊C8C2×D13semidirect
74. C13#949semidirect
102. C3#88162semidirect

Maximal subgroups

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

subgroupindex
C2×D1562
C3×#61272
C13×#2082
#105976012
#105975962
#881623
#94913