Finite Group Databasebeta

← #11928491

Subgroups — #11928491

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×C13×D12C211yesmaximal, characteristic, complemented
2C3×#6127C211yesmaximal, characteristic, complemented
3#10597662C211yesmaximal, characteristic, complemented
4#10597599C212yesmaximal, complemented
5#10597595C212yesmaximal, complemented
6#88186—31nomaximal, Hall
7C22×D3×C13—21no—
8C2×C3×C4×C13C2211yescharacteristic
9C13×D12—21no—
10C13×D12C2212yes—
11C3×C22⋊D13—21no—
12C3×D52C2211yescharacteristic, complemented
13C3×C4×D13—21no—
14C3×Dic26C2211yescharacteristic, complemented
15C3⋊#1055C2212yescomplemented
16C2×D4×C13—31no—
17#6127D311yescharacteristic, complemented
18#6105—32no—
19#6104—32no—
20#6099—31no—
21C22×C3×C13D411yescharacteristic
22C2×D3×C13—22no—
23C2×D3×C13—42no—
24C2×C3×D13—21no—
25C3×C4×C13D411yescharacteristic
26C3×C4×C13C2311yescharacteristic
27C3×Dic13—21no—
28C23×C13—61no—
29D4×C13—32no—
30D4×C13—61no—
31C2×C4×C13C2×D311yescharacteristic
32C22⋊D13—21no—
33D52C2×D311yescharacteristic, complemented
34C4×D13—21no—
35Dic26C2×D311yescharacteristic, complemented
36#1055—32no—
37#949—131nomaximal, Hall
38C2×C3×C13—21no—
39C2×C3×C13C2×D411yescharacteristic
40C3×D13—41no—
41D3×C13—42no—
42C22×C13—62no—
43C22×C13—122no—
44C22×C13#6711yescharacteristic
45C2×D13—21no—
46C4×C13#6711yescharacteristic
47C4×C13C22×D311yescharacteristic
48Dic13—21no—
49C3×#41—131no—
50C2×D12D1311yescharacteristic, complemented
51#215—132no—
52#213—132no—
53#208—131no—
54C3×C13AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
55AGL(1,ℤ/8)—391noSylow
56C2×C13—21no—
57C2×C13—122no—
58C2×C13C2×#6711yescharacteristic
59D13—41no—
60C22×D3—21no—
61C3×Q8—131no—
62C3×D4—131no—
63C3×D4—261no—
64C2×C3×C4—261no—
65C2×C3×C4C2×D1311yescharacteristic
66D12—21no—
67D12C2×D1312yes—
68C3⋊C8—132no—
69#41—131no—
70C2×D4—31no—
71SD16—392no—
72D8—392no—
73M16—391no—
74C13#94911yescharacteristic, complemented, Sylow
75C22×C3—261no—
76C22×C3C22⋊D1311yescharacteristic
77C2×D3—22no—
78C2×D3—42no—
79C3×C4—261no—
80C3×C4C22⋊D1311yescharacteristic
81C3×C4C22×D1311yescharacteristic
82C23—61no—
83Q8—131no—
84D4—32no—
85D4—61no—
86D4—131no—
87D4—261no—
88C2×C4—261no—
89C2×C4D3×D1311yescharacteristic
90C8—392no—
91C2×C3—21no—
92C2×C3—521no—
93C2×C3C2×C22⋊D1311yescharacteristic
94D3—42no—
95C22—62no—
96C22—122no—
97C22—261no—
98C22#6460211yescharacteristic
99C4—261no—
100C4#6460211yescharacteristic
101C4C2×D3×D1311yescharacteristic
102C3#8818611yescharacteristic, complemented, Sylow
103C2—21no—
104C2—122no—
105C2—521no—
106C2C2×#6460211yescharacteristic
subgroupG/H
centerC2C2×#64602
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×C13×D12C2semidirect
2. C3×#6127C2semidirect
3. #10597662C2semidirect
4. #10597599C2semidirect
5. #10597595C2semidirect
12. C3×D52C22semidirect
14. C3×Dic26C22semidirect
15. C3⋊#1055C22semidirect
17. #6127D3semidirect
33. D52C2×D3semidirect
35. Dic26C2×D3semidirect
50. C2×D12D13semidirect
54. C3×C13AGL(1,ℤ/8)semidirect
74. C13#949semidirect
102. C3#88186semidirect

Maximal subgroups

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

subgroupindex
C2×C13×D122
C3×#61272
#105976622
#105975992
#105975952
#881863
#94913