Finite Group Databasebeta

← #11928504

Subgroups — #11928504

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
1#10597790C211yesmaximal, characteristic, complemented
2C2×C3×D52C211yesmaximal, characteristic, complemented
3C13×#208C211yesmaximal, characteristic, complemented
4#10597600C212yesmaximal, complemented
5#10597596C212yesmaximal, complemented
6#88162—31nomaximal, Hall
7C22×C3×D13—21no—
8C2×C3×C4×C13C2211yescharacteristic
9#64625—21no—
10D156C2211yescharacteristic, complemented
11C4×D39—21no—
12Dic78C2211yescharacteristic, complemented
13C3×D52—21no—
14C3×D52C2212yes—
15C13×C3⋊C8C2212yescomplemented
16#6127—31no—
17C2×D52D311yescharacteristic, complemented
18C13×M16—31no—
19D104—32no—
20#6095—32no—
21C22×C3×C13D411yescharacteristic
22C2×D39—21no—
23C2×C3×D13—22no—
24C2×C3×D13—42no—
25C3×C4×C13D411yescharacteristic
26C3×C4×C13C2311yescharacteristic
27Dic39—21no—
28C22×D13—21no—
29C2×C4×C13C2×D311yescharacteristic
30C22⋊D13—61no—
31D52—21no—
32D52—31no—
33D52C2×D312yes—
34C4×D13—61no—
35Dic26—31no—
36C8×C13—32no—
37#932—131nomaximal, Hall
38C2×C3×C13—21no—
39C2×C3×C13C2×D411yescharacteristic
40D39—41no—
41C3×D13—42no—
42C22×C13#6711yescharacteristic
43C2×D13—22no—
44C2×D13—42no—
45C2×D13—61no—
46C4×C13#6711yescharacteristic
47C4×C13C22×D311yescharacteristic
48Dic13—61no—
49C2×C3×D4—131no—
50#235—131no—
51#214—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—42no—
59D13—121no—
60C23×C3—261no—
61C3×D4—132no—
62C3×D4—261no—
63C2×C3×C4C2×D1311yescharacteristic
64#67—261no—
65D12—131no—
66C4×D3—261no—
67Dic6—131no—
68C3⋊C8C2×D1312yescomplemented
69#41—391no—
70C2×D4—131no—
71SD16—392no—
72D8—392no—
73M16—31no—
74C13#93211yescharacteristic, complemented, Sylow
75C22×C3—262no—
76C22×C3—522no—
77C22×C3D5211yescharacteristic
78C2×D3—261no—
79C3×C4D5211yescharacteristic
80C3×C4C22×D1311yescharacteristic
81Dic3—261no—
82C23—261no—
83Q8—391no—
84D4—132no—
85D4—261no—
86D4—391no—
87D4—781no—
88C2×C4—781no—
89C2×C4D3×D1311yescharacteristic
90C8—32no—
91C2×C3—21no—
92C2×C3—522no—
93C2×C3C2×D5211yescharacteristic
94D3—521no—
95C22—262no—
96C22—522no—
97C22—781no—
98C22#6460311yescharacteristic
99C4—781no—
100C4#6460311yescharacteristic
101C4C2×D3×D1311yescharacteristic
102C3#8816211yescharacteristic, complemented, Sylow
103C2—21no—
104C2—522no—
105C2—1561no—
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. #10597790C2semidirect
2. C2×C3×D52C2semidirect
3. C13×#208C2semidirect
4. #10597600C2semidirect
5. #10597596C2semidirect
10. D156C22semidirect
12. Dic78C22semidirect
15. C13×C3⋊C8C22semidirect
17. C2×D52D3semidirect
53. #208D13semidirect
54. C3×C13AGL(1,ℤ/8)semidirect
68. C3⋊C8C2×D13semidirect
74. C13#932semidirect
102. C3#88162semidirect

Maximal subgroups

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

subgroupindex
#105977902
C2×C3×D522
C13×#2082
#105976002
#105975962
#881623
#93213