Finite Group Databasebeta

← #11928999

Subgroups — #11928999

Order 1248.

136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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×C3×D4×C13C211yesmaximal, characteristic, complemented
2#10597790C211yesmaximal, characteristic, complemented
3#10597668C212yesmaximal, complemented
4#10597667C212yesmaximal, complemented
5#10597662C211yesmaximal, characteristic, complemented
6#88186—31nomaximal, Hall
7C23×C3×C13—21no—
8C3×D4×C13—21no—
9C3×D4×C13C2212yes—
10C2×C3×C4×C13C2211yescharacteristic
11#64625—21no—
12D156C2211yescharacteristic, complemented
13C4×D39—21no—
14Dic78C2211yescharacteristic, complemented
15C3⋊#1055C2212yescomplemented
16C2×D4×C13D311yescharacteristic, complemented
17#6127—31no—
18#6105—32no—
19#6104—32no—
20#6099—31no—
21C22×C3×C13—22no—
22C22×C3×C13—42no—
23C22×C3×C13D411yescharacteristic
24C2×D39—21no—
25C3×C4×C13D411yescharacteristic
26C3×C4×C13C2311yescharacteristic
27Dic39—21no—
28C23×C13—21no—
29D4×C13—21no—
30D4×C13C2×D312yes—
31C2×C4×C13C2×D311yescharacteristic
32C22⋊D13—61no—
33D52—31no—
34C4×D13—61no—
35Dic26—31no—
36#1055—32no—
37#932—131nomaximal, Hall
38C2×C3×C13—21no—
39C2×C3×C13—42no—
40C2×C3×C13C2×D411yescharacteristic
41D39—41no—
42C22×C13—22no—
43C22×C13—42no—
44C22×C13#6711yescharacteristic
45C2×D13—61no—
46C4×C13#6711yescharacteristic
47C4×C13C22×D311yescharacteristic
48Dic13—61no—
49C2×C3×D4D1311yescharacteristic, complemented
50#235—131no—
51#214—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—42no—
58C2×C13C2×#6711yescharacteristic
59D13—121no—
60C23×C3—21no—
61C3×D4—21no—
62C3×D4C2×D1312yes—
63C2×C3×C4C2×D1311yescharacteristic
64#67—261no—
65D12—131no—
66C4×D3—261no—
67Dic6—131no—
68C3⋊C8—132no—
69#41—391no—
70C2×D4D3911yescharacteristic, complemented
71SD16—392no—
72D8—392no—
73M16—391no—
74C13#93211yescharacteristic, complemented, Sylow
75C22×C3—22no—
76C22×C3—42no—
77C22×C3C22⋊D1311yescharacteristic
78C2×D3—261no—
79C3×C4C22⋊D1311yescharacteristic
80C3×C4C22×D1311yescharacteristic
81Dic3—261no—
82C23—21no—
83Q8—391no—
84D4—21no—
85D4—391no—
86D4—781no—
87D4C2×D3912yes—
88C2×C4—781no—
89C2×C4C2×D3911yescharacteristic
90C8—392no—
91C2×C3—21no—
92C2×C3—42no—
93C2×C3C2×C22⋊D1311yescharacteristic
94D3—521no—
95C22—22no—
96C22—42no—
97C22—781no—
98C22#6462511yescharacteristic
99C4—781no—
100C4#6462511yescharacteristic
101C4C22×D3911yescharacteristic
102C3#8818611yescharacteristic, complemented, Sylow
103C2—21no—
104C2—42no—
105C2—1561no—
106C2C2×#6462511yescharacteristic
subgroupG/H
centerC2C2×#64625
commutator, cosocleC3×C4×C13C23
FrattiniC4C22×D39
FittingC2×C3×D4×C13C2
socleC2×C3×C13C2×D4
hypercenterC2×D4D39
hypocenterC3×C13AGL(1,ℤ/8)
LCSG ▷ C3×C4×C13 ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C13C2semidirect
2. #10597790C2semidirect
3. #10597668C2semidirect
4. #10597667C2semidirect
5. #10597662C2semidirect
12. D156C22semidirect
14. Dic78C22semidirect
15. C3⋊#1055C22semidirect
16. C2×D4×C13D3semidirect
49. C2×C3×D4D13semidirect
54. C3×C13AGL(1,ℤ/8)semidirect
70. C2×D4D39semidirect
74. C13#932semidirect
102. C3#88186semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C132
#105977902
#105976682
#105976672
#105976622
#881863
#93213