Finite Group Databasebeta

← #11928633

Subgroups — #11928633

Order 1248.

124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C3×#6129C211yesmaximal, characteristic, complemented
2#10597739C211yesmaximal, characteristic, complemented
3#10597667C211yesmaximal, characteristic, complemented
4C13×#214C211yesmaximal, characteristic, complemented
5#10597604C211yesmaximal, characteristic, complemented
6#10597601C211yesmaximal, characteristic, complemented
7C3⋊C8×D13C211yesmaximal, characteristic, complemented
8#88170—31nomaximal, Hall
9C3×D4×C13C2211yescharacteristic
10D156C2211yescharacteristic
11C13×Dic6C2211yescharacteristic
12C3×C22⋊D13—21no—
13C2×C3×Dic13—21no—
14C3×C4×D13C2211yescharacteristic
15C3×Dic26C2211yescharacteristic
16#64603—21no—
17#64601—21no—
18C3⋊#1055C2211yescharacteristic
19C13×C3⋊C8C2211yescharacteristic
20#6131—31no—
21#6129D311yescharacteristic, complemented
22C13×SD16—31no—
23#6107—31no—
24#6104—31no—
25#6095—31no—
26C8×D13—31no—
27C22×C3×C13—21no—
28C2×D39—21no—
29C2×C3×D13D411yescharacteristic
30C3×C4×C13C2311yescharacteristic
31C3×Dic13—21no—
32C3×Dic13D411yescharacteristic
33Dic3×C13—21no—
34Q8×C13—31no—
35D4×C13C2×D311yescharacteristic
36C22⋊D13—21no—
37C2×Dic13—21no—
38D52—31no—
39D52—61no—
40C4×D13—61no—
41C4×D13C2×D311yescharacteristic
42Dic26C2×D311yescharacteristic
43C8×C13—31no—
44#1055—31no—
45#950—131nomaximal, Hall
46C2×C3×C13—41no—
47C2×C3×C13C2×D411yescharacteristic
48D39—41no—
49C3×D13—21no—
50C22×C13—21no—
51C2×D13—61no—
52C2×D13#6711yescharacteristic
53C4×C13—61no—
54C4×C13C22×D311yescharacteristic
55Dic13—21no—
56Dic13#6711yescharacteristic
57C3×#41—131no—
58#235—131no—
59#216—131no—
60#215—131no—
61#214D1311yescharacteristic, complemented
62#213—131no—
63C2×C3⋊C8—131no—
64C3×C13#13511yescharacteristic, complemented, Hall
65#135—391noSylow
66C2×C13—41no—
67C2×C13C2×#6711yescharacteristic
68D13—21no—
69D13—121no—
70C3×Q8—131no—
71C3×D4—261no—
72C3×D4C2×D1311yescharacteristic
73C2×C3×C4—131no—
74C2×C3×C4—261no—
75#67—261no—
76D12—131no—
77C4×D3—261no—
78Dic6C2×D1311yescharacteristic
79C3⋊C8—131no—
80C3⋊C8C2×D1311yescharacteristic
81#41—131no—
82#41—391no—
83Q16—391no—
84SD16—31no—
85SD16—391no—
86D8—391no—
87C2×C8—391no—
88C13#95011yescharacteristic, complemented, Sylow
89C22×C3—21no—
90C22×C3—131no—
91C2×D3—261no—
92C3×C4—131no—
93C3×C4—261no—
94C3×C4C22×D1311yescharacteristic
95Dic3—21no—
96Q8—31no—
97Q8—131no—
98D4—261no—
99D4—391no—
100D4—781no—
101D4D3×D1311yescharacteristic
102C2×C4—131no—
103C2×C4—261no—
104C2×C4—781no—
105C8—31no—
106C8—391no—
107C2×C3—41no—
108C2×C3—261no—
109C2×C3D4×D1311yescharacteristic
110D3—521no—
111C22—21no—
112C22—131no—
113C22—781no—
114C4—61no—
115C4—131no—
116C4—261no—
117C4C2×D3×D1311yescharacteristic
118C3#8817011yescharacteristic, complemented, Sylow
119C2—41no—
120C2—261no—
121C2—1561no—
122C2#67×D1311yescharacteristic
subgroupG/H
centerC2#67×D13
commutator, cosocleC3×C4×C13C23
FrattiniC4C2×D3×D13
FittingC3×D4×C13C22
socleC2×C3×C13C2×D4
hypercenterD4D3×D13
hypocenterC3×C13#135
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. C3×#6129C2semidirect
2. #10597739C2semidirect
3. #10597667C2semidirect
4. C13×#214C2semidirect
5. #10597604C2semidirect
6. #10597601C2semidirect
7. C3⋊C8×D13C2semidirect
21. #6129D3semidirect
61. #214D13semidirect
64. C3×C13#135semidirect
88. C13#950semidirect
118. C3#88170semidirect

Maximal subgroups

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

subgroupindex
C3×#61292
#105977392
#105976672
C13×#2142
#105976042
#105976012
C3⋊C8×D132
#881703
#95013