Finite Group Databasebeta

← #11928607

Subgroups — #11928607

Order 1248.

136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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×Dic78C211yesmaximal, characteristic
2C2×#64605C211yesmaximal, characteristic
3C13×Dic3⋊C4C211yesmaximal, characteristic
4C3×#6101C211yesmaximal, characteristic
5Dic3⋊Dic13C211yesmaximal, characteristic
6#10597611C211yesmaximal, characteristic
7Dic3×Dic13C211yesmaximal, characteristic
8#88142—31nomaximal, Hall
9C2×C3×C4×C13C2211yescharacteristic
10C2×Dic39C2211yescharacteristic
11C2×Dic39C2211yescharacteristic
12Dic78—22no—
13C2×Dic3×C13C2211yescharacteristic
14C2×Dic3×C13C2211yescharacteristic
15C2×C3×Dic13C2211yescharacteristic
16C2×C3×Dic13C2211yescharacteristic
17#64605—22no—
18C2×Dic26—31no—
19C2×Dic26—31no—
20C13×C4⋊C4—31no—
21C4⋊Dic13—31no—
22#6101—31no—
23#6101D311yescharacteristic
24C4×Dic13—31no—
25C22×C3×C13C2311yescharacteristic
26C3×C4×C13—21no—
27Dic39—21no—
28Dic39D412yes—
29C3×Dic13—21no—
30C3×Dic13Q812yescomplemented
31Dic3×C13—21no—
32Dic3×C13Q812yescomplemented
33C2×C4×C13—31no—
34C2×C4×C13—31no—
35C2×C4×C13C2×D311yescharacteristic
36C2×Dic13—31no—
37C2×Dic13—31no—
38C2×Dic13C2×D311yescharacteristic
39C2×Dic13C2×D311yescharacteristic
40Dic26—62no—
41Dic26—62no—
42#888—131nomaximal, Hall
43C2×C3×C13C2×D411yescharacteristic
44C2×C3×C13C2×Q811yescharacteristic
45C2×C3×C13C2×Q811yescharacteristic
46C22×C13C22×D311yescharacteristic
47C4×C13—21no—
48C4×C13—32no—
49C4×C13—61no—
50Dic13—21no—
51Dic13—32no—
52Dic13—61no—
53Dic13Dic612yescomplemented
54C2×Dic6—131no—
55C2×Dic6—131no—
56C3×C4⋊C4—131no—
57C4⋊Dic3—131no—
58Dic3⋊C4—131no—
59Dic3⋊C4D1311yescharacteristic
60C4×Dic3—131no—
61C3×C13C4⋊Q811yescharacteristic, complemented, Hall
62C4⋊Q8—391noSylow
63C2×C13C2×Dic611yescharacteristic
64C2×C13D3×D411yescharacteristic
65C2×C13D3×Q811yescharacteristic
66C2×C3×C4—131no—
67C2×C3×C4—131no—
68C2×C3×C4C2×D1311yescharacteristic
69C2×Dic3—131no—
70C2×Dic3—131no—
71C2×Dic3C2×D1311yescharacteristic
72C2×Dic3C2×D1311yescharacteristic
73Dic6—262no—
74Dic6—262no—
75C2×Q8—391no—
76C2×Q8—391no—
77C4⋊C4—31no—
78C4⋊C4—131no—
79C4⋊C4—391no—
80C4⋊C4—391no—
81C42—391no—
82C13#88811yescharacteristic, complemented, Sylow
83C22×C3C22×D1311yescharacteristic
84C3×C4—21no—
85C3×C4—132no—
86C3×C4—261no—
87Dic3—21no—
88Dic3—132no—
89Dic3—261no—
90Dic3Dic2612yescomplemented
91Q8—782no—
92Q8—782no—
93C2×C4—31no—
94C2×C4—31no—
95C2×C4—131no—
96C2×C4—131no—
97C2×C4—391no—
98C2×C4—391no—
99C2×C4D3×D1311yescharacteristic
100C2×C3C2×Dic2611yescharacteristic
101C2×C3D4×D1311yescharacteristic
102C2×C3Q8×D1311yescharacteristic
103C22C2×D3×D1311yescharacteristic
104C4—21no—
105C4—32no—
106C4—61no—
107C4—132no—
108C4—261no—
109C4—392no—
110C4—781no—
111C3#8814211yescharacteristic, complemented, Sylow
112C2Dic6×D1311yescharacteristic
113C2D3×Dic2611yescharacteristic
114C2#1059775611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D13
commutator, socle, prime radical, cosocleC22×C3×C13C23
FittingC2×C3×C4×C13C22
hypercenterC2×C4D3×D13
hypocenterC3×C13C4⋊Q8
LCSG ▷ C22×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
30. C3×Dic13Q8semidirect
32. Dic3×C13Q8semidirect
53. Dic13Dic6semidirect
61. C3×C13C4⋊Q8semidirect
82. C13#888semidirect
90. Dic3Dic26semidirect
111. C3#88142semidirect

Maximal subgroups

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

subgroupindex
C2×Dic782
C2×#646052
C13×Dic3⋊C42
C3×#61012
Dic3⋊Dic132
#105976112
Dic3×Dic132
#881423
#88813