Finite Group Databasebeta

← #11928669

Subgroups — #11928669

Order 1248.

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 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#10597671C211yesmaximal, characteristic
2C13×#217C211yesmaximal, characteristic
3C3×C22⋊Dic13C211yesmaximal, characteristic
4Dic3⋊Dic13C211yesmaximal, characteristic, complemented
5#10597612C211yesmaximal, characteristic, complemented
6#10597611C211yesmaximal, characteristic, complemented
7Dic3×Dic13C211yesmaximal, characteristic, complemented
8#88133—31nomaximal, Hall
9C23×C3×C13C2211yescharacteristic
10C2×Dic39C2211yescharacteristic
11C2×Dic39C2211yescharacteristic
12C2×Dic3×C13C2211yescharacteristic
13C2×Dic3×C13C2211yescharacteristic
14C2×C3×Dic13C2211yescharacteristic
15C2×C3×Dic13C2211yescharacteristic
16C13×C22⋊C4—31no—
17C22⋊Dic13—31no—
18C22⋊Dic13D311yescharacteristic
19C4⋊Dic13—31no—
20#6101—31no—
21#6101—31no—
22C4×Dic13—31no—
23C22×C3×C13—21no—
24C22×C3×C13—21no—
25C22×C3×C13—21no—
26C22×C3×C13C2311yescharacteristic
27Dic39—21no—
28Dic39—21no—
29C3×Dic13—21no—
30C3×Dic13—21no—
31Dic3×C13—21no—
32Dic3×C13—21no—
33C23×C13C2×D311yescharacteristic
34C2×C4×C13—31no—
35C2×C4×C13—31no—
36C2×Dic13—31no—
37C2×Dic13—31no—
38C2×Dic13C2×D311yescharacteristic
39C2×Dic13C2×D311yescharacteristic
40#879—131nomaximal, Hall
41C2×C3×C13—41no—
42C2×C3×C13#4111yescharacteristic
43C2×C3×C13#4111yescharacteristic
44C2×C3×C13#4111yescharacteristic
45C22×C13—21no—
46C22×C13—21no—
47C22×C13—21no—
48C22×C13C22×D311yescharacteristic
49C4×C13—61no—
50C4×C13—61no—
51Dic13—21no—
52Dic13—21no—
53Dic13—61no—
54Dic13—61no—
55C3×C22⋊C4—131no—
56#217—131no—
57#217D1311yescharacteristic
58C4⋊Dic3—131no—
59Dic3⋊C4—131no—
60Dic3⋊C4—131no—
61C4×Dic3—131no—
62C3×C13#12611yescharacteristic, complemented, Hall
63#126—391noSylow
64C2×C13—41no—
65C2×C13#23511yescharacteristic
66C2×C13#23711yescharacteristic
67C2×C13#23711yescharacteristic
68C23×C3C2×D1311yescharacteristic
69C2×C3×C4—131no—
70C2×C3×C4—131no—
71C2×Dic3—131no—
72C2×Dic3—131no—
73C2×Dic3C2×D1311yescharacteristic
74C2×Dic3C2×D1311yescharacteristic
75C4⋊C4—391no—
76C4⋊C4—391no—
77C4⋊C4—391no—
78C22⋊C4—31no—
79C22⋊C4—131no—
80C22⋊C4—391no—
81C42—391no—
82C13#87911yescharacteristic, complemented, Sylow
83C22×C3—21no—
84C22×C3—21no—
85C22×C3—21no—
86C22×C3C22×D1311yescharacteristic
87C3×C4—261no—
88C3×C4—261no—
89Dic3—21no—
90Dic3—21no—
91Dic3—261no—
92Dic3—261no—
93C23D3×D1311yescharacteristic
94C2×C4—31no—
95C2×C4—31no—
96C2×C4—131no—
97C2×C4—131no—
98C2×C4—391no—
99C2×C4—391no—
100C2×C3—41no—
101C2×C3#612711yescharacteristic
102C2×C3#612911yescharacteristic
103C2×C3#612911yescharacteristic
104C22—21no—
105C22—21no—
106C22—21no—
107C22C2×D3×D1311yescharacteristic
108C4—61no—
109C4—61no—
110C4—261no—
111C4—261no—
112C4—781no—
113C4—781no—
114C3#8813311yescharacteristic, complemented, Sylow
115C2—41no—
116C2#1059774511yescharacteristic
117C2#1059774611yescharacteristic
118C2#1059774811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D13
commutator, socle, cosocleC22×C3×C13C23
Fitting, prime radicalC23×C3×C13C22
hypercenterC23D3×D13
hypocenterC3×C13#126
LCSG ▷ C22×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
4. Dic3⋊Dic13C2semidirect
5. #10597612C2semidirect
6. #10597611C2semidirect
7. Dic3×Dic13C2semidirect
62. C3×C13#126semidirect
82. C13#879semidirect
114. C3#88133semidirect

Maximal subgroups

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

subgroupindex
#105976712
C13×#2172
C3×C22⋊Dic132
Dic3⋊Dic132
#105976122
#105976112
Dic3×Dic132
#881333
#87913