Finite Group Databasebeta

← C3×#88165 #11928801

Subgroups — C3×#88165 #11928801

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
1C3×#6129C211yesmaximal, characteristic, complemented
2C3×D4×D13C211yesmaximal, characteristic, complemented
3C3×C13×D8C211yesmaximal, characteristic, complemented
4C3×#6105C211yesmaximal, characteristic, complemented
5C3×#6104C211yesmaximal, characteristic, complemented
6C3×#6095C211yesmaximal, characteristic, complemented
7C3×#6094C211yesmaximal, characteristic, complemented
8#88165C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×D13—21no—
10C3×D4×C13C2211yescharacteristic
11C3×D4×C13C2211yescharacteristic, complemented
12C3×C22⋊D13—21no—
13C3×C22⋊D13—21no—
14C2×C3×Dic13—21no—
15C3×D52C2211yescharacteristic
16C3×C4×D13C2211yescharacteristic
17C3×Dic26C2211yescharacteristic, complemented
18C3×C8×C13C2211yescharacteristic, complemented
19C3×#1055C2211yescharacteristic, complemented
20#6129C2×C311yescharacteristic, complemented
21D4×D13C2×C311yescharacteristic, complemented
22C13×D8C2×C311yescharacteristic, complemented
23#6105C2×C311yescharacteristic, complemented
24#6104C2×C311yescharacteristic, complemented
25#6095C2×C311yescharacteristic, complemented
26#6094C2×C311yescharacteristic, complemented
27C22×C3×C13—21no—
28C22×C3×C13—21no—
29C2×C3×D13—21no—
30C2×C3×D13—42no—
31C2×C3×D13D411yescharacteristic
32C3×C4×C13C2311yescharacteristic
33C3×Dic13—21no—
34C3×Dic13D411yescharacteristic
35C22×D13—21no—
36D4×C13C22×C311yescharacteristic
37D4×C13C22×C311yescharacteristic, complemented
38C22⋊D13—21no—
39C22⋊D13—21no—
40C2×Dic13—21no—
41D52C22×C311yescharacteristic
42C4×D13C22×C311yescharacteristic
43Dic26C22×C311yescharacteristic, complemented
44C8×C13C22×C311yescharacteristic, complemented
45#1055C22×C311yescharacteristic, complemented
46C3×AGL(1,ℤ/8)—131nomaximal, Hall
47C2×C3×C13—41no—
48C2×C3×C13—41no—
49C2×C3×C13C2×D411yescharacteristic
50C3×D13—21no—
51C3×D13—41no—
52C22×C13—21no—
53C22×C13—21no—
54C2×D13—21no—
55C2×D13—42no—
56C2×D13C3×D411yescharacteristic
57C4×C13C23×C311yescharacteristic
58Dic13—21no—
59Dic13C3×D411yescharacteristic
60C3×#41—131no—
61C2×C3×D4—131no—
62C3×SD16—131no—
63C3×SD16—131no—
64C3×D8—131no—
65C3×D8D1311yescharacteristic, complemented
66C3×M16—131no—
67C3×C13AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
68AGL(1,ℤ/8)—131noSylow
69C2×C13—41no—
70C2×C13—41no—
71C2×C13C2×C3×D411yescharacteristic
72D13—21no—
73D13—41no—
74C23×C3—261no—
75C3×Q8—131no—
76C3×D4—131no—
77C3×D4—261no—
78C3×D4—261no—
79C3×D4C2×D1311yescharacteristic
80C3×D4C2×D1311yescharacteristic, complemented
81C2×C3×C4—131no—
82C2×C3×C4—261no—
83C3×C8—131no—
84C3×C8C2×D1311yescharacteristic, complemented
85#41—131no—
86C2×D4—131no—
87SD16—131no—
88SD16—131no—
89D8—131no—
90D8C3×D1311yescharacteristic, complemented
91M16—131no—
92C13C3×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
93C22×C3—21no—
94C22×C3—21no—
95C22×C3—131no—
96C22×C3—261no—
97C22×C3—522no—
98C3×C4—131no—
99C3×C4—261no—
100C3×C4C22×D1311yescharacteristic
101C23—261no—
102Q8—131no—
103D4—131no—
104D4—261no—
105D4—261no—
106D4C2×C3×D1311yescharacteristic
107D4C2×C3×D1311yescharacteristic, complemented
108C2×C4—131no—
109C2×C4—261no—
110C8—131no—
111C8C2×C3×D1311yescharacteristic, complemented
112C2×C3—41no—
113C2×C3—41no—
114C2×C3—261no—
115C2×C3—521no—
116C2×C3D4×D1311yescharacteristic
117C22—21no—
118C22—21no—
119C22—131no—
120C22—261no—
121C22—522no—
122C4—131no—
123C4—261no—
124C4C22×C3×D1311yescharacteristic
125C3#8816511yescharacteristic, direct product factor, Sylow
126C2—41no—
127C2—41no—
128C2—261no—
129C2—521no—
130C2C3×D4×D1311yescharacteristic
subgroupG/H
centerC2×C3D4×D13
commutator, cosocleC4×C13C23×C3
FrattiniC4C22×C3×D13
FittingC3×C13×D8C2
socleC2×C3×C13C2×D4
hypercenterC3×D8D13
hypocenterC13C3×AGL(1,ℤ/8)
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D8

Complements

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

NH ≅ G/Ntype
1. C3×#6129C2semidirect
2. C3×D4×D13C2semidirect
3. C3×C13×D8C2semidirect
4. C3×#6105C2semidirect
5. C3×#6104C2semidirect
6. C3×#6095C2semidirect
7. C3×#6094C2semidirect
8. #88165C3direct (N × H)
11. C3×D4×C13C22semidirect
17. C3×Dic26C22semidirect
18. C3×C8×C13C22semidirect
19. C3×#1055C22semidirect
20. #6129C2×C3semidirect
21. D4×D13C2×C3semidirect
22. C13×D8C2×C3semidirect
23. #6105C2×C3semidirect
24. #6104C2×C3semidirect
25. #6095C2×C3semidirect
26. #6094C2×C3semidirect
37. D4×C13C22×C3semidirect
43. Dic26C22×C3semidirect
44. C8×C13C22×C3semidirect
45. #1055C22×C3semidirect
65. C3×D8D13semidirect
67. C3×C13AGL(1,ℤ/8)semidirect
80. C3×D4C2×D13semidirect
84. C3×C8C2×D13semidirect
90. D8C3×D13semidirect
92. C13C3×AGL(1,ℤ/8)semidirect
107. D4C2×C3×D13semidirect
111. C8C2×C3×D13semidirect
125. C3#88165direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#61292
C3×D4×D132
C3×C13×D82
C3×#61052
C3×#61042
C3×#60952
C3×#60942
#881653
C3×AGL(1,ℤ/8)13