Finite Group Databasebeta

← C3×SD16×D13 #11928803

Subgroups — C3×SD16×D13 #11928803

Order 1248.

136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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×Q8×D13C211yesmaximal, characteristic, complemented
2C3×D4×D13C211yesmaximal, characteristic
3C3×C13×SD16C211yesmaximal, characteristic, complemented
4C3×#6106C211yesmaximal, characteristic, complemented
5C3×#6105C211yesmaximal, characteristic, complemented
6C3×#6095C211yesmaximal, characteristic, complemented
7C3×C8×D13C211yesmaximal, characteristic, complemented
8SD16×D13C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×D13—21no—
10C3×Q8×C13C2211yescharacteristic, complemented
11C3×D4×C13C2211yescharacteristic
12C3×C22⋊D13—21no—
13C3×D52C2211yescharacteristic
14C3×C4×D13—21no—
15C3×C4×D13C2211yescharacteristic
16C3×Dic26—21no—
17C3×Dic26C2211yescharacteristic, complemented
18C3×C8×C13C2211yescharacteristic, complemented
19C3×#1055C2211yescharacteristic, complemented
20Q8×D13C2×C311yescharacteristic, complemented
21D4×D13C2×C311yescharacteristic
22C13×SD16C2×C311yescharacteristic, complemented
23#6106C2×C311yescharacteristic, complemented
24#6105C2×C311yescharacteristic, complemented
25#6095C2×C311yescharacteristic, complemented
26C8×D13C2×C311yescharacteristic, complemented
27C22×C3×C13—21no—
28C2×C3×D13—21no—
29C2×C3×D13—42no—
30C2×C3×D13D411yescharacteristic
31C3×C4×C13—21no—
32C3×C4×C13C2311yescharacteristic
33C3×Dic13—21no—
34C3×Dic13D411yescharacteristic
35C22×D13—21no—
36Q8×C13C22×C311yescharacteristic, complemented
37D4×C13C22×C311yescharacteristic
38C22⋊D13—21no—
39D52C22×C311yescharacteristic
40C4×D13—21no—
41C4×D13C22×C311yescharacteristic
42Dic26—21no—
43Dic26C22×C311yescharacteristic, complemented
44C8×C13C22×C311yescharacteristic, complemented
45#1055C22×C311yescharacteristic, complemented
46C2×C3×SD16—131nomaximal, Hall
47C2×C3×C13—41no—
48C2×C3×C13C2×D411yescharacteristic
49C3×D13—41no—
50C3×D13SD1612yesdirect product factor
51C22×C13—21no—
52C2×D13—21no—
53C2×D13—42no—
54C2×D13C3×D411yescharacteristic
55C4×C13—21no—
56C4×C13C23×C311yescharacteristic
57Dic13—21no—
58Dic13C3×D411yescharacteristic
59C2×C3×Q8—131no—
60C2×C3×D4—131no—
61C3×SD16—131no—
62C3×SD16—131no—
63C3×SD16—131no—
64C3×SD16D1311yescharacteristic, direct product factor
65C2×C3×C8—131no—
66C3×C13C2×SD1611yescharacteristic, complemented, Hall
67C2×SD16—131noSylow
68C2×C13—41no—
69C2×C13C2×C3×D411yescharacteristic
70D13—41no—
71D13C3×SD1612yesdirect product factor
72C23×C3—261no—
73C3×Q8—131no—
74C3×Q8—261no—
75C3×Q8C2×D1311yescharacteristic, complemented
76C3×D4—131no—
77C3×D4—261no—
78C3×D4C2×D1311yescharacteristic
79C2×C3×C4—131no—
80C2×C3×C4—261no—
81C3×C8—131no—
82C3×C8C2×D1311yescharacteristic, complemented
83C2×Q8—131no—
84C2×D4—131no—
85SD16—131no—
86SD16—131no—
87SD16—131no—
88SD16C3×D1311yescharacteristic, direct product factor
89C2×C8—131no—
90C13C2×C3×SD1611yescharacteristic, complemented, Sylow
91C22×C3—21no—
92C22×C3—131no—
93C22×C3—261no—
94C22×C3—522no—
95C3×C4—21no—
96C3×C4—131no—
97C3×C4—261no—
98C3×C4C22×D1311yescharacteristic
99C23—261no—
100Q8—131no—
101Q8—261no—
102Q8C2×C3×D1311yescharacteristic, complemented
103D4—131no—
104D4—261no—
105D4C2×C3×D1311yescharacteristic
106C2×C4—131no—
107C2×C4—261no—
108C8—131no—
109C8C2×C3×D1311yescharacteristic, complemented
110C2×C3—41no—
111C2×C3—132no—
112C2×C3—521no—
113C2×C3D4×D1311yescharacteristic
114C22—21no—
115C22—131no—
116C22—261no—
117C22—522no—
118C4—21no—
119C4—131no—
120C4—261no—
121C4C22×C3×D1311yescharacteristic
122C3SD16×D1311yescharacteristic, direct product factor, Sylow
123C2—41no—
124C2—132no—
125C2—521no—
126C2C3×D4×D1311yescharacteristic
subgroupG/H
centerC2×C3D4×D13
commutator, cosocleC4×C13C23×C3
FrattiniC4C22×C3×D13
FittingC3×C13×SD16C2
socleC2×C3×C13C2×D4
prime radicalC3×D4×D13C2
hypercenterC3×SD16D13
hypocenterC13C2×C3×SD16
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×SD16

Complements

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

NH ≅ G/Ntype
1. C3×Q8×D13C2semidirect
3. C3×C13×SD16C2semidirect
4. C3×#6106C2semidirect
5. C3×#6105C2semidirect
6. C3×#6095C2semidirect
7. C3×C8×D13C2semidirect
8. SD16×D13C3direct (N × H)
10. C3×Q8×C13C22semidirect
17. C3×Dic26C22semidirect
18. C3×C8×C13C22semidirect
19. C3×#1055C22semidirect
20. Q8×D13C2×C3semidirect
22. C13×SD16C2×C3semidirect
23. #6106C2×C3semidirect
24. #6105C2×C3semidirect
25. #6095C2×C3semidirect
26. C8×D13C2×C3semidirect
36. Q8×C13C22×C3semidirect
43. Dic26C22×C3semidirect
44. C8×C13C22×C3semidirect
45. #1055C22×C3semidirect
50. C3×D13SD16direct (N × H)
64. C3×SD16D13direct (N × H)
66. C3×C13C2×SD16semidirect
71. D13C3×SD16direct (N × H)
75. C3×Q8C2×D13semidirect
82. C3×C8C2×D13semidirect
88. SD16C3×D13direct (N × H)
90. C13C2×C3×SD16semidirect
102. Q8C2×C3×D13semidirect
109. C8C2×C3×D13semidirect
122. C3SD16×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C3×Q8×D132
C3×D4×D132
C3×C13×SD162
C3×#61062
C3×#61052
C3×#60952
C3×C8×D132
SD16×D133
C2×C3×SD1613