Finite Group Databasebeta

← D3×C13×SD16 #11928889

Subgroups — D3×C13×SD16 #11928889

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
1D3×Q8×C13C211yesmaximal, characteristic, complemented
2D3×D4×C13C211yesmaximal, characteristic
3C3×C13×SD16C211yesmaximal, characteristic, complemented
4C13×#215C211yesmaximal, characteristic, complemented
5C13×#214C211yesmaximal, characteristic, complemented
6C13×#204C211yesmaximal, characteristic, complemented
7D3×C8×C13C211yesmaximal, characteristic, complemented
8C2×C13×SD16—31nomaximal, Hall
9C22×D3×C13—21no—
10C3×Q8×C13C2211yescharacteristic, complemented
11C3×D4×C13C2211yescharacteristic
12C13×#67—21no—
13C13×D12C2211yescharacteristic
14C4×D3×C13—21no—
15C4×D3×C13C2211yescharacteristic
16C13×Dic6—21no—
17C13×Dic6C2211yescharacteristic, complemented
18C3×C8×C13C2211yescharacteristic, complemented
19C13×C3⋊C8C2211yescharacteristic, complemented
20C2×Q8×C13—31no—
21C2×D4×C13—31no—
22C13×SD16—31no—
23C13×SD16—31no—
24C13×SD16—31no—
25C13×SD16D311yescharacteristic, direct product factor
26C2×C8×C13—31no—
27C22×C3×C13—21no—
28C2×D3×C13—21no—
29C2×D3×C13—42no—
30C2×D3×C13D411yescharacteristic
31C3×C4×C13—21no—
32C3×C4×C13C2311yescharacteristic
33Dic3×C13—21no—
34Dic3×C13D411yescharacteristic
35C23×C13—61no—
36Q8×C13—31no—
37Q8×C13—61no—
38Q8×C13C2×D311yescharacteristic, complemented
39D4×C13—31no—
40D4×C13—61no—
41D4×C13C2×D311yescharacteristic
42C2×C4×C13—31no—
43C2×C4×C13—61no—
44C8×C13—31no—
45C8×C13C2×D311yescharacteristic, complemented
46D3×SD16C1311yesmaximal, characteristic, direct product factor, Hall
47C2×C3×C13—41no—
48C2×C3×C13C2×D411yescharacteristic
49D3×C13—41no—
50D3×C13SD1612yesdirect product factor
51C22×C13—21no—
52C22×C13—31no—
53C22×C13—61no—
54C22×C13—122no—
55C4×C13—21no—
56C4×C13—31no—
57C4×C13—61no—
58C4×C13C22×D311yescharacteristic
59D3×Q8C2×C1311yescharacteristic, complemented
60D3×D4C2×C1311yescharacteristic
61C3×SD16C2×C1311yescharacteristic, complemented
62#215C2×C1311yescharacteristic, complemented
63#214C2×C1311yescharacteristic, complemented
64#204C2×C1311yescharacteristic, complemented
65D3×C8C2×C1311yescharacteristic, complemented
66C3×C13C2×SD1611yescharacteristic, complemented, Hall
67C2×SD16—31noSylow
68C2×C13—32no—
69C2×C13—41no—
70C2×C13—121no—
71C2×C13D3×D411yescharacteristic
72C22×D3—21no—
73C3×Q8C22×C1311yescharacteristic, complemented
74C3×D4C22×C1311yescharacteristic
75#67—21no—
76D12C22×C1311yescharacteristic
77C4×D3—21no—
78C4×D3C22×C1311yescharacteristic
79Dic6—21no—
80Dic6C22×C1311yescharacteristic, complemented
81C3×C8C22×C1311yescharacteristic, complemented
82C3⋊C8C22×C1311yescharacteristic, complemented
83C2×Q8—31no—
84C2×D4—31no—
85SD16—31no—
86SD16—31no—
87SD16—31no—
88SD16D3×C1311yescharacteristic, direct product factor
89C2×C8—31no—
90C13D3×SD1611yescharacteristic, direct product factor, Sylow
91C22×C3—21no—
92C2×D3—21no—
93C2×D3—42no—
94C2×D3D4×C1311yescharacteristic
95C3×C4—21no—
96C3×C4C23×C1311yescharacteristic
97Dic3—21no—
98Dic3D4×C1311yescharacteristic
99C23—61no—
100Q8—31no—
101Q8—61no—
102Q8C2×D3×C1311yescharacteristic, complemented
103D4—31no—
104D4—61no—
105D4C2×D3×C1311yescharacteristic
106C2×C4—31no—
107C2×C4—61no—
108C8—31no—
109C8C2×D3×C1311yescharacteristic, complemented
110C2×C3—41no—
111C2×C3C2×D4×C1311yescharacteristic
112D3—41no—
113D3C13×SD1612yesdirect product factor
114C22—21no—
115C22—31no—
116C22—61no—
117C22—122no—
118C4—21no—
119C4—31no—
120C4—61no—
121C4C22×D3×C1311yescharacteristic
122C3C2×C13×SD1611yescharacteristic, complemented, Sylow
123C2—32no—
124C2—41no—
125C2—121no—
126C2D3×D4×C1311yescharacteristic
subgroupG/H
centerC2×C13D3×D4
commutator, cosocleC3×C4C23×C13
FrattiniC4C22×D3×C13
FittingC3×C13×SD16C2
socleC2×C3×C13C2×D4
prime radicalD3×D4×C13C2
hypercenterC13×SD16D3
hypocenterC3C2×C13×SD16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C13 ◁ C4×C13 ◁ C13×SD16

Complements

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

NH ≅ G/Ntype
1. D3×Q8×C13C2semidirect
3. C3×C13×SD16C2semidirect
4. C13×#215C2semidirect
5. C13×#214C2semidirect
6. C13×#204C2semidirect
7. D3×C8×C13C2semidirect
10. C3×Q8×C13C22semidirect
17. C13×Dic6C22semidirect
18. C3×C8×C13C22semidirect
19. C13×C3⋊C8C22semidirect
25. C13×SD16D3direct (N × H)
38. Q8×C13C2×D3semidirect
45. C8×C13C2×D3semidirect
46. D3×SD16C13direct (N × H)
50. D3×C13SD16direct (N × H)
59. D3×Q8C2×C13semidirect
61. C3×SD16C2×C13semidirect
62. #215C2×C13semidirect
63. #214C2×C13semidirect
64. #204C2×C13semidirect
65. D3×C8C2×C13semidirect
66. C3×C13C2×SD16semidirect
73. C3×Q8C22×C13semidirect
80. Dic6C22×C13semidirect
81. C3×C8C22×C13semidirect
82. C3⋊C8C22×C13semidirect
88. SD16D3×C13direct (N × H)
90. C13D3×SD16direct (N × H)
102. Q8C2×D3×C13semidirect
109. C8C2×D3×C13semidirect
113. D3C13×SD16direct (N × H)
122. C3C2×C13×SD16semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×C132
D3×D4×C132
C3×C13×SD162
C13×#2152
C13×#2142
C13×#2042
D3×C8×C132
C2×C13×SD163
D3×SD1613