Finite Group Databasebeta

← D3×C7×SD16 #10621310

Subgroups — D3×C7×SD16 #10621310

Order 672.

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×C7×Q8C211yesmaximal, characteristic, complemented
2D3×C7×D4C211yesmaximal, characteristic
3C3×C7×SD16C211yesmaximal, characteristic, complemented
4C7×#215C211yesmaximal, characteristic, complemented
5C7×#214C211yesmaximal, characteristic, complemented
6C7×#204C211yesmaximal, characteristic, complemented
7D3×C7×C8C211yesmaximal, characteristic, complemented
8C2×C7×SD16—31nomaximal, Hall
9C22×D3×C7—21no—
10C3×C7×Q8C2211yescharacteristic, complemented
11C3×C7×D4C2211yescharacteristic
12C7×#67—21no—
13C7×D12C2211yescharacteristic
14C4×D3×C7—21no—
15C4×D3×C7C2211yescharacteristic
16C7×Dic6—21no—
17C7×Dic6C2211yescharacteristic, complemented
18C3×C7×C8C2211yescharacteristic, complemented
19C7×C3⋊C8C2211yescharacteristic, complemented
20C2×C7×Q8—31no—
21C2×C7×D4—31no—
22C7×SD16—31no—
23C7×SD16—31no—
24C7×SD16—31no—
25C7×SD16D311yescharacteristic, direct product factor
26C2×C7×C8—31no—
27D3×SD16C711yesmaximal, characteristic, direct product factor, Hall
28C22×C3×C7—21no—
29C2×D3×C7—21no—
30C2×D3×C7—42no—
31C2×D3×C7D411yescharacteristic
32C3×C4×C7—21no—
33C3×C4×C7C2311yescharacteristic
34C7×Dic3—21no—
35C7×Dic3D411yescharacteristic
36C23×C7—61no—
37C7×Q8—31no—
38C7×Q8—61no—
39C7×Q8C2×D311yescharacteristic, complemented
40C7×D4—31no—
41C7×D4—61no—
42C7×D4C2×D311yescharacteristic
43C2×C4×C7—31no—
44C2×C4×C7—61no—
45C7×C8—31no—
46C7×C8C2×D311yescharacteristic, complemented
47D3×Q8C2×C711yescharacteristic, complemented
48D3×D4C2×C711yescharacteristic
49C3×SD16C2×C711yescharacteristic, complemented
50#215C2×C711yescharacteristic, complemented
51#214C2×C711yescharacteristic, complemented
52#204C2×C711yescharacteristic, complemented
53D3×C8C2×C711yescharacteristic, complemented
54C2×C3×C7—41no—
55C2×C3×C7C2×D411yescharacteristic
56D3×C7—41no—
57D3×C7SD1612yesdirect product factor
58C2×SD16—31noSylow
59C22×C7—21no—
60C22×C7—31no—
61C22×C7—61no—
62C22×C7—122no—
63C4×C7—21no—
64C4×C7—31no—
65C4×C7—61no—
66C4×C7C22×D311yescharacteristic
67C22×D3—21no—
68C3×Q8C22×C711yescharacteristic, complemented
69C3×D4C22×C711yescharacteristic
70#67—21no—
71D12C22×C711yescharacteristic
72C4×D3—21no—
73C4×D3C22×C711yescharacteristic
74Dic6—21no—
75Dic6C22×C711yescharacteristic, complemented
76C3×C8C22×C711yescharacteristic, complemented
77C3⋊C8C22×C711yescharacteristic, complemented
78C3×C7C2×SD1611yescharacteristic, complemented, Hall
79C2×Q8—31no—
80C2×D4—31no—
81SD16—31no—
82SD16—31no—
83SD16—31no—
84SD16D3×C711yescharacteristic, direct product factor
85C2×C8—31no—
86C2×C7—32no—
87C2×C7—41no—
88C2×C7—121no—
89C2×C7D3×D411yescharacteristic
90C22×C3—21no—
91C2×D3—21no—
92C2×D3—42no—
93C2×D3C7×D411yescharacteristic
94C3×C4—21no—
95C3×C4C23×C711yescharacteristic
96Dic3—21no—
97Dic3C7×D411yescharacteristic
98C23—61no—
99Q8—31no—
100Q8—61no—
101Q8C2×D3×C711yescharacteristic, complemented
102D4—31no—
103D4—61no—
104D4C2×D3×C711yescharacteristic
105C2×C4—31no—
106C2×C4—61no—
107C8—31no—
108C8C2×D3×C711yescharacteristic, complemented
109C7D3×SD1611yescharacteristic, direct product factor, Sylow
110C2×C3—41no—
111C2×C3C2×C7×D411yescharacteristic
112D3—41no—
113D3C7×SD1612yesdirect product factor
114C22—21no—
115C22—31no—
116C22—61no—
117C22—122no—
118C4—21no—
119C4—31no—
120C4—61no—
121C4C22×D3×C711yescharacteristic
122C3C2×C7×SD1611yescharacteristic, complemented, Sylow
123C2—32no—
124C2—41no—
125C2—121no—
126C2D3×C7×D411yescharacteristic
subgroupG/H
centerC2×C7D3×D4
commutator, cosocleC3×C4C23×C7
FrattiniC4C22×D3×C7
FittingC3×C7×SD16C2
socleC2×C3×C7C2×D4
prime radicalD3×C7×D4C2
hypercenterC7×SD16D3
hypocenterC3C2×C7×SD16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C7 ◁ C4×C7 ◁ C7×SD16

Complements

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

NH ≅ G/Ntype
1. D3×C7×Q8C2semidirect
3. C3×C7×SD16C2semidirect
4. C7×#215C2semidirect
5. C7×#214C2semidirect
6. C7×#204C2semidirect
7. D3×C7×C8C2semidirect
10. C3×C7×Q8C22semidirect
17. C7×Dic6C22semidirect
18. C3×C7×C8C22semidirect
19. C7×C3⋊C8C22semidirect
25. C7×SD16D3direct (N × H)
27. D3×SD16C7direct (N × H)
39. C7×Q8C2×D3semidirect
46. C7×C8C2×D3semidirect
47. D3×Q8C2×C7semidirect
49. C3×SD16C2×C7semidirect
50. #215C2×C7semidirect
51. #214C2×C7semidirect
52. #204C2×C7semidirect
53. D3×C8C2×C7semidirect
57. D3×C7SD16direct (N × H)
68. C3×Q8C22×C7semidirect
75. Dic6C22×C7semidirect
76. C3×C8C22×C7semidirect
77. C3⋊C8C22×C7semidirect
78. C3×C7C2×SD16semidirect
84. SD16D3×C7direct (N × H)
101. Q8C2×D3×C7semidirect
108. C8C2×D3×C7semidirect
109. C7D3×SD16direct (N × H)
113. D3C7×SD16direct (N × H)
122. C3C2×C7×SD16semidirect

Maximal subgroups

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

subgroupindex
D3×C7×Q82
D3×C7×D42
C3×C7×SD162
C7×#2152
C7×#2142
C7×#2042
D3×C7×C82
C2×C7×SD163
D3×SD167