Finite Group Databasebeta

← C2×SD16×D313 #34094923

Subgroups — C2×SD16×D313 #34094923

Order 20032.

298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×Q8×D313C211yesmaximal, characteristic, complemented
2C2×D4×D313C211yesmaximal, characteristic
3C2×#19097550C211yesmaximal, characteristic, complemented
4C2×#19097549C211yesmaximal, characteristic, complemented
5C2×#19097548C211yesmaximal, characteristic, complemented
6SD16×D313C218yesmaximal, direct product factor
7C2×C8×D313C211yesmaximal, characteristic, complemented
8C2×SD16×C313C211yesmaximal, characteristic, complemented
9C23×D313—21no—
10C2×Dic626—21no—
11C2×Dic626C2211yescharacteristic, complemented
12Q8×D313—22no—
13Q8×D313C2214yescomplemented
14C2×D1252C2211yescharacteristic
15C2×C22⋊D313—21no—
16D4×D313—22no—
17D4×D313C2214yes—
18C2×C4×D313—21no—
19C2×C4×D313C2211yescharacteristic
20#19097550C2214yescomplemented
21#19097549C2214yescomplemented
22#19097548C2214yescomplemented
23C2×#14578809C2211yescharacteristic, complemented
24C8×D313C2214yescomplemented
25C2×Q8×C313C2211yescharacteristic, complemented
26C2×D4×C313C2211yescharacteristic
27SD16×C313C2214yescomplemented
28C2×C8×C313C2211yescharacteristic, complemented
29C22×D313—21no—
30C22×D313—24no—
31C22×D313—44no—
32C22×D313D411yescharacteristic
33Dic626—21no—
34Dic626—24no—
35Dic626C2312yescomplemented
36D1252—21no—
37D1252C2312yes—
38C22⋊D313—24no—
39C2×Dic313—21no—
40C2×Dic313D411yescharacteristic
41C4×D313—24no—
42C4×D313D412yes—
43C4×D313C2312yes—
44#14578809C2312yescomplemented
45C23×C313—21no—
46Q8×C313—21no—
47Q8×C313C2312yescomplemented
48D4×C313—21no—
49D4×C313C2312yes—
50C2×C4×C313—21no—
51C2×C4×C313C2311yescharacteristic
52C8×C313C2312yescomplemented
53C22×C313—22no—
54C22×C313—42no—
55C22×C313C2×D411yescharacteristic
56C2×D313—22no—
57C2×D313—42no—
58C2×D313—48no—
59C2×D313SD1614yesdirect product factor
60C2×D313C2×D412yes—
61C4×C313—22no—
62C4×C313C2×D411yescharacteristic
63C4×C313C2411yescharacteristic
64Dic313—22no—
65Dic313C2×D412yes—
66C2×C313—42no—
67C2×C313C2×SD1612yescomplemented
68C2×C313C22×D411yescharacteristic
69D313—42no—
70D313C2×SD1614yesdirect product factor
71C313C22×SD1611yescharacteristic, complemented, Sylow
72C22×SD16—3131nomaximal, Sylow
73C22×Q8—3131no—
74C22×D4—3131no—
75C2×SD16—3131no—
76C2×SD16—3131no—
77C2×SD16—3138no—
78C2×SD16—3131no—
79C2×SD16D31311yescharacteristic, direct product factor
80C22×C8—3131no—
81C24—6261no—
82C2×Q8—3134no—
83C2×Q8—3131no—
84C2×Q8—6261no—
85C2×Q8—6262no—
86C2×Q8C2×D31311yescharacteristic, complemented
87C2×D4—3134no—
88C2×D4—3131no—
89C2×D4—6262no—
90C2×D4—6261no—
91C2×D4C2×D31311yescharacteristic
92C22×C4—3131no—
93C22×C4—6261no—
94SD16—3134no—
95SD16—3134no—
96SD16—3134no—
97SD16C2×D31314yesdirect product factor
98C2×C8—3131no—
99C2×C8—3134no—
100C2×C8C2×D31311yescharacteristic, complemented
101C23—21no—
102C23—3131no—
103C23—6264no—
104C23—6261no—
105C23—12524no—
106Q8—21no—
107Q8—3132no—
108Q8—6264no—
109Q8—6261no—
110Q8C22×D31312yescomplemented
111D4—21no—
112D4—3132no—
113D4—6264no—
114D4—6261no—
115D4C22×D31312yes—
116C2×C4—21no—
117C2×C4—3131no—
118C2×C4—3132no—
119C2×C4—3132no—
120C2×C4—6264no—
121C2×C4—6261no—
122C2×C4C22×D31311yescharacteristic
123C8—3132no—
124C8C22×D31312yescomplemented
125C22—22no—
126C22—42no—
127C22—3134no—
128C22—3132no—
129C22—6262no—
130C22—12528no—
131C22—12522no—
132C22D4×D31311yescharacteristic
133C4—22no—
134C4—3132no—
135C4—6262no—
136C4D4×D31311yescharacteristic
137C4C23×D31311yescharacteristic
138C2—42no—
139C2—3134no—
140C2—12522no—
141C2SD16×D31312yesdirect product factor
142C2C2×D4×D31311yescharacteristic
subgroupG/H
centerC22D4×D313
commutator, cosocleC4×C313C24
FrattiniC4C23×D313
FittingC2×SD16×C313C2
socleC22×C313C2×D4
prime radicalC2×D4×D313C2
hypercenterC2×SD16D313
hypocenterC313C22×SD16
LCSG ▷ C4×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D313C2semidirect
3. C2×#19097550C2semidirect
4. C2×#19097549C2semidirect
5. C2×#19097548C2semidirect
6. SD16×D313C2direct (N × H)
7. C2×C8×D313C2semidirect
8. C2×SD16×C313C2semidirect
11. C2×Dic626C22semidirect
13. Q8×D313C22semidirect
20. #19097550C22semidirect
21. #19097549C22semidirect
22. #19097548C22semidirect
23. C2×#14578809C22semidirect
24. C8×D313C22semidirect
25. C2×Q8×C313C22semidirect
27. SD16×C313C22semidirect
28. C2×C8×C313C22semidirect
35. Dic626C23semidirect
44. #14578809C23semidirect
47. Q8×C313C23semidirect
52. C8×C313C23semidirect
59. C2×D313SD16direct (N × H)
67. C2×C313C2×SD16semidirect
70. D313C2×SD16direct (N × H)
71. C313C22×SD16semidirect
79. C2×SD16D313direct (N × H)
86. C2×Q8C2×D313semidirect
97. SD16C2×D313direct (N × H)
100. C2×C8C2×D313semidirect
110. Q8C22×D313semidirect
124. C8C22×D313semidirect
141. C2SD16×D313direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D3132
C2×D4×D3132
C2×#190975502
C2×#190975492
C2×#190975482
SD16×D3132
C2×C8×D3132
C2×SD16×C3132
C22×SD16313