Finite Group Databasebeta

← C2×D13×D16 #13127940

Subgroups — C2×D13×D16 #13127940

Order 1664.

440 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 125 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×D8×D13C212yesmaximal, complemented
2C2×C13×D16C211yesmaximal, characteristic, complemented
3C2×#88066C212yesmaximal, complemented
4D13×D16C218yesmaximal, direct product factor
5C2×D208C211yesmaximal, characteristic, complemented
6C2×C16×D13C211yesmaximal, characteristic, complemented
7C2×D4×D13—22no—
8C2×C13×D8C2212yescomplemented
9C2×#6104—22no—
10D8×D13—24no—
11D8×D13C2218yescomplemented
12C2×D104C2212yescomplemented
13C2×C8×D13C2211yescharacteristic
14C13×D16C2214yescomplemented
15C2×C13×C16C2211yescharacteristic, complemented
16#88066C2218yescomplemented
17C2×#6090C2211yescharacteristic, complemented
18D208C2214yescomplemented
19C16×D13C2214yescomplemented
20C23×D13—42no—
21C2×D4×C13—22no—
22C2×C22⋊D13—42no—
23D4×D13—28no—
24D4×D13—44no—
25C2×D52—22no—
26C2×C4×D13D411yescharacteristic
27C13×D8—22no—
28C13×D8C2314yescomplemented
29C2×C8×C13C2311yescharacteristic
30#6104—28no—
31C2×#1055D411yescharacteristic
32D104—22no—
33D104C2314yescomplemented
34C8×D13D412yes—
35C8×D13C2312yes—
36C13×C16C2312yescomplemented
37#6090C2312yescomplemented
38C22×D16—131nomaximal, Sylow
39C23×C13—42no—
40C22×D13—42no—
41C22×D13—48no—
42C22×D13—88no—
43C22×D13D811yescharacteristic
44D4×C13—24no—
45D4×C13—42no—
46C2×C4×C13C2×D411yescharacteristic
47C22⋊D13—48no—
48C2×Dic13D811yescharacteristic
49D52—24no—
50D52—42no—
51C4×D13D812yes—
52C4×D13C2×D412yes—
53C8×C13C2×D411yescharacteristic
54C8×C13C2411yescharacteristic
55#1055C2×D412yes—
56C22×D8—132no—
57C2×D16—132no—
58C2×D16—138no—
59C2×D16—131no—
60C2×D16D1311yescharacteristic, direct product factor
61C22×C16—131no—
62C22×C13—44no—
63C22×C13—84no—
64C22×C13C2×D811yescharacteristic
65C2×D13—44no—
66C2×D13—84no—
67C2×D13—816no—
68C2×D13D1614yesdirect product factor
69C2×D13C2×D812yes—
70C4×C13C2×D811yescharacteristic
71C4×C13C22×D411yescharacteristic
72Dic13C2×D812yes—
73C22×D4—262no—
74C2×D8—138no—
75C2×D8—132no—
76C2×D8—264no—
77C2×D8—262no—
78C2×D8C2×D1312yescomplemented
79C22×C8—131no—
80D16—138no—
81D16—134no—
82D16C2×D1314yesdirect product factor
83C2×C16—131no—
84C2×C16—134no—
85C2×C16C2×D1311yescharacteristic, complemented
86C2×C13—84no—
87C2×C13C2×D1612yescomplemented
88C2×C13C22×D811yescharacteristic
89D13—84no—
90D13C2×D1614yesdirect product factor
91C24—522no—
92C2×D4—22no—
93C2×D4—268no—
94C2×D4—262no—
95C2×D4—524no—
96C2×D4—522no—
97C22×C4—131no—
98D8—22no—
99D8—134no—
100D8—268no—
101D8—262no—
102D8C22×D1314yescomplemented
103C2×C8—131no—
104C2×C8—132no—
105C2×C8—132no—
106C2×C8C22×D1311yescharacteristic
107C16—132no—
108C16C22×D1312yescomplemented
109C13C22×D1611yescharacteristic, complemented, Sylow
110C23—42no—
111C23—131no—
112C23—528no—
113C23—522no—
114C23—1048no—
115D4—24no—
116D4—42no—
117D4—264no—
118D4—528no—
119D4—522no—
120C2×C4—131no—
121C2×C4—132no—
122C2×C4—132no—
123C2×C4D4×D1311yescharacteristic
124C8—132no—
125C8D4×D1311yescharacteristic
126C8C23×D1311yescharacteristic
127C22—44no—
128C22—84no—
129C22—132no—
130C22—134no—
131C22—524no—
132C22—10416no—
133C22—1044no—
134C22D8×D1311yescharacteristic
135C4—132no—
136C4D8×D1311yescharacteristic
137C4C2×D4×D1311yescharacteristic
138C2—84no—
139C2—134no—
140C2—1044no—
141C2D13×D1612yesdirect product factor
142C2C2×D8×D1311yescharacteristic
subgroupG/H
centerC22D8×D13
commutator, cosocleC8×C13C24
FrattiniC8C23×D13
FittingC2×C13×D16C2
socleC22×C13C2×D8
hypercenterC2×D16D13
hypocenterC13C22×D16
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×D13C2semidirect
2. C2×C13×D16C2semidirect
3. C2×#88066C2semidirect
4. D13×D16C2direct (N × H)
5. C2×D208C2semidirect
6. C2×C16×D13C2semidirect
8. C2×C13×D8C22semidirect
11. D8×D13C22semidirect
12. C2×D104C22semidirect
14. C13×D16C22semidirect
15. C2×C13×C16C22semidirect
16. #88066C22semidirect
17. C2×#6090C22semidirect
18. D208C22semidirect
19. C16×D13C22semidirect
28. C13×D8C23semidirect
33. D104C23semidirect
36. C13×C16C23semidirect
37. #6090C23semidirect
60. C2×D16D13direct (N × H)
68. C2×D13D16direct (N × H)
78. C2×D8C2×D13semidirect
82. D16C2×D13direct (N × H)
85. C2×C16C2×D13semidirect
87. C2×C13C2×D16semidirect
90. D13C2×D16direct (N × H)
102. D8C22×D13semidirect
108. C16C22×D13semidirect
109. C13C22×D16semidirect
141. C2D13×D16direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×D132
C2×C13×D162
C2×#880662
D13×D162
C2×D2082
C2×C16×D132
C22×D1613