Finite Group Databasebeta

← C2×SD16×D29 #14271934

Subgroups — C2×SD16×D29 #14271934

Order 1856.

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×D29C211yesmaximal, characteristic, complemented
2C2×D4×D29C211yesmaximal, characteristic
3C2×SD16×C29C211yesmaximal, characteristic, complemented
4C2×#90784C211yesmaximal, characteristic, complemented
5C2×#90783C211yesmaximal, characteristic, complemented
6SD16×D29C218yesmaximal, direct product factor
7C2×#90773C211yesmaximal, characteristic, complemented
8C2×C8×D29C211yesmaximal, characteristic, complemented
9C23×D29—21no—
10C2×Q8×C29C2211yescharacteristic, complemented
11C2×D4×C29C2211yescharacteristic
12C2×C22⋊D29—21no—
13Q8×D29—22no—
14Q8×D29C2214yescomplemented
15D4×D29—22no—
16D4×D29C2214yes—
17C2×D116C2211yescharacteristic
18C2×C4×D29—21no—
19C2×C4×D29C2211yescharacteristic
20C2×Dic58—21no—
21C2×Dic58C2211yescharacteristic, complemented
22SD16×C29C2214yescomplemented
23C2×C8×C29C2211yescharacteristic, complemented
24#90784C2214yescomplemented
25#90783C2214yescomplemented
26C2×#6597C2211yescharacteristic, complemented
27#90773C2214yescomplemented
28C8×D29C2214yescomplemented
29C23×C29—21no—
30C22×D29—21no—
31C22×D29—24no—
32C22×D29—44no—
33C22×D29D411yescharacteristic
34Q8×C29—21no—
35Q8×C29C2312yescomplemented
36D4×C29—21no—
37D4×C29C2312yes—
38C2×C4×C29—21no—
39C2×C4×C29C2311yescharacteristic
40C22⋊D29—24no—
41C2×Dic29—21no—
42C2×Dic29D411yescharacteristic
43D116—21no—
44D116C2312yes—
45C4×D29—24no—
46C4×D29D412yes—
47C4×D29C2312yes—
48Dic58—21no—
49Dic58—24no—
50Dic58C2312yescomplemented
51C8×C29C2312yescomplemented
52#6597C2312yescomplemented
53C22×C29—22no—
54C22×C29—42no—
55C22×C29C2×D411yescharacteristic
56C2×D29—22no—
57C2×D29—42no—
58C2×D29—48no—
59C2×D29SD1614yesdirect product factor
60C2×D29C2×D412yes—
61C4×C29—22no—
62C4×C29C2×D411yescharacteristic
63C4×C29C2411yescharacteristic
64Dic29—22no—
65Dic29C2×D412yes—
66C22×SD16—291nomaximal, Sylow
67C2×C29—42no—
68C2×C29C2×SD1612yescomplemented
69C2×C29C22×D411yescharacteristic
70D29—42no—
71D29C2×SD1614yesdirect product factor
72C22×Q8—291no—
73C22×D4—291no—
74C2×SD16—291no—
75C2×SD16—291no—
76C2×SD16—298no—
77C2×SD16—291no—
78C2×SD16D2911yescharacteristic, direct product factor
79C22×C8—291no—
80C29C22×SD1611yescharacteristic, complemented, Sylow
81C24—581no—
82C2×Q8—294no—
83C2×Q8—291no—
84C2×Q8—581no—
85C2×Q8—582no—
86C2×Q8C2×D2911yescharacteristic, complemented
87C2×D4—294no—
88C2×D4—291no—
89C2×D4—582no—
90C2×D4—581no—
91C2×D4C2×D2911yescharacteristic
92C22×C4—291no—
93C22×C4—581no—
94SD16—294no—
95SD16—294no—
96SD16—294no—
97SD16C2×D2914yesdirect product factor
98C2×C8—291no—
99C2×C8—294no—
100C2×C8C2×D2911yescharacteristic, complemented
101C23—21no—
102C23—291no—
103C23—584no—
104C23—581no—
105C23—1164no—
106Q8—21no—
107Q8—292no—
108Q8—584no—
109Q8—581no—
110Q8C22×D2912yescomplemented
111D4—21no—
112D4—292no—
113D4—584no—
114D4—581no—
115D4C22×D2912yes—
116C2×C4—21no—
117C2×C4—291no—
118C2×C4—292no—
119C2×C4—292no—
120C2×C4—584no—
121C2×C4—581no—
122C2×C4C22×D2911yescharacteristic
123C8—292no—
124C8C22×D2912yescomplemented
125C22—22no—
126C22—42no—
127C22—292no—
128C22—294no—
129C22—582no—
130C22—1168no—
131C22—1162no—
132C22D4×D2911yescharacteristic
133C4—22no—
134C4—292no—
135C4—582no—
136C4D4×D2911yescharacteristic
137C4C23×D2911yescharacteristic
138C2—42no—
139C2—294no—
140C2—1162no—
141C2SD16×D2912yesdirect product factor
142C2C2×D4×D2911yescharacteristic
subgroupG/H
centerC22D4×D29
commutator, cosocleC4×C29C24
FrattiniC4C23×D29
FittingC2×SD16×C29C2
socleC22×C29C2×D4
prime radicalC2×D4×D29C2
hypercenterC2×SD16D29
hypocenterC29C22×SD16
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D29C2semidirect
3. C2×SD16×C29C2semidirect
4. C2×#90784C2semidirect
5. C2×#90783C2semidirect
6. SD16×D29C2direct (N × H)
7. C2×#90773C2semidirect
8. C2×C8×D29C2semidirect
10. C2×Q8×C29C22semidirect
14. Q8×D29C22semidirect
21. C2×Dic58C22semidirect
22. SD16×C29C22semidirect
23. C2×C8×C29C22semidirect
24. #90784C22semidirect
25. #90783C22semidirect
26. C2×#6597C22semidirect
27. #90773C22semidirect
28. C8×D29C22semidirect
35. Q8×C29C23semidirect
50. Dic58C23semidirect
51. C8×C29C23semidirect
52. #6597C23semidirect
59. C2×D29SD16direct (N × H)
68. C2×C29C2×SD16semidirect
71. D29C2×SD16direct (N × H)
78. C2×SD16D29direct (N × H)
80. C29C22×SD16semidirect
86. C2×Q8C2×D29semidirect
97. SD16C2×D29direct (N × H)
100. C2×C8C2×D29semidirect
110. Q8C22×D29semidirect
124. C8C22×D29semidirect
141. C2SD16×D29direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D292
C2×D4×D292
C2×SD16×C292
C2×#907842
C2×#907832
SD16×D292
C2×#907732
C2×C8×D292
C22×SD1629