Finite Group Databasebeta

← C2×SD16×D409 #39910018

Subgroups — C2×SD16×D409 #39910018

Order 26176.

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×D409C211yesmaximal, characteristic, complemented
2C2×D4×D409C211yesmaximal, characteristic
3C2×#20266977C211yesmaximal, characteristic, complemented
4C2×#20266976C211yesmaximal, characteristic, complemented
5C2×#20266975C211yesmaximal, characteristic, complemented
6SD16×D409C218yesmaximal, direct product factor
7C2×C8×D409C211yesmaximal, characteristic, complemented
8C2×SD16×C409C211yesmaximal, characteristic, complemented
9C23×D409—21no—
10C2×Dic818—21no—
11C2×Dic818C2211yescharacteristic, complemented
12Q8×D409—22no—
13Q8×D409C2214yescomplemented
14C2×D1636C2211yescharacteristic
15C2×C22⋊D409—21no—
16D4×D409—22no—
17D4×D409C2214yes—
18C2×C4×D409—21no—
19C2×C4×D409C2211yescharacteristic
20#20266977C2214yescomplemented
21#20266976C2214yescomplemented
22#20266975C2214yescomplemented
23C2×#15692543C2211yescharacteristic, complemented
24C8×D409C2214yescomplemented
25C2×Q8×C409C2211yescharacteristic, complemented
26C2×D4×C409C2211yescharacteristic
27SD16×C409C2214yescomplemented
28C2×C8×C409C2211yescharacteristic, complemented
29C22×D409—21no—
30C22×D409—24no—
31C22×D409—44no—
32C22×D409D411yescharacteristic
33Dic818—21no—
34Dic818—24no—
35Dic818C2312yescomplemented
36D1636—21no—
37D1636C2312yes—
38C22⋊D409—24no—
39C2×Dic409—21no—
40C2×Dic409D411yescharacteristic
41C4×D409—24no—
42C4×D409D412yes—
43C4×D409C2312yes—
44#15692543C2312yescomplemented
45C23×C409—21no—
46Q8×C409—21no—
47Q8×C409C2312yescomplemented
48D4×C409—21no—
49D4×C409C2312yes—
50C2×C4×C409—21no—
51C2×C4×C409C2311yescharacteristic
52C8×C409C2312yescomplemented
53C22×C409—22no—
54C22×C409—42no—
55C22×C409C2×D411yescharacteristic
56C2×D409—22no—
57C2×D409—42no—
58C2×D409—48no—
59C2×D409SD1614yesdirect product factor
60C2×D409C2×D412yes—
61C4×C409—22no—
62C4×C409C2×D411yescharacteristic
63C4×C409C2411yescharacteristic
64Dic409—22no—
65Dic409C2×D412yes—
66C2×C409—42no—
67C2×C409C2×SD1612yescomplemented
68C2×C409C22×D411yescharacteristic
69D409—42no—
70D409C2×SD1614yesdirect product factor
71C409C22×SD1611yescharacteristic, complemented, Sylow
72C22×SD16—4091nomaximal, Sylow
73C22×Q8—4091no—
74C22×D4—4091no—
75C2×SD16—4091no—
76C2×SD16—4091no—
77C2×SD16—4098no—
78C2×SD16—4091no—
79C2×SD16D40911yescharacteristic, direct product factor
80C22×C8—4091no—
81C24—8181no—
82C2×Q8—8181no—
83C2×Q8—8182no—
84C2×Q8—4094no—
85C2×Q8—4091no—
86C2×Q8C2×D40911yescharacteristic, complemented
87C2×D4—8182no—
88C2×D4—8181no—
89C2×D4—4094no—
90C2×D4—4091no—
91C2×D4C2×D40911yescharacteristic
92C22×C4—8181no—
93C22×C4—4091no—
94SD16—4094no—
95SD16—4094no—
96SD16—4094no—
97SD16C2×D40914yesdirect product factor
98C2×C8—4091no—
99C2×C8—4094no—
100C2×C8C2×D40911yescharacteristic, complemented
101C23—21no—
102C23—8184no—
103C23—8181no—
104C23—16364no—
105C23—4091no—
106Q8—21no—
107Q8—8184no—
108Q8—8181no—
109Q8—4092no—
110Q8C22×D40912yescomplemented
111D4—21no—
112D4—8184no—
113D4—8181no—
114D4—4092no—
115D4C22×D40912yes—
116C2×C4—21no—
117C2×C4—8184no—
118C2×C4—8181no—
119C2×C4—4091no—
120C2×C4—4092no—
121C2×C4—4092no—
122C2×C4C22×D40911yescharacteristic
123C8—4092no—
124C8C22×D40912yescomplemented
125C22—22no—
126C22—42no—
127C22—8182no—
128C22—16368no—
129C22—16362no—
130C22—4094no—
131C22—4092no—
132C22D4×D40911yescharacteristic
133C4—22no—
134C4—8182no—
135C4—4092no—
136C4D4×D40911yescharacteristic
137C4C23×D40911yescharacteristic
138C2—42no—
139C2—16362no—
140C2—4094no—
141C2SD16×D40912yesdirect product factor
142C2C2×D4×D40911yescharacteristic
subgroupG/H
centerC22D4×D409
commutator, cosocleC4×C409C24
FrattiniC4C23×D409
FittingC2×SD16×C409C2
socleC22×C409C2×D4
prime radicalC2×D4×D409C2
hypercenterC2×SD16D409
hypocenterC409C22×SD16
LCSG ▷ C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D409C2semidirect
3. C2×#20266977C2semidirect
4. C2×#20266976C2semidirect
5. C2×#20266975C2semidirect
6. SD16×D409C2direct (N × H)
7. C2×C8×D409C2semidirect
8. C2×SD16×C409C2semidirect
11. C2×Dic818C22semidirect
13. Q8×D409C22semidirect
20. #20266977C22semidirect
21. #20266976C22semidirect
22. #20266975C22semidirect
23. C2×#15692543C22semidirect
24. C8×D409C22semidirect
25. C2×Q8×C409C22semidirect
27. SD16×C409C22semidirect
28. C2×C8×C409C22semidirect
35. Dic818C23semidirect
44. #15692543C23semidirect
47. Q8×C409C23semidirect
52. C8×C409C23semidirect
59. C2×D409SD16direct (N × H)
67. C2×C409C2×SD16semidirect
70. D409C2×SD16direct (N × H)
71. C409C22×SD16semidirect
79. C2×SD16D409direct (N × H)
86. C2×Q8C2×D409semidirect
97. SD16C2×D409direct (N × H)
100. C2×C8C2×D409semidirect
110. Q8C22×D409semidirect
124. C8C22×D409semidirect
141. C2SD16×D409direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D4092
C2×D4×D4092
C2×#202669772
C2×#202669762
C2×#202669752
SD16×D4092
C2×C8×D4092
C2×SD16×C4092
C22×SD16409