Finite Group Databasebeta

← C2×SD16×D47 #15689894

Subgroups — C2×SD16×D47 #15689894

Order 3008.

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×D47C211yesmaximal, characteristic, complemented
2C2×D4×D47C211yesmaximal, characteristic
3C2×#10625325C211yesmaximal, characteristic, complemented
4C2×#10625335C211yesmaximal, characteristic, complemented
5C2×#10625336C211yesmaximal, characteristic, complemented
6SD16×D47C218yesmaximal, direct product factor
7C2×C8×D47C211yesmaximal, characteristic, complemented
8C2×SD16×C47C211yesmaximal, characteristic, complemented
9C23×D47—21no—
10C2×Q8×C47C2211yescharacteristic, complemented
11C2×D4×C47C2211yescharacteristic
12C2×C22⋊D47—21no—
13Q8×D47—22no—
14Q8×D47C2214yescomplemented
15D4×D47—22no—
16D4×D47C2214yes—
17C2×D188C2211yescharacteristic
18C2×C4×D47—21no—
19C2×C4×D47C2211yescharacteristic
20C2×Dic94—21no—
21C2×Dic94C2211yescharacteristic, complemented
22SD16×C47C2214yescomplemented
23C2×C8×C47C2211yescharacteristic, complemented
24#10625336C2214yescomplemented
25#10625335C2214yescomplemented
26C2×C47⋊C8C2211yescharacteristic, complemented
27#10625325C2214yescomplemented
28C8×D47C2214yescomplemented
29C23×C47—21no—
30C22×D47—21no—
31C22×D47—24no—
32C22×D47—44no—
33C22×D47D411yescharacteristic
34Q8×C47—21no—
35Q8×C47C2312yescomplemented
36D4×C47—21no—
37D4×C47C2312yes—
38C2×C4×C47—21no—
39C2×C4×C47C2311yescharacteristic
40C22⋊D47—24no—
41C2×Dic47—21no—
42C2×Dic47D411yescharacteristic
43D188—21no—
44D188C2312yes—
45C4×D47—24no—
46C4×D47D412yes—
47C4×D47C2312yes—
48Dic94—21no—
49Dic94—24no—
50Dic94C2312yescomplemented
51C8×C47C2312yescomplemented
52C47⋊C8C2312yescomplemented
53C22×C47—22no—
54C22×C47—42no—
55C22×C47C2×D411yescharacteristic
56C2×D47—22no—
57C2×D47—42no—
58C2×D47—48no—
59C2×D47SD1614yesdirect product factor
60C2×D47C2×D412yes—
61C4×C47—22no—
62C4×C47C2×D411yescharacteristic
63C4×C47C2411yescharacteristic
64Dic47—22no—
65Dic47C2×D412yes—
66C2×C47—42no—
67C2×C47C2×SD1612yescomplemented
68C2×C47C22×D411yescharacteristic
69D47—42no—
70D47C2×SD1614yesdirect product factor
71C22×SD16—471nomaximal, Sylow
72C47C22×SD1611yescharacteristic, complemented, Sylow
73C22×Q8—471no—
74C22×D4—471no—
75C2×SD16—471no—
76C2×SD16—471no—
77C2×SD16—478no—
78C2×SD16—471no—
79C2×SD16D4711yescharacteristic, direct product factor
80C22×C8—471no—
81C24—941no—
82C2×Q8—474no—
83C2×Q8—471no—
84C2×Q8—941no—
85C2×Q8—942no—
86C2×Q8C2×D4711yescharacteristic, complemented
87C2×D4—474no—
88C2×D4—471no—
89C2×D4—942no—
90C2×D4—941no—
91C2×D4C2×D4711yescharacteristic
92C22×C4—471no—
93C22×C4—941no—
94SD16—474no—
95SD16—474no—
96SD16—474no—
97SD16C2×D4714yesdirect product factor
98C2×C8—471no—
99C2×C8—474no—
100C2×C8C2×D4711yescharacteristic, complemented
101C23—21no—
102C23—471no—
103C23—944no—
104C23—941no—
105C23—1884no—
106Q8—21no—
107Q8—472no—
108Q8—944no—
109Q8—941no—
110Q8C22×D4712yescomplemented
111D4—21no—
112D4—472no—
113D4—944no—
114D4—941no—
115D4C22×D4712yes—
116C2×C4—21no—
117C2×C4—471no—
118C2×C4—472no—
119C2×C4—472no—
120C2×C4—944no—
121C2×C4—941no—
122C2×C4C22×D4711yescharacteristic
123C8—472no—
124C8C22×D4712yescomplemented
125C22—22no—
126C22—42no—
127C22—474no—
128C22—472no—
129C22—942no—
130C22—1888no—
131C22—1882no—
132C22D4×D4711yescharacteristic
133C4—22no—
134C4—472no—
135C4—942no—
136C4D4×D4711yescharacteristic
137C4C23×D4711yescharacteristic
138C2—42no—
139C2—474no—
140C2—1882no—
141C2SD16×D4712yesdirect product factor
142C2C2×D4×D4711yescharacteristic
subgroupG/H
centerC22D4×D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
FittingC2×SD16×C47C2
socleC22×C47C2×D4
prime radicalC2×D4×D47C2
hypercenterC2×SD16D47
hypocenterC47C22×SD16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D47C2semidirect
3. C2×#10625325C2semidirect
4. C2×#10625335C2semidirect
5. C2×#10625336C2semidirect
6. SD16×D47C2direct (N × H)
7. C2×C8×D47C2semidirect
8. C2×SD16×C47C2semidirect
10. C2×Q8×C47C22semidirect
14. Q8×D47C22semidirect
21. C2×Dic94C22semidirect
22. SD16×C47C22semidirect
23. C2×C8×C47C22semidirect
24. #10625336C22semidirect
25. #10625335C22semidirect
26. C2×C47⋊C8C22semidirect
27. #10625325C22semidirect
28. C8×D47C22semidirect
35. Q8×C47C23semidirect
50. Dic94C23semidirect
51. C8×C47C23semidirect
52. C47⋊C8C23semidirect
59. C2×D47SD16direct (N × H)
67. C2×C47C2×SD16semidirect
70. D47C2×SD16direct (N × H)
72. C47C22×SD16semidirect
79. C2×SD16D47direct (N × H)
86. C2×Q8C2×D47semidirect
97. SD16C2×D47direct (N × H)
100. C2×C8C2×D47semidirect
110. Q8C22×D47semidirect
124. C8C22×D47semidirect
141. C2SD16×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D472
C2×D4×D472
C2×#106253252
C2×#106253352
C2×#106253362
SD16×D472
C2×C8×D472
C2×SD16×C472
C22×SD1647