Finite Group Databasebeta

← SD16×Dic97 #20260824

Subgroups — SD16×Dic97 #20260824

Order 6208.

122 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic97C211yesmaximal, characteristic, complemented
2D4×Dic97C211yesmaximal, characteristic
3#15690742C211yesmaximal, characteristic, complemented
4#15690734C211yesmaximal, characteristic, complemented
5#15690731C211yesmaximal, characteristic
6C8×Dic97C211yesmaximal, characteristic, complemented
7C2×SD16×C97C211yesmaximal, characteristic
8C22×Dic97—21no—
9C2×#11715895C2211yescharacteristic
10C4⋊Dic97—21no—
11C4⋊Dic97C2211yescharacteristic
12C4⋊Dic97C2211yescharacteristic
13C22⋊Dic97—21no—
14C4×Dic97—21no—
15C4×Dic97C2211yescharacteristic
16C2×Q8×C97C2211yescharacteristic
17C2×D4×C97C2211yescharacteristic
18SD16×C97C414yescomplemented
19C2×C8×C97C2211yescharacteristic
20C23×C97—21no—
21Q8×C97—21no—
22Q8×C97C2×C412yescomplemented
23D4×C97—21no—
24D4×C97C2×C412yes—
25C2×C4×C97—21no—
26C2×C4×C97C2311yescharacteristic
27C2×Dic97—21no—
28C2×Dic97—21no—
29C2×Dic97—42no—
30C2×Dic97D411yescharacteristic
31C2×Dic97D411yescharacteristic
32C8×C97C2×C412yescomplemented
33#11715895—21no—
34C22×C97—22no—
35C22×C97—41no—
36C22×C97—41no—
37C22×C97C2×D411yescharacteristic
38C4×C97—22no—
39C4×C97C22×C411yescharacteristic
40C4×C97#4111yescharacteristic
41Dic97—21no—
42Dic97—41no—
43Dic97—41no—
44Dic97SD1612yesdirect product factor
45C2×C97—42no—
46C2×C97C4×D411yescharacteristic
47C2×C97C2×SD1611yescharacteristic
48C2×C97#13511yescharacteristic
49C97C4×SD1611yescharacteristic, complemented, Sylow
50C4×SD16—971nomaximal, Sylow
51C2×SD16D9711yescharacteristic
52C4×Q8—971no—
53C4×D4—971no—
54#106—971no—
55#103—971no—
56#102—971no—
57C4×C8—971no—
58C2×Q8C2×D9711yescharacteristic
59C2×D4C2×D9711yescharacteristic
60C22×C4—1941no—
61SD16Dic9714yesdirect product factor
62C2×C8—971no—
63C2×C8C2×D9711yescharacteristic
64C4⋊C4—971no—
65C4⋊C4—971no—
66C4⋊C4—1941no—
67C22⋊C4—1941no—
68C42—971no—
69C42—1941no—
70C23—21no—
71Q8—21no—
72Q8C2×Dic9712yescomplemented
73D4—21no—
74D4C2×Dic9712yes—
75C2×C4—21no—
76C2×C4—971no—
77C2×C4—971no—
78C2×C4—3882no—
79C2×C4—1941no—
80C2×C4—1941no—
81C2×C4C22×D9711yescharacteristic
82C8—1941no—
83C8C2×Dic9712yescomplemented
84C22—22no—
85C22—41no—
86C22—41no—
87C22D4×D9711yescharacteristic
88C4—22no—
89C4—972no—
90C4—3881no—
91C4—3881no—
92C4—1941no—
93C4C22×Dic9711yescharacteristic
94C4#1309551011yescharacteristic
95C2—42no—
96C2D4×Dic9711yescharacteristic
97C2SD16×D9711yescharacteristic
98C2#1569083111yescharacteristic
subgroupG/H
centerC22D4×D97
commutatorC4×C97C22×C4
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC22×C97C2×D4
hypercenterC2×SD16D97
hypocenterC97C4×SD16
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×Dic97C2semidirect
3. #15690742C2semidirect
4. #15690734C2semidirect
6. C8×Dic97C2semidirect
18. SD16×C97C4semidirect
22. Q8×C97C2×C4semidirect
32. C8×C97C2×C4semidirect
44. Dic97SD16direct (N × H)
49. C97C4×SD16semidirect
61. SD16Dic97direct (N × H)
72. Q8C2×Dic97semidirect
83. C8C2×Dic97semidirect