Finite Group Databasebeta

← SD16×Dic373 #37559511

Subgroups — SD16×Dic373 #37559511

Order 23872.

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×Dic373C211yesmaximal, characteristic, complemented
2D4×Dic373C211yesmaximal, characteristic
3#26045724C211yesmaximal, characteristic, complemented
4#26045716C211yesmaximal, characteristic, complemented
5#26045713C211yesmaximal, characteristic
6C8×Dic373C211yesmaximal, characteristic, complemented
7C2×SD16×C373C211yesmaximal, characteristic
8C22×Dic373—21no—
9C2×#15688412C2211yescharacteristic
10C4⋊Dic373—21no—
11C4⋊Dic373C2211yescharacteristic
12C4⋊Dic373C2211yescharacteristic
13C22⋊Dic373—21no—
14C4×Dic373—21no—
15C4×Dic373C2211yescharacteristic
16C2×Q8×C373C2211yescharacteristic
17C2×D4×C373C2211yescharacteristic
18SD16×C373C414yescomplemented
19C2×C8×C373C2211yescharacteristic
20C2×Dic373—21no—
21C2×Dic373—21no—
22C2×Dic373—42no—
23C2×Dic373D411yescharacteristic
24C2×Dic373D411yescharacteristic
25#15688412—21no—
26C23×C373—21no—
27Q8×C373—21no—
28Q8×C373C2×C412yescomplemented
29D4×C373—21no—
30D4×C373C2×C412yes—
31C2×C4×C373—21no—
32C2×C4×C373C2311yescharacteristic
33C8×C373C2×C412yescomplemented
34C22×C373—22no—
35C22×C373—41no—
36C22×C373—41no—
37C22×C373C2×D411yescharacteristic
38C4×C373—22no—
39C4×C373C22×C411yescharacteristic
40C4×C373#4111yescharacteristic
41Dic373—21no—
42Dic373—41no—
43Dic373—41no—
44Dic373SD1612yesdirect product factor
45C2×C373—42no—
46C2×C373C4×D411yescharacteristic
47C2×C373C2×SD1611yescharacteristic
48C2×C373#13511yescharacteristic
49C373C4×SD1611yescharacteristic, complemented, Sylow
50C4×SD16—3731nomaximal, Sylow
51C2×SD16D37311yescharacteristic
52C4×Q8—3731no—
53C4×D4—3731no—
54#106—3731no—
55#103—3731no—
56#102—3731no—
57C4×C8—3731no—
58C2×Q8C2×D37311yescharacteristic
59C2×D4C2×D37311yescharacteristic
60C22×C4—7461no—
61SD16Dic37314yesdirect product factor
62C2×C8—3731no—
63C2×C8C2×D37311yescharacteristic
64C4⋊C4—3731no—
65C4⋊C4—3731no—
66C4⋊C4—7461no—
67C22⋊C4—7461no—
68C42—3731no—
69C42—7461no—
70C23—21no—
71Q8—21no—
72Q8C2×Dic37312yescomplemented
73D4—21no—
74D4C2×Dic37312yes—
75C2×C4—21no—
76C2×C4—3731no—
77C2×C4—3731no—
78C2×C4—14922no—
79C2×C4—7461no—
80C2×C4—7461no—
81C2×C4C22×D37311yescharacteristic
82C8—7461no—
83C8C2×Dic37312yescomplemented
84C22—22no—
85C22—41no—
86C22—41no—
87C22D4×D37311yescharacteristic
88C4—22no—
89C4—3732no—
90C4—14921no—
91C4—14921no—
92C4—7461no—
93C4C22×Dic37311yescharacteristic
94C4#2023860911yescharacteristic
95C2—42no—
96C2D4×Dic37311yescharacteristic
97C2SD16×D37311yescharacteristic
98C2#2604581311yescharacteristic
subgroupG/H
centerC22D4×D373
commutatorC4×C373C22×C4
FrattiniC2×C4C22×D373
FittingC2×SD16×C373C2
socleC22×C373C2×D4
prime radicalC2×D4×C373C22
cosocleC2×C4×C373C23
hypercenterC2×SD16D373
hypocenterC373C4×SD16
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×Dic373C2semidirect
3. #26045724C2semidirect
4. #26045716C2semidirect
6. C8×Dic373C2semidirect
18. SD16×C373C4semidirect
28. Q8×C373C2×C4semidirect
33. C8×C373C2×C4semidirect
44. Dic373SD16direct (N × H)
49. C373C4×SD16semidirect
61. SD16Dic373direct (N × H)
72. Q8C2×Dic373semidirect
83. C8C2×Dic373semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic3732
D4×Dic3732
#260457242
#260457162
#260457132
C8×Dic3732
C2×SD16×C3732
C4×SD16373