Finite Group Databasebeta

← #20260886

Subgroups — #20260886

Order 6208.

188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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×#13095499C212yesmaximal, complemented
2#15690789C211yesmaximal, characteristic, complemented
3#15690731C212yesmaximal, complemented
4C22⋊#11715895C211yesmaximal, characteristic, complemented
5C22×D4×C97C211yesmaximal, characteristic
6C2×Dic194C2211yescharacteristic, complemented
7#13095499—24no—
8C2×#11715895C2212yescomplemented
9C4⋊Dic97C2211yescharacteristic, complemented
10#13095490—21no—
11C22⋊Dic97—21no—
12C24×C97—21no—
13C2×D4×C97—24no—
14C2×D4×C97—21no—
15C2×D4×C97C2212yes—
16C22×C4×C97C2211yescharacteristic
17C23×C97—24no—
18C23×C97—22no—
19C23×C97—42no—
20C23×C97—42no—
21C23×C97D411yescharacteristic
22D4×C97—24no—
23D4×C97—22no—
24D4×C97D414yes—
25C2×C4×C97—22no—
26C2×C4×C97D411yescharacteristic
27C2×C4×C97C2311yescharacteristic
28C2×Dic97—21no—
29C2×Dic97—21no—
30Dic194—22no—
31#11715895—22no—
32C22×C97—21no—
33C22×C97—21no—
34C22×C97—24no—
35C22×C97—48no—
36C22×C97—42no—
37C22×C97—42no—
38C22×C97SD1612yescomplemented
39C22×C97C2×D411yescharacteristic
40C4×C97—21no—
41C4×C97C2×D412yes—
42Dic97—41no—
43Dic97—41no—
44C2×C97—22no—
45C2×C97—44no—
46C2×C97#12011yescharacteristic
47C2×C97C2×SD1611yescharacteristic
48C2×C97AGL(1,ℤ/8)11yescharacteristic
49C97#45011yescharacteristic, complemented, Sylow
50#450—971nomaximal, Sylow
51C22×D4D9711yescharacteristic
52C2×SD16—972no—
53C22⋊Q8—971no—
54#102—972no—
55C22⋊C8—971no—
56C24—21no—
57C2×Q8—971no—
58C2×D4—24no—
59C2×D4—21no—
60C2×D4C2×D9712yes—
61C22×C4C2×D9711yescharacteristic
62SD16—1944no—
63C2×C8—972no—
64C4⋊C4—971no—
65C4⋊C4—1941no—
66C22⋊C4—1941no—
67C23—24no—
68C23—22no—
69C23—42no—
70C23—42no—
71C23C22⋊D9711yescharacteristic
72Q8—1942no—
73D4—24no—
74D4—22no—
75D4C22⋊D9714yes—
76C2×C4—22no—
77C2×C4—1941no—
78C2×C4—1941no—
79C2×C4C22⋊D9711yescharacteristic
80C2×C4C22×D9711yescharacteristic
81C8—1942no—
82C22—21no—
83C22—21no—
84C22—24no—
85C22—48no—
86C22—42no—
87C22—42no—
88C22#1309549912yescomplemented
89C22C2×C22⋊D9711yescharacteristic
90C4—21no—
91C4—3881no—
92C4—3881no—
93C4C2×C22⋊D9712yes—
94C2—22no—
95C2—44no—
96C2#1569077911yescharacteristic
97C2C2×#1309549911yescharacteristic
98C2#1569083611yescharacteristic
subgroupG/H
centerC22C2×C22⋊D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC22×D4×C97C2
socleC22×C97C2×D4
hypercenterC22×D4D97
hypocenterC97#450
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13095499C2semidirect
2. #15690789C2semidirect
3. #15690731C2semidirect
4. C22⋊#11715895C2semidirect
6. C2×Dic194C22semidirect
8. C2×#11715895C22semidirect
9. C4⋊Dic97C22semidirect
38. C22×C97SD16semidirect
49. C97#450semidirect
88. C22#13095499semidirect