Finite Group Databasebeta

← #20261637

Subgroups — #20261637

Order 6208.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690870C211yesmaximal, characteristic
2#15690868C211yesmaximal, characteristic
3#15690793C211yesmaximal, characteristic
4#13095520—21no—
5C22⋊#87604—21no—
6C2×C22⋊D97C2211yescharacteristic
7#13095490—21no—
8C22⋊Dic97C411yescharacteristic, complemented
9#13095488—21no—
10C22×C4×C97C411yescharacteristic, complemented
11C23×C97C2×C411yescharacteristic
12C22×D97D411yescharacteristic
13C2×#87604—41no—
14C2×C4×C97—21no—
15C2×C4×C97—41no—
16C22⋊D97—41no—
17C2×Dic97—21no—
18C2×Dic97D411yescharacteristic
19#11715897—41no—
20C22×C97—21no—
21C22×C97—41no—
22C22×C97C22⋊C411yescharacteristic
23C2×D97—21no—
24C2×D97—41no—
25#87604—81no—
26C4×C97—41no—
27Dic97—21no—
28Dic97—41no—
29C2×C97—21no—
30C2×C97—41no—
31C2×C97#9911yescharacteristic
32D97—41no—
33C97#35211yescharacteristic, complemented, Sylow
34#352—971nomaximal, Sylow
35#123—971no—
36#100—971no—
37#99—971no—
38C2×D4—971no—
39C22×C4#8760411yescharacteristic, complemented
40M16—1941no—
41C4⋊C4—1941no—
42C22⋊C4—971no—
43C22⋊C4—1941no—
44C22⋊C4—1941no—
45C23—971no—
46C23C2×#8760411yescharacteristic
47D4—3881no—
48C2×C4—21no—
49C2×C4—41no—
50C2×C4—971no—
51C2×C4—3881no—
52C2×C4—1941no—
53C8—3881no—
54C22—21no—
55C22—41no—
56C22—3881no—
57C22—1941no—
58C22C22⋊#8760411yescharacteristic
59C4—41no—
60C4—7761no—
61C4—3881no—
62C4—1941no—
63C2—21no—
64C2—41no—
65C2—3881no—
66C2#1569086811yescharacteristic
subgroupG/H
centerC2#15690868
commutatorC23×C97C2×C4
FrattiniC23C2×#87604
FittingC22×C4×C97C4
socleC2×C97#99
hypercenterC22×C4#87604
hypocenterC97#352
LCSG ▷ C23×C97 ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C22⋊Dic97C4semidirect
10. C22×C4×C97C4semidirect
33. C97#352semidirect
39. C22×C4#87604semidirect