Finite Group Databasebeta

← #20260524

Subgroups — #20260524

Order 6208.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690791C211yesmaximal, characteristic
2#15690727C211yesmaximal, characteristic
3#99×C97C211yesmaximal, characteristic
4C22×Dic97C411yescharacteristic, complemented
5#13095495—21no—
6#13095490—21no—
7C22⋊Dic97—21no—
8C22⋊Dic97C411yescharacteristic, complemented
9C2×D4×C97C2211yescharacteristic
10C22⋊C4×C97—21no—
11C23×C97C2×C411yescharacteristic
12C23×C97D411yescharacteristic
13D4×C97—41no—
14C2×C4×C97—41no—
15C2×C4×C97D411yescharacteristic
16C2×Dic97—21no—
17C2×Dic97—21no—
18C2×Dic97—41no—
19#11715895—41no—
20C22×C97—21no—
21C22×C97—21no—
22C22×C97—41no—
23C22×C97—41no—
24C22×C97C22⋊C411yescharacteristic
25C4×C97—21no—
26C4×C97—81no—
27Dic97—41no—
28Dic97—41no—
29C2×C97—21no—
30C2×C97—41no—
31C2×C97—41no—
32C2×C97#9911yescharacteristic
33C97#35211yescharacteristic, complemented, Sylow
34#352—971nomaximal, Sylow
35#123—971no—
36#100—971no—
37#99D9711yescharacteristic
38C2×D4C2×D9711yescharacteristic
39C22×C4—971no—
40M16—1941no—
41C4⋊C4—1941no—
42C22⋊C4—21no—
43C22⋊C4—971no—
44C22⋊C4—1941no—
45C23C4×D9711yescharacteristic
46C23C22⋊D9711yescharacteristic
47D4—41no—
48C2×C4—41no—
49C2×C4—3881no—
50C2×C4—1941no—
51C2×C4—1941no—
52C2×C4D38811yescharacteristic
53C8—3881no—
54C22—21no—
55C22—21no—
56C22—41no—
57C22—41no—
58C22#1309548811yescharacteristic
59C4—21no—
60C4—81no—
61C4—3881no—
62C4—3881no—
63C2—21no—
64C2—41no—
65C2—41no—
66C2#1569072411yescharacteristic
subgroupG/H
centerC2#15690724
commutatorC23×C97C2×C4
FrattiniC2×D4C2×D97
Fitting#99×C97C2
socleC2×C97#99
hypercenter#99D97
hypocenterC97#352
LCSG ▷ C23×C97 ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C22×Dic97C4semidirect
8. C22⋊Dic97C4semidirect
33. C97#352semidirect