Finite Group Databasebeta

← #34059836

Subgroups — #34059836

Order 19072.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750534C211yesmaximal, characteristic
2#23750532C211yesmaximal, characteristic
3#23749982C211yesmaximal, characteristic
4#18011972—21no—
5#18011970—21no—
6#18011899C2211yescharacteristic
7#18011834—21no—
8#18011831—21no—
9C4×#11924746C411yescharacteristic, complemented
10#125×C149C411yescharacteristic, complemented
11#14558745—41no—
12C22⋊#10597010—41no—
13C2×Dic298D411yescharacteristic
14C2×D596D411yescharacteristic
15C2×#11924746—21no—
16#14558713—41no—
17C4⋊C4×C149—21no—
18C4⋊C4×C149—41no—
19C42×C149C2×C411yescharacteristic
20C2×#10597010—81no—
21#11924753—81no—
22C22×D149—21no—
23Dic298—41no—
24D596—41no—
25C2×Dic149—21no—
26#11924746—41no—
27C2×C4×C149—21no—
28C2×C4×C149—41no—
29C2×C4×C149C22⋊C411yescharacteristic
30C22×C149#9911yescharacteristic
31C2×D149—41no—
32C2×D149—81no—
33#10597010—161no—
34C4×C149—21no—
35C4×C149—41no—
36C4×C149—81no—
37Dic149—41no—
38C2×C149—21no—
39C2×C149#35411yescharacteristic
40D149—81no—
41C149#141411yescharacteristic, complemented, Sylow
42#1414—1491nomaximal, Sylow
43#488—1491no—
44#355—1491no—
45#354—1491no—
46#125#1059701011yescharacteristic, complemented
47#124—1491no—
48#103—2981no—
49#102—2981no—
50#101—2981no—
51#99—2981no—
52C4×C8—1491no—
53C2×Q8—1491no—
54C2×D4—1491no—
55M16—5961no—
56C2×C8—2981no—
57C4⋊C4—21no—
58C4⋊C4—41no—
59C22⋊C4—5961no—
60C22⋊C4—5961no—
61C42C2×#1059701011yescharacteristic
62C23—2981no—
63Q8—5961no—
64D4—5961no—
65C2×C4—21no—
66C2×C4—41no—
67C2×C4—2981no—
68C2×C4—11921no—
69C2×C4C22⋊#1059701011yescharacteristic
70C8—5961no—
71C8—11921no—
72C22—5961no—
73C22—11921no—
74C22#1801196911yescharacteristic
75C4—21no—
76C4—41no—
77C4—81no—
78C4—23841no—
79C4—5961no—
80C2—21no—
81C2—11921no—
82C2#2375053111yescharacteristic
subgroupG/H
centerC2#23750531
commutatorC42×C149C2×C4
FrattiniC42C2×#10597010
Fitting#125×C149C4
socleC2×C149#354
prime radicalC2×D596D4
cosocle#18011899C22
hypercenter#125#10597010
hypocenterC149#1414
LCSG ▷ C42×C149 ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. C4×#11924746C4semidirect
10. #125×C149C4semidirect
41. C149#1414semidirect
46. #125#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505342
#237505322
#237499822
#1414149