Finite Group Databasebeta

← #18070383

Subgroups — #18070383

Order 4864.

134 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 25 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
1#14562936C211yesmaximal, characteristic
2#14561806C211yesmaximal, characteristic
3C19×#1355C211yesmaximal, characteristic
4C19⋊#564C411yescharacteristic, complemented
5#11926908—21no—
6#11926337—21no—
7#11926286C411yescharacteristic, complemented
8#11926285—21no—
9C19×#490C2211yescharacteristic
10C19×#347—21no—
11C19×#127D411yescharacteristic
12C19×#125C2×C411yescharacteristic
13#10597336—41no—
14#10597335—41no—
15#10597335—41no—
16#10597316—21no—
17C19×M32—41no—
18C19×#102—41no—
19C19×#97D411yescharacteristic
20#10597291—41no—
21#10597289—41no—
22#10597289—41no—
23#10597260—21no—
24C2×D4×C19—21no—
25C2×D4×C19—41no—
26C2×C8×C19—21no—
27C4⋊C4×C19—21no—
28C4⋊C4×C19—41no—
29C42×C19C22⋊C411yescharacteristic
30C22⋊Dic19—81no—
31C4⋊Dic19—21no—
32C4⋊Dic19—21no—
33C4⋊Dic19—41no—
34Dic19⋊C4—41no—
35Dic19⋊C4—41no—
36Dic19⋊C4—41no—
37Dic19⋊C4—41no—
38C4×Dic19—41no—
39C2×C19⋊C8—41no—
40C16×C19—42no—
41#7524—191nomaximal, Sylow
42C23×C19—41no—
43D4×C19—81no—
44D4×C19—82no—
45C2×C4×C19—21no—
46C2×C4×C19—41no—
47C2×C4×C19#9911yescharacteristic
48C2×Dic19—41no—
49C2×Dic19—41no—
50C2×Dic19—161no—
51C8×C19—41no—
52C19⋊C8—81no—
53#1658—191no—
54#1412—191no—
55#1355D1911yescharacteristic
56C22×C19—81no—
57C22×C19—161no—
58C22×C19AΣL(1,𝔽16)11yescharacteristic
59C4×C19—21no—
60C4×C19—41no—
61C4×C19—81no—
62Dic19—81no—
63Dic19—81no—
64Dic19—321no—
65#564—191no—
66#490—381no—
67#490C2×D1911yescharacteristic
68#353—381no—
69#347—21no—
70#330—191no—
71#330—381no—
72C2×C19—21no—
73C2×C19—161no—
74C2×C19#140411yescharacteristic
75#127D7611yescharacteristic
76#125—381no—
77#125—761no—
78#125—761no—
79#125—761no—
80#125C4×D1911yescharacteristic
81M32—41no—
82#102—41no—
83#102—761no—
84#102—761no—
85#99—761no—
86#97—381no—
87#97C22⋊D1911yescharacteristic
88C19#752411yescharacteristic, complemented, Sylow
89C2×D4—21no—
90C2×D4—41no—
91C2×C8—21no—
92C2×C8—761no—
93C4⋊C4—21no—
94C4⋊C4—41no—
95C4⋊C4—381no—
96C4⋊C4—381no—
97C4⋊C4—761no—
98C4⋊C4—761no—
99C4⋊C4—761no—
100C4⋊C4—761no—
101C4⋊C4—761no—
102C22⋊C4—1521no—
103C42—761no—
104C42(C2×D19)⋊C411yescharacteristic
105C16—42no—
106C23—41no—
107D4—81no—
108D4—82no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—3041no—
112C2×C4—761no—
113C2×C4—761no—
114C2×C4#1059726311yescharacteristic
115C8—41no—
116C8—1521no—
117C22—81no—
118C22—161no—
119C22#1192633211yescharacteristic
120C4—21no—
121C4—41no—
122C4—81no—
123C4—6081no—
124C4—1521no—
125C4—1521no—
126C2—21no—
127C2—161no—
128C2#1456178711yescharacteristic
subgroupG/H
centerC2#14561787
commutatorC19×#125C2×C4
Frattini#490C2×D19
FittingC19×#1355C2
socleC2×C19#1404
prime radicalC19×#127D4
cosocleC19×#490C22
hypercenter#1355D19
hypocenterC19#7524
LCSG ▷ C19×#125 ▷ C42×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #490 ◁ #1355

Complements

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

NH ≅ G/Ntype
4. C19⋊#564C4semidirect
7. #11926286C4semidirect
88. C19#7524semidirect

Maximal subgroups

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

subgroupindex
#145629362
#145618062
C19×#13552
#752419