Finite Group Databasebeta

← #18070368

Subgroups — #18070368

Order 4864.

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

normal subgroups only

This group has 162 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#14562716C211yesmaximal, characteristic
2#14561800C211yesmaximal, characteristic, complemented
3C19×#1359C211yesmaximal, characteristic, complemented
4#11927260C411yescharacteristic, complemented
5#11926736—21no—
6#11926337—21no—
7#11926293C411yescharacteristic, complemented
8#11926273—21no—
9C19×#492C2211yescharacteristic
10C19×#364—21no—
11C2×SD16×C19—41no—
12C19×C4⋊Q8C2×C411yescharacteristic
13C19×#127D411yescharacteristic
14#10597393—41no—
15C2×#64525—41no—
16#10597341—41no—
17#10597338—41no—
18C4×D76—21no—
19C19×M32—41no—
20C4×C8×C19D411yescharacteristic
21#10597291—41no—
22#10597289—41no—
23C4⋊(C19⋊C8)—21no—
24C2×Q8×C19—21no—
25C2×D4×C19—21no—
26C2×D4×C19—41no—
27C2×D76—21no—
28C2×D76—41no—
29C2×C4×D19—41no—
30SD16×C19—81no—
31SD16×C19—81no—
32C2×C8×C19—21no—
33C4⋊C4×C19—41no—
34C42×C19C22⋊C411yescharacteristic
35C22⋊Dic19—81no—
36#64525—82no—
37(C2×D19)⋊C4—42no—
38(C2×D19)⋊C4—41no—
39C4⋊Dic19—21no—
40C4×Dic19—41no—
41C2×C19⋊C8—41no—
42C16×C19—81no—
43#7519—191nomaximal, Sylow
44C23×C19—41no—
45C22×D19—41no—
46Q8×C19—81no—
47D4×C19—81no—
48D4×C19—81no—
49D4×C19—81no—
50C2×C4×C19—21no—
51C2×C4×C19—41no—
52C2×C4×C19#9911yescharacteristic
53C2×Dic19—41no—
54C2×Dic19—161no—
55D76—41no—
56D76—41no—
57D76—161no—
58C4×D19—81no—
59C4×D19—81no—
60C8×C19—21no—
61C8×C19—21no—
62C19⋊C8—81no—
63#1624—191no—
64#1409—191no—
65#1359D1911yescharacteristic, complemented
66C22×C19—81no—
67C22×C19—161no—
68C22×C19AΣL(1,𝔽16)11yescharacteristic
69C2×D19—81no—
70C2×D19—81no—
71C2×D19—81no—
72C4×C19—21no—
73C4×C19—21no—
74C4×C19—21no—
75C4×C19—81no—
76Dic19—81no—
77Dic19—321no—
78#555—191no—
79#492C2×D1911yescharacteristic
80#459—381no—
81#364—21no—
82#353—381no—
83#333—191no—
84D4⋊C8—381no—
85C2×C19—21no—
86C2×C19—161no—
87C2×C19#140211yescharacteristic
88D19—161no—
89C2×SD16—41no—
90C2×D8—761no—
91C4⋊Q8C4×D1911yescharacteristic
92#127D7611yescharacteristic
93#124—761no—
94#121—761no—
95C4×D4—381no—
96#117—761no—
97M32—41no—
98C4⋊C8—381no—
99#102—761no—
100#99—761no—
101C4×C8C22⋊D1911yescharacteristic
102C19#751911yescharacteristic, complemented, Sylow
103C2×Q8—21no—
104C2×D4—21no—
105C2×D4—41no—
106C2×D4—381no—
107C2×D4—761no—
108C22×C4—761no—
109SD16—81no—
110SD16—81no—
111D8—1522no—
112C2×C8—21no—
113C2×C8—761no—
114C4⋊C4—41no—
115C4⋊C4—381no—
116C22⋊C4—762no—
117C22⋊C4—761no—
118C22⋊C4—1521no—
119C42—761no—
120C42(C2×D19)⋊C411yescharacteristic
121C16—81no—
122C23—41no—
123C23—761no—
124Q8—81no—
125D4—81no—
126D4—81no—
127D4—81no—
128D4—3041no—
129D4—761no—
130D4—761no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—3041no—
134C2×C4—761no—
135C2×C4—1521no—
136C2×C4—1521no—
137C2×C4#1059726311yescharacteristic
138C8—21no—
139C8—21no—
140C8—1521no—
141C22—81no—
142C22—161no—
143C22—1521no—
144C22—1521no—
145C22—1521no—
146C22#1192633211yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—81no—
151C4—6081no—
152C4—1521no—
153C2—21no—
154C2—161no—
155C2—3041no—
156C2#1456178111yescharacteristic
subgroupG/H
centerC2#14561781
commutatorC19×C4⋊Q8C2×C4
Frattini#492C2×D19
FittingC19×#1359C2
socleC2×C19#1402
prime radical#14562716C2
cosocleC19×#492C22
hypercenter#1359D19
hypocenterC19#7519
LCSG ▷ C19×C4⋊Q8 ▷ C42×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1359

Complements

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

NH ≅ G/Ntype
2. #14561800C2semidirect
3. C19×#1359C2semidirect
4. #11927260C4semidirect
7. #11926293C4semidirect
65. #1359D19semidirect
102. C19#7519semidirect

Maximal subgroups

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

subgroupindex
#145627162
#145618002
C19×#13592
#751919