Finite Group Databasebeta

← #18070372

Subgroups — #18070372

Order 4864.

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

normal subgroups only

This group has 148 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#14562778C211yesmaximal, characteristic
2#14561674C211yesmaximal, characteristic, complemented
3C19×#1411C211yesmaximal, characteristic, complemented
4#11927260C411yescharacteristic
5#11926831—21no—
6#11926365—21no—
7#11926293C411yescharacteristic
8#11926273—21no—
9C19×#494C2211yescharacteristic
10C19×#356—21no—
11C2×Q16×C19—41no—
12C19×C4⋊Q8C2×C411yescharacteristic
13C19×C4⋊Q8D411yescharacteristic
14#10597393—41no—
15#10597341—41no—
16#10597338—41no—
17C4×D76—21no—
18C19×#101—41no—
19C4×C8×C19D411yescharacteristic
20#10597269—41no—
21#10597266—41no—
22#10597265—41no—
23C4⋊(C19⋊C8)—21no—
24C2×Q8×C19—21no—
25C2×Q8×C19—21no—
26C2×D76—21no—
27C2×D76—41no—
28C2×C4×D19—41no—
29Q16×C19—81no—
30Q16×C19—81no—
31M16×C19—81no—
32C2×C8×C19—21no—
33C4⋊C4×C19—41no—
34C4⋊C4×C19—41no—
35C42×C19C22⋊C411yescharacteristic
36(C2×D19)⋊C4—42no—
37(C2×D19)⋊C4—41no—
38C4⋊Dic19—21no—
39C4×Dic19—41no—
40C2×C19⋊C8—41no—
41C19⋊C16—81no—
42#7521—191nomaximal, Sylow
43C22×D19—41no—
44Q8×C19—81no—
45Q8×C19—81no—
46C2×C4×C19—21no—
47C2×C4×C19—41no—
48C2×C4×C19—41no—
49C2×C4×C19#9911yescharacteristic
50C2×Dic19—41no—
51D76—41no—
52D76—41no—
53D76—161no—
54C4×D19—81no—
55C4×D19—81no—
56C8×C19—21no—
57C8×C19—21no—
58C8×C19—161no—
59C19⋊C8—81no—
60#1634—191no—
61#1411D1911yescharacteristic, complemented
62#1358—191no—
63C22×C19AΣL(1,𝔽16)11yescharacteristic
64C2×D19—81no—
65C2×D19—81no—
66C2×D19—81no—
67C4×C19—21no—
68C4×C19—21no—
69C4×C19—21no—
70C4×C19—81no—
71C4×C19—81no—
72Dic19—81no—
73#555—191no—
74#494C2×D1911yescharacteristic
75#476—381no—
76#364—381no—
77#356—21no—
78#333—191no—
79D4⋊C8—381no—
80C2×C19—21no—
81C2×C19#140211yescharacteristic
82D19—161no—
83C2×Q16—41no—
84C4⋊Q8C4×D1911yescharacteristic
85C4⋊Q8C22⋊D1911yescharacteristic
86#124—761no—
87#121—761no—
88C4×D4—381no—
89#117—761no—
90M32—761no—
91#106—761no—
92C4⋊C8—381no—
93#102—761no—
94#101—41no—
95C4×C8D7611yescharacteristic
96C19#752111yescharacteristic, complemented, Sylow
97C2×Q8—21no—
98C2×Q8—21no—
99C2×D4—381no—
100C2×D4—761no—
101C22×C4—761no—
102Q16—81no—
103Q16—81no—
104M16—81no—
105C2×C8—21no—
106C2×C8—761no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C4⋊C4—381no—
110C22⋊C4—762no—
111C22⋊C4—761no—
112C42—761no—
113C42(C2×D19)⋊C411yescharacteristic
114C16—1521no—
115C23—761no—
116Q8—81no—
117Q8—81no—
118D4—3041no—
119D4—761no—
120D4—761no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—761no—
125C2×C4—1521no—
126C2×C4—1521no—
127C2×C4#1059726311yescharacteristic
128C8—21no—
129C8—21no—
130C8—161no—
131C8—1521no—
132C22—1521no—
133C22—1521no—
134C22—1521no—
135C22#1192633011yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—81no—
140C4—81no—
141C4—1521no—
142C2—21no—
143C2—3041no—
144C2#1456177911yescharacteristic
subgroupG/H
centerC2#14561779
commutatorC19×C4⋊Q8C2×C4
Frattini#494C2×D19
FittingC19×#1411C2
socleC2×C19#1402
prime radical#11927260C4
cosocleC19×#494C22
hypercenter#1411D19
hypocenterC19#7521
LCSG ▷ C19×C4⋊Q8 ▷ C42×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
2. #14561674C2semidirect
3. C19×#1411C2semidirect
61. #1411D19semidirect
96. C19#7521semidirect

Maximal subgroups

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

subgroupindex
#145627782
#145616742
C19×#14112
#752119