Finite Group Databasebeta

← #14561782

Subgroups — #14561782

Order 2432.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#11926721C211yesmaximal, characteristic
2#11926284C211yesmaximal, characteristic, complemented
3C19×#355C211yesmaximal, characteristic, complemented
4#10597430C411yescharacteristic
5C19×#124C2211yescharacteristic
6#10597388—21no—
7C19×#101—21no—
8#10597290C411yescharacteristic
9#10597262—21no—
10#10597260—21no—
11C2×Q8×C19D411yescharacteristic
12C2×D4×C19C2×C411yescharacteristic
13C2×C22⋊D19—41no—
14#64543—41no—
15D4×D19—41no—
16#64541—21no—
17M16×C19—41no—
18C22⋊C4×C19—41no—
19C42×C19D411yescharacteristic
20#64528—41no—
21#64527—41no—
22#64520—21no—
23C2×C19⋊C8—41no—
24C23×C19—21no—
25C22×D19—41no—
26Q8×C19—41no—
27D4×C19—41no—
28C2×C4×C19—21no—
29C2×C4×C19—21no—
30C2×C4×C19C22⋊C411yescharacteristic
31C22⋊D19—42no—
32C22⋊D19—41no—
33C2×Dic19—41no—
34D76—21no—
35C4×D19—41no—
36Dic38—21no—
37C8×C19—81no—
38C19⋊C8—41no—
39C19⋊C8—42no—
40#1403—191nomaximal, Sylow
41C22×C19—41no—
42C22×C19—81no—
43C22×C19#9911yescharacteristic
44C2×D19—41no—
45C2×D19—161no—
46C4×C19—21no—
47C4×C19—41no—
48C4×C19—41no—
49Dic19—41no—
50#455—191no—
51#355D1911yescharacteristic, complemented
52#329—191no—
53C2×C19—21no—
54C2×C19—81no—
55C2×C19AΣL(1,𝔽16)11yescharacteristic
56D19—81no—
57H(5,𝔽2)—191no—
58#137—381no—
59#124C2×D1911yescharacteristic
60#104—381no—
61#101—21no—
62#100—191no—
63#97—381no—
64C19#140311yescharacteristic, complemented, Sylow
65#41—381no—
66#41—761no—
67C2×Q8C22⋊D1911yescharacteristic
68C2×D4—761no—
69C2×D4—761no—
70C2×D4C4×D1911yescharacteristic
71Q16—761no—
72SD16—761no—
73M16—41no—
74M16—381no—
75C2×C8—761no—
76C22⋊C4—41no—
77C42D7611yescharacteristic
78C23—21no—
79C23—761no—
80Q8—41no—
81Q8—381no—
82D4—41no—
83D4—381no—
84D4—762no—
85D4—761no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—761no—
89C2×C4—761no—
90C2×C4(C2×D19)⋊C411yescharacteristic
91C8—81no—
92C8—761no—
93C8—762no—
94C22—41no—
95C22—81no—
96C22—3041no—
97C22—761no—
98C22#1059726311yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—761no—
103C2—21no—
104C2—81no—
105C2—1521no—
106C2#1192633011yescharacteristic
subgroupG/H
centerC2#11926330
commutatorC2×D4×C19C2×C4
Frattini#124C2×D19
FittingC19×#355C2
socleC2×C19AΣL(1,𝔽16)
prime radical#10597430C4
cosocleC19×#124C22
hypercenter#355D19
hypocenterC19#1403
LCSG ▷ C2×D4×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #11926284C2semidirect
3. C19×#355C2semidirect
51. #355D19semidirect
64. C19#1403semidirect

Maximal subgroups

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

subgroupindex
#119267212
#119262842
C19×#3552
#140319