Finite Group Databasebeta

← #18070387

Subgroups — #18070387

Order 4864.

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

normal subgroups only

This group has 126 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#14562961C211yesmaximal, characteristic
2#14561670C211yesmaximal, characteristic
3C19×#1413C211yesmaximal, characteristic
4C19⋊#564C411yescharacteristic
5#11926950—21no—
6#11926322—21no—
7#11926286C411yescharacteristic
8#11926285—21no—
9C19×#491C2211yescharacteristic
10C19×#356—21no—
11C19×C4⋊Q8D411yescharacteristic
12C19×#125C2×C411yescharacteristic
13#10597336—41no—
14#10597335—41no—
15#10597335—41no—
16#10597316—21no—
17C19×#103—41no—
18C19×#101—41no—
19C19×#97D411yescharacteristic
20#10597269—41no—
21#10597265—41no—
22#10597264—41no—
23#10597260—21no—
24C2×Q8×C19—21no—
25M16×C19—81no—
26C2×C8×C19—21no—
27C4⋊C4×C19—21no—
28C4⋊C4×C19—41no—
29C4⋊C4×C19—41no—
30C42×C19C22⋊C411yescharacteristic
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—
40C19⋊C16—42no—
41#7526—191nomaximal, Sylow
42Q8×C19—81no—
43C2×C4×C19—21no—
44C2×C4×C19—41no—
45C2×C4×C19—41no—
46C2×C4×C19#9911yescharacteristic
47C2×Dic19—41no—
48C2×Dic19—41no—
49C8×C19—41no—
50C8×C19—161no—
51C19⋊C8—42no—
52#1663—191no—
53#1413D1911yescharacteristic
54#1356—191no—
55C22×C19AΣL(1,𝔽16)11yescharacteristic
56C4×C19—21no—
57C4×C19—41no—
58C4×C19—81no—
59C4×C19—81no—
60Dic19—81no—
61Dic19—81no—
62#564—191no—
63#501—381no—
64#491C2×D1911yescharacteristic
65#356—21no—
66#347—381no—
67#330—191no—
68#330—381no—
69C2×C19—21no—
70C2×C19#140411yescharacteristic
71C4⋊Q8C22⋊D1911yescharacteristic
72#125—381no—
73#125—761no—
74#125—761no—
75#125—761no—
76#125C4×D1911yescharacteristic
77M32—761no—
78#107—761no—
79#106—761no—
80#103—41no—
81#101—41no—
82#97—381no—
83#97D7611yescharacteristic
84C19#752611yescharacteristic, complemented, Sylow
85C2×Q8—21no—
86M16—81no—
87C2×C8—21no—
88C2×C8—761no—
89C4⋊C4—21no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—381no—
93C4⋊C4—381no—
94C4⋊C4—761no—
95C4⋊C4—761no—
96C4⋊C4—761no—
97C4⋊C4—761no—
98C4⋊C4—761no—
99C42—761no—
100C42(C2×D19)⋊C411yescharacteristic
101C16—762no—
102Q8—81no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—761no—
107C2×C4—761no—
108C2×C4#1059726311yescharacteristic
109C8—41no—
110C8—161no—
111C8—762no—
112C22#1192633011yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—81no—
117C4—1521no—
118C4—1521no—
119C2—21no—
120C2#1456178511yescharacteristic
subgroupG/H
centerC2#14561785
commutatorC19×#125C2×C4
Frattini#491C2×D19
FittingC19×#1413C2
socleC2×C19#1404
prime radicalC22×C19AΣL(1,𝔽16)
cosocleC19×#491C22
hypercenter#1413D19
hypocenterC19#7526
LCSG ▷ C19×#125 ▷ C42×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #491 ◁ #1413

Complements

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

NH ≅ G/Ntype
84. C19#7526semidirect

Maximal subgroups

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

subgroupindex
#145629612
#145616702
C19×#14132
#752619