Finite Group Databasebeta

← #18070384

Subgroups — #18070384

Order 4864.

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

normal subgroups only

This group has 138 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#14562956C211yesmaximal, characteristic
2#14561670C211yesmaximal, characteristic, complemented
3C19×#1413C211yesmaximal, characteristic, complemented
4#11927292C411yescharacteristic
5#11926906—21no—
6#11926322—21no—
7#11926286C411yescharacteristic
8#11926283—21no—
9C19×#491C2211yescharacteristic
10C19×#356—21no—
11C19×C4⋊Q8D411yescharacteristic
12C19×#125C2×C411yescharacteristic
13#10597342—41no—
14#10597341—41no—
15#10597340—41no—
16#10597321—21no—
17C19×#103—41no—
18C19×#101—41no—
19C19×#97D411yescharacteristic
20#10597269—41no—
21#10597267—41no—
22#10597266—41no—
23#10597260—21no—
24C2×Q8×C19—21no—
25C2×D76—21no—
26C2×D76—41no—
27C2×C4×D19—41no—
28C2×Dic38—21no—
29M16×C19—81no—
30C2×C8×C19—21no—
31C4⋊C4×C19—21no—
32C4⋊C4×C19—41no—
33C4⋊C4×C19—41no—
34C42×C19C22⋊C411yescharacteristic
35(C2×D19)⋊C4—41no—
36(C2×D19)⋊C4—41no—
37(C2×D19)⋊C4—41no—
38Dic19⋊C4—41no—
39C2×C19⋊C8—41no—
40C19⋊C16—42no—
41#7525—191nomaximal, Sylow
42C22×D19—41no—
43Q8×C19—81no—
44C2×C4×C19—21no—
45C2×C4×C19—41no—
46C2×C4×C19—41no—
47C2×C4×C19#9911yescharacteristic
48C2×Dic19—41no—
49D76—81no—
50D76—161no—
51C4×D19—161no—
52Dic38—81no—
53C8×C19—41no—
54C8×C19—161no—
55C19⋊C8—81no—
56#1662—191no—
57#1413D1911yescharacteristic, complemented
58#1356—191no—
59C22×C19AΣL(1,𝔽16)11yescharacteristic
60C2×D19—81no—
61C2×D19—81no—
62C2×D19—81no—
63C4×C19—21no—
64C4×C19—41no—
65C4×C19—81no—
66C4×C19—81no—
67Dic19—81no—
68#562—191no—
69#491C2×D1911yescharacteristic
70#489—381no—
71#356—21no—
72#347—381no—
73#330—191no—
74#329—381no—
75C2×C19—21no—
76C2×C19#140411yescharacteristic
77D19—161no—
78C4⋊Q8C22⋊D1911yescharacteristic
79#125C4×D1911yescharacteristic
80#124—381no—
81#123—761no—
82C22⋊Q8—761no—
83#121—761no—
84M32—761no—
85#103—41no—
86#103—761no—
87#102—761no—
88#101—41no—
89#97—381no—
90#97D7611yescharacteristic
91C19#752511yescharacteristic, complemented, Sylow
92C2×Q8—21no—
93C2×Q8—381no—
94C2×D4—381no—
95C2×D4—761no—
96C22×C4—761no—
97M16—81no—
98C2×C8—21no—
99C2×C8—761no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—761no—
104C22⋊C4—761no—
105C22⋊C4—761no—
106C22⋊C4—761no—
107C42(C2×D19)⋊C411yescharacteristic
108C16—762no—
109C23—761no—
110Q8—81no—
111Q8—1521no—
112D4—3041no—
113D4—1521no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—3041no—
118C2×C4—761no—
119C2×C4#1059726311yescharacteristic
120C8—41no—
121C8—161no—
122C8—1521no—
123C22—1521no—
124C22—1521no—
125C22—1521no—
126C22#1192633011yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—1521no—
132C2—21no—
133C2—3041no—
134C2#1456178511yescharacteristic
subgroupG/H
centerC2#14561785
commutatorC19×#125C2×C4
Frattini#491C2×D19
FittingC19×#1413C2
socleC2×C19#1404
prime radical#11927292C4
cosocleC19×#491C22
hypercenter#1413D19
hypocenterC19#7525
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
2. #14561670C2semidirect
3. C19×#1413C2semidirect
57. #1413D19semidirect
91. C19#7525semidirect

Maximal subgroups

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

subgroupindex
#145629562
#145616702
C19×#14132
#752519