Finite Group Databasebeta

← #18070167

Subgroups — #18070167

Order 4864.

194 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 41 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#14564985C211yesmaximal, characteristic
2#14561516C211yesmaximal, characteristic
3C19×#1324C211yesmaximal, characteristic
4#11927175C411yescharacteristic
5#11926584—21no—
6C2×#10597260—21no—
7#11926313C411yescharacteristic
8#11926304—21no—
9C19×#382C2211yescharacteristic
10C19×#324—21no—
11C2×C4⋊C4×C19C2×C411yescharacteristic
12C2×C4⋊C4×C19D411yescharacteristic
13C2×C42×C19D411yescharacteristic
14#10597372—21no—
15#10597370—41no—
16C2×#64520—21no—
17C22×C19⋊C8—41no—
18#10597336—41no—
19#10597334—41no—
20C19×C22⋊C8—41no—
21C19×#95—41no—
22#10597265—41no—
23#10597264—41no—
24#10597260—22no—
25#10597260—41no—
26C22×C4×C19—21no—
27C22×C4×C19—21no—
28C22×C4×C19—21no—
29C22×C4×C19C22⋊C411yescharacteristic
30C2×Dic38—41no—
31C2×C8×C19—81no—
32C4⋊C4×C19—41no—
33C4⋊C4×C19—41no—
34C42×C19—21no—
35C42×C19SD1611yescharacteristic
36C42×C19Q1611yescharacteristic
37C22⋊Dic19—41no—
38C4⋊Dic19—21no—
39C4⋊Dic19—21no—
40C4⋊Dic19—41no—
41Dic19⋊C4—42no—
42C4×Dic19—41no—
43#64520—22no—
44#64520—41no—
45C2×C19⋊C8—42no—
46C2×C19⋊C8—41no—
47C2×C19⋊C8—42no—
48C2×C19⋊C8—42no—
49#7442—191nomaximal, Sylow
50C23×C19#9911yescharacteristic
51C2×C4×C19—21no—
52C2×C4×C19—21no—
53C2×C4×C19—21no—
54C2×C4×C19—21no—
55C2×C4×C19—41no—
56C2×C4×C19—41no—
57C2×C4×C19—41no—
58C2×C4×C19—41no—
59C2×C4×C19—81no—
60C2×C4×C19—81no—
61C2×C4×C19#10311yescharacteristic
62C2×C4×C19#10411yescharacteristic
63C2×Dic19—41no—
64C2×Dic19—41no—
65Dic38—161no—
66C8×C19—161no—
67C19⋊C8—42no—
68C19⋊C8—44no—
69#2061—191no—
70#1324D1911yescharacteristic
71#1295—191no—
72C22×C19—21no—
73C22×C19—21no—
74C22×C19#32811yescharacteristic
75C22×C19AΣL(1,𝔽16)11yescharacteristic
76C22×C19#35611yescharacteristic
77C4×C19—21no—
78C4×C19—21no—
79C4×C19—41no—
80C4×C19—41no—
81C4×C19—81no—
82C4×C19—81no—
83Dic19—81no—
84Dic19—81no—
85#544—191no—
86#428—381no—
87C2×#97—381no—
88#382C2×D1911yescharacteristic
89#343—191no—
90#339—381no—
91#324—21no—
92C2×C19—21no—
93C2×C19—21no—
94C2×C19#135411yescharacteristic
95C2×C19#140311yescharacteristic
96C2×C19#140411yescharacteristic
97C2×M16—381no—
98C22×C8—761no—
99C4⋊Q8—761no—
100#125—761no—
101C22⋊Q8—761no—
102#117—381no—
103C2×C4⋊C4C4×D1911yescharacteristic
104C2×C4⋊C4C22⋊D1911yescharacteristic
105C2×C42D7611yescharacteristic
106#107—761no—
107#106—761no—
108C22⋊C8—41no—
109#97—382no—
110#97—761no—
111#95—41no—
112C19#744211yescharacteristic, complemented, Sylow
113C2×Q8—761no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4(C2×D19)⋊C411yescharacteristic
118M16—382no—
119M16—761no—
120C2×C8—81no—
121C2×C8—762no—
122C2×C8—761no—
123C2×C8—762no—
124C2×C8—762no—
125C4⋊C4—41no—
126C4⋊C4—41no—
127C4⋊C4—381no—
128C4⋊C4—381no—
129C4⋊C4—761no—
130C4⋊C4—762no—
131C22⋊C4—761no—
132C42—21no—
133C42—761no—
134C42#6451611yescharacteristic
135C42Dic7611yescharacteristic
136C23#1059726311yescharacteristic
137Q8—3041no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—761no—
149C2×C4—761no—
150C2×C4#1059727311yescharacteristic
151C2×C4#1059728211yescharacteristic
152C8—161no—
153C8—762no—
154C8—764no—
155C22—21no—
156C22—21no—
157C22#1192628211yescharacteristic
158C22#1192633011yescharacteristic
159C22#1192634211yescharacteristic
160C4—21no—
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—81no—
166C4—1521no—
167C4—1521no—
168C2—21no—
169C2—21no—
170C2#1456166611yescharacteristic
171C2#1456178211yescharacteristic
172C2#1456178511yescharacteristic
subgroupG/H
centerC22#11926330
commutatorC2×C4⋊C4×C19C2×C4
Frattini#382C2×D19
FittingC19×#1324C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC23×C19#99
cosocleC19×#382C22
hypercenter#1324D19
hypocenterC19#7442
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
112. C19#7442semidirect

Maximal subgroups

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

subgroupindex
#145649852
#145615162
C19×#13242
#744219