Finite Group Databasebeta

← #18070170

Subgroups — #18070170

Order 4864.

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

normal subgroups only

This group has 198 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#14564980C211yesmaximal, characteristic
2#14561518C211yesmaximal, characteristic
3C19×#1325C211yesmaximal, characteristic
4#11927175C411yescharacteristic
5#11926584—21no—
6C2×C4⋊(C19⋊C8)—21no—
7#11926313C411yescharacteristic
8#11926304—21no—
9C19×#384C2211yescharacteristic
10C19×#324—21no—
11C2×C4⋊C4×C19—41no—
12C2×C4⋊C4×C19C2×C411yescharacteristic
13C2×C4⋊C4×C19D411yescharacteristic
14C2×C42×C19D411yescharacteristic
15#10597372—21no—
16#10597370—41no—
17C2×#64520—21no—
18C22×C19⋊C8—41no—
19#10597336—41no—
20#10597334—41no—
21C19×C22⋊C8—41no—
22#10597265—41no—
23#10597264—41no—
24C4⋊(C19⋊C8)—22no—
25C4⋊(C19⋊C8)—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—
34C4⋊C4×C19—81no—
35C4⋊C4×C19—81no—
36C42×C19—21no—
37C42×C19SD1611yescharacteristic
38C42×C19Q1611yescharacteristic
39C22⋊Dic19—41no—
40C4⋊Dic19—21no—
41C4⋊Dic19—21no—
42C4⋊Dic19—41no—
43Dic19⋊C4—42no—
44C4×Dic19—41no—
45#64520—22no—
46#64520—41no—
47C2×C19⋊C8—41no—
48C2×C19⋊C8—42no—
49C2×C19⋊C8—81no—
50C2×C19⋊C8—81no—
51#7443—191nomaximal, Sylow
52C23×C19#9911yescharacteristic
53C2×C4×C19—21no—
54C2×C4×C19—21no—
55C2×C4×C19—21no—
56C2×C4×C19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—41no—
62C2×C4×C19—41no—
63C2×C4×C19—81no—
64C2×C4×C19—81no—
65C2×C4×C19#10311yescharacteristic
66C2×C4×C19#10411yescharacteristic
67C2×Dic19—41no—
68C2×Dic19—41no—
69Dic38—161no—
70C8×C19—161no—
71C19⋊C8—42no—
72C19⋊C8—82no—
73#2060—191no—
74#1325D1911yescharacteristic
75#1296—191no—
76C22×C19—21no—
77C22×C19—21no—
78C22×C19#32811yescharacteristic
79C22×C19AΣL(1,𝔽16)11yescharacteristic
80C22×C19#35611yescharacteristic
81C4×C19—21no—
82C4×C19—21no—
83C4×C19—21no—
84C4×C19—21no—
85C4×C19—21no—
86C4×C19—21no—
87C4×C19—81no—
88C4×C19—81no—
89Dic19—81no—
90Dic19—81no—
91#544—191no—
92#428—381no—
93C2×C4⋊C8—381no—
94#384C2×D1911yescharacteristic
95#343—191no—
96#339—381no—
97#324—21no—
98C2×C19—21no—
99C2×C19—21no—
100C2×C19#135411yescharacteristic
101C2×C19#140211yescharacteristic
102C2×C19#140511yescharacteristic
103C2×M16—381no—
104C22×C8—761no—
105C4⋊Q8—761no—
106#125—761no—
107C22⋊Q8—761no—
108#117—381no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4C4×D1911yescharacteristic
111C2×C4⋊C4C22⋊D1911yescharacteristic
112C2×C42D7611yescharacteristic
113#107—761no—
114#106—761no—
115C4⋊C8—382no—
116C4⋊C8—761no—
117C22⋊C8—41no—
118C19#744311yescharacteristic, complemented, Sylow
119C2×Q8—761no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4(C2×D19)⋊C411yescharacteristic
124M16—382no—
125M16—761no—
126C2×C8—81no—
127C2×C8—761no—
128C2×C8—762no—
129C2×C8—1521no—
130C2×C8—1521no—
131C4⋊C4—41no—
132C4⋊C4—41no—
133C4⋊C4—81no—
134C4⋊C4—81no—
135C4⋊C4—381no—
136C4⋊C4—381no—
137C4⋊C4—761no—
138C4⋊C4—762no—
139C22⋊C4—761no—
140C42—21no—
141C42—761no—
142C42#6451611yescharacteristic
143C42Dic7611yescharacteristic
144C23#1059726311yescharacteristic
145Q8—3041no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—761no—
159C2×C4—761no—
160C2×C4#1059727311yescharacteristic
161C2×C4#1059728211yescharacteristic
162C8—161no—
163C8—762no—
164C8—1522no—
165C22—21no—
166C22—21no—
167C22#1192628211yescharacteristic
168C22#1192633011yescharacteristic
169C22#1192634211yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—1521no—
179C4—1521no—
180C2—21no—
181C2—21no—
182C2#1456166611yescharacteristic
183C2#1456177911yescharacteristic
184C2#1456178811yescharacteristic
subgroupG/H
centerC22#11926330
commutatorC2×C4⋊C4×C19C2×C4
Frattini#384C2×D19
FittingC19×#1325C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC23×C19#99
cosocleC19×#384C22
hypercenter#1325D19
hypocenterC19#7443
LCSG ▷ C2×C4⋊C4×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
118. C19#7443semidirect

Maximal subgroups

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

subgroupindex
#145649802
#145615182
C19×#13252
#744319