Finite Group Databasebeta

← #18070121

Subgroups — #18070121

Order 4864.

214 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 39 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#14561565C211yesmaximal, characteristic
2#14561543C211yesmaximal, characteristic
3C19×#2030C211yesmaximal, characteristic
4#11926508—21no—
5#11926268—21no—
6C19×#543C411yescharacteristic
7C19×#381—21no—
8C19×#381C2211yescharacteristic
9C19×#342—21no—
10C19×#342C411yescharacteristic
11C23×C4×C19D411yescharacteristic
12C19×C22⋊Q8—42no—
13C19×C22⋊Q8—41no—
14C2×C22⋊C4×C19—21no—
15C2×C22⋊C4×C19—21no—
16C2×C22⋊C4×C19C2×C411yescharacteristic
17C2×C22⋊C4×C19D411yescharacteristic
18C2×#64520—41no—
19C19×#95—41no—
20C19×#95—42no—
21C22⋊(C19⋊C8)—22no—
22C22⋊(C19⋊C8)—41no—
23C22⋊(C19⋊C8)—41no—
24C24×C19C22⋊C411yescharacteristic
25C2×Q8×C19—41no—
26C22×C4×C19—21no—
27C22×C4×C19—21no—
28C22×C4×C19—22no—
29C22×C4×C19—21no—
30C22×C4×C19—21no—
31C22×C4×C19—41no—
32C22×C4×C19—41no—
33C22×C4×C19—41no—
34C22×C4×C19SD1611yescharacteristic
35C22×C4×C19Q1611yescharacteristic
36C4⋊C4×C19—42no—
37C4⋊C4×C19—41no—
38C22⋊C4×C19—41no—
39C22⋊C4×C19—41no—
40C22⋊C4×C19—41no—
41C22⋊C4×C19—41no—
42C22⋊C4×C19—41no—
43C22⋊C4×C19—41no—
44#64520—81no—
45#64520—81no—
46C2×C19⋊C8—42no—
47C2×C19⋊C8—81no—
48#7427—191nomaximal, Sylow
49C23×C19—21no—
50C23×C19—21no—
51C23×C19—81no—
52C23×C19#9911yescharacteristic
53C23×C19#10311yescharacteristic
54C23×C19#10411yescharacteristic
55Q8×C19—161no—
56C2×C4×C19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—41no—
59C2×C4×C19—41no—
60C2×C4×C19—41no—
61C2×C4×C19—41no—
62C2×C4×C19—42no—
63C2×C4×C19—41no—
64C2×C4×C19—41no—
65C2×C4×C19—81no—
66C2×C4×C19—81no—
67C2×C4×C19—81no—
68C2×C4×C19—82no—
69C2×C4×C19—81no—
70C2×C4×C19—82no—
71C19⋊C8—82no—
72C19⋊C8—161no—
73#2030D1911yescharacteristic
74#1317—191no—
75#1306—191no—
76C22×C19—21no—
77C22×C19—21no—
78C22×C19—41no—
79C22×C19—41no—
80C22×C19—41no—
81C22×C19—42no—
82C22×C19—81no—
83C22×C19#32811yescharacteristic
84C22×C19AΣL(1,𝔽16)11yescharacteristic
85C22×C19#35411yescharacteristic
86C4×C19—41no—
87C4×C19—41no—
88C4×C19—81no—
89C4×C19—82no—
90C4×C19—81no—
91C4×C19—161no—
92#543Dic1911yescharacteristic
93#407—381no—
94#381—21no—
95#381C2×D1911yescharacteristic
96#342—21no—
97#342Dic1911yescharacteristic
98#323—381no—
99C2×C19—21no—
100C2×C19—21no—
101C2×C19—21no—
102C2×C19—41no—
103C2×C19—41no—
104C2×C19#135111yescharacteristic
105C23×C4C22⋊D1911yescharacteristic
106C2×M16—761no—
107C22⋊Q8—42no—
108C22⋊Q8—41no—
109C2×C22⋊C4—21no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4C2×Dic1911yescharacteristic
112C2×C22⋊C4C22⋊D1911yescharacteristic
113C22⋊C8—382no—
114C22⋊C8—761no—
115C22⋊C8—761no—
116#95—41no—
117#95—42no—
118C19#742711yescharacteristic, complemented, Sylow
119C24C22⋊Dic1911yescharacteristic
120C2×Q8—41no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—22no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4—41no—
129C22×C4#6452711yescharacteristic
130C22×C4#6452811yescharacteristic
131M16—1521no—
132M16—1521no—
133C2×C8—762no—
134C2×C8—1521no—
135C4⋊C4—42no—
136C4⋊C4—41no—
137C22⋊C4—41no—
138C22⋊C4—41no—
139C22⋊C4—41no—
140C22⋊C4—41no—
141C22⋊C4—41no—
142C22⋊C4—41no—
143C23—21no—
144C23—21no—
145C23—81no—
146C23#1059729111yescharacteristic
147C23#1059729211yescharacteristic
148C23#1059729411yescharacteristic
149Q8—161no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—82no—
163C2×C4—81no—
164C2×C4—82no—
165C8—3041no—
166C8—1522no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#1192628111yescharacteristic
175C22#1192633111yescharacteristic
176C22#1192633911yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—82no—
181C4—81no—
182C4—161no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#1456165611yescharacteristic
subgroupG/H
centerC2#14561656
commutatorC2×C22⋊C4×C19C2×C4
Frattini#381C2×D19
FittingC19×#2030C2
socleC2×C19#1351
prime radicalC24×C19C22⋊C4
cosocleC19×#381C22
hypercenter#2030D19
hypocenterC19#7427
LCSG ▷ C2×C22⋊C4×C19 ▷ C24×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #2030

Complements

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

NH ≅ G/Ntype
118. C19#7427semidirect

Maximal subgroups

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

subgroupindex
#145615652
#145615432
C19×#20302
#742719