Finite Group Databasebeta

← #18070025

Subgroups — #18070025

Order 4864.

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

normal subgroups only

This group has 284 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, complemented
2#14561543C211yesmaximal, characteristic, complemented
3C19×#2022C211yesmaximal, characteristic
4#11926508—21no—
5#11926268—21no—
6C19×#534C411yescharacteristic
7C2×C19×#123—21no—
8C2×C19×#99—21no—
9C19×#381C2211yescharacteristic
10C19×#342C411yescharacteristic
11C22×D4×C19—21no—
12C23×C4×C19D411yescharacteristic
13C19×#123—42no—
14C19×#123—41no—
15C19×#123—41no—
16C19×#123—41no—
17C19×#121—41no—
18C19×#120—41no—
19C2×C4⋊C4×C19—41no—
20C2×C22⋊C4×C19—21no—
21C2×C22⋊C4×C19—41no—
22C2×C22⋊C4×C19C2×C411yescharacteristic
23C2×C22⋊C4×C19D411yescharacteristic
24C2×#64520—41no—
25C19×#99—42no—
26C19×#95—41no—
27C22⋊(C19⋊C8)—22no—
28C22⋊(C19⋊C8)—41no—
29C22⋊(C19⋊C8)—41no—
30C24×C19—21no—
31C24×C19C22⋊C411yescharacteristic
32C2×D4×C19—41no—
33C2×D4×C19—41no—
34C2×D4×C19—41no—
35C2×D4×C19—41no—
36C2×D4×C19—41no—
37C2×D4×C19—41no—
38C2×D4×C19—41no—
39C22×C4×C19—21no—
40C22×C4×C19—21no—
41C22×C4×C19—21no—
42C22×C4×C19—21no—
43C22×C4×C19—21no—
44C22×C4×C19—41no—
45C22×C4×C19—41no—
46C22×C4×C19—41no—
47C22×C4×C19D811yescharacteristic
48C22×C4×C19SD1611yescharacteristic
49C4⋊C4×C19—41no—
50C4⋊C4×C19—42no—
51C4⋊C4×C19—42no—
52C22⋊C4×C19—22no—
53C22⋊C4×C19—42no—
54C22⋊C4×C19—42no—
55C22⋊C4×C19—42no—
56C22⋊C4×C19—41no—
57C22⋊C4×C19—41no—
58C22⋊C4×C19—41no—
59#64520—81no—
60#64520—81no—
61C2×C19⋊C8—42no—
62C2×C19⋊C8—81no—
63#7395—191nomaximal, Sylow
64C23×C19—21no—
65C23×C19—21no—
66C23×C19—41no—
67C23×C19—41no—
68C23×C19—41no—
69C23×C19—81no—
70C23×C19—82no—
71C23×C19#9911yescharacteristic
72C23×C19#10211yescharacteristic
73C23×C19#10411yescharacteristic
74D4×C19—81no—
75D4×C19—81no—
76D4×C19—81no—
77D4×C19—81no—
78D4×C19—161no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—41no—
82C2×C4×C19—41no—
83C2×C4×C19—41no—
84C2×C4×C19—41no—
85C2×C4×C19—42no—
86C2×C4×C19—41no—
87C2×C4×C19—41no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—41no—
91C2×C4×C19—81no—
92C2×C4×C19—82no—
93C2×C4×C19—81no—
94C2×C4×C19—81no—
95C19⋊C8—82no—
96C19⋊C8—161no—
97#2022D1911yescharacteristic
98#1317—191no—
99#1306—191no—
100C22×C19—21no—
101C22×C19—21no—
102C22×C19—41no—
103C22×C19—41no—
104C22×C19—41no—
105C22×C19—42no—
106C22×C19—81no—
107C22×C19—82no—
108C22×C19—82no—
109C22×C19—81no—
110C22×C19—161no—
111C22×C19#32711yescharacteristic
112C22×C19AΣL(1,𝔽16)11yescharacteristic
113C22×C19#35311yescharacteristic
114C4×C19—41no—
115C4×C19—41no—
116C4×C19—81no—
117C4×C19—81no—
118C4×C19—82no—
119C4×C19—81no—
120#534Dic1911yescharacteristic
121C2×#123—21no—
122C2×#99—21no—
123#407—381no—
124#381C2×D1911yescharacteristic
125#342Dic1911yescharacteristic
126#323—381no—
127C2×C19—21no—
128C2×C19—21no—
129C2×C19—21no—
130C2×C19—41no—
131C2×C19—41no—
132C2×C19—161no—
133C2×C19#134311yescharacteristic
134C22×D4—21no—
135C23×C4C22⋊D1911yescharacteristic
136C2×M16—761no—
137#123—42no—
138#123—41no—
139#123—41no—
140#123—41no—
141#121—41no—
142#120—41no—
143C2×C4⋊C4—41no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—41no—
146C2×C22⋊C4C2×Dic1911yescharacteristic
147C2×C22⋊C4C22⋊D1911yescharacteristic
148#99—42no—
149C22⋊C8—382no—
150C22⋊C8—761no—
151C22⋊C8—761no—
152#95—41no—
153C19#739511yescharacteristic, complemented, Sylow
154C24—21no—
155C24C22⋊Dic1911yescharacteristic
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4#6452511yescharacteristic
172C22×C4#6452611yescharacteristic
173M16—1521no—
174M16—1521no—
175C2×C8—762no—
176C2×C8—1521no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C22⋊C4—22no—
181C22⋊C4—42no—
182C22⋊C4—42no—
183C22⋊C4—42no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C23—21no—
188C23—21no—
189C23—41no—
190C23—41no—
191C23—41no—
192C23—81no—
193C23—82no—
194C23#1059728911yescharacteristic
195C23#1059729111yescharacteristic
196C23#1059729411yescharacteristic
197D4—81no—
198D4—81no—
199D4—81no—
200D4—81no—
201D4—161no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4—81no—
217C2×C4—81no—
218C8—3041no—
219C8—1522no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22—82no—
228C22—82no—
229C22—81no—
230C22—161no—
231C22#1192627811yescharacteristic
232C22#1192633111yescharacteristic
233C22#1192633711yescharacteristic
234C4—41no—
235C4—41no—
236C4—81no—
237C4—81no—
238C4—82no—
239C4—81no—
240C2—21no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2—161no—
246C2#1456163211yescharacteristic
subgroupG/H
centerC2#14561632
commutatorC2×C22⋊C4×C19C2×C4
Frattini#381C2×D19
FittingC19×#2022C2
socleC2×C19#1343
prime radicalC19×#534C4
cosocleC19×#381C22
hypercenter#2022D19
hypocenterC19#7395
LCSG ▷ C2×C22⋊C4×C19 ▷ C24×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #14561565C2semidirect
2. #14561543C2semidirect
153. C19#7395semidirect

Maximal subgroups

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

subgroupindex
#145615652
#145615432
C19×#20222
#739519