Finite Group Databasebeta

← #18069236

Subgroups — #18069236

Order 4864.

316 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 47 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#14561559C211yesmaximal, characteristic, complemented
2#14561512C211yesmaximal, characteristic, complemented
3C19×#1999C211yesmaximal, characteristic
4#11926508—21no—
5C22⋊(C19⋊C16)—21no—
6C22×D8×C19C411yescharacteristic
7C2×C19×#121—21no—
8C2×C19×#102—21no—
9C2×C19×C22⋊C8C2211yescharacteristic
10C19×#340C411yescharacteristic
11C22×D4×C19—21no—
12C22×D4×C19—41no—
13C23×C4×C19D411yescharacteristic
14C2×D8×C19—41no—
15C2×D8×C19—42no—
16C22×C8×C19C2×C411yescharacteristic
17C22×C8×C19D411yescharacteristic
18C19×#121—42no—
19C19×#121—42no—
20C2×C4⋊C4×C19—21no—
21C2×C22⋊C4×C19—41no—
22C2×#64520—41no—
23C19×#102—42no—
24C19×C22⋊C8—41no—
25C22⋊(C19⋊C8)—22no—
26C22⋊(C19⋊C8)—41no—
27C2×C19⋊C16—41no—
28C24×C19—41no—
29C24×C19SD1611yescharacteristic
30C2×D4×C19—22no—
31C2×D4×C19—41no—
32C2×D4×C19—41no—
33C2×D4×C19—41no—
34C2×D4×C19—44no—
35C2×D4×C19—41no—
36C2×D4×C19—41no—
37C2×D4×C19—82no—
38C2×D4×C19—82no—
39C22×C4×C19—21no—
40C22×C4×C19—21no—
41C22×C4×C19—41no—
42C22×C4×C19—41no—
43C22×C4×C19—41no—
44C22×C4×C19C22⋊C411yescharacteristic
45C22×C4×C19D811yescharacteristic
46D8×C19—42no—
47D8×C19—42no—
48C2×C8×C19—21no—
49C2×C8×C19—21no—
50C2×C8×C19—41no—
51C2×C8×C19—41no—
52C4⋊C4×C19—22no—
53C4⋊C4×C19—41no—
54C22⋊C4×C19—44no—
55#64520—81no—
56#64520—81no—
57C2×C19⋊C8—42no—
58C19⋊C16—81no—
59#7084—191nomaximal, Sylow
60C23×C19—21no—
61C23×C19—21no—
62C23×C19—21no—
63C23×C19—41no—
64C23×C19—41no—
65C23×C19—42no—
66C23×C19—81no—
67C23×C19—81no—
68C23×C19—81no—
69C23×C19—81no—
70C23×C19—81no—
71C23×C19—81no—
72C23×C19#10211yescharacteristic
73D4×C19—42no—
74D4×C19—42no—
75D4×C19—81no—
76D4×C19—88no—
77D4×C19—81no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—41no—
82C2×C4×C19—41no—
83C2×C4×C19—41no—
84C2×C4×C19—42no—
85C2×C4×C19—81no—
86C2×C4×C19—81no—
87C2×C4×C19—81no—
88C2×C4×C19#9911yescharacteristic
89C2×C4×C19#10411yescharacteristic
90C8×C19—41no—
91C8×C19—41no—
92C19⋊C8—82no—
93#1999D1911yescharacteristic
94#1314—191no—
95#1293—191no—
96C22×C19—21no—
97C22×C19—21no—
98C22×C19—42no—
99C22×C19—41no—
100C22×C19—41no—
101C22×C19—41no—
102C22×C19—81no—
103C22×C19—82no—
104C22×C19—82no—
105C22×C19—82no—
106C22×C19—161no—
107C22×C19—161no—
108C22×C19—161no—
109C22×C19—161no—
110C22×C19#32711yescharacteristic
111C22×C19#35911yescharacteristic
112C22×C19#36111yescharacteristic
113C4×C19—21no—
114C4×C19—41no—
115C4×C19—82no—
116C4×C19AΣL(1,𝔽16)11yescharacteristic
117C4×C19#35311yescharacteristic
118C22×D8Dic1911yescharacteristic
119C2×#121—21no—
120C2×#102—21no—
121#407—381no—
122C2×C22⋊C8C2×D1911yescharacteristic
123C22⋊C16—381no—
124#340Dic1911yescharacteristic
125C2×C19—21no—
126C2×C19—21no—
127C2×C19—81no—
128C2×C19—162no—
129C2×C19#134111yescharacteristic
130C2×C19#134311yescharacteristic
131C2×C19#134911yescharacteristic
132C22×D4—21no—
133C22×D4—41no—
134C23×C4C22⋊D1911yescharacteristic
135C2×D8—41no—
136C2×D8—42no—
137C2×M16—761no—
138C22×C8C2×Dic1911yescharacteristic
139C22×C8C22⋊D1911yescharacteristic
140#121—42no—
141#121—42no—
142C2×C4⋊C4—21no—
143C2×C22⋊C4—41no—
144C2×C16—761no—
145#102—42no—
146C22⋊C8—41no—
147C22⋊C8—382no—
148C22⋊C8—761no—
149C19#708411yescharacteristic, complemented, Sylow
150C24—41no—
151C24#6452611yescharacteristic
152C2×D4—22no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—41no—
156C2×D4—44no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—82no—
160C2×D4—82no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4#6452511yescharacteristic
167C22×C4C22⋊Dic1911yescharacteristic
168D8—42no—
169D8—42no—
170M16—1521no—
171M16—1521no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—762no—
177C4⋊C4—22no—
178C4⋊C4—41no—
179C22⋊C4—44no—
180C16—1521no—
181C23—21no—
182C23—21no—
183C23—21no—
184C23—41no—
185C23—41no—
186C23—42no—
187C23—81no—
188C23—81no—
189C23—81no—
190C23—81no—
191C23—81no—
192C23—81no—
193C23#1059728911yescharacteristic
194D4—42no—
195D4—42no—
196D4—81no—
197D4—88no—
198D4—81no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—81no—
207C2×C4—81no—
208C2×C4—81no—
209C2×C4#1059729111yescharacteristic
210C2×C4#1059729411yescharacteristic
211C8—41no—
212C8—41no—
213C8—1522no—
214C22—21no—
215C22—21no—
216C22—42no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—82no—
222C22—82no—
223C22—82no—
224C22—161no—
225C22—161no—
226C22—161no—
227C22—161no—
228C22#1192627811yescharacteristic
229C22#1192635111yescharacteristic
230C22#1192635711yescharacteristic
231C4—21no—
232C4—41no—
233C4—82no—
234C4#1192633111yescharacteristic
235C4#1192633711yescharacteristic
236C2—21no—
237C2—21no—
238C2—81no—
239C2—162no—
240C2#1456162611yescharacteristic
241C2#1456163211yescharacteristic
242C2#1456165011yescharacteristic
subgroupG/H
centerC22#11926278
commutatorC22×C8×C19C2×C4
FrattiniC2×C22⋊C8C2×D19
Fitting, prime radicalC19×#1999C2
socleC22×C19#327
cosocleC2×C19×C22⋊C8C22
hypercenter#1999D19
hypocenterC19#7084
LCSG ▷ C22×C8×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. #14561559C2semidirect
2. #14561512C2semidirect
149. C19#7084semidirect

Maximal subgroups

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

subgroupindex
#145615592
#145615122
C19×#19992
#708419