Finite Group Databasebeta

← C19×#11514 #18017473

Subgroups — C19×#11514 #18017473

Order 4864.

434 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C19×#2317C211yesmaximal, characteristic
2C19×#1463C212yesmaximal
3C19×#1325C212yesmaximal, complemented
4C19×#1324C212yesmaximal, complemented
5C2×C19×#117C411yescharacteristic
6C2×C19×#117C411yescharacteristic
7C22×C4⋊C4×C19C2211yescharacteristic
8C19×#407—22no—
9C19×#389—22no—
10C19×#385—22no—
11C19×#384C411yescharacteristic
12C19×#384C2211yescharacteristic
13C19×#382C411yescharacteristic
14C19×#382C2211yescharacteristic
15C19×#324—22no—
16C19×#324C2214yes—
17C23×C4×C19C2×C411yescharacteristic
18C23×C4×C19D412yes—
19C2×M16×C19—42no—
20C19×#117—22no—
21C19×#117—22no—
22C19×#117—42no—
23C2×C4⋊C4×C19—21no—
24C2×C4⋊C4×C19—22no—
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—42no—
27C2×C4⋊C4×C19C2×C411yescharacteristic
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19D412yes—
31C2×C4⋊C4×C19C2311yescharacteristic
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C42×C19—21no—
35C2×C42×C19C2×C411yescharacteristic
36C2×C42×C19C2×C411yescharacteristic
37C19×C22⋊C8—24no—
38C19×C22⋊C8—42no—
39C19×#95—22no—
40C19×#95—22no—
41C24×C19C22⋊C411yescharacteristic
42C22×C4×C19—22no—
43C22×C4×C19—22no—
44C22×C4×C19—21no—
45C22×C4×C19—21no—
46C22×C4×C19—22no—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—22no—
50C22×C4×C19—21no—
51C22×C4×C19—21no—
52C22×C4×C19—82no—
53C22×C4×C19C22⋊C411yescharacteristic
54C22×C4×C19C22⋊C412yes—
55C22×C4×C19C22×C411yescharacteristic
56C22×C4×C19C2×D412yes—
57M16×C19—84no—
58C2×C8×C19—44no—
59C4⋊C4×C19—24no—
60C4⋊C4×C19—41no—
61C4⋊C4×C19—42no—
62C4⋊C4×C19—41no—
63C4⋊C4×C19—41no—
64C4⋊C4×C19—41no—
65C4⋊C4×C19—82no—
66C4⋊C4×C19—82no—
67C22⋊C4×C19—24no—
68C22⋊C4×C19—42no—
69C42×C19—21no—
70C42×C19—21no—
71C42×C19—42no—
72C42×C19M1612yescomplemented
73C42×C19M1612yescomplemented
74#11514C1911yesmaximal, characteristic, direct product factor, Sylow
75C23×C19—21no—
76C23×C19—21no—
77C23×C19—41no—
78C23×C19—41no—
79C23×C19#9912yes—
80C23×C19C2×C22⋊C411yescharacteristic
81C2×C4×C19—24no—
82C2×C4×C19—24no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—21no—
87C2×C4×C19—22no—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—41no—
92C2×C4×C19—41no—
93C2×C4×C19—44no—
94C2×C4×C19—41no—
95C2×C4×C19—41no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19—41no—
101C2×C4×C19—41no—
102C2×C4×C19—82no—
103C2×C4×C19#10112yes—
104C2×C4×C19C2×M1611yescharacteristic
105C2×C4×C19C2×M1611yescharacteristic
106C8×C19—84no—
107#2317C2×C1911yescharacteristic
108#1463C2×C1912yes—
109#1325C2×C1912yescomplemented
110#1324C2×C1912yescomplemented
111C22×C19—21no—
112C22×C19—21no—
113C22×C19—22no—
114C22×C19—22no—
115C22×C19—22no—
116C22×C19—42no—
117C22×C19—42no—
118C22×C19#40711yescharacteristic
119C22×C19C2×#9911yescharacteristic
120C22×C19C2×#10111yescharacteristic
121C4×C19—22no—
122C4×C19—21no—
123C4×C19—21no—
124C4×C19—42no—
125C4×C19—42no—
126C4×C19—42no—
127C4×C19—42no—
128C4×C19—81no—
129C4×C19—81no—
130C2×#117C4×C1911yescharacteristic
131C2×#117C4×C1911yescharacteristic
132C22×C4⋊C4C22×C1911yescharacteristic
133#407—22no—
134#389—22no—
135#385—22no—
136#384C4×C1911yescharacteristic
137#384C22×C1911yescharacteristic
138#382C4×C1911yescharacteristic
139#382C22×C1911yescharacteristic
140#324—22no—
141#324C22×C1914yes—
142C2×C19—21no—
143C2×C19—21no—
144C2×C19—42no—
145C2×C19#146311yescharacteristic
146C2×C19#212711yescharacteristic
147C2×C19#213311yescharacteristic
148C23×C4C2×C4×C1911yescharacteristic
149C23×C4D4×C1912yes—
150C2×M16—42no—
151#117—22no—
152#117—22no—
153#117—42no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4C2×C4×C1911yescharacteristic
159C2×C4⋊C4C2×C4×C1911yescharacteristic
160C2×C4⋊C4C2×C4×C1911yescharacteristic
161C2×C4⋊C4D4×C1912yes—
162C2×C4⋊C4C23×C1911yescharacteristic
163C2×C22⋊C4—21no—
164C2×C22⋊C4—21no—
165C2×C42—21no—
166C2×C42C2×C4×C1911yescharacteristic
167C2×C42C2×C4×C1911yescharacteristic
168C22⋊C8—24no—
169C22⋊C8—42no—
170#95—22no—
171#95—22no—
172C19#1151411yescharacteristic, direct product factor, Sylow
173C24C22⋊C4×C1911yescharacteristic
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—82no—
185C22×C4C22⋊C4×C1911yescharacteristic
186C22×C4C22⋊C4×C1912yes—
187C22×C4C22×C4×C1911yescharacteristic
188C22×C4C2×D4×C1912yes—
189M16—84no—
190C2×C8—44no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C22⋊C4—24no—
200C22⋊C4—42no—
201C42—21no—
202C42—21no—
203C42—42no—
204C42M16×C1912yescomplemented
205C42M16×C1912yescomplemented
206C23—21no—
207C23—21no—
208C23—41no—
209C23—41no—
210C23C19×#9912yes—
211C23C2×C22⋊C4×C1911yescharacteristic
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—44no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—82no—
234C2×C4C19×#10112yes—
235C2×C4C2×M16×C1911yescharacteristic
236C2×C4C2×M16×C1911yescharacteristic
237C8—84no—
238C22—21no—
239C22—21no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—42no—
244C22—42no—
245C22C19×#40711yescharacteristic
246C22C2×C19×#9911yescharacteristic
247C22C2×C19×#10111yescharacteristic
248C4—21no—
249C4—21no—
250C4—22no—
251C4—42no—
252C4—42no—
253C4—42no—
254C4—42no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—21no—
259C2—42no—
260C2C19×#146311yescharacteristic
261C2C19×#212711yescharacteristic
262C2C19×#213311yescharacteristic
subgroupG/H
center, socleC22×C19C2×#99
commutatorC22×C4C22×C4×C19
Frattini, cosocleC2×C4⋊C4C23×C19
prime radicalC24×C19C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C24×C19 ◁ C22×C4⋊C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
3. C19×#1325C2semidirect
4. C19×#1324C2semidirect
72. C42×C19M16semidirect
73. C42×C19M16semidirect
74. #11514C19direct (N × H)
109. #1325C2×C19semidirect
110. #1324C2×C19semidirect
172. C19#11514direct (N × H)
204. C42M16×C19semidirect
205. C42M16×C19semidirect

Maximal subgroups

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

subgroupindex
C19×#23172
C19×#14632
C19×#13252
C19×#13242
#1151419