Finite Group Databasebeta

← C19×#11535 #18017494

Subgroups — C19×#11535 #18017494

Order 4864.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2326C211yesmaximal, characteristic
2C19×#1465C212yesmaximal
3C19×#1325C212yesmaximal, complemented
4C19×#1319C212yesmaximal, complemented
5C2×C19×#124C411yescharacteristic
6C2×C4×Q8×C19C411yescharacteristic
7C2×C4×D4×C19C2211yescharacteristic
8C19×#407—22no—
9C19×#391C2211yescharacteristic
10C19×#390C411yescharacteristic
11C19×#388—22no—
12C19×#385—22no—
13C19×#384C2211yescharacteristic
14C19×#376C411yescharacteristic
15C19×#324C2214yes—
16C19×#323—22no—
17C22×Q8×C19C2×C411yescharacteristic
18C22×D4×C19C2×C411yescharacteristic
19C23×C4×C19D412yes—
20C2×M16×C19—42no—
21C19×#124—22no—
22C19×#124—22no—
23C4×Q8×C19—42no—
24C4×D4×C19—42no—
25C2×C4⋊C4×C19—21no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19C2×C411yescharacteristic
28C2×C4⋊C4×C19C2311yescharacteristic
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19D412yes—
32C2×C42×C19—21no—
33C2×C42×C19C2×C411yescharacteristic
34C2×C42×C19C2×C411yescharacteristic
35C2×C42×C19C2×C411yescharacteristic
36C19×C22⋊C8—24no—
37C19×C22⋊C8—42no—
38C19×#95—21no—
39C19×#95—21no—
40C19×#95—22no—
41C24×C19C22⋊C412yes—
42C2×Q8×C19—21no—
43C2×Q8×C19—41no—
44C2×Q8×C19—41no—
45C2×Q8×C19M1612yescomplemented
46C2×D4×C19—21no—
47C2×D4×C19—21no—
48C2×D4×C19—41no—
49C2×D4×C19—41no—
50C22×C4×C19—21no—
51C22×C4×C19—21no—
52C22×C4×C19—22no—
53C22×C4×C19—22no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—82no—
57C22×C4×C19C22⋊C411yescharacteristic
58C22×C4×C19C22⋊C411yescharacteristic
59C22×C4×C19C22×C411yescharacteristic
60C22×C4×C19C2×D412yes—
61M16×C19—84no—
62C2×C8×C19—44no—
63C4⋊C4×C19—41no—
64C4⋊C4×C19—41no—
65C4⋊C4×C19—42no—
66C4⋊C4×C19—82no—
67C22⋊C4×C19—28no—
68C22⋊C4×C19—42no—
69C22⋊C4×C19—82no—
70C42×C19—22no—
71C42×C19—21no—
72C42×C19—41no—
73C42×C19—42no—
74C42×C19M1612yescomplemented
75#11535C1911yesmaximal, characteristic, direct product factor, Sylow
76C23×C19—22no—
77C23×C19—22no—
78C23×C19—22no—
79C23×C19—42no—
80C23×C19—42no—
81C23×C19C2×C22⋊C411yescharacteristic
82Q8×C19—42no—
83Q8×C19—42no—
84D4×C19—42no—
85D4×C19—42no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—21no—
91C2×C4×C19—22no—
92C2×C4×C19—41no—
93C2×C4×C19—44no—
94C2×C4×C19—41no—
95C2×C4×C19—41no—
96C2×C4×C19—41no—
97C2×C4×C19—41no—
98C2×C4×C19—42no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—42no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
104C2×C4×C19—41no—
105C2×C4×C19—82no—
106C2×C4×C19#9912yes—
107C2×C4×C19C2×M1611yescharacteristic
108C2×C4×C19C2×M1611yescharacteristic
109C8×C19—84no—
110#2326C2×C1911yescharacteristic
111#1465C2×C1912yes—
112#1325C2×C1912yescomplemented
113#1319C2×C1912yescomplemented
114C22×C19—21no—
115C22×C19—21no—
116C22×C19—44no—
117C22×C19—42no—
118C22×C19—42no—
119C22×C19—42no—
120C22×C19—82no—
121C22×C19#40711yescharacteristic
122C22×C19C2×#9911yescharacteristic
123C22×C19#41311yescharacteristic
124C4×C19—22no—
125C4×C19—21no—
126C4×C19—21no—
127C4×C19—42no—
128C4×C19—42no—
129C4×C19—41no—
130C4×C19—42no—
131C4×C19—81no—
132C4×C19—81no—
133C2×#124C4×C1911yescharacteristic
134C2×C4×Q8C4×C1911yescharacteristic
135C2×C4×D4C22×C1911yescharacteristic
136#407—22no—
137#391C22×C1911yescharacteristic
138#390C4×C1911yescharacteristic
139#388—22no—
140#385—22no—
141#384C22×C1911yescharacteristic
142#376C4×C1911yescharacteristic
143#324C22×C1914yes—
144#323—22no—
145C2×C19—21no—
146C2×C19—21no—
147C2×C19—82no—
148C2×C19#146511yescharacteristic
149C2×C19#212711yescharacteristic
150C2×C19#213511yescharacteristic
151C22×Q8C2×C4×C1911yescharacteristic
152C22×D4C2×C4×C1911yescharacteristic
153C23×C4D4×C1912yes—
154C2×M16—42no—
155#124—22no—
156#124—22no—
157C4×Q8—42no—
158C4×D4—42no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4C2×C4×C1911yescharacteristic
162C2×C4⋊C4C23×C1911yescharacteristic
163C2×C22⋊C4—22no—
164C2×C22⋊C4—22no—
165C2×C22⋊C4D4×C1912yes—
166C2×C42—21no—
167C2×C42C2×C4×C1911yescharacteristic
168C2×C42C2×C4×C1911yescharacteristic
169C2×C42C2×C4×C1911yescharacteristic
170C22⋊C8—24no—
171C22⋊C8—42no—
172#95—21no—
173#95—21no—
174#95—22no—
175C19#1153511yescharacteristic, direct product factor, Sylow
176C24C22⋊C4×C1912yes—
177C2×Q8—21no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8M16×C1912yescomplemented
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—41no—
184C2×D4—41no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—82no—
192C22×C4C22⋊C4×C1911yescharacteristic
193C22×C4C22⋊C4×C1911yescharacteristic
194C22×C4C22×C4×C1911yescharacteristic
195C22×C4C2×D4×C1912yes—
196M16—84no—
197C2×C8—44no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—82no—
202C22⋊C4—28no—
203C22⋊C4—42no—
204C22⋊C4—82no—
205C42—21no—
206C42—22no—
207C42—41no—
208C42—42no—
209C42M16×C1912yescomplemented
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×C22⋊C4×C1911yescharacteristic
216Q8—42no—
217Q8—42no—
218D4—42no—
219D4—42no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—44no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—82no—
240C2×C4C19×#9912yes—
241C2×C4C2×M16×C1911yescharacteristic
242C2×C4C2×M16×C1911yescharacteristic
243C8—84no—
244C22—21no—
245C22—21no—
246C22—44no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—82no—
251C22C19×#40711yescharacteristic
252C22C2×C19×#9911yescharacteristic
253C22C19×#41311yescharacteristic
254C4—21no—
255C4—21no—
256C4—22no—
257C4—42no—
258C4—42no—
259C4—42no—
260C4—41no—
261C4—81no—
262C4—81no—
263C2—21no—
264C2—21no—
265C2—82no—
266C2C19×#146511yescharacteristic
267C2C19×#212711yescharacteristic
268C2C19×#213511yescharacteristic
subgroupG/H
center, socleC22×C19C2×#99
commutatorC22×C4C22×C4×C19
Frattini, cosocleC2×C4⋊C4C23×C19
prime radicalC22×D4×C19C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C4×D4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
3. C19×#1325C2semidirect
4. C19×#1319C2semidirect
45. C2×Q8×C19M16semidirect
74. C42×C19M16semidirect
75. #11535C19direct (N × H)
112. #1325C2×C19semidirect
113. #1319C2×C19semidirect
175. C19#11535direct (N × H)
180. C2×Q8M16×C19semidirect
209. C42M16×C19semidirect

Maximal subgroups

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

subgroupindex
C19×#23262
C19×#14652
C19×#13252
C19×#13192
#1153519