Finite Group Databasebeta

← C19×#9408 #18015367

Subgroups — C19×#9408 #18015367

Order 4864.

618 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2583C211yesmaximal, characteristic
2C19×#2274C211yesmaximal, characteristic
3C19×#1508C212yesmaximal
4C19×#1463C211yesmaximal, characteristic
5C19×#1297C212yesmaximal
6C2×C19×C22⋊Q8C2211yescharacteristic
7C2×C19×#117—21no—
8C22×C4⋊C4×C19C2211yescharacteristic
9C19×#407C2212yes—
10C19×#398C412yescomplemented
11C19×#395C412yescomplemented
12C19×#389—22no—
13C19×#385—21no—
14C19×#385—21no—
15C4×C4⋊C4×C19—24no—
16C4×C22⋊C4×C19—21no—
17C4×C22⋊C4×C19C2211yescharacteristic
18C4×C22⋊C4×C19C2212yes—
19C19×#328—24no—
20C19×#324—22no—
21C22×Q8×C19C2×C411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C2×M16×C19—22no—
26C19×C22⋊Q8—22no—
27C19×C22⋊Q8—22no—
28C19×#117—28no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19C2×C412yes—
37C2×C4⋊C4×C19D412yes—
38C2×C22⋊C4×C19—22no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C42×C19—22no—
42C2×C42×C19—22no—
43C2×C42×C19—22no—
44C2×C42×C19—21no—
45C19×C22⋊C8—22no—
46C19×C22⋊C8—22no—
47C19×#95—22no—
48C19×#95—22no—
49C19×#95—22no—
50C19×#95C2×C412yes—
51C19×#95D414yes—
52C24×C19C2×D411yescharacteristic
53C2×Q8×C19—22no—
54C2×Q8×C19—81no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—24no—
58C22×C4×C19—22no—
59C22×C4×C19—24no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—81no—
65C22×C4×C19—81no—
66C22×C4×C19C22⋊C412yes—
67C22×C4×C19C22⋊C412yes—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D412yes—
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19#4112yes—
72M16×C19—82no—
73C2×C8×C19—42no—
74C4⋊C4×C19—28no—
75C4⋊C4×C19—24no—
76C4⋊C4×C19—24no—
77C4⋊C4×C19—22no—
78C4⋊C4×C19—44no—
79C4⋊C4×C19—42no—
80C4⋊C4×C19—82no—
81C22⋊C4×C19—24no—
82C22⋊C4×C19—28no—
83C22⋊C4×C19—41no—
84C22⋊C4×C19—41no—
85C42×C19—28no—
86C42×C19—82no—
87C42×C19—81no—
88C42×C19—82no—
89#9408C1911yesmaximal, characteristic, direct product factor, Sylow
90C23×C19—22no—
91C23×C19—22no—
92C23×C19—41no—
93C23×C19C2×C22⋊C411yescharacteristic
94C23×C19#12011yescharacteristic
95C23×C19#12311yescharacteristic
96Q8×C19—82no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—24no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—28no—
103C2×C4×C19—24no—
104C2×C4×C19—22no—
105C2×C4×C19—41no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—41no—
109C2×C4×C19—44no—
110C2×C4×C19—42no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—44no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—42no—
119C2×C4×C19—81no—
120C2×C4×C19#10414yes—
121C2×C4×C19C4×D412yes—
122C2×C4×C19#12112yes—
123C8×C19—82no—
124#2583C2×C1911yescharacteristic
125#2274C2×C1911yescharacteristic
126#1508C2×C1912yes—
127#1463C2×C1911yescharacteristic
128#1297C2×C1912yes—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—44no—
137C22×C19#38611yescharacteristic
138C22×C19C2×#10412yes—
139C22×C19#45612yes—
140C4×C19—24no—
141C4×C19—22no—
142C4×C19—22no—
143C4×C19—48no—
144C4×C19—44no—
145C4×C19—42no—
146C4×C19—81no—
147C4×C19—81no—
148C2×C22⋊Q8C22×C1911yescharacteristic
149C2×#117—21no—
150C22×C4⋊C4C22×C1911yescharacteristic
151#407C22×C1912yes—
152#398C4×C1912yescomplemented
153#395C4×C1912yescomplemented
154#389—22no—
155#385—21no—
156#385—21no—
157C4×C4⋊C4—24no—
158C4×C22⋊C4—21no—
159C4×C22⋊C4C22×C1911yescharacteristic
160C4×C22⋊C4C22×C1912yes—
161#328—24no—
162#324—22no—
163C2×C19—22no—
164C2×C19—22no—
165C2×C19—41no—
166C2×C19#188611yescharacteristic
167C2×C19#189611yescharacteristic
168C2×C19#191311yescharacteristic
169C22×Q8C2×C4×C1911yescharacteristic
170C23×C4D4×C1911yescharacteristic
171C23×C4D4×C1911yescharacteristic
172C23×C4C23×C1911yescharacteristic
173C2×M16—22no—
174C22⋊Q8—22no—
175C22⋊Q8—22no—
176#117—28no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4C2×C4×C1911yescharacteristic
184C2×C4⋊C4C2×C4×C1912yes—
185C2×C4⋊C4D4×C1912yes—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—21no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195#95—22no—
196#95—22no—
197#95—22no—
198#95C2×C4×C1912yes—
199#95D4×C1914yes—
200C19#940811yescharacteristic, direct product factor, Sylow
201C24C2×D4×C1911yescharacteristic
202C2×Q8—22no—
203C2×Q8—81no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—24no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—81no—
214C22×C4—81no—
215C22×C4C22⋊C4×C1912yes—
216C22×C4C22⋊C4×C1912yes—
217C22×C4C22×C4×C1911yescharacteristic
218C22×C4C2×D4×C1912yes—
219C22×C4C2×D4×C1911yescharacteristic
220C22×C4#41×C1912yes—
221M16—82no—
222C2×C8—42no—
223C4⋊C4—28no—
224C4⋊C4—24no—
225C4⋊C4—24no—
226C4⋊C4—22no—
227C4⋊C4—42no—
228C4⋊C4—44no—
229C4⋊C4—82no—
230C22⋊C4—24no—
231C22⋊C4—28no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C42—28no—
235C42—82no—
236C42—81no—
237C42—82no—
238C23—22no—
239C23—22no—
240C23—41no—
241C23C2×C22⋊C4×C1911yescharacteristic
242C23C19×#12011yescharacteristic
243C23C19×#12311yescharacteristic
244Q8—82no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—28no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—81no—
268C2×C4C19×#10414yes—
269C2×C4C4×D4×C1912yes—
270C2×C4C19×#12112yes—
271C8—82no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—44no—
280C22C19×#38611yescharacteristic
281C22C2×C19×#10412yes—
282C22C19×#45612yes—
283C4—24no—
284C4—22no—
285C4—22no—
286C4—48no—
287C4—44no—
288C4—42no—
289C4—81no—
290C4—81no—
291C2—22no—
292C2—22no—
293C2—41no—
294C2C19×#188611yescharacteristic
295C2C19×#189611yescharacteristic
296C2C19×#191311yescharacteristic
subgroupG/H
center, socleC22×C19#386
commutatorC22×C4C22×C4×C19
Frattini, cosocleC23×C4C23×C19
prime radicalC24×C19C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
10. C19×#398C4semidirect
11. C19×#395C4semidirect
89. #9408C19direct (N × H)
152. #398C4×C19semidirect
153. #395C4×C19semidirect
200. C19#9408direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#25832
C19×#22742
C19×#15082
C19×#14632
C19×#12972
#940819