Finite Group Databasebeta

← C19×#11531 #18017490

Subgroups — C19×#11531 #18017490

Order 4864.

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

normal subgroups only

This group has 460 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
1C4×C19×#124C211yesmaximal, characteristic
2C19×#1465C212yesmaximal
3C19×#1324C212yesmaximal, 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×#382C2211yescharacteristic
13C4×C22⋊C4×C19—22no—
14C43×C19C411yescharacteristic
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—41no—
24C4×Q8×C19—41no—
25C4×D4×C19—41no—
26C4×D4×C19—41no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C4⋊C4×C19C2311yescharacteristic
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—22no—
32C2×C22⋊C4×C19D412yes—
33C2×C42×C19—21no—
34C2×C42×C19—21no—
35C2×C42×C19—21no—
36C2×C42×C19C2×C411yescharacteristic
37C2×C42×C19C2×C411yescharacteristic
38C2×C42×C19C2×C411yescharacteristic
39C19×C22⋊C8—24no—
40C19×C22⋊C8—42no—
41C19×#95—22no—
42C19×#95—22no—
43C24×C19C22⋊C412yes—
44C2×Q8×C19—21no—
45C2×Q8×C19—41no—
46C2×Q8×C19—41no—
47C2×Q8×C19M1612yescomplemented
48C2×D4×C19—21no—
49C2×D4×C19—21no—
50C2×D4×C19—41no—
51C2×D4×C19—41no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—21no—
58C22×C4×C19—44no—
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C2×D412yes—
63M16×C19—84no—
64C2×C8×C19—44no—
65C4⋊C4×C19—41no—
66C4⋊C4×C19—41no—
67C4⋊C4×C19—42no—
68C22⋊C4×C19—28no—
69C22⋊C4×C19—42no—
70C22⋊C4×C19—44no—
71C42×C19—21no—
72C42×C19—21no—
73C42×C19—21no—
74C42×C19—41no—
75C42×C19—42no—
76C42×C19—42no—
77C42×C19—41no—
78C42×C19—41no—
79C42×C19M1612yescomplemented
80#11531C1911yesmaximal, characteristic, direct product factor, Sylow
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—42no—
85C23×C19—42no—
86C23×C19C2×C22⋊C411yescharacteristic
87Q8×C19—42no—
88Q8×C19—42no—
89D4×C19—42no—
90D4×C19—42no—
91C2×C4×C19—21no—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—21no—
98C2×C4×C19—22no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
104C2×C4×C19—41no—
105C2×C4×C19—44no—
106C2×C4×C19—41no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19—41no—
110C2×C4×C19—82no—
111C2×C4×C19#9911yescharacteristic
112C2×C4×C19#9911yescharacteristic
113C2×C4×C19C2×M1611yescharacteristic
114C2×C4×C19C2×M1611yescharacteristic
115C8×C19—84no—
116C4×#124C2×C1911yescharacteristic
117#1465C2×C1912yes—
118#1324C2×C1912yescomplemented
119#1319C2×C1912yescomplemented
120C22×C19—21no—
121C22×C19—21no—
122C22×C19—44no—
123C22×C19—42no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19—82no—
127C22×C19#40711yescharacteristic
128C22×C19C2×#9911yescharacteristic
129C22×C19#41311yescharacteristic
130C4×C19—21no—
131C4×C19—21no—
132C4×C19—21no—
133C4×C19—42no—
134C4×C19—42no—
135C4×C19—42no—
136C4×C19—41no—
137C4×C19—42no—
138C4×C19—81no—
139C4×C19#35412yes—
140C2×#124C4×C1911yescharacteristic
141C2×C4×Q8C4×C1911yescharacteristic
142C2×C4×D4C22×C1911yescharacteristic
143#407—22no—
144#391C22×C1911yescharacteristic
145#390C4×C1911yescharacteristic
146#388—22no—
147#382C22×C1911yescharacteristic
148C4×C22⋊C4—22no—
149C43C4×C1911yescharacteristic
150#324C22×C1914yes—
151#323—22no—
152C2×C19—21no—
153C2×C19—21no—
154C2×C19—82no—
155C2×C19#146511yescharacteristic
156C2×C19C2×#35411yescharacteristic
157C2×C19#213211yescharacteristic
158C22×Q8C2×C4×C1911yescharacteristic
159C22×D4C2×C4×C1911yescharacteristic
160C23×C4D4×C1912yes—
161C2×M16—42no—
162#124—22no—
163#124—22no—
164C4×Q8—41no—
165C4×Q8—41no—
166C4×D4—41no—
167C4×D4—41no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4C2×C4×C1911yescharacteristic
170C2×C4⋊C4C23×C1911yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4D4×C1912yes—
174C2×C42—21no—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42C2×C4×C1911yescharacteristic
178C2×C42C2×C4×C1911yescharacteristic
179C2×C42C2×C4×C1911yescharacteristic
180C22⋊C8—24no—
181C22⋊C8—42no—
182#95—22no—
183#95—22no—
184C19#1153111yescharacteristic, direct product factor, Sylow
185C24C22⋊C4×C1912yes—
186C2×Q8—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8M16×C1912yescomplemented
190C2×D4—21no—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—44no—
201C22×C4C22⋊C4×C1911yescharacteristic
202C22×C4C22⋊C4×C1911yescharacteristic
203C22×C4C22×C4×C1911yescharacteristic
204C22×C4C2×D4×C1912yes—
205M16—84no—
206C2×C8—44no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—42no—
210C22⋊C4—28no—
211C22⋊C4—42no—
212C22⋊C4—44no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—41no—
217C42—42no—
218C42—42no—
219C42—41no—
220C42—41no—
221C42M16×C1912yescomplemented
222C23—22no—
223C23—22no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23C2×C22⋊C4×C1911yescharacteristic
228Q8—42no—
229Q8—42no—
230D4—42no—
231D4—42no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—44no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—82no—
252C2×C4C19×#9911yescharacteristic
253C2×C4C19×#9911yescharacteristic
254C2×C4C2×M16×C1911yescharacteristic
255C2×C4C2×M16×C1911yescharacteristic
256C8—84no—
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—82no—
264C22C19×#40711yescharacteristic
265C22C2×C19×#9911yescharacteristic
266C22C19×#41311yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—42no—
272C4—42no—
273C4—42no—
274C4—41no—
275C4—81no—
276C4C19×#35412yes—
277C2—21no—
278C2—21no—
279C2—82no—
280C2C19×#146511yescharacteristic
281C2C2×C19×#35411yescharacteristic
282C2C19×#213211yescharacteristic
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×#1324C2semidirect
4. C19×#1319C2semidirect
47. C2×Q8×C19M16semidirect
79. C42×C19M16semidirect
80. #11531C19direct (N × H)
118. #1324C2×C19semidirect
119. #1319C2×C19semidirect
184. C19#11531direct (N × H)
189. C2×Q8M16×C19semidirect
221. C42M16×C19semidirect

Maximal subgroups

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

subgroupindex
C4×C19×#1242
C19×#14652
C19×#13242
C19×#13192
#1153119