Finite Group Databasebeta

← C19×#8469 #18014428

Subgroups — C19×#8469 #18014428

Order 4864.

1092 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3498C211yesmaximal, characteristic
2C19×#1965C212yesmaximal, complemented
3C19×#1560C211yesmaximal, characteristic, complemented
4C19×#1525C211yesmaximal, characteristic, complemented
5C19×#1489C212yesmaximal, complemented
6C2×C19×H(5,𝔽2)C412yes—
7C19×#550—22no—
8D42×C19—24no—
9D42×C19—22no—
10C19×#535—22no—
11C19×#535C412yes—
12C19×#532—21no—
13C19×#532C2211yescharacteristic
14C2×C19×#127—21no—
15C2×C19×#127C2211yescharacteristic
16C4×#41×C19C2211yescharacteristic
17C19×#423C2212yescomplemented
18C2×C19×#100—24no—
19C4×M16×C19C2212yescomplemented
20C19×#333—21no—
21C19×#331—21no—
22C19×#329—22no—
23C19×Q8⋊C8—22no—
24C19×D4⋊C8—22no—
25C19×H(5,𝔽2)—44no—
26C19×H(5,𝔽2)—44no—
27C2×#41×C19—22no—
28C2×#41×C19—22no—
29C2×#41×C19C2×C411yescharacteristic
30C2×#41×C19C2×C412yes—
31C22×D4×C19—24no—
32C22×D4×C19—24no—
33C22×D4×C19—22no—
34C22×D4×C19—22no—
35C22×D4×C19C2×C412yes—
36C22×D4×C19D414yes—
37C2×M16×C19—22no—
38C2×M16×C19—22no—
39C19×C4⋊Q8D411yescharacteristic
40C19×#127—24no—
41C19×#127—22no—
42C19×#127—21no—
43C19×#127—21no—
44C19×#127—22no—
45C19×#127D411yescharacteristic
46C19×#124—22no—
47C19×#124D412yes—
48C19×#121—24no—
49C19×#121—28no—
50C19×#121—22no—
51C19×#121—24no—
52C19×#120—28no—
53C19×#120—24no—
54C4×Q8×C19D412yes—
55C4×D4×C19—24no—
56C4×D4×C19—22no—
57C4×D4×C19—22no—
58C4×D4×C19D412yes—
59C19×#117—21no—
60C19×#117C2×C411yescharacteristic
61C2×C42×C19—21no—
62C2×C42×C19C2311yescharacteristic
63C19×C4⋊C8—22no—
64C19×C4⋊C8—22no—
65C19×#100—48no—
66C19×#97—22no—
67C4×C8×C19—22no—
68C24×C19—24no—
69C24×C19C22⋊C414yes—
70#41×C19—22no—
71#41×C19—22no—
72#41×C19—48no—
73#41×C19—42no—
74#41×C19—42no—
75#41×C19—44no—
76#41×C19—44no—
77C2×Q8×C19C22⋊C411yescharacteristic
78C2×Q8×C19C22⋊C412yes—
79C2×D4×C19—21no—
80C2×D4×C19—24no—
81C2×D4×C19—24no—
82C2×D4×C19—22no—
83C2×D4×C19—28no—
84C2×D4×C19—22no—
85C2×D4×C19—22no—
86C2×D4×C19—24no—
87C2×D4×C19—22no—
88C2×D4×C19—24no—
89C2×D4×C19—48no—
90C2×D4×C19—42no—
91C2×D4×C19—42no—
92C2×D4×C19—44no—
93C2×D4×C19—44no—
94C2×D4×C19—416no—
95C2×D4×C19—44no—
96C2×D4×C19—44no—
97C2×D4×C19—84no—
98C2×D4×C19—84no—
99C2×D4×C19C22⋊C411yescharacteristic
100C2×D4×C19C22⋊C412yes—
101C22×C4×C19—21no—
102C22×C4×C19—24no—
103C22×C4×C19—22no—
104C22×C4×C19—22no—
105C22×C4×C19C22×C411yescharacteristic
106C22×C4×C19C2×D412yes—
107M16×C19—24no—
108M16×C19—42no—
109M16×C19—44no—
110C2×C8×C19—42no—
111C2×C8×C19—42no—
112C4⋊C4×C19—22no—
113C4⋊C4×C19—22no—
114C4⋊C4×C19C22⋊C412yes—
115C22⋊C4×C19—28no—
116C22⋊C4×C19—21no—
117C22⋊C4×C19—22no—
118C22⋊C4×C19—24no—
119C42×C19—21no—
120C42×C19—22no—
121C42×C19C2×D411yescharacteristic
122C42×C19C2×D411yescharacteristic
123C42×C19C2×D412yes—
124#8469C1911yesmaximal, characteristic, direct product factor, Sylow
125C23×C19—21no—
126C23×C19—24no—
127C23×C19—22no—
128C23×C19—48no—
129C23×C19—44no—
130C23×C19—48no—
131C23×C19—88no—
132C23×C19C2×C22⋊C411yescharacteristic
133Q8×C19—21no—
134Q8×C19—42no—
135Q8×C19#10012yescomplemented
136D4×C19—24no—
137D4×C19—21no—
138D4×C19—42no—
139D4×C19—44no—
140D4×C19—48no—
141D4×C19—44no—
142D4×C19—48no—
143D4×C19—42no—
144D4×C19—42no—
145D4×C19—44no—
146D4×C19—42no—
147D4×C19—44no—
148D4×C19—42no—
149D4×C19—84no—
150D4×C19—88no—
151D4×C19#10012yescomplemented
152C2×C4×C19—24no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—22no—
157C2×C4×C19—22no—
158C2×C4×C19—22no—
159C2×C4×C19—22no—
160C2×C4×C19—48no—
161C2×C4×C19—42no—
162C2×C4×C19—42no—
163C2×C4×C19—42no—
164C2×C4×C19—42no—
165C2×C4×C19C2×C22⋊C411yescharacteristic
166C2×C4×C19C2×C22⋊C411yescharacteristic
167C2×C4×C19#12012yes—
168C2×C4×C19#12012yes—
169C8×C19—44no—
170C8×C19—82no—
171#3498C2×C1911yescharacteristic
172#1965C2×C1912yescomplemented
173#1560C2×C1911yescharacteristic, complemented
174#1525C2×C1911yescharacteristic, complemented
175#1489C2×C1912yescomplemented
176C22×C19—22no—
177C22×C19—21no—
178C22×C19—22no—
179C22×C19—42no—
180C22×C19—48no—
181C22×C19—44no—
182C22×C19—44no—
183C22×C19—42no—
184C22×C19—164no—
185C22×C19—168no—
186C22×C19#37911yescharacteristic
187C4×C19—22no—
188C4×C19—21no—
189C4×C19—22no—
190C4×C19—42no—
191C4×C19—42no—
192C4×C19C2×#10011yescharacteristic
193C4×C19C2×#10011yescharacteristic
194C4×C19#45312yes—
195C4×C19#45512yes—
196C2×H(5,𝔽2)C4×C1912yes—
197#550—22no—
198D42—24no—
199D42—22no—
200#535—22no—
201#535C4×C1912yes—
202#532—21no—
203#532C22×C1911yescharacteristic
204C2×#127—21no—
205C2×#127C22×C1911yescharacteristic
206C4×#41C22×C1911yescharacteristic
207#423C22×C1912yescomplemented
208C2×#100—24no—
209C4×M16C22×C1912yescomplemented
210#333—21no—
211#331—21no—
212#329—22no—
213Q8⋊C8—22no—
214D4⋊C8—22no—
215C2×C19—41no—
216C2×C19—42no—
217C2×C19—84no—
218C2×C19—82no—
219C2×C19#178311yescharacteristic
220C2×C19#179212yes—
221H(5,𝔽2)—44no—
222H(5,𝔽2)—44no—
223C2×#41—22no—
224C2×#41—22no—
225C2×#41C2×C4×C1911yescharacteristic
226C2×#41C2×C4×C1912yes—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4C2×C4×C1912yes—
232C22×D4D4×C1914yes—
233C2×M16—22no—
234C2×M16—22no—
235C4⋊Q8D4×C1911yescharacteristic
236#127—24no—
237#127—22no—
238#127—21no—
239#127—21no—
240#127—22no—
241#127D4×C1911yescharacteristic
242#124—22no—
243#124D4×C1912yes—
244#121—24no—
245#121—28no—
246#121—22no—
247#121—24no—
248#120—28no—
249#120—24no—
250C4×Q8D4×C1912yes—
251C4×D4—24no—
252C4×D4—22no—
253C4×D4—22no—
254C4×D4D4×C1912yes—
255#117—21no—
256#117C2×C4×C1911yescharacteristic
257C2×C42—21no—
258C2×C42C23×C1911yescharacteristic
259C4⋊C8—22no—
260C4⋊C8—22no—
261#100—48no—
262#97—22no—
263C4×C8—22no—
264C19#846911yescharacteristic, direct product factor, Sylow
265C24—24no—
266C24C22⋊C4×C1914yes—
267#41—22no—
268#41—22no—
269#41—48no—
270#41—42no—
271#41—42no—
272#41—44no—
273#41—44no—
274C2×Q8C22⋊C4×C1911yescharacteristic
275C2×Q8C22⋊C4×C1912yes—
276C2×D4—21no—
277C2×D4—24no—
278C2×D4—24no—
279C2×D4—22no—
280C2×D4—28no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—24no—
284C2×D4—22no—
285C2×D4—24no—
286C2×D4—48no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—44no—
290C2×D4—44no—
291C2×D4—416no—
292C2×D4—44no—
293C2×D4—44no—
294C2×D4—84no—
295C2×D4—84no—
296C2×D4C22⋊C4×C1911yescharacteristic
297C2×D4C22⋊C4×C1912yes—
298C22×C4—21no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4C22×C4×C1911yescharacteristic
303C22×C4C2×D4×C1912yes—
304M16—24no—
305M16—42no—
306M16—44no—
307C2×C8—42no—
308C2×C8—42no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4C22⋊C4×C1912yes—
312C22⋊C4—28no—
313C22⋊C4—21no—
314C22⋊C4—22no—
315C22⋊C4—24no—
316C42—21no—
317C42—22no—
318C42C2×D4×C1912yes—
319C42C2×D4×C1911yescharacteristic
320C42C2×D4×C1911yescharacteristic
321C23—21no—
322C23—24no—
323C23—22no—
324C23—48no—
325C23—44no—
326C23—48no—
327C23—88no—
328C23C2×C22⋊C4×C1911yescharacteristic
329Q8—21no—
330Q8—42no—
331Q8C19×#10012yescomplemented
332D4—24no—
333D4—21no—
334D4—42no—
335D4—44no—
336D4—48no—
337D4—44no—
338D4—48no—
339D4—42no—
340D4—42no—
341D4—44no—
342D4—42no—
343D4—44no—
344D4—42no—
345D4—84no—
346D4—88no—
347D4C19×#10012yescomplemented
348C2×C4—24no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—48no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4C2×C22⋊C4×C1911yescharacteristic
362C2×C4C2×C22⋊C4×C1911yescharacteristic
363C2×C4C19×#12012yes—
364C2×C4C19×#12012yes—
365C8—44no—
366C8—82no—
367C22—21no—
368C22—22no—
369C22—22no—
370C22—42no—
371C22—44no—
372C22—42no—
373C22—48no—
374C22—44no—
375C22—164no—
376C22—168no—
377C22C19×#37911yescharacteristic
378C4—21no—
379C4—22no—
380C4—22no—
381C4—42no—
382C4—42no—
383C4C2×C19×#10011yescharacteristic
384C4C2×C19×#10011yescharacteristic
385C4C19×#45312yes—
386C4C19×#45512yes—
387C2—41no—
388C2—42no—
389C2—82no—
390C2—84no—
391C2C19×#178311yescharacteristic
392C2C19×#179212yes—
subgroupG/H
center, socleC22×C19#379
commutatorC22×C4C22×C4×C19
Frattini, cosocleC2×C42C23×C19
prime radicalC19×#3498C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#1965C2semidirect
3. C19×#1560C2semidirect
4. C19×#1525C2semidirect
5. C19×#1489C2semidirect
17. C19×#423C22semidirect
19. C4×M16×C19C22semidirect
124. #8469C19direct (N × H)
135. Q8×C19#100semidirect
151. D4×C19#100semidirect
172. #1965C2×C19semidirect
173. #1560C2×C19semidirect
174. #1525C2×C19semidirect
175. #1489C2×C19semidirect
207. #423C22×C19semidirect
209. C4×M16C22×C19semidirect
264. C19#8469direct (N × H)
331. Q8C19×#100semidirect
347. D4C19×#100semidirect

Maximal subgroups

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

subgroupindex
C19×#34982
C19×#19652
C19×#15602
C19×#15252
C19×#14892
#846919