Finite Group Databasebeta

← C19×#18140 #18024099

Subgroups — C19×#18140 #18024099

Order 4864.

1024 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3459C211yesmaximal, characteristic
2C19×#3092C212yesmaximal, complemented
3C19×#2486C211yesmaximal, characteristic, complemented
4C19×#1609C214yesmaximal, complemented
5C19×#1608C212yesmaximal, complemented
6C19×#1607C212yesmaximal, complemented
7C19×#1513C212yesmaximal, complemented
8C19×#1465C211yesmaximal, characteristic, complemented
9C19×#543C2211yescharacteristic
10C19×#539—22no—
11C19×#539C2212yes—
12C19×#538—22no—
13C19×#538—21no—
14C19×#534—21no—
15C19×#534C2211yescharacteristic
16C19×#529—22no—
17C19×#529—21no—
18C19×#525—22no—
19C19×#525C2212yes—
20C2×C19×#123—21no—
21C2×C4×D4×C19—21no—
22C2×C4×D4×C19C2211yescharacteristic
23C22×C4⋊C4×C19C2211yescharacteristic, complemented
24C19×#484—22no—
25C19×#483C2214yescomplemented
26C19×#481—22no—
27C19×#480C2214yes—
28C19×#428—22no—
29C19×#417—22no—
30C19×#407C2212yescomplemented
31C19×#398C2212yescomplemented
32C19×#397C2212yes—
33C19×#389—21no—
34C19×#381—21no—
35C19×#380—21no—
36C19×#380C2211yescharacteristic, complemented
37C19×#328C2214yescomplemented
38C19×#327C2214yes—
39C19×#324C2212yescomplemented
40C19×#323C2212yes—
41C2×#41×C19D412yes—
42C22×D4×C19—21no—
43C22×D4×C19D411yescharacteristic
44C23×C4×C19—21no—
45C23×C4×C19—21no—
46C23×C4×C19D411yescharacteristic
47C23×C4×C19C2311yescharacteristic
48C2×M16×C19—22no—
49C19×#126—22no—
50C19×#126—22no—
51C19×#126—22no—
52C19×#125—21no—
53C19×#125—22no—
54C19×#124—22no—
55C19×#124—21no—
56C19×#123—22no—
57C19×#123—22no—
58C19×#123—22no—
59C19×#123—22no—
60C19×#123—22no—
61C19×#123—22no—
62C19×#123—44no—
63C19×C22⋊Q8—22no—
64C19×C22⋊Q8—22no—
65C19×C22⋊Q8—21no—
66C19×C22⋊Q8—22no—
67C19×C22⋊Q8D412yes—
68C19×C22⋊Q8C2312yes—
69C19×#121—22no—
70C19×#121—22no—
71C19×#121—22no—
72C19×#121—21no—
73C19×#121D412yes—
74C19×#121C2312yes—
75C19×#120—22no—
76C19×#120—22no—
77C19×#120—22no—
78C4×Q8×C19—21no—
79C4×D4×C19—22no—
80C4×D4×C19—22no—
81C4×D4×C19—21no—
82C4×D4×C19—22no—
83C4×D4×C19—22no—
84C4×D4×C19—22no—
85C4×D4×C19—22no—
86C4×D4×C19—22no—
87C19×#117—22no—
88C19×#117D412yes—
89C2×C4⋊C4×C19—21no—
90C2×C4⋊C4×C19—22no—
91C2×C4⋊C4×C19—22no—
92C2×C4⋊C4×C19—21no—
93C2×C4⋊C4×C19—21no—
94C2×C4⋊C4×C19—22no—
95C2×C4⋊C4×C19C2312yes—
96C2×C4⋊C4×C19C2311yescharacteristic
97C2×C22⋊C4×C19—21no—
98C2×C22⋊C4×C19—21no—
99C2×C22⋊C4×C19—22no—
100C2×C22⋊C4×C19—21no—
101C2×C22⋊C4×C19D411yescharacteristic
102C2×C22⋊C4×C19C2311yescharacteristic
103C2×C42×C19—21no—
104C2×C42×C19D411yescharacteristic
105C19×#107—24no—
106C19×#106—24no—
107C19×#103—24no—
108C19×#102—24no—
109C19×C22⋊C8—22no—
110C19×C22⋊C8C2314yes—
111C19×#95—22no—
112C19×#95—22no—
113C19×#95C2312yes—
114C24×C19—21no—
115C24×C19C2×D411yescharacteristic
116C24×C19C2×D411yescharacteristic
117#41×C19—44no—
118C2×Q8×C19—21no—
119C2×Q8×C19C2×D412yes—
120C2×D4×C19—22no—
121C2×D4×C19—22no—
122C2×D4×C19—22no—
123C2×D4×C19—22no—
124C2×D4×C19—21no—
125C2×D4×C19—22no—
126C2×D4×C19—22no—
127C2×D4×C19—41no—
128C2×D4×C19—42no—
129C2×D4×C19—42no—
130C2×D4×C19C2×D412yes—
131C22×C4×C19—21no—
132C22×C4×C19—21no—
133C22×C4×C19—21no—
134C22×C4×C19—22no—
135C22×C4×C19—21no—
136C22×C4×C19—22no—
137C22×C4×C19—21no—
138C22×C4×C19—22no—
139C22×C4×C19—22no—
140C22×C4×C19—42no—
141C22×C4×C19—42no—
142C22×C4×C19—42no—
143C22×C4×C19—42no—
144C22×C4×C19—42no—
145C22×C4×C19—82no—
146C22×C4×C19C2×D411yescharacteristic
147C22×C4×C19C2×D411yescharacteristic
148C22×C4×C19C2×D412yes—
149C22×C4×C19C2×D411yescharacteristic
150C22×C4×C19C2×D411yescharacteristic
151C22×C4×C19C2×D412yes—
152C22×C4×C19C2411yescharacteristic
153M16×C19—44no—
154C2×C8×C19—24no—
155C4⋊C4×C19—22no—
156C4⋊C4×C19—22no—
157C4⋊C4×C19—22no—
158C4⋊C4×C19—21no—
159C4⋊C4×C19—21no—
160C4⋊C4×C19—22no—
161C4⋊C4×C19—22no—
162C4⋊C4×C19—22no—
163C4⋊C4×C19—22no—
164C4⋊C4×C19—24no—
165C4⋊C4×C19—42no—
166C4⋊C4×C19—44no—
167C4⋊C4×C19—41no—
168C4⋊C4×C19—41no—
169C4⋊C4×C19C2×D412yes—
170C4⋊C4×C19C2×D412yes—
171C22⋊C4×C19—22no—
172C22⋊C4×C19—22no—
173C22⋊C4×C19—22no—
174C22⋊C4×C19—22no—
175C22⋊C4×C19—22no—
176C22⋊C4×C19—22no—
177C22⋊C4×C19—22no—
178C22⋊C4×C19—22no—
179C22⋊C4×C19—22no—
180C22⋊C4×C19—22no—
181C22⋊C4×C19—22no—
182C22⋊C4×C19—22no—
183C22⋊C4×C19—42no—
184C22⋊C4×C19—44no—
185C42×C19—22no—
186C42×C19—22no—
187C42×C19—21no—
188C42×C19—21no—
189#18140C1911yesmaximal, characteristic, direct product factor, Sylow
190C23×C19—21no—
191C23×C19—21no—
192C23×C19—21no—
193C23×C19—21no—
194C23×C19—22no—
195C23×C19—41no—
196C23×C19—41no—
197C23×C19—41no—
198C23×C19—41no—
199C23×C19—42no—
200C23×C19—81no—
201C23×C19—81no—
202C23×C19#12012yes—
203C23×C19AGL(1,ℤ/8)12yes—
204C23×C19C22×D411yescharacteristic
205Q8×C19—42no—
206Q8×C19—81no—
207D4×C19—42no—
208D4×C19—44no—
209D4×C19—44no—
210D4×C19—42no—
211D4×C19—42no—
212D4×C19—82no—
213D4×C19—82no—
214D4×C19—81no—
215C2×C4×C19—22no—
216C2×C4×C19—24no—
217C2×C4×C19—21no—
218C2×C4×C19—22no—
219C2×C4×C19—21no—
220C2×C4×C19—22no—
221C2×C4×C19—21no—
222C2×C4×C19—22no—
223C2×C4×C19—21no—
224C2×C4×C19—21no—
225C2×C4×C19—42no—
226C2×C4×C19—41no—
227C2×C4×C19—42no—
228C2×C4×C19—42no—
229C2×C4×C19—44no—
230C2×C4×C19—41no—
231C2×C4×C19—41no—
232C2×C4×C19—42no—
233C2×C4×C19—42no—
234C2×C4×C19—42no—
235C2×C4×C19—42no—
236C2×C4×C19—42no—
237C2×C4×C19—42no—
238C2×C4×C19—81no—
239C2×C4×C19—81no—
240C2×C4×C19—82no—
241C2×C4×C19—81no—
242C2×C4×C19—84no—
243C2×C4×C19#12011yescharacteristic
244C2×C4×C19#12011yescharacteristic
245C2×C4×C19C22×D412yes—
246C8×C19—44no—
247#3459C2×C1911yescharacteristic
248#3092C2×C1912yescomplemented
249#2486C2×C1911yescharacteristic, complemented
250#1609C2×C1914yescomplemented
251#1608C2×C1912yescomplemented
252#1607C2×C1912yescomplemented
253#1513C2×C1912yescomplemented
254#1465C2×C1911yescharacteristic, complemented
255C22×C19—21no—
256C22×C19—21no—
257C22×C19—22no—
258C22×C19—22no—
259C22×C19—22no—
260C22×C19—22no—
261C22×C19—42no—
262C22×C19—42no—
263C22×C19—42no—
264C22×C19—41no—
265C22×C19—41no—
266C22×C19—42no—
267C22×C19—42no—
268C22×C19—42no—
269C22×C19—81no—
270C22×C19—84no—
271C22×C19C2×#12011yescharacteristic
272C22×C19C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C19#57511yescharacteristic
274C4×C19—22no—
275C4×C19—21no—
276C4×C19—41no—
277C4×C19—42no—
278C4×C19—41no—
279C4×C19—42no—
280C4×C19—41no—
281C4×C19—42no—
282C4×C19—82no—
283C4×C19—82no—
284C4×C19#45812yes—
285#543C22×C1911yescharacteristic
286#539—22no—
287#539C22×C1912yes—
288#538—22no—
289#538—21no—
290#534—21no—
291#534C22×C1911yescharacteristic
292#529—22no—
293#529—21no—
294#525—22no—
295#525C22×C1912yes—
296C2×#123—21no—
297C2×C4×D4—21no—
298C2×C4×D4C22×C1911yescharacteristic
299C22×C4⋊C4C22×C1911yescharacteristic, complemented
300#484—22no—
301#483C22×C1914yescomplemented
302#481—22no—
303#480C22×C1914yes—
304#428—22no—
305#417—22no—
306#407C22×C1912yescomplemented
307#398C22×C1912yescomplemented
308#397C22×C1912yes—
309#389—21no—
310#381—21no—
311#380—21no—
312#380C22×C1911yescharacteristic, complemented
313#328C22×C1914yescomplemented
314#327C22×C1914yes—
315#324C22×C1912yescomplemented
316#323C22×C1912yes—
317C2×C19—21no—
318C2×C19—21no—
319C2×C19—42no—
320C2×C19—42no—
321C2×C19—82no—
322C2×C19#300611yescharacteristic
323C2×C19#302211yescharacteristic
324C2×C19C2×#45811yescharacteristic
325C2×#41D4×C1912yes—
326C22×D4—21no—
327C22×D4D4×C1911yescharacteristic
328C23×C4—21no—
329C23×C4—21no—
330C23×C4D4×C1911yescharacteristic
331C23×C4C23×C1911yescharacteristic
332C2×M16—22no—
333#126—22no—
334#126—22no—
335#126—22no—
336#125—21no—
337#125—22no—
338#124—22no—
339#124—21no—
340#123—22no—
341#123—22no—
342#123—22no—
343#123—22no—
344#123—22no—
345#123—22no—
346#123—44no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—21no—
350C22⋊Q8—22no—
351C22⋊Q8D4×C1912yes—
352C22⋊Q8C23×C1912yes—
353#121—22no—
354#121—22no—
355#121—22no—
356#121—21no—
357#121D4×C1912yes—
358#121C23×C1912yes—
359#120—22no—
360#120—22no—
361#120—22no—
362C4×Q8—21no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—21no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371#117—22no—
372#117D4×C1912yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4C23×C1912yes—
380C2×C4⋊C4C23×C1911yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4D4×C1911yescharacteristic
386C2×C22⋊C4C23×C1911yescharacteristic
387C2×C42—21no—
388C2×C42D4×C1911yescharacteristic
389#107—24no—
390#106—24no—
391#103—24no—
392#102—24no—
393C22⋊C8—22no—
394C22⋊C8C23×C1914yes—
395#95—22no—
396#95—22no—
397#95C23×C1912yes—
398C19#1814011yescharacteristic, direct product factor, Sylow
399C24—21no—
400C24C2×D4×C1911yescharacteristic
401C24C2×D4×C1911yescharacteristic
402#41—44no—
403C2×Q8—21no—
404C2×Q8C2×D4×C1912yes—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4C2×D4×C1912yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—82no—
431C22×C4C2×D4×C1911yescharacteristic
432C22×C4C2×D4×C1911yescharacteristic
433C22×C4C2×D4×C1912yes—
434C22×C4C2×D4×C1911yescharacteristic
435C22×C4C2×D4×C1911yescharacteristic
436C22×C4C2×D4×C1912yes—
437C22×C4C24×C1911yescharacteristic
438M16—44no—
439C2×C8—24no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—24no—
450C4⋊C4—42no—
451C4⋊C4—44no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4C2×D4×C1912yes—
455C4⋊C4C2×D4×C1912yes—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—42no—
469C22⋊C4—44no—
470C42—22no—
471C42—22no—
472C42—21no—
473C42—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—42no—
484C23—81no—
485C23—81no—
486C23C19×#12012yes—
487C23C19×AGL(1,ℤ/8)12yes—
488C23C22×D4×C1911yescharacteristic
489Q8—42no—
490Q8—81no—
491D4—42no—
492D4—44no—
493D4—44no—
494D4—42no—
495D4—42no—
496D4—82no—
497D4—82no—
498D4—81no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—81no—
523C2×C4—82no—
524C2×C4—81no—
525C2×C4—81no—
526C2×C4—84no—
527C2×C4C19×#12011yescharacteristic
528C2×C4C19×#12011yescharacteristic
529C2×C4C22×D4×C1912yes—
530C8—44no—
531C22—21no—
532C22—21no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—84no—
547C22C2×C19×#12011yescharacteristic
548C22C2×C19×AGL(1,ℤ/8)11yescharacteristic
549C22C19×#57511yescharacteristic
550C4—22no—
551C4—21no—
552C4—41no—
553C4—42no—
554C4—41no—
555C4—42no—
556C4—41no—
557C4—42no—
558C4—82no—
559C4—82no—
560C4C19×#45812yes—
561C2—21no—
562C2—21no—
563C2—42no—
564C2—42no—
565C2—82no—
566C2C19×#300611yescharacteristic
567C2C19×#302211yescharacteristic
568C2C2×C19×#45811yescharacteristic
subgroupG/H
center, socleC22×C19C2×#120
commutator, Frattini, cosocleC22×C4C24×C19
prime radicalC19×#3459C2
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
2. C19×#3092C2semidirect
3. C19×#2486C2semidirect
4. C19×#1609C2semidirect
5. C19×#1608C2semidirect
6. C19×#1607C2semidirect
7. C19×#1513C2semidirect
8. C19×#1465C2semidirect
23. C22×C4⋊C4×C19C22semidirect
25. C19×#483C22semidirect
30. C19×#407C22semidirect
31. C19×#398C22semidirect
36. C19×#380C22semidirect
37. C19×#328C22semidirect
39. C19×#324C22semidirect
189. #18140C19direct (N × H)
248. #3092C2×C19semidirect
249. #2486C2×C19semidirect
250. #1609C2×C19semidirect
251. #1608C2×C19semidirect
252. #1607C2×C19semidirect
253. #1513C2×C19semidirect
254. #1465C2×C19semidirect
299. C22×C4⋊C4C22×C19semidirect
301. #483C22×C19semidirect
306. #407C22×C19semidirect
307. #398C22×C19semidirect
312. #380C22×C19semidirect
313. #328C22×C19semidirect
315. #324C22×C19semidirect
398. C19#18140direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#34592
C19×#30922
C19×#24862
C19×#16092
C19×#16082
C19×#16072
C19×#15132
C19×#14652
#1814019