Finite Group Databasebeta

← C19×#8407 #18014366

Subgroups — C19×#8407 #18014366

Order 4864.

900 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#539C211yesmaximal, characteristic
2C19×#1874C211yesmaximal, characteristic
3C19×#1872C211yesmaximal, characteristic, complemented
4C2×C19×#328C211yesmaximal, characteristic, complemented
5C2×C19×#327C211yesmaximal, characteristic
6C2×C19×#324C211yesmaximal, characteristic, complemented
7C19×#1441C211yesmaximal, characteristic, complemented
8C19×#539—22no—
9C19×#539—22no—
10C19×#539—22no—
11C19×#539C414yescomplemented
12C2×C19×#126—21no—
13C2×C19×#125—21no—
14C2×C19×#123—21no—
15C2×C19×#123—21no—
16C2×C19×C22⋊Q8—21no—
17C2×C19×C22⋊Q8C2211yescharacteristic
18C2×C19×#121C2211yescharacteristic
19C2×C4×D4×C19—21no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C22×C4⋊C4×C19C2211yescharacteristic
22C2×C19×#103—21no—
23C2×C19×#102—21no—
24C2×C19×C22⋊C8C2211yescharacteristic
25C2×C19×C22⋊C8C2211yescharacteristic
26C2×C19×#95—21no—
27C2×C19×#95—21no—
28C2×C19×#95C2211yescharacteristic
29C19×#340—21no—
30C19×#340—21no—
31C19×#328—22no—
32C19×#327—22no—
33C19×#324—22no—
34C22×Q8×C19D411yescharacteristic
35C22×D4×C19—21no—
36C22×D4×C19D411yescharacteristic
37C23×C4×C19—21no—
38C23×C4×C19—21no—
39C23×C4×C19—21no—
40C23×C4×C19D411yescharacteristic
41C23×C4×C19D411yescharacteristic
42C23×C4×C19C2311yescharacteristic
43C22×C8×C19—21no—
44C22×C8×C19—21no—
45C19×#126—24no—
46C19×#126—24no—
47C19×#125—24no—
48C19×#125—24no—
49C19×#123—24no—
50C19×#123—24no—
51C19×#123—24no—
52C19×#123—24no—
53C19×C22⋊Q8—24no—
54C19×C22⋊Q8—24no—
55C19×C22⋊Q8—21no—
56C19×C22⋊Q8—21no—
57C19×C22⋊Q8C2×C412yes—
58C19×C22⋊Q8D412yes—
59C19×#121—21no—
60C19×#121—21no—
61C19×#121C2×C412yes—
62C19×#121D412yes—
63C4×D4×C19—24no—
64C4×D4×C19—24no—
65C2×C4⋊C4×C19—21no—
66C2×C4⋊C4×C19—21no—
67C2×C4⋊C4×C19—21no—
68C2×C4⋊C4×C19—21no—
69C2×C4⋊C4×C19—21no—
70C2×C4⋊C4×C19—21no—
71C2×C4⋊C4×C19—21no—
72C2×C4⋊C4×C19—21no—
73C2×C4⋊C4×C19—21no—
74C2×C4⋊C4×C19—21no—
75C2×C4⋊C4×C19—42no—
76C2×C4⋊C4×C19C2×C412yes—
77C2×C4⋊C4×C19D412yes—
78C2×C4⋊C4×C19D411yescharacteristic
79C2×C4⋊C4×C19D411yescharacteristic
80C2×C22⋊C4×C19—21no—
81C2×C22⋊C4×C19—21no—
82C2×C22⋊C4×C19—21no—
83C2×C22⋊C4×C19—21no—
84C2×C22⋊C4×C19—21no—
85C2×C42×C19—21no—
86C19×#103—42no—
87C19×#102—42no—
88C19×C22⋊C8—21no—
89C19×C22⋊C8—21no—
90C19×C22⋊C8—21no—
91C19×C22⋊C8—21no—
92C19×#95—21no—
93C19×#95—21no—
94C19×#95—42no—
95C19×#95—42no—
96C24×C19—21no—
97C24×C19C2×D411yescharacteristic
98C2×Q8×C19—21no—
99C2×Q8×C19—41no—
100C2×Q8×C19—41no—
101C2×Q8×C19C22⋊C412yes—
102C2×D4×C19—22no—
103C2×D4×C19—22no—
104C2×D4×C19—21no—
105C2×D4×C19—41no—
106C2×D4×C19—41no—
107C2×D4×C19—41no—
108C2×D4×C19—41no—
109C2×D4×C19—41no—
110C2×D4×C19—41no—
111C2×D4×C19C22⋊C412yes—
112C22×C4×C19—21no—
113C22×C4×C19—21no—
114C22×C4×C19—21no—
115C22×C4×C19—21no—
116C22×C4×C19—21no—
117C22×C4×C19—21no—
118C22×C4×C19—21no—
119C22×C4×C19—21no—
120C22×C4×C19—21no—
121C22×C4×C19—21no—
122C22×C4×C19—24no—
123C22×C4×C19—21no—
124C22×C4×C19—22no—
125C22×C4×C19—22no—
126C22×C4×C19—41no—
127C22×C4×C19—41no—
128C22×C4×C19—41no—
129C22×C4×C19—41no—
130C22×C4×C19—41no—
131C22×C4×C19—41no—
132C22×C4×C19—41no—
133C22×C4×C19—41no—
134C22×C4×C19—41no—
135C22×C4×C19—41no—
136C22×C4×C19—41no—
137C22×C4×C19—41no—
138C22×C4×C19—41no—
139C22×C4×C19—41no—
140C22×C4×C19—41no—
141C22×C4×C19—41no—
142C22×C4×C19—81no—
143C22×C4×C19—81no—
144C22×C4×C19C22⋊C412yes—
145C22×C4×C19C22⋊C412yes—
146C22×C4×C19C22×C411yescharacteristic
147C22×C4×C19C2×D411yescharacteristic
148C22×C4×C19C2×D411yescharacteristic
149C22×C4×C19C2×D411yescharacteristic
150C22×C4×C19C2×D411yescharacteristic
151C22×C4×C19C2×D411yescharacteristic
152C2×C8×C19—41no—
153C2×C8×C19—41no—
154C2×C8×C19—41no—
155C2×C8×C19—41no—
156C2×C8×C19—41no—
157C2×C8×C19—41no—
158C4⋊C4×C19—24no—
159C4⋊C4×C19—24no—
160C4⋊C4×C19—24no—
161C4⋊C4×C19—22no—
162C4⋊C4×C19—22no—
163C4⋊C4×C19—22no—
164C4⋊C4×C19—22no—
165C4⋊C4×C19—22no—
166C4⋊C4×C19—22no—
167C4⋊C4×C19—21no—
168C4⋊C4×C19—21no—
169C4⋊C4×C19—22no—
170C4⋊C4×C19—22no—
171C4⋊C4×C19—41no—
172C4⋊C4×C19—41no—
173C4⋊C4×C19C22⋊C412yes—
174C4⋊C4×C19C22⋊C412yes—
175C22⋊C4×C19—24no—
176C22⋊C4×C19—24no—
177C22⋊C4×C19—24no—
178C22⋊C4×C19—22no—
179C22⋊C4×C19—22no—
180C22⋊C4×C19—22no—
181C22⋊C4×C19—22no—
182C42×C19—24no—
183#8407C1911yesmaximal, characteristic, direct product factor, Sylow
184C23×C19—21no—
185C23×C19—21no—
186C23×C19—21no—
187C23×C19—21no—
188C23×C19—22no—
189C23×C19—41no—
190C23×C19—41no—
191C23×C19—41no—
192C23×C19—41no—
193C23×C19—41no—
194C23×C19—41no—
195C23×C19C2×C22⋊C411yescharacteristic
196C23×C19#12011yescharacteristic
197C23×C19#12011yescharacteristic
198C23×C19#13511yescharacteristic
199C23×C19#13511yescharacteristic
200C23×C19AGL(1,ℤ/8)11yescharacteristic
201C23×C19#13711yescharacteristic
202Q8×C19—42no—
203Q8×C19—81no—
204D4×C19—42no—
205D4×C19—42no—
206D4×C19—42no—
207D4×C19—42no—
208D4×C19—42no—
209D4×C19—81no—
210C2×C4×C19—21no—
211C2×C4×C19—21no—
212C2×C4×C19—21no—
213C2×C4×C19—21no—
214C2×C4×C19—22no—
215C2×C4×C19—22no—
216C2×C4×C19—22no—
217C2×C4×C19—22no—
218C2×C4×C19—22no—
219C2×C4×C19—22no—
220C2×C4×C19—22no—
221C2×C4×C19—41no—
222C2×C4×C19—41no—
223C2×C4×C19—41no—
224C2×C4×C19—41no—
225C2×C4×C19—41no—
226C2×C4×C19—41no—
227C2×C4×C19—41no—
228C2×C4×C19—41no—
229C2×C4×C19—41no—
230C2×C4×C19—41no—
231C2×C4×C19—41no—
232C2×C4×C19—41no—
233C2×C4×C19—41no—
234C2×C4×C19—41no—
235C2×C4×C19—41no—
236C2×C4×C19—41no—
237C2×C4×C19—42no—
238C2×C4×C19—42no—
239C2×C4×C19—42no—
240C2×C4×C19—42no—
241C2×C4×C19—42no—
242C2×C4×C19—42no—
243C2×C4×C19—42no—
244C2×C4×C19—81no—
245C2×C4×C19—84no—
246C2×C4×C19—81no—
247C2×C4×C19—81no—
248C2×C4×C19—81no—
249C2×C4×C19—81no—
250C2×C4×C19—81no—
251C2×C4×C19—81no—
252C2×C4×C19—81no—
253C2×C4×C19—81no—
254C2×C4×C19C2×C22⋊C411yescharacteristic
255C2×C4×C19C2×C22⋊C411yescharacteristic
256C2×C4×C19#12011yescharacteristic
257C2×C4×C19#12011yescharacteristic
258C8×C19—81no—
259C8×C19—81no—
260C2×#539C2×C1911yescharacteristic
261#1874C2×C1911yescharacteristic
262#1872C2×C1911yescharacteristic, complemented
263C2×#328C2×C1911yescharacteristic, complemented
264C2×#327C2×C1911yescharacteristic
265C2×#324C2×C1911yescharacteristic, complemented
266#1441C2×C1911yescharacteristic, complemented
267C22×C19—21no—
268C22×C19—21no—
269C22×C19—21no—
270C22×C19—21no—
271C22×C19—21no—
272C22×C19—21no—
273C22×C19—21no—
274C22×C19—21no—
275C22×C19—21no—
276C22×C19—21no—
277C22×C19—21no—
278C22×C19—21no—
279C22×C19—42no—
280C22×C19—42no—
281C22×C19—42no—
282C22×C19—81no—
283C22×C19—81no—
284C22×C19—81no—
285C22×C19—81no—
286C22×C19#37911yescharacteristic
287C22×C19#41611yescharacteristic
288C22×C19#41711yescharacteristic
289C22×C19#44911yescharacteristic
290C22×C19#44911yescharacteristic
291C22×C19#45211yescharacteristic
292C22×C19#45211yescharacteristic
293C22×C19#45411yescharacteristic
294C22×C19#45611yescharacteristic
295C22×C19B(4,𝔽2)11yescharacteristic
296C22×C19#45811yescharacteristic
297C4×C19—21no—
298C4×C19—21no—
299C4×C19—21no—
300C4×C19—21no—
301C4×C19—42no—
302C4×C19—42no—
303C4×C19—42no—
304C4×C19—42no—
305C4×C19—42no—
306C4×C19—82no—
307C4×C19—82no—
308#539—22no—
309#539—22no—
310#539—22no—
311#539C4×C1914yescomplemented
312C2×#126—21no—
313C2×#125—21no—
314C2×#123—21no—
315C2×#123—21no—
316C2×C22⋊Q8—21no—
317C2×C22⋊Q8C22×C1911yescharacteristic
318C2×#121C22×C1911yescharacteristic
319C2×C4×D4—21no—
320C22×C4⋊C4C22×C1911yescharacteristic
321C22×C4⋊C4C22×C1911yescharacteristic
322C2×#103—21no—
323C2×#102—21no—
324C2×C22⋊C8C22×C1911yescharacteristic
325C2×C22⋊C8C22×C1911yescharacteristic
326C2×#95—21no—
327C2×#95—21no—
328C2×#95C22×C1911yescharacteristic
329#340—21no—
330#340—21no—
331#328—22no—
332#327—22no—
333#324—22no—
334C2×C19—21no—
335C2×C19—21no—
336C2×C19—21no—
337C2×C19—21no—
338C2×C19—82no—
339C2×C19#159711yescharacteristic
340C2×C19#160311yescharacteristic
341C2×C19#160911yescharacteristic
342C2×C19#161511yescharacteristic
343C2×C19#178811yescharacteristic
344C2×C19#179011yescharacteristic
345C2×C19#179311yescharacteristic
346C22×Q8D4×C1911yescharacteristic
347C22×D4—21no—
348C22×D4D4×C1911yescharacteristic
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4D4×C1911yescharacteristic
353C23×C4D4×C1911yescharacteristic
354C23×C4C23×C1911yescharacteristic
355C22×C8—21no—
356C22×C8—21no—
357#126—24no—
358#126—24no—
359#125—24no—
360#125—24no—
361#123—24no—
362#123—24no—
363#123—24no—
364#123—24no—
365C22⋊Q8—24no—
366C22⋊Q8—24no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8C2×C4×C1912yes—
370C22⋊Q8D4×C1912yes—
371#121—21no—
372#121—21no—
373#121C2×C4×C1912yes—
374#121D4×C1912yes—
375C4×D4—24no—
376C4×D4—24no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4C2×C4×C1912yes—
389C2×C4⋊C4D4×C1912yes—
390C2×C4⋊C4D4×C1911yescharacteristic
391C2×C4⋊C4D4×C1911yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398#103—42no—
399#102—42no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404#95—21no—
405#95—21no—
406#95—42no—
407#95—42no—
408C19#840711yescharacteristic, direct product factor, Sylow
409C24—21no—
410C24C2×D4×C1911yescharacteristic
411C2×Q8—21no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8C22⋊C4×C1912yes—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4C22⋊C4×C1912yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—81no—
456C22×C4—81no—
457C22×C4C22⋊C4×C1912yes—
458C22×C4C22⋊C4×C1912yes—
459C22×C4C22×C4×C1911yescharacteristic
460C22×C4C2×D4×C1911yescharacteristic
461C22×C4C2×D4×C1911yescharacteristic
462C22×C4C2×D4×C1911yescharacteristic
463C22×C4C2×D4×C1911yescharacteristic
464C22×C4C2×D4×C1911yescharacteristic
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C22⋊C4×C1912yes—
487C4⋊C4C22⋊C4×C1912yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C42—24no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C2×C22⋊C4×C1911yescharacteristic
508C23C19×#12011yescharacteristic
509C23C19×#12011yescharacteristic
510C23C19×#13511yescharacteristic
511C23C19×#13511yescharacteristic
512C23C19×AGL(1,ℤ/8)11yescharacteristic
513C23C19×#13711yescharacteristic
514Q8—42no—
515Q8—81no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—81no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—81no—
557C2×C4—84no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4C2×C22⋊C4×C1911yescharacteristic
567C2×C4C2×C22⋊C4×C1911yescharacteristic
568C2×C4C19×#12011yescharacteristic
569C2×C4C19×#12011yescharacteristic
570C8—81no—
571C8—81no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22C19×#37911yescharacteristic
592C22C19×#41611yescharacteristic
593C22C19×#41711yescharacteristic
594C22C19×#44911yescharacteristic
595C22C19×#44911yescharacteristic
596C22C19×#45211yescharacteristic
597C22C19×#45211yescharacteristic
598C22C19×#45411yescharacteristic
599C22C19×#45611yescharacteristic
600C22C19×B(4,𝔽2)11yescharacteristic
601C22C19×#45811yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—82no—
612C4—82no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—82no—
618C2C19×#159711yescharacteristic
619C2C19×#160311yescharacteristic
620C2C19×#160911yescharacteristic
621C2C19×#161511yescharacteristic
622C2C19×#178811yescharacteristic
623C2C19×#179011yescharacteristic
624C2C19×#179311yescharacteristic
subgroupG/H
center, socleC23×C19#120
commutatorC22×C4C22×C4×C19
Frattini, cosocleC23×C4C23×C19
prime radicalC2×C19×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
3. C19×#1872C2semidirect
4. C2×C19×#328C2semidirect
6. C2×C19×#324C2semidirect
7. C19×#1441C2semidirect
11. C19×#539C4semidirect
183. #8407C19direct (N × H)
262. #1872C2×C19semidirect
263. C2×#328C2×C19semidirect
265. C2×#324C2×C19semidirect
266. #1441C2×C19semidirect
311. #539C4×C19semidirect
408. C19#8407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#5392
C19×#18742
C19×#18722
C2×C19×#3282
C2×C19×#3272
C2×C19×#3242
C19×#14412
#840719