Finite Group Databasebeta

← C19×#19581 #18025540

Subgroups — C19×#19581 #18025540

Order 4864.

644 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3248C211yesmaximal, characteristic, complemented
2C19×#3217C211yesmaximal, characteristic
3C19×#3208C211yesmaximal, characteristic, complemented
4C19×#2994C211yesmaximal, characteristic, complemented
5C19×#1702C211yesmaximal, characteristic, complemented
6C19×#1701C211yesmaximal, characteristic, complemented
7C19×#1686C211yesmaximal, characteristic, complemented
8C19×#1685C211yesmaximal, characteristic, complemented
9C19×#1682C211yesmaximal, characteristic, complemented
10C19×#1681C211yesmaximal, characteristic, complemented
11C19×#1666C211yesmaximal, characteristic, complemented
12C19×#1665C211yesmaximal, characteristic, complemented
13C19×#1573C211yesmaximal, characteristic, complemented
14C19×#1552C211yesmaximal, characteristic, complemented
15C2×C19×#331C211yesmaximal, characteristic, complemented
16C19×#533C2211yescharacteristic
17C2×C19×#127C2211yescharacteristic
18C19×#529C2211yescharacteristic
19C19×#496—21no—
20C19×#492C2211yescharacteristic
21C19×#492C2211yescharacteristic
22C19×#490—21no—
23C19×#486C2211yescharacteristic
24C19×#486C2211yescharacteristic
25C19×#479—21no—
26C19×#475C2211yescharacteristic, complemented
27C19×#474C2211yescharacteristic, complemented
28C19×#467—21no—
29C19×#465—21no—
30C19×#464—21no—
31C19×#462C2211yescharacteristic, complemented
32C19×#461C2211yescharacteristic, complemented
33C19×#460—21no—
34C19×#460—21no—
35C19×#460C2211yescharacteristic
36C19×#460C2211yescharacteristic
37C19×#459C2211yescharacteristic
38C19×#459C2211yescharacteristic
39C19×#450—21no—
40C19×#450—21no—
41C19×#450—21no—
42C19×#447—21no—
43C19×#446C2211yescharacteristic, complemented
44C8×Q8×C19C2211yescharacteristic, complemented
45C19×#436C2211yescharacteristic, complemented
46C19×#435—21no—
47C8×D4×C19—21no—
48C8×D4×C19C2211yescharacteristic, complemented
49C19×#433—21no—
50C19×#432C2211yescharacteristic
51C19×#431C2211yescharacteristic
52C19×#424—21no—
53C2×C19×C4⋊C8C2211yescharacteristic
54C2×C19×C4⋊C8C2211yescharacteristic
55C19×#335C2211yescharacteristic, complemented
56C19×#335C2211yescharacteristic, complemented
57C19×#334C2211yescharacteristic, complemented
58C19×#334C2211yescharacteristic, complemented
59C19×#332C2211yescharacteristic, complemented
60C19×#332C2211yescharacteristic, complemented
61C19×#332C2211yescharacteristic, complemented
62C19×#332C2211yescharacteristic, complemented
63C19×#331C2211yescharacteristic
64C19×#331C2211yescharacteristic
65C19×#331C2211yescharacteristic
66C19×#331C2211yescharacteristic
67C22×D4×C19—21no—
68C22×D4×C19—21no—
69C22×D4×C19—21no—
70C2×Q16×C19—21no—
71C2×SD16×C19—21no—
72C2×SD16×C19—21no—
73C2×SD16×C19—21no—
74C2×SD16×C19—21no—
75C2×SD16×C19—21no—
76C2×SD16×C19—21no—
77C2×SD16×C19—21no—
78C2×D8×C19—21no—
79C2×D8×C19—21no—
80C2×M16×C19—21no—
81C22×C8×C19—21no—
82C22×C8×C19—21no—
83C22×C8×C19—21no—
84C19×C4⋊Q8C2311yescharacteristic
85C19×C4⋊Q8C2311yescharacteristic
86C19×#127—21no—
87C19×#127—21no—
88C19×#127—21no—
89C19×#127C2311yescharacteristic
90C19×#127C2311yescharacteristic
91C19×#126—21no—
92C19×#125—21no—
93C19×#125D411yescharacteristic
94C19×#124D411yescharacteristic
95C19×#123—21no—
96C19×C22⋊Q8—21no—
97C19×C22⋊Q8—21no—
98C19×C22⋊Q8D411yescharacteristic
99C19×#121D411yescharacteristic
100C4×Q8×C19—21no—
101C4×Q8×C19—21no—
102C4×Q8×C19C2311yescharacteristic
103C4×D4×C19—21no—
104C4×D4×C19C2311yescharacteristic
105C19×#117—21no—
106C19×#117—21no—
107C2×C42×C19C2311yescharacteristic
108C19×#107—21no—
109C19×#106—21no—
110C19×C4⋊C8—21no—
111C19×C4⋊C8—21no—
112C19×C4⋊C8—21no—
113C19×C4⋊C8—21no—
114C19×C4⋊C8D411yescharacteristic
115C19×C4⋊C8D411yescharacteristic
116C19×C4⋊C8C2311yescharacteristic
117C19×C4⋊C8C2311yescharacteristic
118C19×C4⋊C8C2311yescharacteristic
119C19×C4⋊C8C2311yescharacteristic
120C19×C4⋊C8C2311yescharacteristic
121C19×C4⋊C8C2311yescharacteristic
122C19×#103—21no—
123C19×#103—21no—
124C19×#103—21no—
125C19×#102—21no—
126C19×#102—21no—
127C19×#102—21no—
128C19×#102—21no—
129C19×#102—21no—
130C19×#102—21no—
131C19×#102—21no—
132C19×#102—21no—
133C19×#102—21no—
134C19×C22⋊C8—21no—
135C19×C22⋊C8—21no—
136C19×C22⋊C8—21no—
137C19×C22⋊C8D411yescharacteristic
138C19×C22⋊C8D411yescharacteristic
139C19×#97—21no—
140C19×#97—21no—
141C4×C8×C19—21no—
142C4×C8×C19C2311yescharacteristic
143C4×C8×C19C2311yescharacteristic
144C24×C19—41no—
145C2×Q8×C19—21no—
146C2×Q8×C19—21no—
147C2×Q8×C19C2×D411yescharacteristic
148C2×D4×C19—21no—
149C2×D4×C19—21no—
150C2×D4×C19—21no—
151C2×D4×C19—21no—
152C2×D4×C19—21no—
153C2×D4×C19—21no—
154C2×D4×C19—21no—
155C2×D4×C19—41no—
156C2×D4×C19—41no—
157C2×D4×C19—41no—
158C2×D4×C19—81no—
159C2×D4×C19—81no—
160C2×D4×C19—81no—
161C2×D4×C19—81no—
162C2×D4×C19—82no—
163C2×D4×C19C2×D411yescharacteristic
164C22×C4×C19—21no—
165C22×C4×C19C2×D411yescharacteristic
166C22×C4×C19C2×D411yescharacteristic
167C22×C4×C19#4111yescharacteristic
168Q16×C19—81no—
169SD16×C19—81no—
170SD16×C19—81no—
171SD16×C19—81no—
172SD16×C19—81no—
173SD16×C19—81no—
174SD16×C19—81no—
175SD16×C19—81no—
176D8×C19—81no—
177D8×C19—81no—
178M16×C19—81no—
179C2×C8×C19—21no—
180C2×C8×C19—21no—
181C2×C8×C19—21no—
182C2×C8×C19—21no—
183C2×C8×C19—21no—
184C2×C8×C19—21no—
185C2×C8×C19—81no—
186C2×C8×C19—81no—
187C2×C8×C19—81no—
188C2×C8×C19C2×D411yescharacteristic
189C2×C8×C19C2×D411yescharacteristic
190C2×C8×C19C2×D411yescharacteristic
191C2×C8×C19C2×D411yescharacteristic
192C4⋊C4×C19—21no—
193C4⋊C4×C19—21no—
194C4⋊C4×C19—21no—
195C4⋊C4×C19—21no—
196C4⋊C4×C19—21no—
197C4⋊C4×C19—21no—
198C4⋊C4×C19—21no—
199C4⋊C4×C19—21no—
200C4⋊C4×C19—41no—
201C4⋊C4×C19—41no—
202C4⋊C4×C19C2×D411yescharacteristic
203C4⋊C4×C19C2×D411yescharacteristic
204C22⋊C4×C19—21no—
205C22⋊C4×C19—21no—
206C22⋊C4×C19—21no—
207C22⋊C4×C19—21no—
208C22⋊C4×C19—21no—
209C22⋊C4×C19—41no—
210C42×C19—21no—
211C42×C19—41no—
212C42×C19C2×D411yescharacteristic
213C42×C19C2×D411yescharacteristic
214C42×C19#4111yescharacteristic
215C42×C19C2411yescharacteristic
216#19581C1911yesmaximal, characteristic, direct product factor, Sylow
217C23×C19—21no—
218C23×C19—41no—
219C23×C19—41no—
220C23×C19—82no—
221C23×C19—82no—
222C23×C19—82no—
223C23×C19#12111yescharacteristic
224Q8×C19—21no—
225Q8×C19—21no—
226Q8×C19—41no—
227Q8×C19—41no—
228Q8×C19—41no—
229Q8×C19—41no—
230D4×C19—21no—
231D4×C19—21no—
232D4×C19—42no—
233D4×C19—41no—
234D4×C19—41no—
235D4×C19—41no—
236D4×C19—41no—
237D4×C19—41no—
238D4×C19—41no—
239D4×C19—41no—
240D4×C19—41no—
241D4×C19—81no—
242D4×C19—81no—
243D4×C19—82no—
244D4×C19—82no—
245D4×C19—82no—
246C2×C4×C19—22no—
247C2×C4×C19—21no—
248C2×C4×C19—21no—
249C2×C4×C19—21no—
250C2×C4×C19—21no—
251C2×C4×C19—21no—
252C2×C4×C19—21no—
253C2×C4×C19—21no—
254C2×C4×C19—41no—
255C2×C4×C19—41no—
256C2×C4×C19—41no—
257C2×C4×C19—41no—
258C2×C4×C19#12111yescharacteristic
259C2×C4×C19#12111yescharacteristic
260C2×C4×C19#12111yescharacteristic
261C2×C4×C19C22×D411yescharacteristic
262C2×C4×C19C22×D411yescharacteristic
263C2×C4×C19C2×#4111yescharacteristic
264C8×C19—21no—
265C8×C19—21no—
266C8×C19—21no—
267C8×C19—21no—
268C8×C19—41no—
269C8×C19—41no—
270C8×C19—41no—
271C8×C19—41no—
272C8×C19—41no—
273C8×C19—41no—
274#3248C2×C1911yescharacteristic, complemented
275#3217C2×C1911yescharacteristic
276#3208C2×C1911yescharacteristic, complemented
277#2994C2×C1911yescharacteristic, complemented
278#1702C2×C1911yescharacteristic, complemented
279#1701C2×C1911yescharacteristic, complemented
280#1686C2×C1911yescharacteristic, complemented
281#1685C2×C1911yescharacteristic, complemented
282#1682C2×C1911yescharacteristic, complemented
283#1681C2×C1911yescharacteristic, complemented
284#1666C2×C1911yescharacteristic, complemented
285#1665C2×C1911yescharacteristic, complemented
286#1573C2×C1911yescharacteristic, complemented
287#1552C2×C1911yescharacteristic, complemented
288C2×#331C2×C1911yescharacteristic, complemented
289C22×C19—21no—
290C22×C19—21no—
291C22×C19—41no—
292C22×C19—41no—
293C22×C19—41no—
294C22×C19—81no—
295C22×C19—81no—
296C22×C19—81no—
297C22×C19—81no—
298C22×C19—81no—
299C22×C19—81no—
300C22×C19—164no—
301C22×C19#47112yes—
302C22×C19C2×#12111yescharacteristic
303C4×C19—21no—
304C4×C19—21no—
305C4×C19—21no—
306C4×C19—21no—
307C4×C19—41no—
308C4×C19—41no—
309C4×C19—41no—
310C4×C19—81no—
311C4×C19—81no—
312C4×C19#57611yescharacteristic
313C4×C19#57611yescharacteristic
314C4×C19#57711yescharacteristic
315C4×C19#57711yescharacteristic
316#533C22×C1911yescharacteristic
317C2×#127C22×C1911yescharacteristic
318#529C22×C1911yescharacteristic
319#496—21no—
320#492C22×C1911yescharacteristic
321#492C22×C1911yescharacteristic
322#490—21no—
323#486C22×C1911yescharacteristic
324#486C22×C1911yescharacteristic
325#479—21no—
326#475C22×C1911yescharacteristic, complemented
327#474C22×C1911yescharacteristic, complemented
328#467—21no—
329#465—21no—
330#464—21no—
331#462C22×C1911yescharacteristic, complemented
332#461C22×C1911yescharacteristic, complemented
333#460—21no—
334#460—21no—
335#460C22×C1911yescharacteristic
336#460C22×C1911yescharacteristic
337#459C22×C1911yescharacteristic
338#459C22×C1911yescharacteristic
339#450—21no—
340#450—21no—
341#450—21no—
342#447—21no—
343#446C22×C1911yescharacteristic, complemented
344C8×Q8C22×C1911yescharacteristic, complemented
345#436C22×C1911yescharacteristic, complemented
346#435—21no—
347C8×D4—21no—
348C8×D4C22×C1911yescharacteristic, complemented
349#433—21no—
350#432C22×C1911yescharacteristic
351#431C22×C1911yescharacteristic
352#424—21no—
353C2×C4⋊C8C22×C1911yescharacteristic
354C2×C4⋊C8C22×C1911yescharacteristic
355#335C22×C1911yescharacteristic, complemented
356#335C22×C1911yescharacteristic, complemented
357#334C22×C1911yescharacteristic, complemented
358#334C22×C1911yescharacteristic, complemented
359#332C22×C1911yescharacteristic, complemented
360#332C22×C1911yescharacteristic, complemented
361#332C22×C1911yescharacteristic, complemented
362#332C22×C1911yescharacteristic, complemented
363#331C22×C1911yescharacteristic
364#331C22×C1911yescharacteristic
365#331C22×C1911yescharacteristic
366#331C22×C1911yescharacteristic
367C2×C19—22no—
368C2×C19—81no—
369C2×C19—161no—
370C2×C19—161no—
371C2×C19#304511yescharacteristic
372C2×C19#306211yescharacteristic
373C2×C19C2×#47111yescharacteristic
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—21no—
377C2×Q16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×M16—21no—
388C22×C8—21no—
389C22×C8—21no—
390C22×C8—21no—
391C4⋊Q8C23×C1911yescharacteristic
392C4⋊Q8C23×C1911yescharacteristic
393#127—21no—
394#127—21no—
395#127—21no—
396#127C23×C1911yescharacteristic
397#127C23×C1911yescharacteristic
398#126—21no—
399#125—21no—
400#125D4×C1911yescharacteristic
401#124D4×C1911yescharacteristic
402#123—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8D4×C1911yescharacteristic
406#121D4×C1911yescharacteristic
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8C23×C1911yescharacteristic
410C4×D4—21no—
411C4×D4C23×C1911yescharacteristic
412#117—21no—
413#117—21no—
414C2×C42C23×C1911yescharacteristic
415#107—21no—
416#106—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8D4×C1911yescharacteristic
422C4⋊C8D4×C1911yescharacteristic
423C4⋊C8C23×C1911yescharacteristic
424C4⋊C8C23×C1911yescharacteristic
425C4⋊C8C23×C1911yescharacteristic
426C4⋊C8C23×C1911yescharacteristic
427C4⋊C8C23×C1911yescharacteristic
428C4⋊C8C23×C1911yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8D4×C1911yescharacteristic
445C22⋊C8D4×C1911yescharacteristic
446#97—21no—
447#97—21no—
448C4×C8—21no—
449C4×C8C23×C1911yescharacteristic
450C4×C8C23×C1911yescharacteristic
451C19#1958111yescharacteristic, direct product factor, Sylow
452C24—41no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8C2×D4×C1911yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—81no—
467C2×D4—81no—
468C2×D4—81no—
469C2×D4—81no—
470C2×D4—82no—
471C2×D4C2×D4×C1911yescharacteristic
472C22×C4—21no—
473C22×C4C2×D4×C1911yescharacteristic
474C22×C4C2×D4×C1911yescharacteristic
475C22×C4#41×C1911yescharacteristic
476Q16—81no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482SD16—81no—
483SD16—81no—
484D8—81no—
485D8—81no—
486M16—81no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—81no—
494C2×C8—81no—
495C2×C8—81no—
496C2×C8C2×D4×C1911yescharacteristic
497C2×C8C2×D4×C1911yescharacteristic
498C2×C8C2×D4×C1911yescharacteristic
499C2×C8C2×D4×C1911yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4C2×D4×C1911yescharacteristic
511C4⋊C4C2×D4×C1911yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C42—21no—
519C42—41no—
520C42C2×D4×C1911yescharacteristic
521C42C2×D4×C1911yescharacteristic
522C42#41×C1911yescharacteristic
523C42C24×C1911yescharacteristic
524C23—21no—
525C23—41no—
526C23—41no—
527C23—82no—
528C23—82no—
529C23—82no—
530C23C19×#12111yescharacteristic
531Q8—21no—
532Q8—21no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—21no—
538D4—21no—
539D4—42no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—81no—
550D4—82no—
551D4—82no—
552D4—82no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4C19×#12111yescharacteristic
566C2×C4C19×#12111yescharacteristic
567C2×C4C19×#12111yescharacteristic
568C2×C4C22×D4×C1911yescharacteristic
569C2×C4C22×D4×C1911yescharacteristic
570C2×C4C2×#41×C1911yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—21no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C22—21no—
582C22—21no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—164no—
593C22C19×#47112yes—
594C22C2×C19×#12111yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4C19×#57611yescharacteristic
605C4C19×#57611yescharacteristic
606C4C19×#57711yescharacteristic
607C4C19×#57711yescharacteristic
608C2—22no—
609C2—81no—
610C2—161no—
611C2—161no—
612C2C19×#304511yescharacteristic
613C2C19×#306211yescharacteristic
614C2C2×C19×#47111yescharacteristic
subgroupG/H
center, socleC22×C19C2×#121
commutator, Frattini, cosocleC42C24×C19
prime radicalC19×#3217C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3248C2semidirect
3. C19×#3208C2semidirect
4. C19×#2994C2semidirect
5. C19×#1702C2semidirect
6. C19×#1701C2semidirect
7. C19×#1686C2semidirect
8. C19×#1685C2semidirect
9. C19×#1682C2semidirect
10. C19×#1681C2semidirect
11. C19×#1666C2semidirect
12. C19×#1665C2semidirect
13. C19×#1573C2semidirect
14. C19×#1552C2semidirect
15. C2×C19×#331C2semidirect
26. C19×#475C22semidirect
27. C19×#474C22semidirect
31. C19×#462C22semidirect
32. C19×#461C22semidirect
43. C19×#446C22semidirect
44. C8×Q8×C19C22semidirect
45. C19×#436C22semidirect
48. C8×D4×C19C22semidirect
55. C19×#335C22semidirect
56. C19×#335C22semidirect
57. C19×#334C22semidirect
58. C19×#334C22semidirect
59. C19×#332C22semidirect
60. C19×#332C22semidirect
61. C19×#332C22semidirect
62. C19×#332C22semidirect
216. #19581C19direct (N × H)
274. #3248C2×C19semidirect
276. #3208C2×C19semidirect
277. #2994C2×C19semidirect
278. #1702C2×C19semidirect
279. #1701C2×C19semidirect
280. #1686C2×C19semidirect
281. #1685C2×C19semidirect
282. #1682C2×C19semidirect
283. #1681C2×C19semidirect
284. #1666C2×C19semidirect
285. #1665C2×C19semidirect
286. #1573C2×C19semidirect
287. #1552C2×C19semidirect
288. C2×#331C2×C19semidirect
326. #475C22×C19semidirect
327. #474C22×C19semidirect
331. #462C22×C19semidirect
332. #461C22×C19semidirect
343. #446C22×C19semidirect
344. C8×Q8C22×C19semidirect
345. #436C22×C19semidirect
348. C8×D4C22×C19semidirect
355. #335C22×C19semidirect
356. #335C22×C19semidirect
357. #334C22×C19semidirect
358. #334C22×C19semidirect
359. #332C22×C19semidirect
360. #332C22×C19semidirect
361. #332C22×C19semidirect
362. #332C22×C19semidirect
451. C19#19581direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#32482
C19×#32172
C19×#32082
C19×#29942
C19×#17022
C19×#17012
C19×#16862
C19×#16852
C19×#16822
C19×#16812
C19×#16662
C19×#16652
C19×#15732
C19×#15522
C2×C19×#3312
#1958119