Finite Group Databasebeta

← C19×#19537 #18025496

Subgroups — C19×#19537 #18025496

Order 4864.

628 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3233C211yesmaximal, characteristic, complemented
2C19×#3217C211yesmaximal, characteristic
3C19×#3208C211yesmaximal, characteristic, complemented
4C19×#2993C211yesmaximal, characteristic, complemented
5C19×#1698C211yesmaximal, characteristic, complemented
6C19×#1697C211yesmaximal, characteristic, complemented
7C19×#1686C211yesmaximal, characteristic, complemented
8C19×#1685C211yesmaximal, characteristic, complemented
9C19×#1678C211yesmaximal, characteristic, complemented
10C19×#1677C211yesmaximal, characteristic, complemented
11C19×#1666C211yesmaximal, characteristic, complemented
12C19×#1665C211yesmaximal, characteristic, complemented
13C19×#1572C211yesmaximal, characteristic, complemented
14C19×#1559C211yesmaximal, characteristic, complemented
15C19×#1545C211yesmaximal, characteristic, complemented
16C19×#533C2211yescharacteristic
17C2×C19×#127C2211yescharacteristic
18C19×#529C2211yescharacteristic
19C19×#499—21no—
20C19×#496—21no—
21C19×#492C2211yescharacteristic
22C19×#492C2211yescharacteristic
23C19×#490—21no—
24C19×#488—21no—
25C19×#486C2211yescharacteristic
26C19×#486C2211yescharacteristic
27C19×#485—21no—
28C19×#482—21no—
29C19×#477C2211yescharacteristic, complemented
30C19×#476C2211yescharacteristic, complemented
31C19×#475C2211yescharacteristic, complemented
32C19×#474C2211yescharacteristic, 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×#436—21no—
46C19×#436C2211yescharacteristic, complemented
47C19×#435—21no—
48C8×D4×C19C2211yescharacteristic, complemented
49C19×#433—21no—
50C19×#432C2211yescharacteristic
51C19×#431C2211yescharacteristic
52C19×#431C2211yescharacteristic
53C19×#424—21no—
54C19×#423C2211yescharacteristic
55C19×#335C2211yescharacteristic, complemented
56C19×#335C2211yescharacteristic, complemented
57C19×#334C2211yescharacteristic, complemented
58C19×#334C2211yescharacteristic, complemented
59C19×#333C2211yescharacteristic, complemented
60C19×#333C2211yescharacteristic, 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×SD16×C19—21no—
71C2×SD16×C19—21no—
72C2×SD16×C19—21no—
73C2×SD16×C19—21no—
74C2×SD16×C19—21no—
75C2×SD16×C19—21no—
76C2×D8×C19—21no—
77C2×D8×C19—21no—
78C2×M16×C19—21no—
79C2×M16×C19—21no—
80C22×C8×C19—21no—
81C19×C4⋊Q8C2311yescharacteristic
82C19×C4⋊Q8C2311yescharacteristic
83C19×#127—21no—
84C19×#127—21no—
85C19×#127—21no—
86C19×#127C2311yescharacteristic
87C19×#127C2311yescharacteristic
88C19×#126—21no—
89C19×#125—21no—
90C19×#125D411yescharacteristic
91C19×#124D411yescharacteristic
92C19×#123—21no—
93C19×C22⋊Q8—21no—
94C19×C22⋊Q8—21no—
95C19×C22⋊Q8D411yescharacteristic
96C19×#121D411yescharacteristic
97C4×Q8×C19—21no—
98C4×Q8×C19—21no—
99C4×Q8×C19C2311yescharacteristic
100C4×D4×C19—21no—
101C4×D4×C19C2311yescharacteristic
102C19×#117—21no—
103C19×#117—21no—
104C2×C42×C19C2311yescharacteristic
105C19×#107—21no—
106C19×#107—21no—
107C19×#106—21no—
108C19×#106—21no—
109C19×C4⋊C8—21no—
110C19×C4⋊C8—21no—
111C19×C4⋊C8—21no—
112C19×C4⋊C8D411yescharacteristic
113C19×C4⋊C8D411yescharacteristic
114C19×C4⋊C8C2311yescharacteristic
115C19×C4⋊C8C2311yescharacteristic
116C19×C4⋊C8C2311yescharacteristic
117C19×C4⋊C8C2311yescharacteristic
118C19×C4⋊C8C2311yescharacteristic
119C19×C4⋊C8C2311yescharacteristic
120C19×#103—21no—
121C19×#103—21no—
122C19×#102—21no—
123C19×#102—21no—
124C19×#102—21no—
125C19×#102—21no—
126C19×#102—21no—
127C19×#102—21no—
128C19×#102—21no—
129C19×#102—21no—
130C19×#102—21no—
131C19×#102—21no—
132C19×C22⋊C8—21no—
133C19×C22⋊C8—21no—
134C19×C22⋊C8—21no—
135C19×C22⋊C8—21no—
136C19×C22⋊C8D411yescharacteristic
137C19×C22⋊C8D411yescharacteristic
138C19×#97—21no—
139C19×#97—21no—
140C4×C8×C19—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
168SD16×C19—81no—
169SD16×C19—81no—
170SD16×C19—81no—
171SD16×C19—81no—
172SD16×C19—81no—
173SD16×C19—81no—
174D8×C19—81no—
175D8×C19—81no—
176M16×C19—81no—
177M16×C19—81no—
178C2×C8×C19—21no—
179C2×C8×C19—21no—
180C2×C8×C19—21no—
181C2×C8×C19—21no—
182C2×C8×C19—21no—
183C2×C8×C19—21no—
184C2×C8×C19—81no—
185C2×C8×C19C2×D411yescharacteristic
186C2×C8×C19C2×D411yescharacteristic
187C2×C8×C19C2×D411yescharacteristic
188C2×C8×C19C2×D411yescharacteristic
189C4⋊C4×C19—21no—
190C4⋊C4×C19—21no—
191C4⋊C4×C19—21no—
192C4⋊C4×C19—21no—
193C4⋊C4×C19—21no—
194C4⋊C4×C19—21no—
195C4⋊C4×C19—21no—
196C4⋊C4×C19—21no—
197C4⋊C4×C19—41no—
198C4⋊C4×C19—41no—
199C4⋊C4×C19C2×D411yescharacteristic
200C4⋊C4×C19C2×D411yescharacteristic
201C22⋊C4×C19—21no—
202C22⋊C4×C19—21no—
203C22⋊C4×C19—21no—
204C22⋊C4×C19—21no—
205C22⋊C4×C19—21no—
206C22⋊C4×C19—41no—
207C42×C19—21no—
208C42×C19—41no—
209C42×C19C2×D411yescharacteristic
210C42×C19C2×D411yescharacteristic
211C42×C19#4111yescharacteristic
212C42×C19C2411yescharacteristic
213#19537C1911yesmaximal, characteristic, direct product factor, Sylow
214C23×C19—21no—
215C23×C19—41no—
216C23×C19—41no—
217C23×C19—82no—
218C23×C19—82no—
219C23×C19—82no—
220C23×C19#12111yescharacteristic
221Q8×C19—21no—
222Q8×C19—21no—
223Q8×C19—41no—
224Q8×C19—41no—
225Q8×C19—81no—
226D4×C19—21no—
227D4×C19—21no—
228D4×C19—41no—
229D4×C19—41no—
230D4×C19—41no—
231D4×C19—41no—
232D4×C19—41no—
233D4×C19—41no—
234D4×C19—41no—
235D4×C19—41no—
236D4×C19—81no—
237D4×C19—81no—
238D4×C19—82no—
239D4×C19—82no—
240D4×C19—82no—
241D4×C19—81no—
242C2×C4×C19—21no—
243C2×C4×C19—21no—
244C2×C4×C19—21no—
245C2×C4×C19—21no—
246C2×C4×C19—21no—
247C2×C4×C19—21no—
248C2×C4×C19—21no—
249C2×C4×C19—41no—
250C2×C4×C19—41no—
251C2×C4×C19—41no—
252C2×C4×C19—41no—
253C2×C4×C19—41no—
254C2×C4×C19#12111yescharacteristic
255C2×C4×C19#12111yescharacteristic
256C2×C4×C19#12111yescharacteristic
257C2×C4×C19C22×D411yescharacteristic
258C2×C4×C19C22×D411yescharacteristic
259C2×C4×C19C2×#4111yescharacteristic
260C8×C19—21no—
261C8×C19—21no—
262C8×C19—21no—
263C8×C19—21no—
264C8×C19—41no—
265C8×C19—41no—
266C8×C19—41no—
267C8×C19—41no—
268C8×C19—41no—
269C8×C19—41no—
270#3233C2×C1911yescharacteristic, complemented
271#3217C2×C1911yescharacteristic
272#3208C2×C1911yescharacteristic, complemented
273#2993C2×C1911yescharacteristic, complemented
274#1698C2×C1911yescharacteristic, complemented
275#1697C2×C1911yescharacteristic, complemented
276#1686C2×C1911yescharacteristic, complemented
277#1685C2×C1911yescharacteristic, complemented
278#1678C2×C1911yescharacteristic, complemented
279#1677C2×C1911yescharacteristic, complemented
280#1666C2×C1911yescharacteristic, complemented
281#1665C2×C1911yescharacteristic, complemented
282#1572C2×C1911yescharacteristic, complemented
283#1559C2×C1911yescharacteristic, complemented
284#1545C2×C1911yescharacteristic, complemented
285C22×C19—21no—
286C22×C19—21no—
287C22×C19—21no—
288C22×C19—41no—
289C22×C19—41no—
290C22×C19—41no—
291C22×C19—81no—
292C22×C19—81no—
293C22×C19—81no—
294C22×C19—81no—
295C22×C19—81no—
296C22×C19—81no—
297C22×C19—164no—
298C22×C19C2×#12111yescharacteristic
299C4×C19—21no—
300C4×C19—21no—
301C4×C19—21no—
302C4×C19—21no—
303C4×C19—41no—
304C4×C19—41no—
305C4×C19—41no—
306C4×C19—81no—
307C4×C19—81no—
308C4×C19#57611yescharacteristic
309C4×C19#57711yescharacteristic
310C4×C19#57711yescharacteristic
311C4×C19#57711yescharacteristic
312#533C22×C1911yescharacteristic
313C2×#127C22×C1911yescharacteristic
314#529C22×C1911yescharacteristic
315#499—21no—
316#496—21no—
317#492C22×C1911yescharacteristic
318#492C22×C1911yescharacteristic
319#490—21no—
320#488—21no—
321#486C22×C1911yescharacteristic
322#486C22×C1911yescharacteristic
323#485—21no—
324#482—21no—
325#477C22×C1911yescharacteristic, complemented
326#476C22×C1911yescharacteristic, complemented
327#475C22×C1911yescharacteristic, complemented
328#474C22×C1911yescharacteristic, complemented
329#460—21no—
330#460—21no—
331#460C22×C1911yescharacteristic
332#460C22×C1911yescharacteristic
333#459C22×C1911yescharacteristic
334#459C22×C1911yescharacteristic
335#450—21no—
336#450—21no—
337#450—21no—
338#447—21no—
339#446C22×C1911yescharacteristic, complemented
340C8×Q8C22×C1911yescharacteristic, complemented
341#436—21no—
342#436C22×C1911yescharacteristic, complemented
343#435—21no—
344C8×D4C22×C1911yescharacteristic, complemented
345#433—21no—
346#432C22×C1911yescharacteristic
347#431C22×C1911yescharacteristic
348#431C22×C1911yescharacteristic
349#424—21no—
350#423C22×C1911yescharacteristic
351#335C22×C1911yescharacteristic, complemented
352#335C22×C1911yescharacteristic, complemented
353#334C22×C1911yescharacteristic, complemented
354#334C22×C1911yescharacteristic, complemented
355#333C22×C1911yescharacteristic, complemented
356#333C22×C1911yescharacteristic, complemented
357#332C22×C1911yescharacteristic, complemented
358#332C22×C1911yescharacteristic, complemented
359#331C22×C1911yescharacteristic
360#331C22×C1911yescharacteristic
361#331C22×C1911yescharacteristic
362#331C22×C1911yescharacteristic
363C2×C19—41no—
364C2×C19—81no—
365C2×C19—161no—
366C2×C19—161no—
367C2×C19#304511yescharacteristic
368C2×C19#305711yescharacteristic
369C2×C19#306811yescharacteristic
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×M16—21no—
382C2×M16—21no—
383C22×C8—21no—
384C4⋊Q8C23×C1911yescharacteristic
385C4⋊Q8C23×C1911yescharacteristic
386#127—21no—
387#127—21no—
388#127—21no—
389#127C23×C1911yescharacteristic
390#127C23×C1911yescharacteristic
391#126—21no—
392#125—21no—
393#125D4×C1911yescharacteristic
394#124D4×C1911yescharacteristic
395#123—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8D4×C1911yescharacteristic
399#121D4×C1911yescharacteristic
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8C23×C1911yescharacteristic
403C4×D4—21no—
404C4×D4C23×C1911yescharacteristic
405#117—21no—
406#117—21no—
407C2×C42C23×C1911yescharacteristic
408#107—21no—
409#107—21no—
410#106—21no—
411#106—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8D4×C1911yescharacteristic
416C4⋊C8D4×C1911yescharacteristic
417C4⋊C8C23×C1911yescharacteristic
418C4⋊C8C23×C1911yescharacteristic
419C4⋊C8C23×C1911yescharacteristic
420C4⋊C8C23×C1911yescharacteristic
421C4⋊C8C23×C1911yescharacteristic
422C4⋊C8C23×C1911yescharacteristic
423#103—21no—
424#103—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8D4×C1911yescharacteristic
440C22⋊C8D4×C1911yescharacteristic
441#97—21no—
442#97—21no—
443C4×C8—21no—
444C4×C8—21no—
445C4×C8C23×C1911yescharacteristic
446C4×C8C23×C1911yescharacteristic
447C19#1953711yescharacteristic, direct product factor, Sylow
448C24—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×D4×C1911yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4—82no—
467C2×D4C2×D4×C1911yescharacteristic
468C22×C4—21no—
469C22×C4C2×D4×C1911yescharacteristic
470C22×C4C2×D4×C1911yescharacteristic
471C22×C4#41×C1911yescharacteristic
472SD16—81no—
473SD16—81no—
474SD16—81no—
475SD16—81no—
476SD16—81no—
477SD16—81no—
478D8—81no—
479D8—81no—
480M16—81no—
481M16—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—81no—
489C2×C8C2×D4×C1911yescharacteristic
490C2×C8C2×D4×C1911yescharacteristic
491C2×C8C2×D4×C1911yescharacteristic
492C2×C8C2×D4×C1911yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C1911yescharacteristic
504C4⋊C4C2×D4×C1911yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C42—21no—
512C42—41no—
513C42C2×D4×C1911yescharacteristic
514C42C2×D4×C1911yescharacteristic
515C42#41×C1911yescharacteristic
516C42C24×C1911yescharacteristic
517C23—21no—
518C23—41no—
519C23—41no—
520C23—82no—
521C23—82no—
522C23—82no—
523C23C19×#12111yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—81no—
541D4—82no—
542D4—82no—
543D4—82no—
544D4—81no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4C19×#12111yescharacteristic
558C2×C4C19×#12111yescharacteristic
559C2×C4C19×#12111yescharacteristic
560C2×C4C22×D4×C1911yescharacteristic
561C2×C4C22×D4×C1911yescharacteristic
562C2×C4C2×#41×C1911yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22C2×C19×#12111yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4C19×#57611yescharacteristic
597C4C19×#57711yescharacteristic
598C4C19×#57711yescharacteristic
599C4C19×#57711yescharacteristic
600C2—41no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C19×#304511yescharacteristic
605C2C19×#305711yescharacteristic
606C2C19×#306811yescharacteristic
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×#3233C2semidirect
3. C19×#3208C2semidirect
4. C19×#2993C2semidirect
5. C19×#1698C2semidirect
6. C19×#1697C2semidirect
7. C19×#1686C2semidirect
8. C19×#1685C2semidirect
9. C19×#1678C2semidirect
10. C19×#1677C2semidirect
11. C19×#1666C2semidirect
12. C19×#1665C2semidirect
13. C19×#1572C2semidirect
14. C19×#1559C2semidirect
15. C19×#1545C2semidirect
29. C19×#477C22semidirect
30. C19×#476C22semidirect
31. C19×#475C22semidirect
32. C19×#474C22semidirect
43. C19×#446C22semidirect
44. C8×Q8×C19C22semidirect
46. C19×#436C22semidirect
48. C8×D4×C19C22semidirect
55. C19×#335C22semidirect
56. C19×#335C22semidirect
57. C19×#334C22semidirect
58. C19×#334C22semidirect
59. C19×#333C22semidirect
60. C19×#333C22semidirect
61. C19×#332C22semidirect
62. C19×#332C22semidirect
213. #19537C19direct (N × H)
270. #3233C2×C19semidirect
272. #3208C2×C19semidirect
273. #2993C2×C19semidirect
274. #1698C2×C19semidirect
275. #1697C2×C19semidirect
276. #1686C2×C19semidirect
277. #1685C2×C19semidirect
278. #1678C2×C19semidirect
279. #1677C2×C19semidirect
280. #1666C2×C19semidirect
281. #1665C2×C19semidirect
282. #1572C2×C19semidirect
283. #1559C2×C19semidirect
284. #1545C2×C19semidirect
325. #477C22×C19semidirect
326. #476C22×C19semidirect
327. #475C22×C19semidirect
328. #474C22×C19semidirect
339. #446C22×C19semidirect
340. C8×Q8C22×C19semidirect
342. #436C22×C19semidirect
344. C8×D4C22×C19semidirect
351. #335C22×C19semidirect
352. #335C22×C19semidirect
353. #334C22×C19semidirect
354. #334C22×C19semidirect
355. #333C22×C19semidirect
356. #333C22×C19semidirect
357. #332C22×C19semidirect
358. #332C22×C19semidirect
447. C19#19537direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#32332
C19×#32172
C19×#32082
C19×#29932
C19×#16982
C19×#16972
C19×#16862
C19×#16852
C19×#16782
C19×#16772
C19×#16662
C19×#16652
C19×#15722
C19×#15592
C19×#15452
#1953719