Finite Group Databasebeta

← C19×#33855 #18039814

Subgroups — C19×#33855 #18039814

Order 4864.

640 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3417C211yesmaximal, characteristic, complemented
2C19×#3416C211yesmaximal, characteristic, complemented
3C19×#3293C211yesmaximal, characteristic, complemented
4C19×#3290C211yesmaximal, characteristic, complemented
5C19×#2251C211yesmaximal, characteristic, complemented
6C19×#2223C211yesmaximal, characteristic, complemented
7C19×#2222C211yesmaximal, characteristic, complemented
8C19×#2214C211yesmaximal, characteristic, complemented
9C19×#2212C211yesmaximal, characteristic, complemented
10C19×#2195C211yesmaximal, characteristic, complemented
11C19×#2195C211yesmaximal, characteristic, complemented
12C19×#2194C211yesmaximal, characteristic, complemented
13C19×#2193C211yesmaximal, characteristic, complemented
14C19×#2179C211yesmaximal, characteristic, complemented
15C19×#2171C211yesmaximal, characteristic, complemented
16C19×#578—21no—
17C19×#578C2211yescharacteristic
18C19×#578C2211yescharacteristic
19C19×#578C2211yescharacteristic, complemented
20C19×#577—21no—
21C19×#576C2211yescharacteristic
22C19×#510—21no—
23C19×#510—21no—
24C19×#510—21no—
25C19×#510C2211yescharacteristic
26C19×#510C2211yescharacteristic
27C19×#510C2211yescharacteristic, complemented
28C19×#509—21no—
29C19×#509C2211yescharacteristic
30C19×#508—21no—
31C19×#508—21no—
32C19×#508C2211yescharacteristic
33C2×C19×Q32—21no—
34C2×C19×Q32C2211yescharacteristic, complemented
35C2×C19×Q32C2211yescharacteristic, complemented
36C2×C19×SD32—21no—
37C2×C19×SD32C2211yescharacteristic
38C2×C19×SD32C2211yescharacteristic
39C19×#504C2211yescharacteristic
40C19×#504C2211yescharacteristic, complemented
41C19×#495C2211yescharacteristic
42C19×#494C2211yescharacteristic, complemented
43C19×#473—21no—
44C19×#473C2211yescharacteristic
45C19×#473C2211yescharacteristic
46C19×#473C2211yescharacteristic, complemented
47C19×#472C2211yescharacteristic
48C19×#471—21no—
49C19×#456—21no—
50C19×#456—21no—
51C19×#455—21no—
52C19×#454—21no—
53C19×#443C2211yescharacteristic
54C19×#443C2211yescharacteristic
55C19×#443C2211yescharacteristic, complemented
56C19×#368C2211yescharacteristic, complemented
57C19×#364C2211yescharacteristic, complemented
58C19×#362C2211yescharacteristic, complemented
59C19×#362C2211yescharacteristic, complemented
60C19×#362C2211yescharacteristic, complemented
61C19×#361C2211yescharacteristic
62C19×#359C2211yescharacteristic
63C19×#359C2211yescharacteristic, complemented
64C19×#350C2211yescharacteristic
65C19×#350C2211yescharacteristic, complemented
66C19×#346C2211yescharacteristic, complemented
67C19×2−1+4—21no—
68C19×2−1+4—21no—
69C19×2−1+4—21no—
70C19×H(5,𝔽2)—21no—
71C19×#137—21no—
72C19×#137—21no—
73C19×#137—21no—
74C19×#137—21no—
75C19×#137—21no—
76C19×#137—21no—
77C19×#137—41no—
78C19×#137—41no—
79C19×#137—41no—
80C19×#137—41no—
81C19×#137—41no—
82C19×#137—41no—
83C19×AGL(1,ℤ/8)—21no—
84C19×AGL(1,ℤ/8)—21no—
85C19×AGL(1,ℤ/8)—41no—
86C19×AGL(1,ℤ/8)—41no—
87C19×#135—21no—
88C19×#135—21no—
89C19×#135—21no—
90C19×#135—21no—
91C19×#135—41no—
92C19×#135—41no—
93C19×#135D411yescharacteristic
94C19×#135C2311yescharacteristic
95C19×#135C2311yescharacteristic
96C2×Q16×C19—21no—
97C2×Q16×C19—21no—
98C2×Q16×C19—21no—
99C2×Q16×C19—21no—
100C2×Q16×C19—41no—
101C2×Q16×C19C2311yescharacteristic
102C2×Q16×C19C2311yescharacteristic
103C2×Q16×C19C2311yescharacteristic
104C2×SD16×C19—21no—
105C2×SD16×C19—41no—
106C2×D8×C19—21no—
107C2×D8×C19C2311yescharacteristic
108C19×#131—21no—
109C19×#131—21no—
110C19×#131C2311yescharacteristic
111C19×#131C2311yescharacteristic
112C19×C4⋊Q8—21no—
113C19×#124—21no—
114C19×Q32—21no—
115C19×Q32—21no—
116C19×Q32—21no—
117C19×Q32—21no—
118C19×Q32—21no—
119C19×Q32—41no—
120C19×Q32D411yescharacteristic
121C19×SD32—21no—
122C19×SD32—21no—
123C19×SD32—21no—
124C19×SD32—21no—
125C19×SD32—21no—
126C19×SD32—21no—
127C19×SD32—41no—
128C19×SD32D411yescharacteristic
129C19×SD32D411yescharacteristic
130C19×D16—21no—
131C19×D16D411yescharacteristic
132C19×M32—21no—
133C19×M32—21no—
134C19×M32C2311yescharacteristic
135C19×M32C2311yescharacteristic
136C2×C16×C19—21no—
137C2×C16×C19—21no—
138C2×C16×C19C2311yescharacteristic
139C2×C16×C19C2311yescharacteristic
140C19×#108D411yescharacteristic
141C19×#108C2311yescharacteristic
142C19×#108C2311yescharacteristic
143C19×#104—21no—
144C19×#104—21no—
145C19×#104D411yescharacteristic
146C19×#104D411yescharacteristic
147C19×#101—21no—
148C19×#101—21no—
149C19×#101—21no—
150C19×#100—21no—
151C4×C8×C19C2311yescharacteristic
152#41×C19—21no—
153#41×C19—21no—
154#41×C19—41no—
155#41×C19—41no—
156#41×C19—41no—
157#41×C19—41no—
158#41×C19—41no—
159#41×C19—41no—
160#41×C19—41no—
161#41×C19—41no—
162#41×C19—81no—
163#41×C19—81no—
164#41×C19—81no—
165#41×C19C2×D411yescharacteristic
166#41×C19C2×D411yescharacteristic
167C2×Q8×C19—21no—
168C2×Q8×C19—21no—
169C2×Q8×C19—21no—
170C2×Q8×C19—41no—
171C2×Q8×C19—41no—
172C2×Q8×C19—41no—
173C2×Q8×C19—41no—
174C2×Q8×C19—41no—
175C2×Q8×C19—41no—
176C2×D4×C19—21no—
177C2×D4×C19—41no—
178C2×D4×C19—41no—
179C2×D4×C19—81no—
180Q16×C19—21no—
181Q16×C19—21no—
182Q16×C19—21no—
183Q16×C19—21no—
184Q16×C19—21no—
185Q16×C19—21no—
186Q16×C19—41no—
187Q16×C19—41no—
188Q16×C19—41no—
189Q16×C19—41no—
190Q16×C19—41no—
191Q16×C19—41no—
192Q16×C19—41no—
193Q16×C19—41no—
194Q16×C19D811yescharacteristic
195Q16×C19C2×D411yescharacteristic
196Q16×C19C2×D411yescharacteristic
197SD16×C19—21no—
198SD16×C19—21no—
199SD16×C19—41no—
200SD16×C19—41no—
201SD16×C19—41no—
202SD16×C19—41no—
203SD16×C19—41no—
204SD16×C19—41no—
205SD16×C19—41no—
206SD16×C19—41no—
207SD16×C19—41no—
208SD16×C19—41no—
209SD16×C19D811yescharacteristic
210SD16×C19D811yescharacteristic
211D8×C19—21no—
212D8×C19—21no—
213D8×C19—41no—
214D8×C19—41no—
215D8×C19D811yescharacteristic
216D8×C19C2×D411yescharacteristic
217D8×C19C2×D411yescharacteristic
218M16×C19—21no—
219M16×C19—21no—
220M16×C19—21no—
221M16×C19—21no—
222M16×C19—41no—
223M16×C19—41no—
224M16×C19C2×D411yescharacteristic
225M16×C19C2×D411yescharacteristic
226C2×C8×C19—21no—
227C2×C8×C19—21no—
228C2×C8×C19—41no—
229C2×C8×C19—41no—
230C2×C8×C19C2×D411yescharacteristic
231C2×C8×C19C2411yescharacteristic
232C4⋊C4×C19—81no—
233C22⋊C4×C19—81no—
234C42×C19C2×D411yescharacteristic
235C16×C19—21no—
236C16×C19—21no—
237C16×C19—21no—
238C16×C19C2×D411yescharacteristic
239C16×C19C2×D411yescharacteristic
240#33855C1911yesmaximal, characteristic, direct product factor, Sylow
241C23×C19—41no—
242C23×C19—81no—
243Q8×C19—21no—
244Q8×C19—21no—
245Q8×C19—41no—
246Q8×C19—41no—
247Q8×C19—41no—
248Q8×C19—41no—
249Q8×C19—41no—
250Q8×C19—41no—
251Q8×C19—81no—
252Q8×C19—81no—
253Q8×C19—81no—
254Q8×C19C2×D811yescharacteristic
255Q8×C19C2×D811yescharacteristic
256D4×C19—21no—
257D4×C19—21no—
258D4×C19—21no—
259D4×C19—21no—
260D4×C19—41no—
261D4×C19—41no—
262D4×C19—41no—
263D4×C19—41no—
264D4×C19—81no—
265D4×C19—81no—
266D4×C19—81no—
267D4×C19—81no—
268D4×C19—81no—
269D4×C19C2×D811yescharacteristic
270D4×C19C2×D811yescharacteristic
271C2×C4×C19—21no—
272C2×C4×C19—21no—
273C2×C4×C19—21no—
274C2×C4×C19—41no—
275C2×C4×C19—41no—
276C2×C4×C19—41no—
277C2×C4×C19—41no—
278C2×C4×C19—41no—
279C2×C4×C19—81no—
280C2×C4×C19—81no—
281C2×C4×C19—81no—
282C2×C4×C19—81no—
283C2×C4×C19—81no—
284C2×C4×C19—81no—
285C2×C4×C19—81no—
286C2×C4×C19C22×D411yescharacteristic
287C8×C19—21no—
288C8×C19—21no—
289C8×C19—41no—
290C8×C19—41no—
291C8×C19C2×D811yescharacteristic
292C8×C19C2×D811yescharacteristic
293C8×C19C22×D411yescharacteristic
294C8×C19H(5,𝔽2)11yescharacteristic
295#3417C2×C1911yescharacteristic, complemented
296#3416C2×C1911yescharacteristic, complemented
297#3293C2×C1911yescharacteristic, complemented
298#3290C2×C1911yescharacteristic, complemented
299#2251C2×C1911yescharacteristic, complemented
300#2223C2×C1911yescharacteristic, complemented
301#2222C2×C1911yescharacteristic, complemented
302#2214C2×C1911yescharacteristic, complemented
303#2212C2×C1911yescharacteristic, complemented
304#2195C2×C1911yescharacteristic, complemented
305#2195C2×C1911yescharacteristic, complemented
306#2194C2×C1911yescharacteristic, complemented
307#2193C2×C1911yescharacteristic, complemented
308#2179C2×C1911yescharacteristic, complemented
309#2171C2×C1911yescharacteristic, complemented
310C22×C19—21no—
311C22×C19—21no—
312C22×C19—41no—
313C22×C19—41no—
314C22×C19—81no—
315C22×C19—161no—
316C22×C19—321no—
317C22×C19#57611yescharacteristic
318C4×C19—21no—
319C4×C19—21no—
320C4×C19—41no—
321C4×C19—41no—
322C4×C19—41no—
323C4×C19—81no—
324C4×C19—81no—
325C4×C19—81no—
326C4×C19D4211yescharacteristic
327C4×C19C22×D811yescharacteristic
328#578—21no—
329#578C22×C1911yescharacteristic
330#578C22×C1911yescharacteristic
331#578C22×C1911yescharacteristic, complemented
332#577—21no—
333#576C22×C1911yescharacteristic
334#510—21no—
335#510—21no—
336#510—21no—
337#510C22×C1911yescharacteristic
338#510C22×C1911yescharacteristic
339#510C22×C1911yescharacteristic, complemented
340#509—21no—
341#509C22×C1911yescharacteristic
342#508—21no—
343#508—21no—
344#508C22×C1911yescharacteristic
345C2×Q32—21no—
346C2×Q32C22×C1911yescharacteristic, complemented
347C2×Q32C22×C1911yescharacteristic, complemented
348C2×SD32—21no—
349C2×SD32C22×C1911yescharacteristic
350C2×SD32C22×C1911yescharacteristic
351#504C22×C1911yescharacteristic
352#504C22×C1911yescharacteristic, complemented
353#495C22×C1911yescharacteristic
354#494C22×C1911yescharacteristic, complemented
355#473—21no—
356#473C22×C1911yescharacteristic
357#473C22×C1911yescharacteristic
358#473C22×C1911yescharacteristic, complemented
359#472C22×C1911yescharacteristic
360#471—21no—
361#456—21no—
362#456—21no—
363#455—21no—
364#454—21no—
365#443C22×C1911yescharacteristic
366#443C22×C1911yescharacteristic
367#443C22×C1911yescharacteristic, complemented
368#368C22×C1911yescharacteristic, complemented
369#364C22×C1911yescharacteristic, complemented
370#362C22×C1911yescharacteristic, complemented
371#362C22×C1911yescharacteristic, complemented
372#362C22×C1911yescharacteristic, complemented
373#361C22×C1911yescharacteristic
374#359C22×C1911yescharacteristic
375#359C22×C1911yescharacteristic, complemented
376#350C22×C1911yescharacteristic
377#350C22×C1911yescharacteristic, complemented
378#346C22×C1911yescharacteristic, complemented
379C2×C19—21no—
380C2×C19—41no—
381C2×C19—41no—
382C2×C19—81no—
383C2×C19—81no—
384C2×C19—161no—
385C2×C19D4×D811yescharacteristic
3862−1+4—21no—
3872−1+4—21no—
3882−1+4—21no—
389H(5,𝔽2)—21no—
390#137—21no—
391#137—21no—
392#137—21no—
393#137—21no—
394#137—21no—
395#137—21no—
396#137—41no—
397#137—41no—
398#137—41no—
399#137—41no—
400#137—41no—
401#137—41no—
402AGL(1,ℤ/8)—21no—
403AGL(1,ℤ/8)—21no—
404AGL(1,ℤ/8)—41no—
405AGL(1,ℤ/8)—41no—
406#135—21no—
407#135—21no—
408#135—21no—
409#135—21no—
410#135—41no—
411#135—41no—
412#135D4×C1911yescharacteristic
413#135C23×C1911yescharacteristic
414#135C23×C1911yescharacteristic
415C2×Q16—21no—
416C2×Q16—21no—
417C2×Q16—21no—
418C2×Q16—21no—
419C2×Q16—41no—
420C2×Q16C23×C1911yescharacteristic
421C2×Q16C23×C1911yescharacteristic
422C2×Q16C23×C1911yescharacteristic
423C2×SD16—21no—
424C2×SD16—41no—
425C2×D8—21no—
426C2×D8C23×C1911yescharacteristic
427#131—21no—
428#131—21no—
429#131C23×C1911yescharacteristic
430#131C23×C1911yescharacteristic
431C4⋊Q8—21no—
432#124—21no—
433Q32—21no—
434Q32—21no—
435Q32—21no—
436Q32—21no—
437Q32—21no—
438Q32—41no—
439Q32D4×C1911yescharacteristic
440SD32—21no—
441SD32—21no—
442SD32—21no—
443SD32—21no—
444SD32—21no—
445SD32—21no—
446SD32—41no—
447SD32D4×C1911yescharacteristic
448SD32D4×C1911yescharacteristic
449D16—21no—
450D16D4×C1911yescharacteristic
451M32—21no—
452M32—21no—
453M32C23×C1911yescharacteristic
454M32C23×C1911yescharacteristic
455C2×C16—21no—
456C2×C16—21no—
457C2×C16C23×C1911yescharacteristic
458C2×C16C23×C1911yescharacteristic
459#108D4×C1911yescharacteristic
460#108C23×C1911yescharacteristic
461#108C23×C1911yescharacteristic
462#104—21no—
463#104—21no—
464#104D4×C1911yescharacteristic
465#104D4×C1911yescharacteristic
466#101—21no—
467#101—21no—
468#101—21no—
469#100—21no—
470C4×C8C23×C1911yescharacteristic
471C19#3385511yescharacteristic, direct product factor, Sylow
472#41—21no—
473#41—21no—
474#41—41no—
475#41—41no—
476#41—41no—
477#41—41no—
478#41—41no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—81no—
483#41—81no—
484#41—81no—
485#41C2×D4×C1911yescharacteristic
486#41C2×D4×C1911yescharacteristic
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×D4—21no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—81no—
500Q16—21no—
501Q16—21no—
502Q16—21no—
503Q16—21no—
504Q16—21no—
505Q16—21no—
506Q16—41no—
507Q16—41no—
508Q16—41no—
509Q16—41no—
510Q16—41no—
511Q16—41no—
512Q16—41no—
513Q16—41no—
514Q16D8×C1911yescharacteristic
515Q16C2×D4×C1911yescharacteristic
516Q16C2×D4×C1911yescharacteristic
517SD16—21no—
518SD16—21no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523SD16—41no—
524SD16—41no—
525SD16—41no—
526SD16—41no—
527SD16—41no—
528SD16—41no—
529SD16D8×C1911yescharacteristic
530SD16D8×C1911yescharacteristic
531D8—21no—
532D8—21no—
533D8—41no—
534D8—41no—
535D8D8×C1911yescharacteristic
536D8C2×D4×C1911yescharacteristic
537D8C2×D4×C1911yescharacteristic
538M16—21no—
539M16—21no—
540M16—21no—
541M16—21no—
542M16—41no—
543M16—41no—
544M16C2×D4×C1911yescharacteristic
545M16C2×D4×C1911yescharacteristic
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8C2×D4×C1911yescharacteristic
551C2×C8C24×C1911yescharacteristic
552C4⋊C4—81no—
553C22⋊C4—81no—
554C42C2×D4×C1911yescharacteristic
555C16—21no—
556C16—21no—
557C16—21no—
558C16C2×D4×C1911yescharacteristic
559C16C2×D4×C1911yescharacteristic
560C23—41no—
561C23—81no—
562Q8—21no—
563Q8—21no—
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570Q8—81no—
571Q8—81no—
572Q8—81no—
573Q8C2×D8×C1911yescharacteristic
574Q8C2×D8×C1911yescharacteristic
575D4—21no—
576D4—21no—
577D4—21no—
578D4—21no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—81no—
584D4—81no—
585D4—81no—
586D4—81no—
587D4—81no—
588D4C2×D8×C1911yescharacteristic
589D4C2×D8×C1911yescharacteristic
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4C22×D4×C1911yescharacteristic
606C8—21no—
607C8—21no—
608C8—41no—
609C8—41no—
610C8C2×D8×C1911yescharacteristic
611C8C2×D8×C1911yescharacteristic
612C8C22×D4×C1911yescharacteristic
613C8C19×H(5,𝔽2)11yescharacteristic
614C22—21no—
615C22—21no—
616C22—41no—
617C22—41no—
618C22—81no—
619C22—161no—
620C22—321no—
621C22C19×#57611yescharacteristic
622C4—21no—
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4D42×C1911yescharacteristic
631C4C22×D8×C1911yescharacteristic
632C2—21no—
633C2—41no—
634C2—41no—
635C2—81no—
636C2—81no—
637C2—161no—
638C2D4×D8×C1911yescharacteristic
subgroupG/H
center, socleC2×C19D4×D8
commutator, Frattini, cosocleC2×C8C24×C19
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C19×#443 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3417C2semidirect
2. C19×#3416C2semidirect
3. C19×#3293C2semidirect
4. C19×#3290C2semidirect
5. C19×#2251C2semidirect
6. C19×#2223C2semidirect
7. C19×#2222C2semidirect
8. C19×#2214C2semidirect
9. C19×#2212C2semidirect
10. C19×#2195C2semidirect
11. C19×#2195C2semidirect
12. C19×#2194C2semidirect
13. C19×#2193C2semidirect
14. C19×#2179C2semidirect
15. C19×#2171C2semidirect
19. C19×#578C22semidirect
27. C19×#510C22semidirect
34. C2×C19×Q32C22semidirect
35. C2×C19×Q32C22semidirect
40. C19×#504C22semidirect
42. C19×#494C22semidirect
46. C19×#473C22semidirect
55. C19×#443C22semidirect
56. C19×#368C22semidirect
57. C19×#364C22semidirect
58. C19×#362C22semidirect
59. C19×#362C22semidirect
60. C19×#362C22semidirect
63. C19×#359C22semidirect
65. C19×#350C22semidirect
66. C19×#346C22semidirect
240. #33855C19direct (N × H)
295. #3417C2×C19semidirect
296. #3416C2×C19semidirect
297. #3293C2×C19semidirect
298. #3290C2×C19semidirect
299. #2251C2×C19semidirect
300. #2223C2×C19semidirect
301. #2222C2×C19semidirect
302. #2214C2×C19semidirect
303. #2212C2×C19semidirect
304. #2195C2×C19semidirect
305. #2195C2×C19semidirect
306. #2194C2×C19semidirect
307. #2193C2×C19semidirect
308. #2179C2×C19semidirect
309. #2171C2×C19semidirect
331. #578C22×C19semidirect
339. #510C22×C19semidirect
346. C2×Q32C22×C19semidirect
347. C2×Q32C22×C19semidirect
352. #504C22×C19semidirect
354. #494C22×C19semidirect
358. #473C22×C19semidirect
367. #443C22×C19semidirect
368. #368C22×C19semidirect
369. #364C22×C19semidirect
370. #362C22×C19semidirect
371. #362C22×C19semidirect
372. #362C22×C19semidirect
375. #359C22×C19semidirect
377. #350C22×C19semidirect
378. #346C22×C19semidirect
471. C19#33855direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#34172
C19×#34162
C19×#32932
C19×#32902
C19×#22512
C19×#22232
C19×#22222
C19×#22142
C19×#22122
C19×#21952
C19×#21942
C19×#21932
C19×#21792
C19×#21712
#3385519