Finite Group Databasebeta

← C19×#61848 #18067807

Subgroups — C19×#61848 #18067807

Order 4864.

1660 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3556C211yesmaximal, characteristic, complemented
2C19×#3501C211yesmaximal, characteristic
3C19×#3388C214yesmaximal, complemented
4C19×#3386C212yesmaximal, complemented
5C19×#3381C212yesmaximal, complemented
6C19×#3372C212yesmaximal, complemented
7C19×#3372C214yesmaximal, complemented
8C19×#3359C212yesmaximal, complemented
9C19×#3242C214yesmaximal, complemented
10C19×#3237C211yesmaximal, characteristic, complemented
11C19×#3231C211yesmaximal, characteristic, complemented
12C19×#3123C214yesmaximal
13C19×#3110C211yesmaximal, characteristic
14C19×#3101C211yesmaximal, characteristic
15C19×#2985C211yesmaximal, characteristic, complemented
16C19×#564—22no—
17C19×#557—21no—
18C19×#557—21no—
19C19×#557C2212yescomplemented
20C19×#557C2212yescomplemented
21C19×#557C2212yescomplemented
22C19×#557C2212yescomplemented
23C19×#554—21no—
24C19×#554—22no—
25C19×#554C2212yes—
26C19×#554C2214yes—
27D4×Q8×C19—21no—
28D4×Q8×C19C2212yes—
29C19×#544C2212yes—
30C19×#543—22no—
31C19×#541—22no—
32C19×#541—22no—
33C19×#541C2214yes—
34C19×#533C2211yescharacteristic
35C19×#533C2211yescharacteristic
36C19×#533C2211yescharacteristic
37C19×#533C2211yescharacteristic
38C2×C19×C22⋊Q8—22no—
39C19×#518C2212yes—
40C2×C4×D4×C19C2211yescharacteristic
41C19×#501C2212yescomplemented
42C19×#501C2214yescomplemented
43C19×#500C2211yescharacteristic, complemented
44C19×#499C2214yescomplemented
45C19×#498C2211yescharacteristic, complemented
46C19×#491C2212yescomplemented
47C19×#491C2214yescomplemented
48C19×#487C2211yescharacteristic, complemented
49C19×#487C2211yescharacteristic, complemented
50C19×#487C2214yescomplemented
51C19×#485C2214yes—
52C19×#485C2214yes—
53C19×#484C2212yes—
54C19×#483C2212yes—
55C19×#479C2214yescomplemented
56C19×#479C2214yescomplemented
57C19×#479C2214yescomplemented
58C19×#478C2214yes—
59C19×#478C2214yes—
60C19×#477C2212yescomplemented
61C19×#477C2214yescomplemented
62C19×#476C2212yes—
63C19×#475C2212yescomplemented
64C19×#475C2214yescomplemented
65C19×#474C2212yes—
66C19×#461C2212yes—
67C19×#461C2212yes—
68C19×#461C2214yes—
69C19×#461C2214yes—
70C19×#450C2212yes—
71C19×#450C2212yes—
72C19×#446C2212yescomplemented
73C19×#446C2214yescomplemented
74C8×Q8×C19C2212yescomplemented
75C19×#440C2214yes—
76C19×#440C2214yes—
77C19×#440C2214yes—
78C4×SD16×C19C2212yes—
79C4×SD16×C19C2212yes—
80C4×SD16×C19C2214yes—
81C4×SD16×C19C2214yes—
82C19×#433C2214yes—
83C19×#432C2211yescharacteristic
84C19×#431C2211yescharacteristic
85C22×Q8×C19—22no—
86C22×D4×C19C2311yescharacteristic
87C23×C4×C19—21no—
88C2×SD16×C19C2312yes—
89C2×SD16×C19C2312yes—
90C2×SD16×C19C2314yes—
91C19×C4⋊Q8—22no—
92C19×C4⋊Q8—22no—
93C19×C4⋊Q8—22no—
94C19×C4⋊Q8D411yescharacteristic
95C19×C4⋊Q8D411yescharacteristic
96C19×C4⋊Q8C2311yescharacteristic
97C19×C4⋊Q8C2314yes—
98C19×C4⋊Q8C2311yescharacteristic
99C19×C4⋊Q8C2311yescharacteristic
100C19×C4⋊Q8C2311yescharacteristic
101C19×C4⋊Q8C2314yes—
102C19×C4⋊Q8C2311yescharacteristic
103C19×C4⋊Q8C2311yescharacteristic
104C19×#126—24no—
105C19×#126—24no—
106C19×#125—22no—
107C19×#125—22no—
108C19×#125—24no—
109C19×#125—24no—
110C19×#125—24no—
111C19×#125—24no—
112C19×#125—24no—
113C19×#125—24no—
114C19×#125—22no—
115C19×#125—21no—
116C19×#125—21no—
117C19×#125D412yes—
118C19×#125C2314yes—
119C19×#125C2314yes—
120C19×#125C2312yes—
121C19×C22⋊Q8—22no—
122C19×C22⋊Q8—24no—
123C19×C22⋊Q8—21no—
124C19×C22⋊Q8—21no—
125C19×C22⋊Q8—21no—
126C19×C22⋊Q8—21no—
127C19×C22⋊Q8—22no—
128C19×C22⋊Q8—24no—
129C19×C22⋊Q8—24no—
130C19×C22⋊Q8—24no—
131C19×C22⋊Q8—24no—
132C19×C22⋊Q8—24no—
133C19×C22⋊Q8D412yes—
134C19×C22⋊Q8D412yes—
135C19×C22⋊Q8C2312yes—
136C19×C22⋊Q8C2312yes—
137C4×Q8×C19—22no—
138C4×Q8×C19—22no—
139C4×Q8×C19—22no—
140C4×Q8×C19—22no—
141C4×Q8×C19—21no—
142C4×Q8×C19—21no—
143C4×Q8×C19—21no—
144C4×Q8×C19—21no—
145C4×Q8×C19C2312yes—
146C4×Q8×C19C2314yes—
147C4×Q8×C19C2314yes—
148C4×Q8×C19C2312yes—
149C4×Q8×C19C2312yes—
150C4×Q8×C19C2312yes—
151C4×D4×C19—22no—
152C4×D4×C19—22no—
153C4×D4×C19—21no—
154C4×D4×C19—21no—
155C4×D4×C19C2312yes—
156C4×D4×C19C2314yes—
157C4×D4×C19C2314yes—
158C4×D4×C19C2312yes—
159C19×#117—21no—
160C19×#117—21no—
161C19×#117C2312yes—
162C19×#117C2312yes—
163C2×C4⋊C4×C19—24no—
164C2×C4⋊C4×C19—22no—
165C2×C4⋊C4×C19C2311yescharacteristic
166C2×C22⋊C4×C19—21no—
167C2×C22⋊C4×C19—24no—
168C2×C42×C19C2311yescharacteristic
169C19×#107C2314yes—
170C19×#107C2314yes—
171C19×#107C2314yes—
172C19×#106C2312yes—
173C19×#106C2314yes—
174C19×#106C2312yes—
175C19×#106C2314yes—
176C19×C4⋊C8C2312yes—
177C19×C4⋊C8C2312yes—
178C19×C4⋊C8C2314yes—
179C19×C4⋊C8C2314yes—
180C19×#103C2314yes—
181C19×#103C2312yes—
182C19×#103C2314yes—
183C19×#103C2312yes—
184C19×#103C2314yes—
185C19×#103C2314yes—
186C19×#103C2314yes—
187C19×#102C2312yes—
188C19×#102C2314yes—
189C19×#102C2312yes—
190C19×C22⋊C8C2312yes—
191C19×C22⋊C8C2312yes—
192C19×#97C2312yes—
193C19×#97C2314yes—
194C4×C8×C19C2311yescharacteristic
195C4×C8×C19C2311yescharacteristic
196C4×C8×C19C2314yes—
197C24×C19—21no—
198C2×Q8×C19—21no—
199C2×Q8×C19—21no—
200C2×Q8×C19—21no—
201C2×Q8×C19—21no—
202C2×Q8×C19—24no—
203C2×Q8×C19—84no—
204C2×Q8×C19C2×D412yes—
205C2×Q8×C19C2×D412yes—
206C2×Q8×C19C2412yes—
207C2×Q8×C19C2412yes—
208C2×D4×C19—24no—
209C2×D4×C19—21no—
210C2×D4×C19C2412yes—
211C22×C4×C19—21no—
212C22×C4×C19—22no—
213C22×C4×C19—24no—
214C22×C4×C19—24no—
215C22×C4×C19—22no—
216C22×C4×C19—82no—
217C22×C4×C19C2×D411yescharacteristic
218C22×C4×C19C2×D411yescharacteristic
219C22×C4×C19C2411yescharacteristic
220SD16×C19—24no—
221SD16×C19—24no—
222SD16×C19—28no—
223C2×C8×C19C2412yes—
224C2×C8×C19C2412yes—
225C2×C8×C19C2414yes—
226C4⋊C4×C19—22no—
227C4⋊C4×C19—21no—
228C4⋊C4×C19—24no—
229C4⋊C4×C19—24no—
230C4⋊C4×C19—24no—
231C4⋊C4×C19—21no—
232C4⋊C4×C19—21no—
233C4⋊C4×C19—21no—
234C4⋊C4×C19—21no—
235C4⋊C4×C19—21no—
236C4⋊C4×C19—21no—
237C4⋊C4×C19—21no—
238C4⋊C4×C19—22no—
239C4⋊C4×C19—21no—
240C4⋊C4×C19—22no—
241C4⋊C4×C19—22no—
242C4⋊C4×C19—24no—
243C4⋊C4×C19—24no—
244C4⋊C4×C19—24no—
245C4⋊C4×C19—24no—
246C4⋊C4×C19—22no—
247C4⋊C4×C19—22no—
248C4⋊C4×C19—24no—
249C4⋊C4×C19—24no—
250C4⋊C4×C19C2×D412yes—
251C4⋊C4×C19C2×D414yes—
252C4⋊C4×C19C2×D412yes—
253C4⋊C4×C19C2×D412yes—
254C4⋊C4×C19C2×D412yes—
255C4⋊C4×C19C2×D414yes—
256C4⋊C4×C19C2412yes—
257C4⋊C4×C19C2412yes—
258C4⋊C4×C19C2412yes—
259C4⋊C4×C19C2412yes—
260C4⋊C4×C19C2412yes—
261C22⋊C4×C19—22no—
262C22⋊C4×C19—22no—
263C22⋊C4×C19—22no—
264C22⋊C4×C19—24no—
265C22⋊C4×C19—24no—
266C22⋊C4×C19—22no—
267C22⋊C4×C19—22no—
268C22⋊C4×C19C2×D414yes—
269C42×C19—22no—
270C42×C19—22no—
271C42×C19—22no—
272C42×C19—24no—
273C42×C19—24no—
274C42×C19C2×D411yescharacteristic
275C42×C19C2×D411yescharacteristic
276C42×C19C2411yescharacteristic
277C42×C19C2411yescharacteristic
278C42×C19C2414yes—
279#61848C1911yesmaximal, characteristic, direct product factor, Sylow
280C23×C19—24no—
281C23×C19—22no—
282C23×C19—81no—
283C23×C19—81no—
284C23×C19C22×D411yescharacteristic
285Q8×C19—24no—
286Q8×C19—22no—
287Q8×C19—22no—
288Q8×C19—24no—
289Q8×C19—42no—
290Q8×C19—42no—
291Q8×C19—42no—
292Q8×C19—42no—
293Q8×C19—81no—
294Q8×C19—84no—
295D4×C19—24no—
296D4×C19—22no—
297D4×C192−1+414yes—
298C2×C4×C19—22no—
299C2×C4×C19—22no—
300C2×C4×C19—22no—
301C2×C4×C19—22no—
302C2×C4×C19—22no—
303C2×C4×C19—22no—
304C2×C4×C19—22no—
305C2×C4×C19—22no—
306C2×C4×C19—22no—
307C2×C4×C19—41no—
308C2×C4×C19—44no—
309C2×C4×C19—84no—
310C2×C4×C19—82no—
311C2×C4×C19—84no—
312C2×C4×C19—81no—
313C2×C4×C19C22×D411yescharacteristic
314C2×C4×C19C22×D411yescharacteristic
315C2×C4×C19C22×D414yes—
316C2×C4×C19C22×D414yes—
317C2×C4×C19C22×D411yescharacteristic
318C2×C4×C19C22×D411yescharacteristic
319C2×C4×C19C22×D411yescharacteristic
320C2×C4×C19C2511yescharacteristic
321C8×C19—22no—
322C8×C19—22no—
323C8×C19—24no—
324#3556C2×C1911yescharacteristic, complemented
325#3501C2×C1911yescharacteristic
326#3388C2×C1914yescomplemented
327#3386C2×C1912yescomplemented
328#3381C2×C1912yescomplemented
329#3372C2×C1912yescomplemented
330#3372C2×C1914yescomplemented
331#3359C2×C1912yescomplemented
332#3242C2×C1914yescomplemented
333#3237C2×C1911yescharacteristic, complemented
334#3231C2×C1911yescharacteristic, complemented
335#3123C2×C1914yes—
336#3110C2×C1911yescharacteristic
337#3101C2×C1911yescharacteristic
338#2985C2×C1911yescharacteristic, complemented
339C22×C19—21no—
340C22×C19—21no—
341C22×C19—24no—
342C22×C19—21no—
343C22×C19—42no—
344C22×C19—42no—
345C22×C19—84no—
346C22×C19C23×D411yescharacteristic
347C4×C19—21no—
348C4×C19—21no—
349C4×C19—24no—
350C4×C19—21no—
351C4×C19—21no—
352C4×C19—24no—
353C4×C19—42no—
354C4×C19—42no—
355C4×C19—42no—
356C4×C19—42no—
357C4×C19—42no—
358C4×C19—42no—
359C4×C19—42no—
360C4×C19#57712yes—
361C4×C19C2×2−1+412yes—
362#564—22no—
363#557—21no—
364#557—21no—
365#557C22×C1912yescomplemented
366#557C22×C1912yescomplemented
367#557C22×C1912yescomplemented
368#557C22×C1912yescomplemented
369#554—21no—
370#554—22no—
371#554C22×C1912yes—
372#554C22×C1914yes—
373D4×Q8—21no—
374D4×Q8C22×C1912yes—
375#544C22×C1912yes—
376#543—22no—
377#541—22no—
378#541—22no—
379#541C22×C1914yes—
380#533C22×C1911yescharacteristic
381#533C22×C1911yescharacteristic
382#533C22×C1911yescharacteristic
383#533C22×C1911yescharacteristic
384C2×C22⋊Q8—22no—
385#518C22×C1912yes—
386C2×C4×D4C22×C1911yescharacteristic
387#501C22×C1914yescomplemented
388#501C22×C1912yescomplemented
389#500C22×C1911yescharacteristic, complemented
390#499C22×C1914yescomplemented
391#498C22×C1911yescharacteristic, complemented
392#491C22×C1912yescomplemented
393#491C22×C1914yescomplemented
394#487C22×C1911yescharacteristic, complemented
395#487C22×C1914yescomplemented
396#487C22×C1911yescharacteristic, complemented
397#485C22×C1914yes—
398#485C22×C1914yes—
399#484C22×C1912yes—
400#483C22×C1912yes—
401#479C22×C1914yescomplemented
402#479C22×C1914yescomplemented
403#479C22×C1914yescomplemented
404#478C22×C1914yes—
405#478C22×C1914yes—
406#477C22×C1912yescomplemented
407#477C22×C1914yescomplemented
408#476C22×C1912yes—
409#475C22×C1912yescomplemented
410#475C22×C1914yescomplemented
411#474C22×C1912yes—
412#461C22×C1912yes—
413#461C22×C1912yes—
414#461C22×C1914yes—
415#461C22×C1914yes—
416#450C22×C1912yes—
417#450C22×C1912yes—
418#446C22×C1912yescomplemented
419#446C22×C1914yescomplemented
420C8×Q8C22×C1912yescomplemented
421#440C22×C1914yes—
422#440C22×C1914yes—
423#440C22×C1914yes—
424C4×SD16C22×C1912yes—
425C4×SD16C22×C1912yes—
426C4×SD16C22×C1914yes—
427C4×SD16C22×C1914yes—
428#433C22×C1914yes—
429#432C22×C1911yescharacteristic
430#431C22×C1911yescharacteristic
431C2×C19—41no—
432C2×C19—44no—
433C2×C19#348611yescharacteristic
434C2×C19C2×#57711yescharacteristic
435C2×C19#358611yescharacteristic
436C22×Q8—22no—
437C22×D4C23×C1911yescharacteristic
438C23×C4—21no—
439C2×SD16C23×C1912yes—
440C2×SD16C23×C1912yes—
441C2×SD16C23×C1914yes—
442C4⋊Q8—22no—
443C4⋊Q8—22no—
444C4⋊Q8—22no—
445C4⋊Q8D4×C1911yescharacteristic
446C4⋊Q8D4×C1911yescharacteristic
447C4⋊Q8C23×C1911yescharacteristic
448C4⋊Q8C23×C1911yescharacteristic
449C4⋊Q8C23×C1914yes—
450C4⋊Q8C23×C1911yescharacteristic
451C4⋊Q8C23×C1911yescharacteristic
452C4⋊Q8C23×C1911yescharacteristic
453C4⋊Q8C23×C1911yescharacteristic
454C4⋊Q8C23×C1914yes—
455#126—24no—
456#126—24no—
457#125—22no—
458#125—22no—
459#125—24no—
460#125—24no—
461#125—24no—
462#125—24no—
463#125—24no—
464#125—24no—
465#125—22no—
466#125—21no—
467#125—21no—
468#125D4×C1912yes—
469#125C23×C1912yes—
470#125C23×C1914yes—
471#125C23×C1914yes—
472C22⋊Q8—22no—
473C22⋊Q8—24no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—22no—
479C22⋊Q8—24no—
480C22⋊Q8—24no—
481C22⋊Q8—24no—
482C22⋊Q8—24no—
483C22⋊Q8—24no—
484C22⋊Q8D4×C1912yes—
485C22⋊Q8D4×C1912yes—
486C22⋊Q8C23×C1912yes—
487C22⋊Q8C23×C1912yes—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8C23×C1912yes—
497C4×Q8C23×C1912yes—
498C4×Q8C23×C1914yes—
499C4×Q8C23×C1914yes—
500C4×Q8C23×C1912yes—
501C4×Q8C23×C1912yes—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4C23×C1912yes—
507C4×D4C23×C1912yes—
508C4×D4C23×C1914yes—
509C4×D4C23×C1914yes—
510#117—21no—
511#117—21no—
512#117C23×C1912yes—
513#117C23×C1912yes—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4C23×C1911yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—24no—
519C2×C42C23×C1911yescharacteristic
520#107C23×C1914yes—
521#107C23×C1914yes—
522#107C23×C1914yes—
523#106C23×C1912yes—
524#106C23×C1914yes—
525#106C23×C1912yes—
526#106C23×C1914yes—
527C4⋊C8C23×C1912yes—
528C4⋊C8C23×C1912yes—
529C4⋊C8C23×C1914yes—
530C4⋊C8C23×C1914yes—
531#103C23×C1914yes—
532#103C23×C1912yes—
533#103C23×C1914yes—
534#103C23×C1912yes—
535#103C23×C1914yes—
536#103C23×C1914yes—
537#103C23×C1914yes—
538#102C23×C1912yes—
539#102C23×C1914yes—
540#102C23×C1912yes—
541C22⋊C8C23×C1912yes—
542C22⋊C8C23×C1912yes—
543#97C23×C1912yes—
544#97C23×C1914yes—
545C4×C8C23×C1911yescharacteristic
546C4×C8C23×C1911yescharacteristic
547C4×C8C23×C1914yes—
548C19#6184811yescharacteristic, direct product factor, Sylow
549C24—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—24no—
555C2×Q8—84no—
556C2×Q8C2×D4×C1912yes—
557C2×Q8C2×D4×C1912yes—
558C2×Q8C24×C1912yes—
559C2×Q8C24×C1912yes—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4C24×C1912yes—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—82no—
569C22×C4C2×D4×C1911yescharacteristic
570C22×C4C2×D4×C1911yescharacteristic
571C22×C4C24×C1911yescharacteristic
572SD16—24no—
573SD16—24no—
574SD16—28no—
575C2×C8C24×C1912yes—
576C2×C8C24×C1912yes—
577C2×C8C24×C1914yes—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4C2×D4×C1912yes—
603C4⋊C4C2×D4×C1914yes—
604C4⋊C4C2×D4×C1912yes—
605C4⋊C4C2×D4×C1912yes—
606C4⋊C4C2×D4×C1912yes—
607C4⋊C4C2×D4×C1914yes—
608C4⋊C4C24×C1912yes—
609C4⋊C4C24×C1912yes—
610C4⋊C4C24×C1912yes—
611C4⋊C4C24×C1912yes—
612C4⋊C4C24×C1912yes—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4C2×D4×C1914yes—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—24no—
625C42—24no—
626C42C2×D4×C1911yescharacteristic
627C42C2×D4×C1911yescharacteristic
628C42C24×C1911yescharacteristic
629C42C24×C1914yes—
630C42C24×C1911yescharacteristic
631C23—24no—
632C23—22no—
633C23—81no—
634C23—81no—
635C23C22×D4×C1911yescharacteristic
636Q8—24no—
637Q8—22no—
638Q8—24no—
639Q8—22no—
640Q8—42no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—84no—
645Q8—81no—
646D4—24no—
647D4—22no—
648D4C19×2−1+414yes—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—44no—
660C2×C4—82no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4—81no—
664C2×C4C22×D4×C1911yescharacteristic
665C2×C4C22×D4×C1911yescharacteristic
666C2×C4C22×D4×C1914yes—
667C2×C4C22×D4×C1914yes—
668C2×C4C22×D4×C1911yescharacteristic
669C2×C4C22×D4×C1911yescharacteristic
670C2×C4C22×D4×C1911yescharacteristic
671C2×C4C25×C1911yescharacteristic
672C8—22no—
673C8—22no—
674C8—24no—
675C22—21no—
676C22—24no—
677C22—21no—
678C22—21no—
679C22—42no—
680C22—42no—
681C22—84no—
682C22C23×D4×C1911yescharacteristic
683C4—21no—
684C4—21no—
685C4—24no—
686C4—21no—
687C4—21no—
688C4—24no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4C19×#57712yes—
697C4C2×C19×2−1+412yes—
698C2—41no—
699C2—44no—
700C2C19×#348611yescharacteristic
701C2C2×C19×#57711yescharacteristic
702C2C19×#358611yescharacteristic
subgroupG/H
center, socleC22×C19C23×D4
commutator, Frattini, cosocleC2×C4C25×C19
prime radicalC22×D4×C19C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C19×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3556C2semidirect
3. C19×#3388C2semidirect
4. C19×#3386C2semidirect
5. C19×#3381C2semidirect
6. C19×#3372C2semidirect
7. C19×#3372C2semidirect
8. C19×#3359C2semidirect
9. C19×#3242C2semidirect
10. C19×#3237C2semidirect
11. C19×#3231C2semidirect
15. C19×#2985C2semidirect
19. C19×#557C22semidirect
20. C19×#557C22semidirect
21. C19×#557C22semidirect
22. C19×#557C22semidirect
41. C19×#501C22semidirect
42. C19×#501C22semidirect
43. C19×#500C22semidirect
44. C19×#499C22semidirect
45. C19×#498C22semidirect
46. C19×#491C22semidirect
47. C19×#491C22semidirect
48. C19×#487C22semidirect
49. C19×#487C22semidirect
50. C19×#487C22semidirect
55. C19×#479C22semidirect
56. C19×#479C22semidirect
57. C19×#479C22semidirect
60. C19×#477C22semidirect
61. C19×#477C22semidirect
63. C19×#475C22semidirect
64. C19×#475C22semidirect
72. C19×#446C22semidirect
73. C19×#446C22semidirect
74. C8×Q8×C19C22semidirect
279. #61848C19direct (N × H)
324. #3556C2×C19semidirect
326. #3388C2×C19semidirect
327. #3386C2×C19semidirect
328. #3381C2×C19semidirect
329. #3372C2×C19semidirect
330. #3372C2×C19semidirect
331. #3359C2×C19semidirect
332. #3242C2×C19semidirect
333. #3237C2×C19semidirect
334. #3231C2×C19semidirect
338. #2985C2×C19semidirect
365. #557C22×C19semidirect
366. #557C22×C19semidirect
367. #557C22×C19semidirect
368. #557C22×C19semidirect
387. #501C22×C19semidirect
388. #501C22×C19semidirect
389. #500C22×C19semidirect
390. #499C22×C19semidirect
391. #498C22×C19semidirect
392. #491C22×C19semidirect
393. #491C22×C19semidirect
394. #487C22×C19semidirect
395. #487C22×C19semidirect
396. #487C22×C19semidirect
401. #479C22×C19semidirect
402. #479C22×C19semidirect
403. #479C22×C19semidirect
406. #477C22×C19semidirect
407. #477C22×C19semidirect
409. #475C22×C19semidirect
410. #475C22×C19semidirect
418. #446C22×C19semidirect
419. #446C22×C19semidirect
420. C8×Q8C22×C19semidirect
548. C19#61848direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35562
C19×#35012
C19×#33882
C19×#33862
C19×#33812
C19×#33722
C19×#33592
C19×#32422
C19×#32372
C19×#32312
C19×#31232
C19×#31102
C19×#31012
C19×#29852
#6184819