Finite Group Databasebeta

← #18075911

Subgroups — #18075911

Order 4864.

940 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D19×#380C211yesmaximal, characteristic
2#14563544C211yesmaximal, characteristic
3(C2×D19)⋊#95C211yesmaximal, characteristic
4#14561515C211yesmaximal, characteristic, complemented
5#14561514C211yesmaximal, characteristic, complemented
6#14561513C211yesmaximal, characteristic, complemented
7C19×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D19C2211yescharacteristic
9C2×C4⋊C4×D19C411yescharacteristic, complemented
10C2×C4⋊C4×D19C411yescharacteristic, complemented
11C22×(C2×D19)⋊C4—21no—
12C2×C22⋊C4×D19—21no—
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14C2×(C2×D19)⋊C8—21no—
15C2×(C2×D19)⋊C8—21no—
16#11926404C2211yescharacteristic
17#11926403—21no—
18#11926402—21no—
19#11926401C411yescharacteristic, complemented
20#11926401C411yescharacteristic, complemented
21C2×C19⋊#95—21no—
22C2×C19⋊#95C2211yescharacteristic
23#95×D19—21no—
24C2×C19×C22⋊C8C2211yescharacteristic
25C19×#380C2211yescharacteristic
26C2×C19×#95C2211yescharacteristic
27C24×D19D411yescharacteristic
28C23×C4×C19—21no—
29C23×C4×C19C2311yescharacteristic
30C23×Dic19—21no—
31C23×Dic19D411yescharacteristic
32C22×C4×D19—21no—
33C22×C4×D19—21no—
34C22×C4×D19—21no—
35C22×C4×D19—21no—
36C22×C4×D19—21no—
37C22×C4×D19—21no—
38C22×C4×D19—42no—
39C22×C4×D19—42no—
40C22×C4×D19C2×C411yescharacteristic
41C22×C4×D19C2×C411yescharacteristic
42C22×C4×D19D411yescharacteristic
43C22×C4×D19D411yescharacteristic
44C22×C8×C19—21no—
45C2×C4⋊C4×C19C2×C411yescharacteristic
46C2×C4⋊C4×C19C2×C411yescharacteristic
47C2×C22⋊C4×C19—21no—
48C2×C22⋊Dic19—21no—
49C2×(C2×D19)⋊C4—24no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—21no—
52C2×(C2×D19)⋊C4—42no—
53C2×(C2×D19)⋊C4—42no—
54C2×C4⋊Dic19C2×C411yescharacteristic
55C2×C4⋊Dic19C2×C411yescharacteristic
56C2×Dic19⋊C4—21no—
57C2×Dic19⋊C4—21no—
58C22×C19⋊C8—21no—
59C4⋊C4×D19—42no—
60C4⋊C4×D19—42no—
61C22⋊C4×D19—42no—
62C22⋊C4×D19—42no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×#95—21no—
66C19×#95—21no—
67C19×#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—42no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76(C2×D19)⋊C8—42no—
77(C2×D19)⋊C8—42no—
78C24×C19C2×D411yescharacteristic
79C23×D19—21no—
80C23×D19—21no—
81C23×D19—21no—
82C23×D19—21no—
83C23×D19—22no—
84C23×D19—22no—
85C23×D19—41no—
86C23×D19—41no—
87C23×D19C22⋊C411yescharacteristic
88C23×D19C22⋊C411yescharacteristic
89C23×D19D812yes—
90C23×D19SD1612yes—
91C22×C4×C19—22no—
92C22×C4×C19—21no—
93C22×C4×C19—21no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19C22×C411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19#4111yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C22×C4×C19#4111yescharacteristic
107C22×C4×C19#4111yescharacteristic
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—22no—
111C22×Dic19—22no—
112C22×Dic19—21no—
113C22×Dic19—21no—
114C22×Dic19—41no—
115C22×Dic19—41no—
116C22×Dic19—41no—
117C22×Dic19—41no—
118C22×Dic19—41no—
119C22×Dic19—41no—
120C22×Dic19—41no—
121C22×Dic19C22⋊C411yescharacteristic
122C22×Dic19C22⋊C411yescharacteristic
123C2×C4×D19—22no—
124C2×C4×D19—21no—
125C2×C4×D19—21no—
126C2×C4×D19—22no—
127C2×C4×D19—22no—
128C2×C4×D19—21no—
129C2×C4×D19—21no—
130C2×C4×D19—21no—
131C2×C4×D19—21no—
132C2×C4×D19—21no—
133C2×C4×D19—21no—
134C2×C4×D19—22no—
135C2×C4×D19—44no—
136C2×C4×D19—44no—
137C2×C4×D19—44no—
138C2×C4×D19—44no—
139C2×C4×D19—41no—
140C2×C4×D19—41no—
141C2×C4×D19—41no—
142C2×C4×D19—41no—
143C2×C4×D19—42no—
144C2×C4×D19—42no—
145C2×C4×D19—42no—
146C2×C4×D19—42no—
147C2×C4×D19—42no—
148C2×C4×D19—42no—
149C2×C8×C19—41no—
150C2×C8×C19—41no—
151C2×C8×C19—41no—
152C4⋊C4×C19—41no—
153C4⋊C4×C19—41no—
154C22⋊C4×C19—41no—
155C22⋊C4×C19—41no—
156C22⋊Dic19—41no—
157C22⋊Dic19—41no—
158(C2×D19)⋊C4—48no—
159(C2×D19)⋊C4—42no—
160(C2×D19)⋊C4—42no—
161C4⋊Dic19—41no—
162C4⋊Dic19—41no—
163Dic19⋊C4—42no—
164Dic19⋊C4—42no—
165C2×C19⋊C8—41no—
166C2×C19⋊C8—41no—
167C2×C19⋊C8—41no—
168#8712—191nomaximal, Sylow
169C23×C19—21no—
170C23×C19—21no—
171C23×C19—21no—
172C23×C19—21no—
173C23×C19C2×C22⋊C411yescharacteristic
174C23×C19#12311yescharacteristic
175C23×C19#12311yescharacteristic
176C23×C19C2×D811yescharacteristic
177C23×C19C2×SD1611yescharacteristic
178C23×C19#13711yescharacteristic
179C23×C19#13711yescharacteristic
180C22×D19—21no—
181C22×D19—21no—
182C22×D19—21no—
183C22×D19—21no—
184C22×D19—21no—
185C22×D19—21no—
186C22×D19—21no—
187C22×D19—21no—
188C22×D19—21no—
189C22×D19—21no—
190C22×D19—22no—
191C22×D19—22no—
192C22×D19—22no—
193C22×D19—22no—
194C22×D19—24no—
195C22×D19—24no—
196C22×D19—42no—
197C22×D19—42no—
198C22×D19—42no—
199C22×D19—42no—
200C22×D19—42no—
201C22×D19—42no—
202C22×D19—42no—
203C22×D19—42no—
204C22×D19—42no—
205C22×D19—42no—
206C22×D19#9912yes—
207C22×D19#10212yes—
208C22×D19#10212yes—
209C22×D19#10412yes—
210C2×C4×C19—21no—
211C2×C4×C19—21no—
212C2×C4×C19—21no—
213C2×C4×C19—21no—
214C2×C4×C19—41no—
215C2×C4×C19—41no—
216C2×C4×C19—41no—
217C2×C4×C19—41no—
218C2×C4×C19—42no—
219C2×C4×C19—42no—
220C2×C4×C19—42no—
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—81no—
228C2×C4×C19—81no—
229C2×C4×C19—81no—
230C2×C4×C19—81no—
231C2×C4×C19#11711yescharacteristic
232C2×C4×C19#11711yescharacteristic
233C2×C4×C19#12311yescharacteristic
234C2×C4×C19#12311yescharacteristic
235C2×Dic19—21no—
236C2×Dic19—21no—
237C2×Dic19—21no—
238C2×Dic19—21no—
239C2×Dic19—21no—
240C2×Dic19—42no—
241C2×Dic19—42no—
242C2×Dic19—42no—
243C2×Dic19—42no—
244C2×Dic19—42no—
245C2×Dic19—41no—
246C2×Dic19—41no—
247C2×Dic19—41no—
248C2×Dic19—41no—
249C2×Dic19—41no—
250C2×Dic19—41no—
251C2×Dic19—81no—
252C2×Dic19—81no—
253C2×Dic19—81no—
254C2×Dic19—81no—
255C2×Dic19#9912yes—
256C4×D19—24no—
257C4×D19—24no—
258C4×D19—42no—
259C4×D19—42no—
260C4×D19—42no—
261C4×D19—42no—
262C4×D19—42no—
263C4×D19—42no—
264C4×D19—84no—
265C4×D19—84no—
266C8×C19—81no—
267C19⋊C8—81no—
268C2×#380—191no—
269#1779—191no—
270C22⋊#95—191no—
271#1294—191no—
272#1294—191no—
273#1294—191no—
274#1294D1911yescharacteristic, complemented
275C22×C19—21no—
276C22×C19—21no—
277C22×C19—21no—
278C22×C19—21no—
279C22×C19—21no—
280C22×C19—21no—
281C22×C19—21no—
282C22×C19—21no—
283C22×C19—21no—
284C22×C19—21no—
285C22×C19—21no—
286C22×C19—21no—
287C22×C19#38111yescharacteristic
288C22×C19C2×#9911yescharacteristic
289C22×C19C2×#9911yescharacteristic
290C22×C19C2×#10211yescharacteristic
291C22×C19#41911yescharacteristic
292C22×C19C2×#10411yescharacteristic
293C22×C19#42111yescharacteristic
294C22×C19#48011yescharacteristic
295C22×C19#48011yescharacteristic
296C22×C19#48311yescharacteristic
297C22×C19#48311yescharacteristic
298C2×D19—22no—
299C2×D19—22no—
300C2×D19—22no—
301C2×D19—22no—
302C2×D19—22no—
303C2×D19—22no—
304C2×D19—22no—
305C2×D19—22no—
306C2×D19—22no—
307C2×D19—44no—
308C2×D19—44no—
309C2×D19—44no—
310C2×D19—44no—
311C2×D19—41no—
312C2×D19—41no—
313C2×D19—41no—
314C2×D19—41no—
315C2×D19#32714yes—
316C4×C19—21no—
317C4×C19—21no—
318C4×C19—21no—
319C4×C19—21no—
320C4×C19—82no—
321C4×C19—81no—
322C4×C19—81no—
323Dic19—22no—
324Dic19—41no—
325Dic19—82no—
326Dic19—81no—
327Dic19—81no—
328C24×C4—191no—
329C22×C4⋊C4—191no—
330C22×C4⋊C4—191no—
331C22×C22⋊C4—381no—
332C22×C22⋊C4—381no—
333C2×C22⋊C8—191no—
334C2×C22⋊C8—381no—
335C2×C22⋊C8—381no—
336C2×C22⋊C8C2×D1911yescharacteristic
337#380—191no—
338#380—191no—
339#380—191no—
340#380—381no—
341#380—381no—
342#380C2×D1911yescharacteristic
343C2×#95—191no—
344C2×#95—381no—
345C2×#95—381no—
346C2×#95C2×D1911yescharacteristic
347C2×C19—21no—
348C2×C19—21no—
349C2×C19—21no—
350C2×C19—21no—
351C2×C19C2×#32711yescharacteristic
352C2×C19#150811yescharacteristic
353C2×C19#151111yescharacteristic
354C2×C19#151911yescharacteristic
355C2×C19#181911yescharacteristic
356C2×C19#182311yescharacteristic
357C2×C19#182611yescharacteristic
358D19—24no—
359D19—42no—
360C25—191no—
361C23×C4—21no—
362C23×C4—191no—
363C23×C4—191no—
364C23×C4—191no—
365C23×C4—191no—
366C23×C4—191no—
367C23×C4—381no—
368C23×C4—381no—
369C23×C4—381no—
370C23×C4—381no—
371C23×C4—381no—
372C23×C4—381no—
373C23×C4—381no—
374C23×C4—762no—
375C23×C4—762no—
376C23×C4C22×D1911yescharacteristic
377C22×C8—21no—
378C22×C8—381no—
379C2×C4⋊C4—191no—
380C2×C4⋊C4—191no—
381C2×C4⋊C4—381no—
382C2×C4⋊C4—381no—
383C2×C4⋊C4—762no—
384C2×C4⋊C4—762no—
385C2×C4⋊C4C4×D1911yescharacteristic
386C2×C4⋊C4C4×D1911yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—381no—
389C2×C22⋊C4—381no—
390C2×C22⋊C4—384no—
391C2×C22⋊C4—381no—
392C2×C22⋊C4—762no—
393C2×C22⋊C4—762no—
394C2×C22⋊C4—762no—
395C2×C22⋊C4—762no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—381no—
399C22⋊C8—381no—
400C22⋊C8—762no—
401C22⋊C8—762no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—381no—
406#95—381no—
407#95—381no—
408#95—381no—
409#95—381no—
410#95—762no—
411C19#871211yescharacteristic, complemented, Sylow
412C24—191no—
413C24—191no—
414C24—192no—
415C24—192no—
416C24—382no—
417C24—382no—
418C24—381no—
419C24—381no—
420C24—381no—
421C24—381no—
422C24—761no—
423C24—761no—
424C24D4×D1911yescharacteristic
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—191no—
437C22×C4—191no—
438C22×C4—382no—
439C22×C4—382no—
440C22×C4—382no—
441C22×C4—382no—
442C22×C4—382no—
443C22×C4—381no—
444C22×C4—381no—
445C22×C4—381no—
446C22×C4—381no—
447C22×C4—381no—
448C22×C4—381no—
449C22×C4—381no—
450C22×C4—381no—
451C22×C4—381no—
452C22×C4—381no—
453C22×C4—382no—
454C22×C4—381no—
455C22×C4—381no—
456C22×C4—761no—
457C22×C4—761no—
458C22×C4—761no—
459C22×C4—761no—
460C22×C4—764no—
461C22×C4—764no—
462C22×C4—764no—
463C22×C4—764no—
464C22×C4—762no—
465C22×C4—762no—
466C22×C4—762no—
467C22×C4—762no—
468C22×C4—762no—
469C22×C4—762no—
470C22×C4—761no—
471C22×C4—761no—
472C22×C4—761no—
473C22×C4—761no—
474C22×C4—761no—
475C22×C4—761no—
476C22×C4—761no—
477C22×C4C2×C4×D1911yescharacteristic
478C22×C4#6454111yescharacteristic
479C22×C4#6454111yescharacteristic
480C22×C4D4×D1911yescharacteristic
481C22×C4#6454311yescharacteristic
482C22×C4#6454511yescharacteristic
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—761no—
487C2×C8—761no—
488C2×C8—761no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—761no—
492C4⋊C4—761no—
493C4⋊C4—762no—
494C4⋊C4—762no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—762no—
498C22⋊C4—762no—
499C22⋊C4—768no—
500C22⋊C4—761no—
501C22⋊C4—761no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—192no—
507C23—192no—
508C23—192no—
509C23—192no—
510C23—384no—
511C23—384no—
512C23—381no—
513C23—381no—
514C23—381no—
515C23—381no—
516C23—381no—
517C23—381no—
518C23—381no—
519C23—382no—
520C23—382no—
521C23—382no—
522C23—382no—
523C23—381no—
524C23—381no—
525C23—381no—
526C23—762no—
527C23—762no—
528C23—762no—
529C23—762no—
530C23—762no—
531C23—762no—
532C23—762no—
533C23—762no—
534C23—762no—
535C23—762no—
536C23C22⋊C4×D1911yescharacteristic
537C23#1059732911yescharacteristic
538C23#1059734011yescharacteristic
539C23D8×D1911yescharacteristic
540C23SD16×D1911yescharacteristic
541C23#1059736111yescharacteristic
542C23#1059736411yescharacteristic
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—192no—
565C2×C4—384no—
566C2×C4—384no—
567C2×C4—381no—
568C2×C4—381no—
569C2×C4—381no—
570C2×C4—381no—
571C2×C4—381no—
572C2×C4—762no—
573C2×C4—762no—
574C2×C4—762no—
575C2×C4—762no—
576C2×C4—762no—
577C2×C4—762no—
578C2×C4—762no—
579C2×C4—762no—
580C2×C4—762no—
581C2×C4—762no—
582C2×C4—762no—
583C2×C4—761no—
584C2×C4—761no—
585C2×C4—761no—
586C2×C4—761no—
587C2×C4—761no—
588C2×C4—761no—
589C2×C4—1524no—
590C2×C4—1524no—
591C2×C4—1521no—
592C2×C4—1521no—
593C2×C4—1521no—
594C2×C4—1521no—
595C2×C4#1059731811yescharacteristic
596C2×C4#1059732911yescharacteristic
597C2×C4#1059733811yescharacteristic
598C2×C4#1059734011yescharacteristic
599C8—81no—
600C8—1521no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—194no—
614C22—382no—
615C22—382no—
616C22—382no—
617C22—382no—
618C22—382no—
619C22—382no—
620C22—382no—
621C22—382no—
622C22—382no—
623C22—764no—
624C22—764no—
625C22—764no—
626C22—764no—
627C22—761no—
628C22—761no—
629C22—761no—
630C22—761no—
631C22#1192640611yescharacteristic
632C22#99×D1911yescharacteristic
633C22#99×D1911yescharacteristic
634C22#102×D1911yescharacteristic
635C22#1192655111yescharacteristic
636C22#104×D1911yescharacteristic
637C22#1192655911yescharacteristic
638C22#1192685611yescharacteristic
639C22#1192685911yescharacteristic
640C22#1192687311yescharacteristic
641C22#1192687611yescharacteristic
642C4—21no—
643C4—21no—
644C4—21no—
645C4—21no—
646C4—82no—
647C4—81no—
648C4—81no—
649C4—382no—
650C4—761no—
651C4—1522no—
652C4—1521no—
653C4—1521no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—384no—
659C2—762no—
660C2D19×#32711yescharacteristic
661C2#1456215311yescharacteristic
662C2#1456216611yescharacteristic
663C2#1456220111yescharacteristic
664C2#1456370811yescharacteristic
665C2#1456372011yescharacteristic
666C2#1456373311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1294C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19D4
cosocleC23×C4×C19C23
hypercenter#1294D19
hypocenterC19#8712
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. #14561515C2semidirect
5. #14561514C2semidirect
6. #14561513C2semidirect
7. C19×#1294C2semidirect
9. C2×C4⋊C4×D19C4semidirect
10. C2×C4⋊C4×D19C4semidirect
19. #11926401C4semidirect
20. #11926401C4semidirect
274. #1294D19semidirect
411. C19#8712semidirect

Maximal subgroups

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

subgroupindex
D19×#3802
#145635442
(C2×D19)⋊#952
#145615152
#145615142
#145615132
C19×#12942
#871219