Finite Group Databasebeta

← #18077939

Subgroups — #18077939

Order 4864.

928 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926506C211yesmaximal, characteristic
2C2×#11926418C211yesmaximal, characteristic
3#14563544C211yesmaximal, characteristic
4C2×#11926269C211yesmaximal, characteristic, complemented
5C2×#11926269C211yesmaximal, characteristic, complemented
6#14561478C211yesmaximal, characteristic, complemented
7C19×#1280C211yesmaximal, characteristic, complemented
8C23×C4×D19C2211yescharacteristic
9C22×#64515—21no—
10C22×C4⋊Dic19C411yescharacteristic
11C22×Dic19⋊C4C2211yescharacteristic
12C22×(C2×D19)⋊C4C411yescharacteristic
13C22×(C2×D19)⋊C4C411yescharacteristic
14#11926506—22no—
15#11926506—22no—
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18C2×(C2×D19)⋊C8—21no—
19C2×(C2×D19)⋊C8—21no—
20C2×(C2×D19)⋊C8—21no—
21#11926418—21no—
22#11926418—21no—
23#11926418—21no—
24#11926418—21no—
25C2×C19⋊#95C411yescharacteristic
26#11926269—22no—
27#11926269—22no—
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×C22⋊C8C2211yescharacteristic
30C2×C19×#95C2211yescharacteristic
31C24×D19C2×C411yescharacteristic
32C23×C4×C19C2×C411yescharacteristic
33C23×C4×C19C2×C411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C23×Dic19C2×C411yescharacteristic
36C23×Dic19C2×C411yescharacteristic
37C23×Dic19C2×C411yescharacteristic
38C22×C4×D19—21no—
39C22×C4×D19—21no—
40C22×C4×D19—21no—
41C22×C4×D19—21no—
42C22×C4×D19—42no—
43C22×C4×D19—42no—
44C22×C4×D19D411yescharacteristic
45C22×C4×D19D411yescharacteristic
46C22×C4×D19D411yescharacteristic
47C22×C4×D19D411yescharacteristic
48C22×C8×C19—21no—
49C22×C8×C19—21no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—21no—
52C2×(C2×D19)⋊C4—22no—
53C2×(C2×D19)⋊C4—22no—
54C2×(C2×D19)⋊C4—21no—
55C2×(C2×D19)⋊C4—21no—
56C2×(C2×D19)⋊C4—42no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19—21no—
59C2×C4⋊Dic19—42no—
60C2×Dic19⋊C4—21no—
61C2×Dic19⋊C4—21no—
62C2×Dic19⋊C4—21no—
63C2×Dic19⋊C4—21no—
64C2×Dic19⋊C4—21no—
65C2×Dic19⋊C4—21no—
66C22×C19⋊C8—21no—
67C22×C19⋊C8—21no—
68C2×#64515—24no—
69C2×#64515—42no—
70C2×#64515—42no—
71C19×C22⋊C8—21no—
72C19×C22⋊C8—21no—
73C19×C22⋊C8—21no—
74C19×C22⋊C8D412yes—
75C19×#95—21no—
76C19×#95—21no—
77C19⋊#95—21no—
78C19⋊#95—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)D412yes—
83(C2×D19)⋊C8—24no—
84(C2×D19)⋊C8—42no—
85(C2×D19)⋊C8—42no—
86C24×C19C22×C411yescharacteristic
87C23×D19—21no—
88C23×D19—21no—
89C23×D19—22no—
90C23×D19—22no—
91C23×D19—21no—
92C23×D19—21no—
93C23×D19—21no—
94C23×D19—21no—
95C23×D19—41no—
96C23×D19—41no—
97C23×D19C22⋊C411yescharacteristic
98C23×D19C22⋊C411yescharacteristic
99C22×C4×C19—21no—
100C22×C4×C19—21no—
101C22×C4×C19—21no—
102C22×C4×C19—21no—
103C22×C4×C19—21no—
104C22×C4×C19—41no—
105C22×C4×C19—41no—
106C22×C4×C19—41no—
107C22×C4×C19—41no—
108C22×C4×C19—41no—
109C22×C4×C19—41no—
110C22×C4×C19M1612yescomplemented
111C22×C4×C19C2×D411yescharacteristic
112C22×C4×C19C2×D411yescharacteristic
113C22×C4×C19C2×D411yescharacteristic
114C22×C4×C19C2×D411yescharacteristic
115C22×C4×C19#4111yescharacteristic
116C22×C4×C19#4111yescharacteristic
117C22×Dic19—21no—
118C22×Dic19—21no—
119C22×Dic19—21no—
120C22×Dic19—21no—
121C22×Dic19—21no—
122C22×Dic19—21no—
123C22×Dic19—21no—
124C22×Dic19—21no—
125C22×Dic19—22no—
126C22×Dic19—21no—
127C22×Dic19—21no—
128C22×Dic19—21no—
129C22×Dic19—41no—
130C22×Dic19—41no—
131C22×Dic19—41no—
132C22×Dic19C22⋊C411yescharacteristic
133C22×Dic19C22⋊C411yescharacteristic
134C22×Dic19M1612yescomplemented
135C2×C4×D19—22no—
136C2×C4×D19—21no—
137C2×C4×D19—21no—
138C2×C4×D19—22no—
139C2×C4×D19—22no—
140C2×C4×D19—21no—
141C2×C4×D19—21no—
142C2×C4×D19—21no—
143C2×C4×D19—21no—
144C2×C4×D19—21no—
145C2×C4×D19—21no—
146C2×C4×D19—22no—
147C2×C4×D19—44no—
148C2×C4×D19—44no—
149C2×C4×D19—44no—
150C2×C4×D19—44no—
151C2×C4×D19—41no—
152C2×C4×D19—41no—
153C2×C4×D19—41no—
154C2×C4×D19—41no—
155C2×C8×C19—22no—
156C2×C8×C19—41no—
157C2×C8×C19—41no—
158C2×C8×C19—41no—
159C2×C8×C19—41no—
160C2×C8×C19—41no—
161(C2×D19)⋊C4—24no—
162(C2×D19)⋊C4—24no—
163(C2×D19)⋊C4—42no—
164(C2×D19)⋊C4—42no—
165C4⋊Dic19—42no—
166C4⋊Dic19—42no—
167Dic19⋊C4—41no—
168Dic19⋊C4—41no—
169Dic19⋊C4—41no—
170Dic19⋊C4—41no—
171C2×C19⋊C8—22no—
172C2×C19⋊C8—41no—
173C2×C19⋊C8—41no—
174C2×C19⋊C8—41no—
175C2×C19⋊C8—41no—
176C2×C19⋊C8—41no—
177#64515—48no—
178#9085—191nomaximal, Sylow
179C23×C19—21no—
180C23×C19—21no—
181C23×C19—21no—
182C23×C19—21no—
183C23×C19C2×C22⋊C411yescharacteristic
184C23×C19C4×D411yescharacteristic
185C23×C19C4×D411yescharacteristic
186C23×C19C2×M1611yescharacteristic
187C23×C19C2×M1611yescharacteristic
188C23×C19#13111yescharacteristic
189C23×C19#13111yescharacteristic
190C22×D19—24no—
191C22×D19—24no—
192C22×D19—21no—
193C22×D19—21no—
194C22×D19—21no—
195C22×D19—21no—
196C22×D19—21no—
197C22×D19—21no—
198C22×D19—21no—
199C22×D19—21no—
200C22×D19—21no—
201C22×D19—21no—
202C22×D19—21no—
203C22×D19—21no—
204C22×D19—42no—
205C22×D19—42no—
206C22×D19—42no—
207C22×D19—42no—
208C22×D19—42no—
209C22×D19—42no—
210C22×D19—42no—
211C22×D19—42no—
212C22×D19—42no—
213C22×D19—42no—
214C22×D19—41no—
215C22×D19—41no—
216C22×D19—41no—
217C22×D19—41no—
218C22×D19#9912yes—
219C22×D19#10112yes—
220C2×C4×C19—21no—
221C2×C4×C19—21no—
222C2×C4×C19—21no—
223C2×C4×C19—21no—
224C2×C4×C19—22no—
225C2×C4×C19—41no—
226C2×C4×C19—41no—
227C2×C4×C19—41no—
228C2×C4×C19—41no—
229C2×C4×C19—42no—
230C2×C4×C19—41no—
231C2×C4×C19—41no—
232C2×C4×C19—42no—
233C2×C4×C19—41no—
234C2×C4×C19—41no—
235C2×C4×C19—41no—
236C2×C4×C19—81no—
237C2×C4×C19—81no—
238C2×C4×C19#12011yescharacteristic
239C2×C4×C19#12111yescharacteristic
240C2×C4×C19#12111yescharacteristic
241C2×C4×C19#12311yescharacteristic
242C2×Dic19—21no—
243C2×Dic19—21no—
244C2×Dic19—21no—
245C2×Dic19—22no—
246C2×Dic19—21no—
247C2×Dic19—21no—
248C2×Dic19—22no—
249C2×Dic19—22no—
250C2×Dic19—42no—
251C2×Dic19—42no—
252C2×Dic19—41no—
253C2×Dic19—41no—
254C2×Dic19—41no—
255C2×Dic19—41no—
256C2×Dic19—41no—
257C2×Dic19—41no—
258C2×Dic19—41no—
259C2×Dic19—81no—
260C2×Dic19—81no—
261C2×Dic19#9912yes—
262C4×D19—24no—
263C4×D19—24no—
264C4×D19—42no—
265C4×D19—42no—
266C4×D19—42no—
267C4×D19—42no—
268C4×D19—42no—
269C4×D19—42no—
270C8×C19—42no—
271C8×C19—81no—
272C19⋊C8—42no—
273C19⋊C8—81no—
274C2×#407—191no—
275C2×#385—191no—
276#1779—191no—
277C2×#324—191no—
278C2×#324—191no—
279#1280—191no—
280#1280D1911yescharacteristic, complemented
281C22×C19—21no—
282C22×C19—21no—
283C22×C19—21no—
284C22×C19—21no—
285C22×C19—21no—
286C22×C19—21no—
287C22×C19—21no—
288C22×C19—21no—
289C22×C19—21no—
290C22×C19—21no—
291C22×C19—21no—
292C22×C19—21no—
293C22×C19#38611yescharacteristic
294C22×C19#40711yescharacteristic
295C22×C19#40811yescharacteristic
296C22×C19C2×#9911yescharacteristic
297C22×C19C2×#9911yescharacteristic
298C22×C19C2×#10111yescharacteristic
299C22×C19#41311yescharacteristic
300C22×C19#43511yescharacteristic
301C22×C19#43511yescharacteristic
302C22×C19#43611yescharacteristic
303C22×C19#43611yescharacteristic
304C2×D19—22no—
305C2×D19—22no—
306C2×D19—22no—
307C2×D19—22no—
308C2×D19—22no—
309C2×D19—22no—
310C2×D19—44no—
311C2×D19—44no—
312C2×D19—44no—
313C2×D19—44no—
314C2×D19—41no—
315C2×D19—41no—
316C2×D19—41no—
317C2×D19—41no—
318C2×D19—41no—
319C2×D19—41no—
320C2×D19—41no—
321C2×D19—41no—
322C4×C19—21no—
323C4×C19—21no—
324C4×C19—21no—
325C4×C19—21no—
326C4×C19—42no—
327C4×C19—81no—
328Dic19—22no—
329Dic19—42no—
330Dic19—41no—
331Dic19—81no—
332C24×C4—191no—
333C22×M16—381no—
334C22×C4⋊C4—191no—
335C22×C4⋊C4—191no—
336C22×C22⋊C4—191no—
337C22×C22⋊C4—191no—
338#407—382no—
339#407—382no—
340C2×C22⋊C8—191no—
341C2×C22⋊C8—191no—
342C2×C22⋊C8—381no—
343C2×C22⋊C8—381no—
344C2×C22⋊C8—381no—
345C2×C22⋊C8C2×D1911yescharacteristic
346C2×C22⋊C8C2×D1911yescharacteristic
347#385—381no—
348#385—381no—
349#385—381no—
350#385—381no—
351C2×#95—191no—
352C2×#95C2×D1911yescharacteristic
353#324—382no—
354#324—382no—
355C2×C19—21no—
356C2×C19—21no—
357C2×C19—21no—
358C2×C19—21no—
359C2×C19#146311yescharacteristic
360C2×C19#146511yescharacteristic
361C2×C19#146811yescharacteristic
362C2×C19#147211yescharacteristic
363C2×C19#187011yescharacteristic
364C2×C19#189811yescharacteristic
365C2×C19#190111yescharacteristic
366D19—42no—
367D19—42no—
368C25—191no—
369C23×C4—191no—
370C23×C4—191no—
371C23×C4—191no—
372C23×C4—191no—
373C23×C4—191no—
374C23×C4—191no—
375C23×C4—191no—
376C23×C4—381no—
377C23×C4—381no—
378C23×C4—381no—
379C23×C4—381no—
380C23×C4—762no—
381C23×C4—762no—
382C23×C4C4×D1911yescharacteristic
383C23×C4C4×D1911yescharacteristic
384C23×C4C22×D1911yescharacteristic
385C2×M16—384no—
386C2×M16—762no—
387C2×M16—762no—
388C22×C8—21no—
389C22×C8—21no—
390C22×C8—381no—
391C22×C8—381no—
392C2×C4⋊C4—381no—
393C2×C4⋊C4—381no—
394C2×C4⋊C4—381no—
395C2×C4⋊C4—381no—
396C2×C4⋊C4—381no—
397C2×C4⋊C4—381no—
398C2×C4⋊C4—381no—
399C2×C4⋊C4—381no—
400C2×C4⋊C4—762no—
401C2×C22⋊C4—382no—
402C2×C22⋊C4—381no—
403C2×C22⋊C4—381no—
404C2×C22⋊C4—382no—
405C2×C22⋊C4—381no—
406C2×C22⋊C4—381no—
407C2×C22⋊C4—762no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—192no—
412C22⋊C8—384no—
413C22⋊C8—381no—
414C22⋊C8—381no—
415C22⋊C8—381no—
416C22⋊C8—762no—
417C22⋊C8—762no—
418C22⋊C8D7612yes—
419#95—21no—
420#95—21no—
421#95—381no—
422#95—381no—
423C19#908511yescharacteristic, complemented, Sylow
424C24—191no—
425C24—191no—
426C24—382no—
427C24—382no—
428C24—381no—
429C24—381no—
430C24—381no—
431C24—381no—
432C24—381no—
433C24—381no—
434C24—761no—
435C24—761no—
436C24C2×C4×D1911yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—191no—
449C22×C4—191no—
450C22×C4—192no—
451C22×C4—382no—
452C22×C4—382no—
453C22×C4—382no—
454C22×C4—382no—
455C22×C4—382no—
456C22×C4—381no—
457C22×C4—381no—
458C22×C4—381no—
459C22×C4—381no—
460C22×C4—381no—
461C22×C4—381no—
462C22×C4—381no—
463C22×C4—381no—
464C22×C4—381no—
465C22×C4—381no—
466C22×C4—381no—
467C22×C4—381no—
468C22×C4—381no—
469C22×C4—381no—
470C22×C4—381no—
471C22×C4—381no—
472C22×C4—381no—
473C22×C4—381no—
474C22×C4—381no—
475C22×C4—761no—
476C22×C4—761no—
477C22×C4—761no—
478C22×C4—761no—
479C22×C4—764no—
480C22×C4—764no—
481C22×C4—764no—
482C22×C4—764no—
483C22×C4—761no—
484C22×C4—761no—
485C22×C4—761no—
486C22×C4#6451512yescomplemented
487C22×C4C2×D7611yescharacteristic
488C22×C4#6454111yescharacteristic
489C22×C4D4×D1911yescharacteristic
490C22×C4D4×D1911yescharacteristic
491C22×C4D4×D1911yescharacteristic
492C22×C4#6454511yescharacteristic
493M16—768no—
494C2×C8—22no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—382no—
501C2×C8—761no—
502C2×C8—761no—
503C2×C8—761no—
504C2×C8—761no—
505C2×C8—761no—
506C4⋊C4—762no—
507C4⋊C4—762no—
508C4⋊C4—761no—
509C4⋊C4—761no—
510C4⋊C4—761no—
511C4⋊C4—761no—
512C22⋊C4—384no—
513C22⋊C4—384no—
514C22⋊C4—762no—
515C22⋊C4—762no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—192no—
521C23—192no—
522C23—384no—
523C23—384no—
524C23—381no—
525C23—381no—
526C23—381no—
527C23—381no—
528C23—381no—
529C23—381no—
530C23—381no—
531C23—381no—
532C23—381no—
533C23—381no—
534C23—381no—
535C23—381no—
536C23—762no—
537C23—762no—
538C23—762no—
539C23—762no—
540C23—762no—
541C23—762no—
542C23—762no—
543C23—762no—
544C23—762no—
545C23—762no—
546C23—761no—
547C23—761no—
548C23—761no—
549C23—761no—
550C23C4×D7611yescharacteristic
551C23C22⋊C4×D1911yescharacteristic
552C23#1059733911yescharacteristic
553C23C2×#6451511yescharacteristic
554C23#1059734711yescharacteristic
555C23M16×D1911yescharacteristic
556C23#1059735311yescharacteristic
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—81no—
574C2×C4—81no—
575C2×C4—192no—
576C2×C4—384no—
577C2×C4—384no—
578C2×C4—381no—
579C2×C4—381no—
580C2×C4—382no—
581C2×C4—382no—
582C2×C4—381no—
583C2×C4—382no—
584C2×C4—381no—
585C2×C4—381no—
586C2×C4—762no—
587C2×C4—762no—
588C2×C4—762no—
589C2×C4—762no—
590C2×C4—762no—
591C2×C4—762no—
592C2×C4—762no—
593C2×C4—762no—
594C2×C4—761no—
595C2×C4—761no—
596C2×C4—761no—
597C2×C4—761no—
598C2×C4—761no—
599C2×C4—761no—
600C2×C4—761no—
601C2×C4—1521no—
602C2×C4—1521no—
603C2×C4#1059732811yescharacteristic
604C2×C4#1059733011yescharacteristic
605C2×C4#1059734011yescharacteristic
606C2×C4#1059734111yescharacteristic
607C8—42no—
608C8—81no—
609C8—762no—
610C8—1521no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—382no—
624C22—382no—
625C22—382no—
626C22—382no—
627C22—382no—
628C22—382no—
629C22—764no—
630C22—764no—
631C22—764no—
632C22—764no—
633C22—761no—
634C22—761no—
635C22—761no—
636C22—761no—
637C22—761no—
638C22—761no—
639C22—761no—
640C22—761no—
641C22#1192642211yescharacteristic
642C22#1192650611yescharacteristic
643C22#1192650911yescharacteristic
644C22#99×D1911yescharacteristic
645C22#99×D1911yescharacteristic
646C22#101×D1911yescharacteristic
647C22#1192652511yescharacteristic
648C22#1192661411yescharacteristic
649C22#1192661711yescharacteristic
650C22#1192662111yescharacteristic
651C22#1192662311yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—81no—
658C4—382no—
659C4—762no—
660C4—761no—
661C4—1521no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—762no—
667C2—762no—
668C2#1456196311yescharacteristic
669C2#1456197011yescharacteristic
670C2#1456198011yescharacteristic
671C2#1456199711yescharacteristic
672C2#1456393111yescharacteristic
673C2#1456408711yescharacteristic
674C2#1456410211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1280C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1280D19
hypocenterC19#9085
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
4. C2×#11926269C2semidirect
5. C2×#11926269C2semidirect
6. #14561478C2semidirect
7. C19×#1280C2semidirect
110. C22×C4×C19M16semidirect
134. C22×Dic19M16semidirect
280. #1280D19semidirect
423. C19#9085semidirect
486. C22×C4#64515semidirect

Maximal subgroups

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

subgroupindex
C2×#119265062
C2×#119264182
#145635442
C2×#119262692
#145614782
C19×#12802
#908519