Finite Group Databasebeta

← #18075924

Subgroups — #18075924

Order 4864.

868 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566017C211yesmaximal, 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×#10597338C411yescharacteristic, complemented
10C2×#10597338C411yescharacteristic, complemented
11C22×(C2×D19)⋊C4—21no—
12C2×C22⋊(C19⋊C8)C2211yescharacteristic
13C2×(C2×D19)⋊C8—21no—
14C2×(C2×D19)⋊C8—21no—
15#11926406—21no—
16#11926404C2211yescharacteristic
17#11926401C411yescharacteristic, complemented
18#11926401C411yescharacteristic, complemented
19#11926399—21no—
20C22⋊C4×Dic19—21no—
21#11926391—21no—
22C2×C19⋊#95—21no—
23C2×C19⋊#95C2211yescharacteristic
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—42no—
37C22×C4×D19—42no—
38C22×C4×D19C2×C411yescharacteristic
39C22×C4×D19C2×C411yescharacteristic
40C22×C4×D19D411yescharacteristic
41C22×C4×D19D411yescharacteristic
42C22×C8×C19—21no—
43C2×C4⋊C4×C19C2×C411yescharacteristic
44C2×C4⋊C4×C19C2×C411yescharacteristic
45C2×C22⋊C4×C19—21no—
46C2×C22⋊Dic19—21no—
47C2×(C2×D19)⋊C4—24no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—21no—
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×C4×Dic19—21no—
57C2×C4×Dic19—21no—
58C22×C19⋊C8—21no—
59#10597338—42no—
60#10597338—42no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×#95—21no—
64C19×#95—21no—
65C19×#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—42no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74(C2×D19)⋊C8—42no—
75(C2×D19)⋊C8—42no—
76C24×C19C2×D411yescharacteristic
77C23×D19—21no—
78C23×D19—21no—
79C23×D19—22no—
80C23×D19—22no—
81C23×D19—21no—
82C23×D19—21no—
83C23×D19—21no—
84C23×D19—21no—
85C23×D19—41no—
86C23×D19—41no—
87C23×D19C22⋊C411yescharacteristic
88C23×D19C22⋊C411yescharacteristic
89C22×C4×C19—22no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
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×C19C22×C411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19#4111yescharacteristic
103C22×C4×C19#4111yescharacteristic
104C22×C4×C19#4111yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C22×Dic19—21no—
107C22×Dic19—21no—
108C22×Dic19—22no—
109C22×Dic19—22no—
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—41no—
113C22×Dic19—41no—
114C22×Dic19—41no—
115C22×Dic19—41no—
116C22×Dic19—41no—
117C22×Dic19—41no—
118C22×Dic19—41no—
119C22×Dic19C22⋊C411yescharacteristic
120C22×Dic19C22⋊C411yescharacteristic
121C2×C4×D19—22no—
122C2×C4×D19—21no—
123C2×C4×D19—21no—
124C2×C4×D19—22no—
125C2×C4×D19—22no—
126C2×C4×D19—21no—
127C2×C4×D19—21no—
128C2×C4×D19—21no—
129C2×C4×D19—21no—
130C2×C4×D19—21no—
131C2×C4×D19—21no—
132C2×C4×D19—22no—
133C2×C4×D19—44no—
134C2×C4×D19—44no—
135C2×C4×D19—44no—
136C2×C4×D19—44no—
137C2×C4×D19—41no—
138C2×C4×D19—41no—
139C2×C4×D19—41no—
140C2×C4×D19—41no—
141C2×C8×C19—41no—
142C2×C8×C19—41no—
143C2×C8×C19—41no—
144C4⋊C4×C19—41no—
145C4⋊C4×C19—41no—
146C22⋊C4×C19—41no—
147C22⋊C4×C19—41no—
148C22⋊Dic19—41no—
149C22⋊Dic19—41no—
150(C2×D19)⋊C4—42no—
151(C2×D19)⋊C4—42no—
152(C2×D19)⋊C4—48no—
153(C2×D19)⋊C4—42no—
154(C2×D19)⋊C4—42no—
155C4⋊Dic19—41no—
156C4⋊Dic19—41no—
157C4×Dic19—42no—
158C4×Dic19—42no—
159C2×C19⋊C8—41no—
160C2×C19⋊C8—41no—
161C2×C19⋊C8—41no—
162#8715—191nomaximal, Sylow
163C23×C19—21no—
164C23×C19—21no—
165C23×C19—21no—
166C23×C19—21no—
167C23×C19C2×C22⋊C411yescharacteristic
168C23×C19#12311yescharacteristic
169C23×C19#12311yescharacteristic
170C23×C19#13511yescharacteristic
171C23×C19#13511yescharacteristic
172C23×C19AGL(1,ℤ/8)11yescharacteristic
173C23×C19#13711yescharacteristic
174C22×D19—24no—
175C22×D19—24no—
176C22×D19—21no—
177C22×D19—21no—
178C22×D19—21no—
179C22×D19—21no—
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—42no—
189C22×D19—42no—
190C22×D19—42no—
191C22×D19—42no—
192C22×D19—42no—
193C22×D19—42no—
194C22×D19—42no—
195C22×D19—42no—
196C22×D19—42no—
197C22×D19—42no—
198C22×D19—41no—
199C22×D19—41no—
200C22×D19—41no—
201C22×D19—41no—
202C22×D19#9912yes—
203C22×D19#10412yes—
204C2×C4×C19—21no—
205C2×C4×C19—21no—
206C2×C4×C19—21no—
207C2×C4×C19—21no—
208C2×C4×C19—41no—
209C2×C4×C19—41no—
210C2×C4×C19—41no—
211C2×C4×C19—41no—
212C2×C4×C19—42no—
213C2×C4×C19—42no—
214C2×C4×C19—42no—
215C2×C4×C19—41no—
216C2×C4×C19—41no—
217C2×C4×C19—41no—
218C2×C4×C19—41no—
219C2×C4×C19—41no—
220C2×C4×C19—41no—
221C2×C4×C19—81no—
222C2×C4×C19—81no—
223C2×C4×C19—81no—
224C2×C4×C19—81no—
225C2×C4×C19#11711yescharacteristic
226C2×C4×C19#11711yescharacteristic
227C2×C4×C19#12311yescharacteristic
228C2×C4×C19#12311yescharacteristic
229C2×Dic19—21no—
230C2×Dic19—21no—
231C2×Dic19—21no—
232C2×Dic19—21no—
233C2×Dic19—21no—
234C2×Dic19—42no—
235C2×Dic19—42no—
236C2×Dic19—42no—
237C2×Dic19—42no—
238C2×Dic19—42no—
239C2×Dic19—41no—
240C2×Dic19—41no—
241C2×Dic19—41no—
242C2×Dic19—41no—
243C2×Dic19—41no—
244C2×Dic19—41no—
245C2×Dic19—81no—
246C2×Dic19—81no—
247C2×Dic19—81no—
248C2×Dic19—81no—
249C2×Dic19#9912yes—
250C4×D19—24no—
251C4×D19—24no—
252C4×D19—42no—
253C4×D19—42no—
254C4×D19—42no—
255C4×D19—42no—
256C4×D19—42no—
257C4×D19—42no—
258C8×C19—81no—
259C19⋊C8—81no—
260#2280—191no—
261#1779—191no—
262C22⋊#95—191no—
263#1294—191no—
264#1294—191no—
265#1294—191no—
266#1294D1911yescharacteristic, complemented
267C22×C19—21no—
268C22×C19—21no—
269C22×C19—21no—
270C22×C19—21no—
271C22×C19—21no—
272C22×C19—21no—
273C22×C19—21no—
274C22×C19—21no—
275C22×C19—21no—
276C22×C19—21no—
277C22×C19—21no—
278C22×C19—21no—
279C22×C19#38111yescharacteristic
280C22×C19C2×#9911yescharacteristic
281C22×C19C2×#9911yescharacteristic
282C22×C19#41611yescharacteristic
283C22×C19#41711yescharacteristic
284C22×C19C2×#10411yescharacteristic
285C22×C19#42111yescharacteristic
286C22×C19#48211yescharacteristic
287C22×C19#48211yescharacteristic
288C22×C19#48511yescharacteristic
289C22×C19#48511yescharacteristic
290C2×D19—22no—
291C2×D19—22no—
292C2×D19—22no—
293C2×D19—22no—
294C2×D19—22no—
295C2×D19—22no—
296C2×D19—44no—
297C2×D19—44no—
298C2×D19—44no—
299C2×D19—44no—
300C2×D19—41no—
301C2×D19—41no—
302C2×D19—41no—
303C2×D19—41no—
304C2×D19—41no—
305C2×D19—41no—
306C2×D19—41no—
307C2×D19—41no—
308C4×C19—21no—
309C4×C19—21no—
310C4×C19—21no—
311C4×C19—21no—
312C4×C19—82no—
313C4×C19—81no—
314C4×C19—81no—
315Dic19—22no—
316Dic19—41no—
317Dic19—82no—
318Dic19—81no—
319Dic19—81no—
320C24×C4—191no—
321C2×#117—191no—
322C2×#117—191no—
323C22×C22⋊C4—381no—
324C2×C22⋊C8—191no—
325C2×C22⋊C8—381no—
326C2×C22⋊C8—381no—
327C2×C22⋊C8C2×D1911yescharacteristic
328#381—381no—
329#380—191no—
330#380—191no—
331#380—191no—
332#380C2×D1911yescharacteristic
333#379—381no—
334C4×C22⋊C4—381no—
335C4×C22⋊C4—381no—
336C2×#95—191no—
337C2×#95—381no—
338C2×#95C2×D1911yescharacteristic
339C2×C19—21no—
340C2×C19—21no—
341C2×C19—21no—
342C2×C19—21no—
343C2×C19#150111yescharacteristic
344C2×C19#150411yescharacteristic
345C2×C19#151311yescharacteristic
346C2×C19#151611yescharacteristic
347C2×C19#181911yescharacteristic
348C2×C19#182511yescharacteristic
349C2×C19#182611yescharacteristic
350D19—42no—
351D19—42no—
352C25—191no—
353C23×C4—21no—
354C23×C4—191no—
355C23×C4—191no—
356C23×C4—191no—
357C23×C4—191no—
358C23×C4—191no—
359C23×C4—381no—
360C23×C4—381no—
361C23×C4—381no—
362C23×C4—381no—
363C23×C4—381no—
364C23×C4—762no—
365C23×C4—762no—
366C23×C4C22×D1911yescharacteristic
367C22×C8—21no—
368C22×C8—381no—
369#117—762no—
370#117—762no—
371C2×C4⋊C4—191no—
372C2×C4⋊C4—191no—
373C2×C4⋊C4C4×D1911yescharacteristic
374C2×C4⋊C4C4×D1911yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—381no—
377C2×C22⋊C4—381no—
378C2×C22⋊C4—381no—
379C2×C22⋊C4—381no—
380C2×C22⋊C4—384no—
381C2×C22⋊C4—381no—
382C2×C22⋊C4—762no—
383C2×C22⋊C4—762no—
384C2×C42—381no—
385C2×C42—381no—
386C22⋊C8—21no—
387C22⋊C8—21no—
388C22⋊C8—381no—
389C22⋊C8—381no—
390C22⋊C8—762no—
391C22⋊C8—762no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—381no—
396#95—381no—
397#95—381no—
398#95—381no—
399#95—381no—
400#95—762no—
401C19#871511yescharacteristic, complemented, Sylow
402C24—191no—
403C24—191no—
404C24—382no—
405C24—382no—
406C24—381no—
407C24—381no—
408C24—381no—
409C24—381no—
410C24—381no—
411C24—381no—
412C24—761no—
413C24—761no—
414C24D4×D1911yescharacteristic
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—191no—
427C22×C4—191no—
428C22×C4—382no—
429C22×C4—382no—
430C22×C4—382no—
431C22×C4—382no—
432C22×C4—382no—
433C22×C4—381no—
434C22×C4—381no—
435C22×C4—381no—
436C22×C4—381no—
437C22×C4—381no—
438C22×C4—381no—
439C22×C4—381no—
440C22×C4—381no—
441C22×C4—381no—
442C22×C4—381no—
443C22×C4—382no—
444C22×C4—381no—
445C22×C4—381no—
446C22×C4—761no—
447C22×C4—761no—
448C22×C4—761no—
449C22×C4—761no—
450C22×C4—764no—
451C22×C4—764no—
452C22×C4—764no—
453C22×C4—764no—
454C22×C4—761no—
455C22×C4—761no—
456C22×C4—761no—
457C22×C4—761no—
458C22×C4—761no—
459C22×C4—761no—
460C22×C4—761no—
461C22×C4C2×C4×D1911yescharacteristic
462C22×C4#6454111yescharacteristic
463C22×C4#6454111yescharacteristic
464C22×C4D4×D1911yescharacteristic
465C22×C4#6454311yescharacteristic
466C22×C4#6454511yescharacteristic
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—761no—
471C2×C8—761no—
472C2×C8—761no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—761no—
476C4⋊C4—761no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—762no—
480C22⋊C4—762no—
481C22⋊C4—762no—
482C22⋊C4—768no—
483C22⋊C4—762no—
484C22⋊C4—761no—
485C22⋊C4—761no—
486C42—762no—
487C42—762no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—192no—
493C23—192no—
494C23—384no—
495C23—384no—
496C23—381no—
497C23—381no—
498C23—381no—
499C23—381no—
500C23—381no—
501C23—381no—
502C23—381no—
503C23—381no—
504C23—381no—
505C23—381no—
506C23—381no—
507C23—381no—
508C23—762no—
509C23—762no—
510C23—762no—
511C23—762no—
512C23—762no—
513C23—762no—
514C23—762no—
515C23—762no—
516C23—762no—
517C23—762no—
518C23—761no—
519C23—761no—
520C23—761no—
521C23—761no—
522C23C22⋊C4×D1911yescharacteristic
523C23#1059732911yescharacteristic
524C23#1059734011yescharacteristic
525C23#1059735811yescharacteristic
526C23#1059736011yescharacteristic
527C23#1059736211yescharacteristic
528C23#1059736411yescharacteristic
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—192no—
551C2×C4—384no—
552C2×C4—384no—
553C2×C4—381no—
554C2×C4—381no—
555C2×C4—381no—
556C2×C4—381no—
557C2×C4—381no—
558C2×C4—762no—
559C2×C4—762no—
560C2×C4—762no—
561C2×C4—762no—
562C2×C4—762no—
563C2×C4—762no—
564C2×C4—762no—
565C2×C4—762no—
566C2×C4—762no—
567C2×C4—762no—
568C2×C4—762no—
569C2×C4—761no—
570C2×C4—761no—
571C2×C4—761no—
572C2×C4—761no—
573C2×C4—761no—
574C2×C4—761no—
575C2×C4—1521no—
576C2×C4—1521no—
577C2×C4—1521no—
578C2×C4—1521no—
579C2×C4#1059731811yescharacteristic
580C2×C4#1059732911yescharacteristic
581C2×C4#1059733811yescharacteristic
582C2×C4#1059734011yescharacteristic
583C8—81no—
584C8—1521no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—382no—
598C22—382no—
599C22—382no—
600C22—382no—
601C22—382no—
602C22—382no—
603C22—764no—
604C22—764no—
605C22—764no—
606C22—764no—
607C22—761no—
608C22—761no—
609C22—761no—
610C22—761no—
611C22—761no—
612C22—761no—
613C22—761no—
614C22—761no—
615C22#1192640611yescharacteristic
616C22#99×D1911yescharacteristic
617C22#99×D1911yescharacteristic
618C22#1192653711yescharacteristic
619C22#1192654411yescharacteristic
620C22#104×D1911yescharacteristic
621C22#1192655911yescharacteristic
622C22#1192686611yescharacteristic
623C22#1192687011yescharacteristic
624C22#1192688311yescharacteristic
625C22#1192688711yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—82no—
631C4—81no—
632C4—81no—
633C4—382no—
634C4—761no—
635C4—1522no—
636C4—1521no—
637C4—1521no—
638C2—21no—
639C2—21no—
640C2—21no—
641C2—21no—
642C2—762no—
643C2—762no—
644C2#1456212311yescharacteristic
645C2#1456213811yescharacteristic
646C2#1456217711yescharacteristic
647C2#1456218811yescharacteristic
648C2#1456370811yescharacteristic
649C2#1456372811yescharacteristic
650C2#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#8715
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×#10597338C4semidirect
10. C2×#10597338C4semidirect
17. #11926401C4semidirect
18. #11926401C4semidirect
266. #1294D19semidirect
401. C19#8715semidirect

Maximal subgroups

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

subgroupindex
#145660172
#145635442
(C2×D19)⋊#952
#145615152
#145615142
#145615132
C19×#12942
#871519