Finite Group Databasebeta

← #18074810

Subgroups — #18074810

Order 4864.

912 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564472C211yesmaximal, characteristic, complemented
2#14564099C211yesmaximal, characteristic, complemented
3#14564074C211yesmaximal, characteristic, complemented
4#14563938C211yesmaximal, characteristic, complemented
5#14562178C211yesmaximal, characteristic, complemented
6#14562151C211yesmaximal, characteristic, complemented
7C19×#3537C211yesmaximal, characteristic
8C22×#64520C2211yescharacteristic, complemented
9C2×#10597294—21no—
10C2×#10597289—21no—
11C2×#10597290—21no—
12C2×#10597291—22no—
13#11926508C2211yescharacteristic, complemented
14#11926404C2211yescharacteristic, complemented
15C4×C22⋊Dic19C2211yescharacteristic, complemented
16#11926313—21no—
17#11926306—21no—
18#11926303—21no—
19#11926281—21no—
20#11926278—22no—
21#11926278—21no—
22C19×#560—22no—
23C19×#553—21no—
24C19×#553—21no—
25D42×C19—22no—
26D42×C19—21no—
27D42×C19—21no—
28C19×#540—21no—
29C19×#538—21no—
30C19×#538C412yescomplemented
31C19×#535—21no—
32C19×#534—21no—
33C19×#534C412yescomplemented
34C19×#525C2211yescharacteristic
35C2×C19×#121C2211yescharacteristic
36C2×C19×#121C2211yescharacteristic
37C2×#41×C19D411yescharacteristic
38C22×D4×C19—22no—
39C22×D4×C19—21no—
40C22×D4×C19—22no—
41C22×D4×C19—21no—
42C22×D4×C19D412yes—
43C22×D4×C19D411yescharacteristic
44C22×D4×C19D411yescharacteristic
45C23×C4×C19C2311yescharacteristic
46C19×#127—22no—
47C19×#127—21no—
48C19×#126—22no—
49C19×#126—22no—
50C19×#125—21no—
51C19×#124—22no—
52C19×#123—22no—
53C19×#123—21no—
54C19×#123—22no—
55C19×#123—22no—
56C19×#123—22no—
57C19×C22⋊Q8C2×C411yescharacteristic
58C19×C22⋊Q8D411yescharacteristic
59C19×#121—22no—
60C19×#121—21no—
61C19×#121—21no—
62C19×#121—22no—
63C19×#121—22no—
64C19×#121—22no—
65C19×#121—22no—
66C19×#121—22no—
67C19×#121—21no—
68C19×#121—21no—
69C19×#121—21no—
70C19×#121—21no—
71C19×#121—21no—
72C19×#121—21no—
73C19×#121C2×C412yes—
74C19×#121C2×C411yescharacteristic
75C19×#121D412yes—
76C19×#121D411yescharacteristic
77C19×#120—22no—
78C19×#120—22no—
79C19×#120—22no—
80C19×#120—22no—
81C19×#120—21no—
82C19×#120—22no—
83C19×#120—22no—
84C4×D4×C19—22no—
85C4×D4×C19—21no—
86C4×D4×C19—21no—
87C4×D4×C19—22no—
88C4×D4×C19—21no—
89C4×D4×C19—21no—
90C19×#117—21no—
91C19×#117D411yescharacteristic
92C2×C4⋊C4×C19D411yescharacteristic
93C2×C4⋊C4×C19D411yescharacteristic
94C2×C22⋊C4×C19—21no—
95C2×C22⋊C4×C19C2×C412yes—
96C2×C22⋊Dic19—21no—
97C2×C22⋊Dic19—21no—
98C2×C4⋊Dic19—21no—
99C2×C4×Dic19—21no—
100C2×#64520—21no—
101C2×#64520—21no—
102C2×#64520—21no—
103C2×#64520—42no—
104C22×C19⋊C8—21no—
105#10597294—42no—
106#10597291—44no—
107#10597290—42no—
108#10597289—42no—
109C19⋊#95—21no—
110C19⋊#95—21no—
111C22⋊(C19⋊C8)—21no—
112C22⋊(C19⋊C8)—21no—
113C24×C19—22no—
114C24×C19—21no—
115C24×C19C22⋊C412yes—
116C24×C19C2×D411yescharacteristic
117#41×C19—41no—
118#41×C19—41no—
119C2×Q8×C19C22⋊C411yescharacteristic
120C2×D4×C19—22no—
121C2×D4×C19—21no—
122C2×D4×C19—22no—
123C2×D4×C19—21no—
124C2×D4×C19—22no—
125C2×D4×C19—22no—
126C2×D4×C19—22no—
127C2×D4×C19—22no—
128C2×D4×C19—22no—
129C2×D4×C19—21no—
130C2×D4×C19—22no—
131C2×D4×C19—22no—
132C2×D4×C19—21no—
133C2×D4×C19—21no—
134C2×D4×C19—21no—
135C2×D4×C19—41no—
136C2×D4×C19—41no—
137C2×D4×C19—41no—
138C2×D4×C19—41no—
139C2×D4×C19—42no—
140C2×D4×C19—42no—
141C2×D4×C19—81no—
142C2×D4×C19—81no—
143C2×D4×C19—82no—
144C2×D4×C19—84no—
145C2×D4×C19—82no—
146C2×D4×C19—82no—
147C2×D4×C19C22⋊C411yescharacteristic
148C2×D4×C19C22⋊C412yes—
149C22×C4×C19—22no—
150C22×C4×C19—22no—
151C22×C4×C19—21no—
152C22×C4×C19—21no—
153C22×C4×C19—41no—
154C22×C4×C19—41no—
155C22×C4×C19C22⋊C412yes—
156C22×C4×C19C22×C411yescharacteristic
157C22×C4×C19C2×D411yescharacteristic
158C22×C4×C19C2×D411yescharacteristic
159C22×C4×C19C2×D411yescharacteristic
160C22×C4×C19C2×D411yescharacteristic
161C22×C4×C19C2×D411yescharacteristic
162C22×Dic19—41no—
163C22×Dic19—41no—
164C4⋊C4×C19—22no—
165C4⋊C4×C19—22no—
166C4⋊C4×C19—21no—
167C4⋊C4×C19—21no—
168C4⋊C4×C19—21no—
169C4⋊C4×C19—21no—
170C4⋊C4×C19—21no—
171C4⋊C4×C19C22⋊C412yes—
172C4⋊C4×C19C22⋊C411yescharacteristic
173C4⋊C4×C19C22⋊C411yescharacteristic
174C22⋊C4×C19—22no—
175C22⋊C4×C19—22no—
176C22⋊C4×C19—22no—
177C22⋊C4×C19—22no—
178C22⋊C4×C19—22no—
179C22⋊C4×C19—21no—
180C22⋊C4×C19—21no—
181C22⋊C4×C19—21no—
182C22⋊C4×C19—22no—
183C22⋊C4×C19—22no—
184C22⋊C4×C19—22no—
185C22⋊C4×C19—21no—
186C22⋊C4×C19—22no—
187C22⋊C4×C19—21no—
188C42×C19—22no—
189C42×C19—21no—
190C22⋊Dic19—22no—
191C22⋊Dic19—41no—
192C22⋊Dic19—42no—
193C4⋊Dic19—41no—
194C4⋊Dic19—41no—
195C4×Dic19—41no—
196C4×Dic19—41no—
197#64520—22no—
198#64520—22no—
199#64520—41no—
200#64520—41no—
201#64520—41no—
202#64520—41no—
203C2×C19⋊C8—22no—
204C2×C19⋊C8—41no—
205C2×C19⋊C8—41no—
206C2×C19⋊C8—41no—
207#8479—191nomaximal, Sylow
208C23×C19—21no—
209C23×C19—21no—
210C23×C19—22no—
211C23×C19—22no—
212C23×C19—21no—
213C23×C19—41no—
214C23×C19—41no—
215C23×C19—42no—
216C23×C19—42no—
217C23×C19—42no—
218C23×C19—41no—
219C23×C19—41no—
220C23×C19—81no—
221C23×C19—81no—
222C23×C19—82no—
223C23×C19—82no—
224C23×C19—82no—
225C23×C19C2×C22⋊C411yescharacteristic
226C23×C19#12011yescharacteristic
227C23×C19#12011yescharacteristic
228Q8×C19—41no—
229D4×C19—42no—
230D4×C19—41no—
231D4×C19—44no—
232D4×C19—42no—
233D4×C19—42no—
234D4×C19—41no—
235D4×C19—42no—
236D4×C19—41no—
237D4×C19—41no—
238D4×C19—41no—
239D4×C19—41no—
240D4×C19—41no—
241D4×C19—81no—
242D4×C19—82no—
243D4×C19—82no—
244D4×C19—81no—
245D4×C19—82no—
246D4×C19—82no—
247D4×C19—82no—
248D4×C19—82no—
249D4×C19—82no—
250C2×C4×C19—21no—
251C2×C4×C19—21no—
252C2×C4×C19—21no—
253C2×C4×C19—21no—
254C2×C4×C19—21no—
255C2×C4×C19—21no—
256C2×C4×C19—21no—
257C2×C4×C19—22no—
258C2×C4×C19—21no—
259C2×C4×C19—22no—
260C2×C4×C19—21no—
261C2×C4×C19—41no—
262C2×C4×C19—41no—
263C2×C4×C19—41no—
264C2×C4×C19—41no—
265C2×C4×C19—41no—
266C2×C4×C19—42no—
267C2×C4×C19—81no—
268C2×C4×C19—82no—
269C2×C4×C19—82no—
270C2×C4×C19C2×C22⋊C411yescharacteristic
271C2×C4×C19C2×C22⋊C411yescharacteristic
272C2×C4×C19#12011yescharacteristic
273C2×C4×C19#12011yescharacteristic
274C2×Dic19—42no—
275C2×Dic19—81no—
276C2×Dic19—81no—
277C2×Dic19—81no—
278C2×Dic19—81no—
279C2×Dic19—81no—
280C19⋊C8—42no—
281C19⋊C8—81no—
282#3537D1911yescharacteristic
283#1964—191no—
284#1900—191no—
285#1895—191no—
286#1871—191no—
287#1513—191no—
288#1507—191no—
289C22×C19—21no—
290C22×C19—21no—
291C22×C19—21no—
292C22×C19—21no—
293C22×C19—21no—
294C22×C19—21no—
295C22×C19—21no—
296C22×C19—21no—
297C22×C19—42no—
298C22×C19—42no—
299C22×C19—41no—
300C22×C19—42no—
301C22×C19—42no—
302C22×C19—41no—
303C22×C19—41no—
304C22×C19—42no—
305C22×C19—42no—
306C22×C19—81no—
307C22×C19—81no—
308C22×C19—161no—
309C22×C19—161no—
310C22×C19—162no—
311C22×C19—164no—
312C22×C19#37911yescharacteristic
313C22×C19#45311yescharacteristic
314C22×C19#45511yescharacteristic
315C4×C19—21no—
316C4×C19—21no—
317C4×C19—21no—
318C4×C19—42no—
319C4×C19—41no—
320C4×C19—42no—
321C4×C19—41no—
322C4×C19—41no—
323C4×C19B(4,𝔽2)11yescharacteristic
324C4×C19#45811yescharacteristic
325Dic19—82no—
326Dic19—161no—
327C22×M16—191no—
328#560—22no—
329#553—21no—
330#553—21no—
331D42—22no—
332D42—21no—
333D42—21no—
334#540—21no—
335#538—21no—
336#538Dic1912yescomplemented
337#535—21no—
338#534—21no—
339#534Dic1912yescomplemented
340#525C2×D1911yescharacteristic
341C2×#121C2×D1911yescharacteristic
342C2×#121C2×D1911yescharacteristic
343C2×#104—381no—
344C2×#102—381no—
345C2×#100—381no—
346C2×#99—382no—
347#407—191no—
348#380—191no—
349C4×C22⋊C4—191no—
350#343—381no—
351#340—381no—
352#339—381no—
353#328—381no—
354#327—382no—
355#327—381no—
356C2×C19—21no—
357C2×C19—21no—
358C2×C19—41no—
359C2×C19—41no—
360C2×C19—82no—
361C2×C19—82no—
362C2×C19—81no—
363C2×C19#179011yescharacteristic
364C2×C19#179211yescharacteristic
365C2×C19#179511yescharacteristic
366C2×#41C22⋊D1911yescharacteristic
367C22×D4—22no—
368C22×D4—21no—
369C22×D4—22no—
370C22×D4—21no—
371C22×D4C22⋊D1912yes—
372C22×D4C22⋊D1911yescharacteristic
373C22×D4C22⋊D1911yescharacteristic
374C23×C4C22×D1911yescharacteristic
375C2×M16—381no—
376C2×M16—381no—
377C2×M16—381no—
378C2×M16—762no—
379C22×C8—381no—
380#127—22no—
381#127—21no—
382#126—22no—
383#126—22no—
384#125—21no—
385#124—22no—
386#123—22no—
387#123—21no—
388#123—22no—
389#123—22no—
390#123—22no—
391C22⋊Q8C2×Dic1911yescharacteristic
392C22⋊Q8C22⋊D1911yescharacteristic
393#121—22no—
394#121—21no—
395#121—21no—
396#121—22no—
397#121—22no—
398#121—22no—
399#121—22no—
400#121—22no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121C2×Dic1912yes—
408#121C2×Dic1911yescharacteristic
409#121C22⋊D1912yes—
410#121C22⋊D1911yescharacteristic
411#120—22no—
412#120—22no—
413#120—22no—
414#120—22no—
415#120—21no—
416#120—22no—
417#120—22no—
418C4×D4—22no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—22no—
422C4×D4—21no—
423C4×D4—21no—
424#117—21no—
425#117C22⋊D1911yescharacteristic
426C2×C4⋊C4—381no—
427C2×C4⋊C4C22⋊D1911yescharacteristic
428C2×C4⋊C4C22⋊D1911yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—381no—
431C2×C22⋊C4—381no—
432C2×C22⋊C4C2×Dic1912yes—
433C2×C42—381no—
434#104—762no—
435#102—762no—
436#100—762no—
437#99—764no—
438C22⋊C8—381no—
439C22⋊C8—381no—
440#95—381no—
441#95—381no—
442C19#847911yescharacteristic, complemented, Sylow
443C24—22no—
444C24—21no—
445C24C22⋊Dic1912yes—
446C24C2×C22⋊D1911yescharacteristic
447#41—41no—
448#41—41no—
449C2×Q8C22⋊Dic1911yescharacteristic
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4—82no—
474C2×D4—84no—
475C2×D4—82no—
476C2×D4—82no—
477C2×D4C22⋊Dic1911yescharacteristic
478C2×D4C22⋊Dic1912yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—761no—
486C22×C4—761no—
487C22×C4C22⋊Dic1912yes—
488C22×C4C22×Dic1911yescharacteristic
489C22×C4C2×C22⋊D1911yescharacteristic
490C22×C4C2×C22⋊D1911yescharacteristic
491C22×C4C2×C22⋊D1911yescharacteristic
492C22×C4C2×C22⋊D1911yescharacteristic
493C22×C4C2×C22⋊D1911yescharacteristic
494M16—382no—
495M16—382no—
496M16—761no—
497M16—761no—
498M16—761no—
499M16—761no—
500C2×C8—382no—
501C2×C8—761no—
502C2×C8—761no—
503C2×C8—761no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—761no—
512C4⋊C4—761no—
513C4⋊C4C22⋊Dic1912yes—
514C4⋊C4C22⋊Dic1911yescharacteristic
515C4⋊C4C22⋊Dic1911yescharacteristic
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—382no—
531C22⋊C4—761no—
532C22⋊C4—762no—
533C42—22no—
534C42—21no—
535C42—761no—
536C42—761no—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—22no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—81no—
550C23—81no—
551C23—82no—
552C23—82no—
553C23—82no—
554C23C2×C22⋊Dic1911yescharacteristic
555C23#1059739911yescharacteristic
556C23#1059739911yescharacteristic
557Q8—41no—
558D4—42no—
559D4—41no—
560D4—44no—
561D4—42no—
562D4—42no—
563D4—41no—
564D4—42no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—81no—
571D4—82no—
572D4—82no—
573D4—81no—
574D4—82no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—82no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—81no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—762no—
600C2×C4—1521no—
601C2×C4—1521no—
602C2×C4—1521no—
603C2×C4—1521no—
604C2×C4—1521no—
605C2×C4C2×C22⋊Dic1911yescharacteristic
606C2×C4C2×C22⋊Dic1911yescharacteristic
607C2×C4#1059739911yescharacteristic
608C2×C4#1059739911yescharacteristic
609C8—762no—
610C8—1521no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—42no—
620C22—42no—
621C22—41no—
622C22—42no—
623C22—42no—
624C22—41no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—81no—
629C22—81no—
630C22—161no—
631C22—161no—
632C22—162no—
633C22—164no—
634C22#1192640011yescharacteristic
635C22#1192671211yescharacteristic
636C22#1192672211yescharacteristic
637C4—21no—
638C4—21no—
639C4—21no—
640C4—42no—
641C4—41no—
642C4—42no—
643C4—41no—
644C4—41no—
645C4—3041no—
646C4—1522no—
647C4#1192673111yescharacteristic
648C4#1192673411yescharacteristic
649C2—21no—
650C2—21no—
651C2—41no—
652C2—41no—
653C2—82no—
654C2—81no—
655C2—82no—
656C2#1456358311yescharacteristic
657C2#1456358911yescharacteristic
658C2#1456360511yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3537C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3537D19
hypocenterC19#8479
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3537

Complements

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

NH ≅ G/Ntype
1. #14564472C2semidirect
2. #14564099C2semidirect
3. #14564074C2semidirect
4. #14563938C2semidirect
5. #14562178C2semidirect
6. #14562151C2semidirect
8. C22×#64520C22semidirect
13. #11926508C22semidirect
14. #11926404C22semidirect
15. C4×C22⋊Dic19C22semidirect
30. C19×#538C4semidirect
33. C19×#534C4semidirect
336. #538Dic19semidirect
339. #534Dic19semidirect
442. C19#8479semidirect

Maximal subgroups

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

subgroupindex
#145644722
#145640992
#145640742
#145639382
#145621782
#145621512
C19×#35372
#847919