Finite Group Databasebeta

← #18074081

Subgroups — #18074081

Order 4864.

860 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564064C211yesmaximal, characteristic, complemented
2#14564059C211yesmaximal, characteristic, complemented
3#14563928C211yesmaximal, characteristic, complemented
4#14563623C211yesmaximal, characteristic, complemented
5#14562207C211yesmaximal, characteristic, complemented
6#14562203C211yesmaximal, characteristic, complemented
7C19×#3505C211yesmaximal, characteristic
8C23×C19⋊C8C2211yescharacteristic
9C2×#10597292—21no—
10C2×#10597289—21no—
11C2×#10597291—21no—
12C2×C22⋊(C19⋊C8)—21no—
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14#11926404C2211yescharacteristic
15#11926404C2211yescharacteristic
16#11926311—21no—
17#11926306—21no—
18#11926306—21no—
19#11926299—21no—
20#11926281—22no—
21#11926278—22no—
22C19×#553—22no—
23C19×#553—21no—
24C19×#552—21no—
25C19×#551—22no—
26C19×#548—21no—
27C19×#546—21no—
28C19×#539C412yescomplemented
29C19×#538C412yescomplemented
30C19×#534—21no—
31C19×#529—21no—
32C19×#525—21no—
33C2×C19×C22⋊Q8C2211yescharacteristic
34C2×C19×#121C2211yescharacteristic
35C19×#518—21no—
36C2×C4×D4×C19C2211yescharacteristic
37C2×#41×C19—21no—
38C22×Q8×C19D411yescharacteristic
39C22×D4×C19—21no—
40C22×D4×C19D411yescharacteristic
41C22×D4×C19D411yescharacteristic
42C23×C4×C19D411yescharacteristic
43C23×C4×C19C2311yescharacteristic
44C19×#126—22no—
45C19×#126—22no—
46C19×#126—22no—
47C19×#125—21no—
48C19×#125—22no—
49C19×#124—21no—
50C19×#124—22no—
51C19×#123—22no—
52C19×#123—22no—
53C19×#123—22no—
54C19×#123—22no—
55C19×#123—22no—
56C19×C22⋊Q8—21no—
57C19×C22⋊Q8—22no—
58C19×C22⋊Q8—21no—
59C19×C22⋊Q8—21no—
60C19×C22⋊Q8C2×C412yes—
61C19×C22⋊Q8D412yes—
62C19×#121—21no—
63C19×#121—22no—
64C19×#121—22no—
65C19×#121—22no—
66C19×#121—21no—
67C19×#121—21no—
68C19×#121C2×C412yes—
69C19×#121D412yes—
70C19×#120—22no—
71C19×#120—22no—
72C4×Q8×C19—21no—
73C4×D4×C19—22no—
74C4×D4×C19—22no—
75C4×D4×C19—22no—
76C4×D4×C19—21no—
77C4×D4×C19—22no—
78C4×D4×C19—22no—
79C4×D4×C19—21no—
80C4×D4×C19—21no—
81C4×D4×C19—21no—
82C4×D4×C19—21no—
83C19×#117—22no—
84C19×#117—21no—
85C19×#117—22no—
86C2×C4⋊C4×C19—21no—
87C2×C4⋊C4×C19C2×C411yescharacteristic
88C2×C4⋊C4×C19D411yescharacteristic
89C2×C4⋊C4×C19D411yescharacteristic
90C2×C22⋊C4×C19—22no—
91C2×C22⋊C4×C19—21no—
92C2×C22⋊C4×C19—21no—
93C2×C22⋊C4×C19C2×C411yescharacteristic
94C2×C22⋊C4×C19D411yescharacteristic
95C2×C42×C19D411yescharacteristic
96C2×C22⋊Dic19—21no—
97C2×C22⋊Dic19—21no—
98C2×C4⋊Dic19—21no—
99C2×C4⋊Dic19—21no—
100C22×C19⋊C8—21no—
101C22×C19⋊C8—21no—
102C22×C19⋊C8—21no—
103C22×C19⋊C8—21no—
104C22×C19⋊C8—42no—
105#10597292—42no—
106#10597291—42no—
107#10597289—42no—
108C19⋊#95—21no—
109C19⋊#95—21no—
110C22⋊(C19⋊C8)—21no—
111C22⋊(C19⋊C8)—21no—
112C22⋊(C19⋊C8)—42no—
113C24×C19—21no—
114C24×C19C22⋊C411yescharacteristic
115C24×C19C2×D411yescharacteristic
116#41×C19—81no—
117#41×C19—81no—
118C2×Q8×C19—21no—
119C2×Q8×C19—41no—
120C2×Q8×C19—41no—
121C2×Q8×C19C22⋊C412yes—
122C2×D4×C19—22no—
123C2×D4×C19—21no—
124C2×D4×C19—21no—
125C2×D4×C19—22no—
126C2×D4×C19—21no—
127C2×D4×C19—21no—
128C2×D4×C19—21no—
129C2×D4×C19—21no—
130C2×D4×C19—22no—
131C2×D4×C19—22no—
132C2×D4×C19—21no—
133C2×D4×C19—41no—
134C2×D4×C19—41no—
135C2×D4×C19—41no—
136C2×D4×C19—41no—
137C2×D4×C19—41no—
138C2×D4×C19—41no—
139C2×D4×C19C22⋊C412yes—
140C22×C4×C19—21no—
141C22×C4×C19—22no—
142C22×C4×C19—22no—
143C22×C4×C19—21no—
144C22×C4×C19—21no—
145C22×C4×C19—21no—
146C22×C4×C19—21no—
147C22×C4×C19—41no—
148C22×C4×C19—41no—
149C22×C4×C19—41no—
150C22×C4×C19—41no—
151C22×C4×C19C22⋊C411yescharacteristic
152C22×C4×C19C22⋊C411yescharacteristic
153C22×C4×C19C22⋊C411yescharacteristic
154C22×C4×C19C22×C411yescharacteristic
155C22×C4×C19C2×D411yescharacteristic
156C22×C4×C19C2×D411yescharacteristic
157C22×C4×C19C2×D411yescharacteristic
158C22×C4×C19C2×D411yescharacteristic
159C22×C4×C19C2×D411yescharacteristic
160C22×Dic19—41no—
161C22×Dic19—41no—
162C4⋊C4×C19—22no—
163C4⋊C4×C19—22no—
164C4⋊C4×C19—22no—
165C4⋊C4×C19—22no—
166C4⋊C4×C19—22no—
167C4⋊C4×C19—21no—
168C4⋊C4×C19—21no—
169C4⋊C4×C19—22no—
170C4⋊C4×C19—21no—
171C4⋊C4×C19—21no—
172C4⋊C4×C19C22⋊C412yes—
173C4⋊C4×C19C22⋊C412yes—
174C22⋊C4×C19—22no—
175C22⋊C4×C19—22no—
176C22⋊C4×C19—22no—
177C22⋊C4×C19—22no—
178C22⋊C4×C19—22no—
179C22⋊C4×C19—22no—
180C22⋊C4×C19—22no—
181C22⋊C4×C19—21no—
182C22⋊C4×C19—22no—
183C22⋊C4×C19—21no—
184C22⋊C4×C19—22no—
185C22⋊C4×C19—21no—
186C22⋊C4×C19—21no—
187C22⋊C4×C19—22no—
188C42×C19—22no—
189C42×C19—22no—
190C42×C19—21no—
191C42×C19—21no—
192C22⋊Dic19—41no—
193C22⋊Dic19—41no—
194C22⋊Dic19—41no—
195C22⋊Dic19—41no—
196C4⋊Dic19—41no—
197C4⋊Dic19—41no—
198C4⋊Dic19—41no—
199C4⋊Dic19—41no—
200C2×C19⋊C8—22no—
201C2×C19⋊C8—22no—
202C2×C19⋊C8—22no—
203C2×C19⋊C8—41no—
204C2×C19⋊C8—41no—
205C2×C19⋊C8—41no—
206C2×C19⋊C8—41no—
207C2×C19⋊C8—41no—
208C2×C19⋊C8—41no—
209C2×C19⋊C8—41no—
210#8352—191nomaximal, Sylow
211C23×C19—21no—
212C23×C19—22no—
213C23×C19—21no—
214C23×C19—21no—
215C23×C19—41no—
216C23×C19—41no—
217C23×C19—41no—
218C23×C19—41no—
219C23×C19—41no—
220C23×C19—41no—
221C23×C19—81no—
222C23×C19—81no—
223C23×C19C2×C22⋊C411yescharacteristic
224C23×C19#12011yescharacteristic
225C23×C19#12011yescharacteristic
226C23×C19#13511yescharacteristic
227C23×C19#13511yescharacteristic
228C23×C19AGL(1,ℤ/8)11yescharacteristic
229C23×C19#13711yescharacteristic
230Q8×C19—42no—
231Q8×C19—41no—
232Q8×C19—41no—
233D4×C19—42no—
234D4×C19—42no—
235D4×C19—42no—
236D4×C19—41no—
237D4×C19—41no—
238D4×C19—42no—
239D4×C19—41no—
240D4×C19—41no—
241D4×C19—42no—
242D4×C19—41no—
243D4×C19—41no—
244D4×C19—82no—
245D4×C19—82no—
246C2×C4×C19—21no—
247C2×C4×C19—21no—
248C2×C4×C19—21no—
249C2×C4×C19—21no—
250C2×C4×C19—21no—
251C2×C4×C19—21no—
252C2×C4×C19—21no—
253C2×C4×C19—21no—
254C2×C4×C19—22no—
255C2×C4×C19—21no—
256C2×C4×C19—22no—
257C2×C4×C19—22no—
258C2×C4×C19—21no—
259C2×C4×C19—21no—
260C2×C4×C19—41no—
261C2×C4×C19—41no—
262C2×C4×C19—41no—
263C2×C4×C19—41no—
264C2×C4×C19—41no—
265C2×C4×C19—41no—
266C2×C4×C19—41no—
267C2×C4×C19—41no—
268C2×C4×C19—41no—
269C2×C4×C19—81no—
270C2×C4×C19—81no—
271C2×C4×C19—81no—
272C2×C4×C19—82no—
273C2×C4×C19—82no—
274C2×C4×C19C2×C22⋊C411yescharacteristic
275C2×C4×C19C2×C22⋊C411yescharacteristic
276C2×C4×C19#12011yescharacteristic
277C2×C4×C19#12011yescharacteristic
278C2×Dic19—81no—
279C2×Dic19—81no—
280C2×Dic19—81no—
281C2×Dic19—81no—
282C2×Dic19—81no—
283C2×Dic19—81no—
284C19⋊C8—42no—
285C19⋊C8—81no—
286#3505D1911yescharacteristic
287#1893—191no—
288#1892—191no—
289#1869—191no—
290#1799—191no—
291#1520—191no—
292#1519—191no—
293C22×C19—21no—
294C22×C19—21no—
295C22×C19—21no—
296C22×C19—21no—
297C22×C19—21no—
298C22×C19—21no—
299C22×C19—41no—
300C22×C19—41no—
301C22×C19—41no—
302C22×C19—41no—
303C22×C19—42no—
304C22×C19—42no—
305C22×C19—41no—
306C22×C19—41no—
307C22×C19—42no—
308C22×C19—41no—
309C22×C19—42no—
310C22×C19—81no—
311C22×C19—161no—
312C22×C19—161no—
313C22×C19#37911yescharacteristic
314C22×C19#41611yescharacteristic
315C22×C19#41711yescharacteristic
316C22×C19#44911yescharacteristic
317C22×C19#44911yescharacteristic
318C22×C19#45211yescharacteristic
319C22×C19#45211yescharacteristic
320C4×C19—21no—
321C4×C19—21no—
322C4×C19—21no—
323C4×C19—41no—
324C4×C19—42no—
325C4×C19—41no—
326C4×C19—42no—
327C4×C19—41no—
328C4×C19—42no—
329C4×C19B(4,𝔽2)11yescharacteristic
330C4×C19#45811yescharacteristic
331Dic19—161no—
332Dic19—161no—
333C23×C8—191no—
334#553—22no—
335#553—21no—
336#552—21no—
337#551—22no—
338#548—21no—
339#546—21no—
340#539Dic1912yescomplemented
341#538Dic1912yescomplemented
342#534—21no—
343#529—21no—
344#525—21no—
345C2×C22⋊Q8C2×D1911yescharacteristic
346C2×#121C2×D1911yescharacteristic
347#518—21no—
348C2×C4×D4C2×D1911yescharacteristic
349C2×#103—381no—
350C2×#102—381no—
351C2×#99—381no—
352C2×C22⋊C8—191no—
353C2×C22⋊C8—381no—
354#380—191no—
355#380—191no—
356#342—381no—
357#340—381no—
358#340—381no—
359#336—381no—
360#328—382no—
361#327—382no—
362C2×C19—21no—
363C2×C19—21no—
364C2×C19—21no—
365C2×C19—21no—
366C2×C19—21no—
367C2×C19—21no—
368C2×C19—81no—
369C2×C19—82no—
370C2×C19#178811yescharacteristic
371C2×C19#179011yescharacteristic
372C2×C19#179411yescharacteristic
373C2×#41—21no—
374C22×Q8C22⋊D1911yescharacteristic
375C22×D4—21no—
376C22×D4C22⋊D1911yescharacteristic
377C22×D4C22⋊D1911yescharacteristic
378C23×C4C22⋊D1911yescharacteristic
379C23×C4C22×D1911yescharacteristic
380C22×C8—381no—
381C22×C8—381no—
382C22×C8—381no—
383C22×C8—381no—
384C22×C8—762no—
385#126—22no—
386#126—22no—
387#126—22no—
388#125—21no—
389#125—22no—
390#124—21no—
391#124—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8C2×Dic1912yes—
402C22⋊Q8C22⋊D1912yes—
403#121—21no—
404#121—22no—
405#121—22no—
406#121—22no—
407#121—21no—
408#121—21no—
409#121C2×Dic1912yes—
410#121C22⋊D1912yes—
411#120—22no—
412#120—22no—
413C4×Q8—21no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—21no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424#117—22no—
425#117—21no—
426#117—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—381no—
429C2×C4⋊C4—381no—
430C2×C4⋊C4C2×Dic1911yescharacteristic
431C2×C4⋊C4C22⋊D1911yescharacteristic
432C2×C4⋊C4C22⋊D1911yescharacteristic
433C2×C22⋊C4—22no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—381no—
437C2×C22⋊C4—381no—
438C2×C22⋊C4C2×Dic1911yescharacteristic
439C2×C22⋊C4C22⋊D1911yescharacteristic
440C2×C42C22⋊D1911yescharacteristic
441#103—762no—
442#102—762no—
443#99—762no—
444C22⋊C8—381no—
445C22⋊C8—381no—
446C22⋊C8—762no—
447#95—381no—
448#95—381no—
449C19#835211yescharacteristic, complemented, Sylow
450C24—21no—
451C24C22⋊Dic1911yescharacteristic
452C24C2×C22⋊D1911yescharacteristic
453#41—81no—
454#41—81no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8C22⋊Dic1912yes—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C22⋊Dic1912yes—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—761no—
489C22×C4—761no—
490C22×C4C22⋊Dic1911yescharacteristic
491C22×C4C22⋊Dic1911yescharacteristic
492C22×C4C22⋊Dic1911yescharacteristic
493C22×C4C22×Dic1911yescharacteristic
494C22×C4C2×C22⋊D1911yescharacteristic
495C22×C4C2×C22⋊D1911yescharacteristic
496C22×C4C2×C22⋊D1911yescharacteristic
497C22×C4C2×C22⋊D1911yescharacteristic
498C22×C4C2×C22⋊D1911yescharacteristic
499C2×C8—382no—
500C2×C8—382no—
501C2×C8—382no—
502C2×C8—761no—
503C2×C8—761no—
504C2×C8—761no—
505C2×C8—761no—
506C2×C8—761no—
507C2×C8—761no—
508C2×C8—761no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—761no—
520C4⋊C4—761no—
521C4⋊C4—761no—
522C4⋊C4—761no—
523C4⋊C4C22⋊Dic1912yes—
524C4⋊C4C22⋊Dic1912yes—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—761no—
540C22⋊C4—761no—
541C22⋊C4—761no—
542C22⋊C4—761no—
543C42—22no—
544C42—22no—
545C42—21no—
546C42—21no—
547C23—21no—
548C23—21no—
549C23—22no—
550C23—21no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—81no—
558C23—81no—
559C23#1059739511yescharacteristic
560C23#1059739611yescharacteristic
561C23#1059739611yescharacteristic
562C23#1059739711yescharacteristic
563C23C2×C22⋊Dic1911yescharacteristic
564C23#1059739911yescharacteristic
565C23#1059739911yescharacteristic
566Q8—42no—
567Q8—41no—
568Q8—41no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—41no—
573D4—41no—
574D4—42no—
575D4—41no—
576D4—41no—
577D4—42no—
578D4—41no—
579D4—41no—
580D4—82no—
581D4—82no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—82no—
609C2×C4—82no—
610C2×C4—1521no—
611C2×C4—1521no—
612C2×C4—1521no—
613C2×C4—1521no—
614C2×C4—1521no—
615C2×C4—1521no—
616C2×C4C2×C22⋊Dic1911yescharacteristic
617C2×C4C2×C22⋊Dic1911yescharacteristic
618C2×C4#1059739911yescharacteristic
619C2×C4#1059739911yescharacteristic
620C8—762no—
621C8—1521no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—42no—
633C22—42no—
634C22—41no—
635C22—41no—
636C22—42no—
637C22—41no—
638C22—42no—
639C22—81no—
640C22—161no—
641C22—161no—
642C22#1192640011yescharacteristic
643C22#1192654011yescharacteristic
644C22#1192654511yescharacteristic
645C22#1192668911yescharacteristic
646C22#1192668911yescharacteristic
647C22#1192670611yescharacteristic
648C22#1192670611yescharacteristic
649C4—21no—
650C4—21no—
651C4—21no—
652C4—41no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—42no—
658C4—3041no—
659C4—3041no—
660C4#1192673111yescharacteristic
661C4#1192673411yescharacteristic
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—81no—
669C2—82no—
670C2#1456357511yescharacteristic
671C2#1456358311yescharacteristic
672C2#1456359911yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3505C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3505D19
hypocenterC19#8352
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #14564064C2semidirect
2. #14564059C2semidirect
3. #14563928C2semidirect
4. #14563623C2semidirect
5. #14562207C2semidirect
6. #14562203C2semidirect
28. C19×#539C4semidirect
29. C19×#538C4semidirect
340. #539Dic19semidirect
341. #538Dic19semidirect
449. C19#8352semidirect

Maximal subgroups

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

subgroupindex
#145640642
#145640592
#145639282
#145636232
#145622072
#145622032
C19×#35052
#835219