Finite Group Databasebeta

← #18074050

Subgroups — #18074050

Order 4864.

1052 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564079C212yesmaximal, complemented
2#14562139C212yesmaximal, complemented
3#14561962C211yesmaximal, characteristic, complemented
4#14561872C211yesmaximal, characteristic, complemented
5C19×#3490C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C22×C4×Dic19C2211yescharacteristic, complemented
8C2×#10597294—22no—
9#11926508C2212yescomplemented
10C2×C19⋊#95—21no—
11C2×C19⋊#95C2211yescharacteristic, complemented
12#11926303—22no—
13#11926281—22no—
14#11926278—22no—
15#11926268—21no—
16#11926268—21no—
17C19×#551—22no—
18C19×#551—22no—
19C19×#546—22no—
20C19×#546—22no—
21C19×#543C411yescharacteristic, complemented
22C19×#538—21no—
23C19×#538C412yescomplemented
24C19×#534C411yescharacteristic, complemented
25C19×#525—21no—
26C19×#525C2212yes—
27C2×C19×#120—21no—
28C19×#518—21no—
29C22×C22⋊C4×C19C2211yescharacteristic
30C25×C19D411yescharacteristic
31C2×#41×C19—21no—
32C2×#41×C19D412yes—
33C22×D4×C19—21no—
34C22×D4×C19—21no—
35C22×D4×C19—21no—
36C23×C4×C19D411yescharacteristic
37C23×C4×C19C2311yescharacteristic
38C23×Dic19—21no—
39C23×Dic19—21no—
40C19×#126—22no—
41C19×#126—22no—
42C19×#124—22no—
43C19×#124—22no—
44C19×#123—22no—
45C19×#123—22no—
46C19×#123—22no—
47C19×#123—22no—
48C19×#123—22no—
49C19×C22⋊Q8—21no—
50C19×C22⋊Q8—22no—
51C19×C22⋊Q8—21no—
52C19×C22⋊Q8—22no—
53C19×C22⋊Q8C2×C412yes—
54C19×C22⋊Q8D412yes—
55C19×#121—21no—
56C19×#121—22no—
57C19×#121—22no—
58C19×#121—21no—
59C19×#121C2×C412yes—
60C19×#121D412yes—
61C19×#120—22no—
62C19×#120—22no—
63C19×#120—22no—
64C19×#120—22no—
65C19×#120—22no—
66C4×D4×C19—22no—
67C4×D4×C19—22no—
68C4×D4×C19—22no—
69C4×D4×C19—22no—
70C4×D4×C19—22no—
71C4×D4×C19—22no—
72C19×#117—22no—
73C19×#117—21no—
74C19×#117D412yes—
75C2×C22⋊C4×C19—22no—
76C2×C22⋊C4×C19—21no—
77C2×C22⋊C4×C19—21no—
78C2×C22⋊C4×C19—21no—
79C2×C22⋊C4×C19—22no—
80C2×C22⋊C4×C19—22no—
81C2×C22⋊C4×C19C2×C411yescharacteristic
82C2×C22⋊C4×C19C2×C411yescharacteristic
83C2×C22⋊C4×C19D411yescharacteristic
84C2×C22⋊C4×C19D411yescharacteristic
85C2×C22⋊Dic19—24no—
86C2×C22⋊Dic19—42no—
87C2×C22⋊Dic19—42no—
88C2×C4×Dic19—22no—
89C2×C4×Dic19—42no—
90C2×#64520—22no—
91#10597294—44no—
92C19⋊#95—22no—
93C19⋊#95—42no—
94C22⋊(C19⋊C8)—22no—
95C22⋊(C19⋊C8)—22no—
96C24×C19—21no—
97C24×C19—22no—
98C24×C19—21no—
99C24×C19—21no—
100C24×C19—41no—
101C24×C19—41no—
102C24×C19—41no—
103C24×C19—41no—
104C24×C19—41no—
105C24×C19C22⋊C411yescharacteristic
106C24×C19C22⋊C411yescharacteristic
107C24×C19C2×D411yescharacteristic
108#41×C19—42no—
109#41×C19—42no—
110#41×C19—81no—
111#41×C19—81no—
112C2×Q8×C19—21no—
113C2×Q8×C19C22⋊C412yescomplemented
114C2×D4×C19—22no—
115C2×D4×C19—22no—
116C2×D4×C19—22no—
117C2×D4×C19—22no—
118C2×D4×C19—21no—
119C2×D4×C19—22no—
120C2×D4×C19—22no—
121C2×D4×C19—42no—
122C2×D4×C19—42no—
123C2×D4×C19—81no—
124C2×D4×C19—81no—
125C2×D4×C19—81no—
126C2×D4×C19—81no—
127C2×D4×C19C22⋊C412yescomplemented
128C22×C4×C19—21no—
129C22×C4×C19—21no—
130C22×C4×C19—21no—
131C22×C4×C19—21no—
132C22×C4×C19—22no—
133C22×C4×C19—21no—
134C22×C4×C19—22no—
135C22×C4×C19—41no—
136C22×C4×C19—41no—
137C22×C4×C19—41no—
138C22×C4×C19—41no—
139C22×C4×C19C22⋊C411yescharacteristic
140C22×C4×C19C22⋊C411yescharacteristic
141C22×C4×C19C22×C411yescharacteristic
142C22×C4×C19C2×D412yes—
143C22×C4×C19C2×D412yes—
144C22×C4×C19C2×D411yescharacteristic
145C22×Dic19—22no—
146C22×Dic19—22no—
147C22×Dic19—22no—
148C22×Dic19—22no—
149C22×Dic19—41no—
150C22×Dic19—41no—
151C22×Dic19—41no—
152C22×Dic19—41no—
153C22×Dic19—41no—
154C22×Dic19—41no—
155C22×Dic19—41no—
156C22×Dic19—41no—
157C22×Dic19—41no—
158C22×Dic19—41no—
159C4⋊C4×C19—22no—
160C4⋊C4×C19—21no—
161C4⋊C4×C19—21no—
162C4⋊C4×C19—22no—
163C4⋊C4×C19—22no—
164C4⋊C4×C19—22no—
165C4⋊C4×C19C22⋊C412yescomplemented
166C4⋊C4×C19C22⋊C412yescomplemented
167C22⋊C4×C19—22no—
168C22⋊C4×C19—22no—
169C22⋊C4×C19—22no—
170C22⋊C4×C19—22no—
171C22⋊C4×C19—22no—
172C22⋊C4×C19—22no—
173C22⋊C4×C19—22no—
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—
181C42×C19—22no—
182C42×C19—22no—
183C22⋊Dic19—48no—
184C4×Dic19—24no—
185C4×Dic19—42no—
186#64520—42no—
187#64520—42no—
188C2×C19⋊C8—42no—
189#8346—191nomaximal, Sylow
190C23×C19—21no—
191C23×C19—21no—
192C23×C19—21no—
193C23×C19—21no—
194C23×C19—21no—
195C23×C19—21no—
196C23×C19—21no—
197C23×C19—21no—
198C23×C19—21no—
199C23×C19—22no—
200C23×C19—21no—
201C23×C19—21no—
202C23×C19—42no—
203C23×C19—42no—
204C23×C19—41no—
205C23×C19—41no—
206C23×C19—41no—
207C23×C19—41no—
208C23×C19—42no—
209C23×C19—42no—
210C23×C19—42no—
211C23×C19—42no—
212C23×C19—42no—
213C23×C19—41no—
214C23×C19—41no—
215C23×C19—41no—
216C23×C19—41no—
217C23×C19—81no—
218C23×C19—81no—
219C23×C19—81no—
220C23×C19—81no—
221C23×C19—81no—
222C23×C19—81no—
223C23×C19—81no—
224C23×C19—81no—
225C23×C19#10412yescomplemented
226C23×C19C2×C22⋊C411yescharacteristic
227C23×C19#12011yescharacteristic
228C23×C19#12011yescharacteristic
229Q8×C19—42no—
230Q8×C19—81no—
231D4×C19—42no—
232D4×C19—44no—
233D4×C19—42no—
234D4×C19—42no—
235D4×C19—42no—
236D4×C19—42no—
237D4×C19—42no—
238D4×C19—42no—
239D4×C19—82no—
240D4×C19—82no—
241D4×C19—81no—
242C2×C4×C19—22no—
243C2×C4×C19—22no—
244C2×C4×C19—22no—
245C2×C4×C19—21no—
246C2×C4×C19—22no—
247C2×C4×C19—22no—
248C2×C4×C19—21no—
249C2×C4×C19—41no—
250C2×C4×C19—41no—
251C2×C4×C19—42no—
252C2×C4×C19—42no—
253C2×C4×C19—41no—
254C2×C4×C19—41no—
255C2×C4×C19—41no—
256C2×C4×C19—41no—
257C2×C4×C19—82no—
258C2×C4×C19—81no—
259C2×C4×C19—81no—
260C2×C4×C19—81no—
261C2×C4×C19—82no—
262C2×C4×C19C2×C22⋊C412yes—
263C2×C4×C19#12012yes—
264C2×Dic19—24no—
265C2×Dic19—42no—
266C2×Dic19—42no—
267C2×Dic19—42no—
268C2×Dic19—42no—
269C2×Dic19—42no—
270C2×Dic19—42no—
271C2×Dic19—42no—
272C2×Dic19—42no—
273C2×Dic19—42no—
274C2×Dic19—81no—
275C2×Dic19—81no—
276C2×Dic19—81no—
277C2×Dic19—81no—
278C19⋊C8—82no—
279#3490D1911yescharacteristic
280#1896—192no—
281#1504—192no—
282#1462—191no—
283#1437—191no—
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—21no—
294C22×C19—21no—
295C22×C19—21no—
296C22×C19—21no—
297C22×C19—21no—
298C22×C19—22no—
299C22×C19—42no—
300C22×C19—42no—
301C22×C19—41no—
302C22×C19—41no—
303C22×C19—42no—
304C22×C19—41no—
305C22×C19—42no—
306C22×C19—41no—
307C22×C19—42no—
308C22×C19—41no—
309C22×C19—81no—
310C22×C19—82no—
311C22×C19—82no—
312C22×C19—82no—
313C22×C19—82no—
314C22×C19—81no—
315C22×C19—162no—
316C22×C19#37911yescharacteristic
317C22×C19C2×#10411yescharacteristic
318C22×C19#42111yescharacteristic
319C22×C19#45311yescharacteristic
320C22×C19#45511yescharacteristic
321C22×C19B(4,𝔽2)11yescharacteristic
322C22×C19#45811yescharacteristic
323C4×C19—22no—
324C4×C19—22no—
325C4×C19—41no—
326C4×C19—41no—
327C4×C19—42no—
328C4×C19—42no—
329C4×C19—42no—
330Dic19—44no—
331Dic19—82no—
332#551—22no—
333#551—22no—
334#546—22no—
335#546—22no—
336#543Dic1911yescharacteristic, complemented
337#538—21no—
338#538Dic1912yescomplemented
339#534Dic1911yescharacteristic, complemented
340#525—21no—
341#525C2×D1912yes—
342C2×#120—21no—
343#518—21no—
344C22×C22⋊C4—381no—
345C22×C22⋊C4C2×D1911yescharacteristic
346C22×C42—191no—
347C2×#104—382no—
348#407—192no—
349C2×#95—191no—
350C2×#95—381no—
351#339—382no—
352#328—382no—
353#327—382no—
354#323—381no—
355#323—381no—
356C2×C19—21no—
357C2×C19—21no—
358C2×C19—21no—
359C2×C19—21no—
360C2×C19—21no—
361C2×C19—21no—
362C2×C19—42no—
363C2×C19—81no—
364C2×C19—82no—
365C2×C19#178911yescharacteristic
366C2×C19#179011yescharacteristic
367C2×C19#179211yescharacteristic
368C25C22⋊D1911yescharacteristic
369C2×#41—21no—
370C2×#41C22⋊D1912yes—
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—21no—
374C23×C4—381no—
375C23×C4—381no—
376C23×C4C22⋊D1911yescharacteristic
377C23×C4C22×D1911yescharacteristic
378C2×M16—382no—
379#126—22no—
380#126—22no—
381#124—22no—
382#124—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386#123—22no—
387#123—22no—
388C22⋊Q8—21no—
389C22⋊Q8—22no—
390C22⋊Q8—21no—
391C22⋊Q8—22no—
392C22⋊Q8C2×Dic1912yes—
393C22⋊Q8C22⋊D1912yes—
394#121—21no—
395#121—22no—
396#121—22no—
397#121—21no—
398#121C2×Dic1912yes—
399#121C22⋊D1912yes—
400#120—22no—
401#120—22no—
402#120—22no—
403#120—22no—
404#120—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411#117—22no—
412#117—21no—
413#117C22⋊D1912yes—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—384no—
421C2×C22⋊C4—762no—
422C2×C22⋊C4—762no—
423C2×C22⋊C4C2×Dic1911yescharacteristic
424C2×C22⋊C4C2×Dic1911yescharacteristic
425C2×C22⋊C4C22⋊D1911yescharacteristic
426C2×C22⋊C4C22⋊D1911yescharacteristic
427C2×C42—382no—
428C2×C42—762no—
429#104—764no—
430C22⋊C8—382no—
431C22⋊C8—382no—
432#95—382no—
433#95—762no—
434C19#834611yescharacteristic, complemented, Sylow
435C24—21no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24—41no—
440C24—41no—
441C24—41no—
442C24—41no—
443C24—41no—
444C24C22⋊Dic1911yescharacteristic
445C24C22⋊Dic1911yescharacteristic
446C24C2×C22⋊D1911yescharacteristic
447#41—42no—
448#41—42no—
449#41—81no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8C22⋊Dic1912yescomplemented
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C22⋊Dic1912yescomplemented
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—382no—
479C22×C4—382no—
480C22×C4—382no—
481C22×C4—382no—
482C22×C4—761no—
483C22×C4—761no—
484C22×C4—761no—
485C22×C4—761no—
486C22×C4—761no—
487C22×C4—761no—
488C22×C4—761no—
489C22×C4—761no—
490C22×C4—761no—
491C22×C4—761no—
492C22×C4C22⋊Dic1911yescharacteristic
493C22×C4C22⋊Dic1911yescharacteristic
494C22×C4C22×Dic1911yescharacteristic
495C22×C4C2×C22⋊D1912yes—
496C22×C4C2×C22⋊D1912yes—
497C22×C4C2×C22⋊D1911yescharacteristic
498M16—762no—
499M16—762no—
500C2×C8—762no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4C22⋊Dic1912yescomplemented
508C4⋊C4C22⋊Dic1912yescomplemented
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—768no—
524C42—22no—
525C42—22no—
526C42—384no—
527C42—762no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—22no—
539C23—21no—
540C23—42no—
541C23—42no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—81no—
556C23—81no—
557C23—81no—
558C23—81no—
559C23—81no—
560C23—81no—
561C23—81no—
562C23—81no—
563C23#1059729412yescomplemented
564C23C2×C22⋊Dic1911yescharacteristic
565C23#1059739911yescharacteristic
566C23#1059739911yescharacteristic
567Q8—42no—
568Q8—81no—
569D4—42no—
570D4—44no—
571D4—42no—
572D4—42no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—42no—
577D4—82no—
578D4—82no—
579D4—81no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—82no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—82no—
600C2×C4—384no—
601C2×C4—762no—
602C2×C4—762no—
603C2×C4—762no—
604C2×C4—762no—
605C2×C4—762no—
606C2×C4—762no—
607C2×C4—762no—
608C2×C4—762no—
609C2×C4—762no—
610C2×C4—1521no—
611C2×C4—1521no—
612C2×C4—1521no—
613C2×C4—1521no—
614C2×C4C2×C22⋊Dic1912yes—
615C2×C4#1059739912yes—
616C8—1522no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—22no—
632C22—42no—
633C22—42no—
634C22—41no—
635C22—41no—
636C22—42no—
637C22—41no—
638C22—42no—
639C22—41no—
640C22—42no—
641C22—41no—
642C22—81no—
643C22—82no—
644C22—82no—
645C22—82no—
646C22—82no—
647C22—81no—
648C22—162no—
649C22#1192640011yescharacteristic
650C22C2×#1059729411yescharacteristic
651C22#1192656111yescharacteristic
652C22#1192671211yescharacteristic
653C22#1192672211yescharacteristic
654C22#1192673111yescharacteristic
655C22#1192673411yescharacteristic
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—42no—
661C4—42no—
662C4—42no—
663C4—764no—
664C4—1522no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—21no—
671C2—42no—
672C2—81no—
673C2—82no—
674C2#1456357911yescharacteristic
675C2#1456358311yescharacteristic
676C2#1456358911yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3490C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3490D19
hypocenterC19#8346
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3490

Complements

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

NH ≅ G/Ntype
1. #14564079C2semidirect
2. #14562139C2semidirect
3. #14561962C2semidirect
4. #14561872C2semidirect
7. C22×C4×Dic19C22semidirect
9. #11926508C22semidirect
11. C2×C19⋊#95C22semidirect
21. C19×#543C4semidirect
23. C19×#538C4semidirect
24. C19×#534C4semidirect
113. C2×Q8×C19C22⋊C4semidirect
127. C2×D4×C19C22⋊C4semidirect
165. C4⋊C4×C19C22⋊C4semidirect
166. C4⋊C4×C19C22⋊C4semidirect
225. C23×C19#104semidirect
336. #543Dic19semidirect
338. #538Dic19semidirect
339. #534Dic19semidirect
434. C19#8346semidirect
452. C2×Q8C22⋊Dic19semidirect
466. C2×D4C22⋊Dic19semidirect
507. C4⋊C4C22⋊Dic19semidirect
508. C4⋊C4C22⋊Dic19semidirect
563. C23#10597294semidirect

Maximal subgroups

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

subgroupindex
#145640792
#145621392
#145619622
#145618722
C19×#34902
#834619