Finite Group Databasebeta

← #18074364

Subgroups — #18074364

Order 4864.

900 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11927141C211yesmaximal, characteristic
2#14563952C211yesmaximal, characteristic
3#14563942C211yesmaximal, characteristic, complemented
4C2×#11926280C211yesmaximal, characteristic, complemented
5C2×#11926277C211yesmaximal, characteristic
6C2×#11926270C211yesmaximal, characteristic, complemented
7C19×#1441C211yesmaximal, characteristic, complemented
8#11927141—22no—
9#11927141—22no—
10#11927141—22no—
11#11927141C414yescomplemented
12C2×#10597344—21no—
13C2×#10597335—21no—
14C2×#10597340—21no—
15C2×#10597375—21no—
16C2×#10597370C2211yescharacteristic
17C2×#10597342—21no—
18C2×#10597376C2211yescharacteristic
19C2×C4×C22⋊D19—21no—
20C2×#10597267—21no—
21C2×#10597266—21no—
22C2×C22⋊(C19⋊C8)C2211yescharacteristic
23C2×C22⋊(C19⋊C8)C2211yescharacteristic
24#11926306—21no—
25#11926306—21no—
26#11926280—22no—
27#11926277—22no—
28#11926270—22no—
29C22×C4⋊C4×C19C2211yescharacteristic
30C22×C4⋊C4×C19C2211yescharacteristic
31C2×C19×#95—21no—
32C2×C19×#95—21no—
33C2×C19×#95C2211yescharacteristic
34C23×C4×C19—21no—
35C23×C4×C19—21no—
36C23×C4×C19D411yescharacteristic
37C23×C4×C19D411yescharacteristic
38C23×C4×C19C2311yescharacteristic
39C22×C22⋊D19—21no—
40C22×D76D411yescharacteristic
41C22×C4×D19—21no—
42C22×Dic38D411yescharacteristic
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19—42no—
50C2×C4⋊C4×C19C2×C412yes—
51C2×C4⋊C4×C19D412yes—
52C2×C22⋊Dic19—21no—
53#10597376—21no—
54#10597376—21no—
55#10597376C2×C412yes—
56#10597376D412yes—
57#10597375—24no—
58#10597375—24no—
59C4×C22⋊D19—24no—
60C4×C22⋊D19—24no—
61C2×(C2×D19)⋊C4—21no—
62C2×(C2×D19)⋊C4—21no—
63C2×(C2×D19)⋊C4—21no—
64C2×(C2×D19)⋊C4—21no—
65C2×C4⋊Dic19D411yescharacteristic
66C2×C4⋊Dic19D411yescharacteristic
67#10597370—21no—
68#10597370—21no—
69#10597370C2×C412yes—
70#10597370D412yes—
71C2×Dic19⋊C4—21no—
72C2×Dic19⋊C4—21no—
73C2×Dic19⋊C4—21no—
74C2×Dic19⋊C4—21no—
75C2×C4×Dic19—21no—
76C22×C19⋊C8—21no—
77C22×C19⋊C8—21no—
78#10597344—24no—
79#10597344—24no—
80#10597342—24no—
81#10597342—24no—
82#10597340—24no—
83#10597340—24no—
84#10597335—24no—
85#10597335—24no—
86C19×#95—21no—
87C19×#95—21no—
88C19×#95—42no—
89C19×#95—42no—
90C22⋊(C19⋊C8)—21no—
91C22⋊(C19⋊C8)—21no—
92C22⋊(C19⋊C8)—21no—
93C22⋊(C19⋊C8)—21no—
94#10597267—42no—
95#10597266—42no—
96C24×C19C2×D411yescharacteristic
97C23×D19—21no—
98C22×C4×C19—21no—
99C22×C4×C19—21no—
100C22×C4×C19—21no—
101C22×C4×C19—21no—
102C22×C4×C19—21no—
103C22×C4×C19—21no—
104C22×C4×C19—21no—
105C22×C4×C19—21no—
106C22×C4×C19—22no—
107C22×C4×C19—22no—
108C22×C4×C19—41no—
109C22×C4×C19—41no—
110C22×C4×C19—41no—
111C22×C4×C19—41no—
112C22×C4×C19—41no—
113C22×C4×C19—41no—
114C22×C4×C19—41no—
115C22×C4×C19—41no—
116C22×C4×C19—41no—
117C22×C4×C19—41no—
118C22×C4×C19—41no—
119C22×C4×C19—41no—
120C22×C4×C19—41no—
121C22×C4×C19—41no—
122C22×C4×C19—41no—
123C22×C4×C19—41no—
124C22×C4×C19C22⋊C412yes—
125C22×C4×C19C22⋊C412yes—
126C22×C4×C19C22×C411yescharacteristic
127C22×C4×C19C2×D411yescharacteristic
128C22×C4×C19C2×D411yescharacteristic
129C22×C4×C19C2×D411yescharacteristic
130C22×C4×C19C2×D411yescharacteristic
131C22×C4×C19C2×D411yescharacteristic
132C2×C22⋊D19—22no—
133C2×C22⋊D19—22no—
134C2×C22⋊D19—41no—
135C2×C22⋊D19—41no—
136C2×C22⋊D19—41no—
137C2×C22⋊D19—41no—
138C22×Dic19—21no—
139C22×Dic19—21no—
140C22×Dic19—21no—
141C2×D76—21no—
142C2×D76—41no—
143C2×D76—41no—
144C2×D76C22⋊C412yes—
145C2×C4×D19—24no—
146C2×C4×D19—81no—
147C2×C4×D19—81no—
148C2×Dic38—21no—
149C2×Dic38—41no—
150C2×Dic38—41no—
151C2×Dic38C22⋊C412yes—
152C4⋊C4×C19—22no—
153C4⋊C4×C19—22no—
154C4⋊C4×C19—22no—
155C4⋊C4×C19—22no—
156C4⋊C4×C19—22no—
157C4⋊C4×C19—22no—
158C4⋊C4×C19—41no—
159C4⋊C4×C19—41no—
160C22⋊Dic19—22no—
161C22⋊Dic19—22no—
162(C2×D19)⋊C4—24no—
163(C2×D19)⋊C4—24no—
164(C2×D19)⋊C4—24no—
165(C2×D19)⋊C4—22no—
166(C2×D19)⋊C4—22no—
167C4⋊Dic19—21no—
168C4⋊Dic19—21no—
169C4⋊Dic19C22⋊C412yes—
170C4⋊Dic19C22⋊C412yes—
171Dic19⋊C4—24no—
172Dic19⋊C4—24no—
173Dic19⋊C4—24no—
174Dic19⋊C4—22no—
175Dic19⋊C4—22no—
176C4×Dic19—24no—
177C2×C19⋊C8—41no—
178C2×C19⋊C8—41no—
179C2×C19⋊C8—41no—
180C2×C19⋊C8—41no—
181C2×C19⋊C8—41no—
182C2×C19⋊C8—41no—
183#8407—191nomaximal, Sylow
184C23×C19—21no—
185C23×C19—21no—
186C23×C19—21no—
187C23×C19—21no—
188C23×C19C2×C22⋊C411yescharacteristic
189C23×C19#12011yescharacteristic
190C23×C19#12011yescharacteristic
191C23×C19#13511yescharacteristic
192C23×C19#13511yescharacteristic
193C23×C19AGL(1,ℤ/8)11yescharacteristic
194C23×C19#13711yescharacteristic
195C22×D19—22no—
196C22×D19—41no—
197C22×D19—41no—
198C22×D19—41no—
199C22×D19—41no—
200C22×D19—41no—
201C22×D19—41no—
202C2×C4×C19—21no—
203C2×C4×C19—21no—
204C2×C4×C19—21no—
205C2×C4×C19—21no—
206C2×C4×C19—22no—
207C2×C4×C19—22no—
208C2×C4×C19—22no—
209C2×C4×C19—22no—
210C2×C4×C19—41no—
211C2×C4×C19—41no—
212C2×C4×C19—41no—
213C2×C4×C19—41no—
214C2×C4×C19—41no—
215C2×C4×C19—41no—
216C2×C4×C19—41no—
217C2×C4×C19—41no—
218C2×C4×C19—41no—
219C2×C4×C19—41no—
220C2×C4×C19—42no—
221C2×C4×C19—42no—
222C2×C4×C19—42no—
223C2×C4×C19—42no—
224C2×C4×C19—42no—
225C2×C4×C19—42no—
226C2×C4×C19—42no—
227C2×C4×C19—81no—
228C2×C4×C19—81no—
229C2×C4×C19—81no—
230C2×C4×C19—81no—
231C2×C4×C19—81no—
232C2×C4×C19—81no—
233C2×C4×C19—81no—
234C2×C4×C19—81no—
235C2×C4×C19—81no—
236C2×C4×C19C2×C22⋊C411yescharacteristic
237C2×C4×C19C2×C22⋊C411yescharacteristic
238C2×C4×C19#12011yescharacteristic
239C2×C4×C19#12011yescharacteristic
240C22⋊D19—42no—
241C22⋊D19—42no—
242C22⋊D19—42no—
243C22⋊D19—42no—
244C2×Dic19—22no—
245C2×Dic19—22no—
246C2×Dic19—22no—
247C2×Dic19—41no—
248C2×Dic19—41no—
249C2×Dic19—41no—
250C2×Dic19—41no—
251C2×Dic19—41no—
252C2×Dic19—41no—
253D76—42no—
254D76—81no—
255C4×D19—84no—
256Dic38—42no—
257Dic38—81no—
258C19⋊C8—81no—
259C19⋊C8—81no—
260C2×#539—191no—
261#1874—191no—
262#1872—191no—
263C2×#328—191no—
264C2×#327—191no—
265C2×#324—191no—
266#1441D1911yescharacteristic, 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#37911yescharacteristic
280C22×C19#41611yescharacteristic
281C22×C19#41711yescharacteristic
282C22×C19#44911yescharacteristic
283C22×C19#44911yescharacteristic
284C22×C19#45211yescharacteristic
285C22×C19#45211yescharacteristic
286C22×C19#45411yescharacteristic
287C22×C19#45611yescharacteristic
288C22×C19B(4,𝔽2)11yescharacteristic
289C22×C19#45811yescharacteristic
290C2×D19—42no—
291C2×D19—42no—
292C2×D19—42no—
293C2×D19—81no—
294C2×D19—81no—
295C2×D19—81no—
296C2×D19—81no—
297C4×C19—21no—
298C4×C19—21no—
299C4×C19—21no—
300C4×C19—21no—
301C4×C19—42no—
302C4×C19—42no—
303C4×C19—82no—
304C4×C19—82no—
305Dic19—42no—
306Dic19—42no—
307Dic19—42no—
308#539—194no—
309#539—382no—
310#539—382no—
311#539—382no—
312C2×#126—381no—
313C2×#125—381no—
314C2×#123—381no—
315C2×#123—381no—
316C2×C22⋊Q8—191no—
317C2×C22⋊Q8—381no—
318C2×#121—191no—
319C2×C4×D4—381no—
320C22×C4⋊C4C2×D1911yescharacteristic
321C22×C4⋊C4C2×D1911yescharacteristic
322C2×#103—381no—
323C2×#102—381no—
324C2×C22⋊C8—191no—
325C2×C22⋊C8—191no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95C2×D1911yescharacteristic
329#340—381no—
330#340—381no—
331#328—382no—
332#327—382no—
333#324—382no—
334C2×C19—21no—
335C2×C19—21no—
336C2×C19—21no—
337C2×C19—21no—
338C2×C19#159711yescharacteristic
339C2×C19#160311yescharacteristic
340C2×C19#160911yescharacteristic
341C2×C19#161511yescharacteristic
342C2×C19#178811yescharacteristic
343C2×C19#179011yescharacteristic
344C2×C19#179311yescharacteristic
345D19—82no—
346C22×Q8—191no—
347C22×D4—191no—
348C22×D4—381no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—381no—
352C23×C4C22⋊D1911yescharacteristic
353C23×C4C22⋊D1911yescharacteristic
354C23×C4C22×D1911yescharacteristic
355C22×C8—381no—
356C22×C8—381no—
357#126—384no—
358#126—384no—
359#125—384no—
360#125—384no—
361#123—384no—
362#123—384no—
363#123—384no—
364#123—384no—
365C22⋊Q8—192no—
366C22⋊Q8—192no—
367C22⋊Q8—384no—
368C22⋊Q8—384no—
369C22⋊Q8—381no—
370C22⋊Q8—381no—
371#121—192no—
372#121—192no—
373#121—381no—
374#121—381no—
375C4×D4—384no—
376C4×D4—384no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—191no—
385C2×C4⋊C4—191no—
386C2×C4⋊C4—381no—
387C2×C4⋊C4—381no—
388C2×C4⋊C4—381no—
389C2×C4⋊C4—381no—
390C2×C4⋊C4C4×D1912yes—
391C2×C4⋊C4D7612yes—
392C2×C22⋊C4—381no—
393C2×C22⋊C4—381no—
394C2×C22⋊C4—381no—
395C2×C22⋊C4—381no—
396C2×C22⋊C4—381no—
397C2×C42—381no—
398#103—762no—
399#102—762no—
400C22⋊C8—381no—
401C22⋊C8—381no—
402C22⋊C8—381no—
403C22⋊C8—381no—
404#95—21no—
405#95—21no—
406#95—42no—
407#95—42no—
408C19#840711yescharacteristic, complemented, Sylow
409C24—381no—
410C24C2×C22⋊D1911yescharacteristic
411C2×Q8—192no—
412C2×Q8—381no—
413C2×Q8—761no—
414C2×Q8—761no—
415C2×D4—192no—
416C2×D4—382no—
417C2×D4—382no—
418C2×D4—381no—
419C2×D4—761no—
420C2×D4—761no—
421C2×D4—761no—
422C2×D4—761no—
423C2×D4—761no—
424C2×D4—761no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—384no—
452C22×C4—381no—
453C22×C4—381no—
454C22×C4—381no—
455C22×C4—1521no—
456C22×C4—1521no—
457C22×C4(C2×D19)⋊C412yes—
458C22×C4(C2×D19)⋊C412yes—
459C22×C4C2×C4×D1911yescharacteristic
460C22×C4C2×D7611yescharacteristic
461C22×C4D4×D1911yescharacteristic
462C22×C4D4×D1911yescharacteristic
463C22×C4D4×D1911yescharacteristic
464C22×C4D4×D1911yescharacteristic
465C2×C8—761no—
466C2×C8—761no—
467C2×C8—761no—
468C2×C8—761no—
469C2×C8—761no—
470C2×C8—761no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—192no—
480C4⋊C4—192no—
481C4⋊C4—384no—
482C4⋊C4—384no—
483C4⋊C4—384no—
484C4⋊C4—382no—
485C4⋊C4—382no—
486C4⋊C4—381no—
487C4⋊C4—381no—
488C22⋊C4—384no—
489C22⋊C4—384no—
490C22⋊C4—384no—
491C22⋊C4—382no—
492C22⋊C4—382no—
493C22⋊C4—382no—
494C22⋊C4—382no—
495C42—384no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—382no—
501C23—761no—
502C23—761no—
503C23—761no—
504C23—761no—
505C23—761no—
506C23—761no—
507C23C2×(C2×D19)⋊C411yescharacteristic
508C23#1059737811yescharacteristic
509C23#1059738311yescharacteristic
510C23#1059738311yescharacteristic
511C23#1059738811yescharacteristic
512C23#1059739611yescharacteristic
513C23#1059739611yescharacteristic
514Q8—762no—
515Q8—1521no—
516D4—762no—
517D4—762no—
518D4—762no—
519D4—762no—
520D4—762no—
521D4—1521no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—382no—
557C2×C4—382no—
558C2×C4—382no—
559C2×C4—761no—
560C2×C4—761no—
561C2×C4—761no—
562C2×C4—761no—
563C2×C4—761no—
564C2×C4—761no—
565C2×C4—1524no—
566C2×C4C22⋊C4×D1911yescharacteristic
567C2×C4C22⋊C4×D1911yescharacteristic
568C2×C4#1059732811yescharacteristic
569C2×C4#1059732811yescharacteristic
570C8—1521no—
571C8—1521no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—762no—
585C22—762no—
586C22—762no—
587C22—1521no—
588C22—1521no—
589C22—1521no—
590C22—1521no—
591C22#1192639911yescharacteristic
592C22#1192653811yescharacteristic
593C22#1192654311yescharacteristic
594C22#1192668711yescharacteristic
595C22#1192668711yescharacteristic
596C22#1192670411yescharacteristic
597C22#1192670411yescharacteristic
598C22#1192671611yescharacteristic
599C22#1192672611yescharacteristic
600C22#1192673011yescharacteristic
601C22#1192673311yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—762no—
611C4—762no—
612C4—762no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—1522no—
618C2#1456256211yescharacteristic
619C2#1456259611yescharacteristic
620C2#1456263011yescharacteristic
621C2#1456266411yescharacteristic
622C2#1456357311yescharacteristic
623C2#1456358211yescharacteristic
624C2#1456359311yescharacteristic
subgroupG/H
centerC23#10597383
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1441C2
socleC23×C19#120
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1441D19
hypocenterC19#8407
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. #14563942C2semidirect
4. C2×#11926280C2semidirect
6. C2×#11926270C2semidirect
7. C19×#1441C2semidirect
11. #11927141C4semidirect
266. #1441D19semidirect
408. C19#8407semidirect

Maximal subgroups

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

subgroupindex
C2×#119271412
#145639522
#145639422
C2×#119262802
C2×#119262772
C2×#119262702
C19×#14412
#840719