Finite Group Databasebeta

← #18077917

Subgroups — #18077917

Order 4864.

964 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D19C211yesmaximal, characteristic
2C2×#11926415C211yesmaximal, characteristic
3#14563544C211yesmaximal, characteristic
4C2×#11926270C211yesmaximal, characteristic, complemented
5#14561477C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C2×C19×#324C211yesmaximal, characteristic, complemented
8C23×C4×D19C2211yescharacteristic
9C22×C8×D19—21no—
10C22×Dic19⋊C4C411yescharacteristic
11C22×(C2×D19)⋊C4C411yescharacteristic
12C22×(C2×D19)⋊C4C411yescharacteristic
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×(C2×D19)⋊C8—21no—
16C2×(C2×D19)⋊C8—21no—
17C2×(C2×D19)⋊C8—21no—
18C22⋊C8×D19—22no—
19C22⋊C8×D19—22no—
20#11926415—21no—
21#11926415—21no—
22#11926415—21no—
23#11926415—21no—
24C2×C19⋊#95C411yescharacteristic
25C2×C19⋊#95C2211yescharacteristic
26#11926270—22no—
27C22×C4⋊C4×C19C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×C22⋊C8C2211yescharacteristic
30C19×#324—22no—
31C24×D19C2×C411yescharacteristic
32C23×C4×C19C2×C411yescharacteristic
33C23×C4×C19C2×C411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C23×Dic19C2×C411yescharacteristic
36C23×Dic19C2×C411yescharacteristic
37C23×Dic19C2×C411yescharacteristic
38C22×C4×D19—21no—
39C22×C4×D19—21no—
40C22×C4×D19—21no—
41C22×C4×D19—21no—
42C22×C4×D19—42no—
43C22×C4×D19—42no—
44C22×C4×D19D411yescharacteristic
45C22×C4×D19D411yescharacteristic
46C22×C4×D19D411yescharacteristic
47C22×C4×D19D411yescharacteristic
48C22×C8×C19—21no—
49C22×C8×C19—21no—
50C2×C4⋊C4×C19—21no—
51C2×C4⋊C4×C19—21no—
52C2×C4⋊C4×C19—21no—
53C2×C4⋊C4×C19—21no—
54C2×C4⋊C4×C19—21no—
55C2×C4⋊C4×C19—21no—
56C2×(C2×D19)⋊C4—21no—
57C2×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—22no—
59C2×(C2×D19)⋊C4—21no—
60C2×(C2×D19)⋊C4—21no—
61C2×(C2×D19)⋊C4—42no—
62C2×(C2×D19)⋊C4C814yescomplemented
63C2×Dic19⋊C4—21no—
64C2×Dic19⋊C4—21no—
65C2×Dic19⋊C4—42no—
66C22×C19⋊C8—21no—
67C22×C19⋊C8—21no—
68C2×C8×D19—24no—
69C2×C8×D19—42no—
70C2×C8×D19—42no—
71C19×C22⋊C8—21no—
72C19×C22⋊C8—21no—
73C19×C22⋊C8—21no—
74C19×C22⋊C8D412yes—
75C19⋊#95—21no—
76C19⋊#95—21no—
77C19⋊#95—21no—
78C19⋊#95—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)D412yes—
83(C2×D19)⋊C8—24no—
84(C2×D19)⋊C8—42no—
85(C2×D19)⋊C8—42no—
86C24×C19C22×C411yescharacteristic
87C23×D19—21no—
88C23×D19—21no—
89C23×D19—21no—
90C23×D19—21no—
91C23×D19—22no—
92C23×D19—22no—
93C23×D19—41no—
94C23×D19—41no—
95C23×D19C22⋊C411yescharacteristic
96C23×D19C22⋊C411yescharacteristic
97C23×D19C2×C812yes—
98C23×D19M1612yes—
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—21no—
107C22×C4×C19—21no—
108C22×C4×C19—41no—
109C22×C4×C19—41no—
110C22×C4×C19—41no—
111C22×C4×C19—41no—
112C22×C4×C19C2×C812yescomplemented
113C22×C4×C19C2×D411yescharacteristic
114C22×C4×C19C2×D411yescharacteristic
115C22×C4×C19C2×D411yescharacteristic
116C22×C4×C19C2×D411yescharacteristic
117C22×C4×C19#4111yescharacteristic
118C22×C4×C19#4111yescharacteristic
119C22×Dic19—21no—
120C22×Dic19—21no—
121C22×Dic19—21no—
122C22×Dic19—21no—
123C22×Dic19—22no—
124C22×Dic19—21no—
125C22×Dic19—21no—
126C22×Dic19—21no—
127C22×Dic19—41no—
128C22×Dic19—41no—
129C22×Dic19—41no—
130C22×Dic19—41no—
131C22×Dic19—41no—
132C22×Dic19C22⋊C411yescharacteristic
133C22×Dic19C22⋊C411yescharacteristic
134C22×Dic19C2×C812yescomplemented
135C2×C4×D19—22no—
136C2×C4×D19—21no—
137C2×C4×D19—21no—
138C2×C4×D19—22no—
139C2×C4×D19—22no—
140C2×C4×D19—21no—
141C2×C4×D19—21no—
142C2×C4×D19—21no—
143C2×C4×D19—21no—
144C2×C4×D19—21no—
145C2×C4×D19—21no—
146C2×C4×D19—22no—
147C2×C4×D19—44no—
148C2×C4×D19—44no—
149C2×C4×D19—44no—
150C2×C4×D19—44no—
151C2×C4×D19—41no—
152C2×C4×D19—41no—
153C2×C4×D19—41no—
154C2×C4×D19—41no—
155C2×C8×C19—22no—
156C2×C8×C19—41no—
157C2×C8×C19—41no—
158C2×C8×C19—41no—
159C2×C8×C19—41no—
160C2×C8×C19—41no—
161C4⋊C4×C19—41no—
162C4⋊C4×C19—41no—
163C4⋊C4×C19—41no—
164C4⋊C4×C19—41no—
165(C2×D19)⋊C4—24no—
166(C2×D19)⋊C4—24no—
167(C2×D19)⋊C4—42no—
168(C2×D19)⋊C4—42no—
169Dic19⋊C4—42no—
170Dic19⋊C4—42no—
171C2×C19⋊C8—22no—
172C2×C19⋊C8—41no—
173C2×C19⋊C8—41no—
174C2×C19⋊C8—41no—
175C2×C19⋊C8—41no—
176C2×C19⋊C8—41no—
177C8×D19—48no—
178#9081—191nomaximal, Sylow
179C23×C19—21no—
180C23×C19—21no—
181C23×C19—21no—
182C23×C19—21no—
183C23×C19C2×C22⋊C411yescharacteristic
184C23×C19C4×D411yescharacteristic
185C23×C19C4×D411yescharacteristic
186C23×C19C22×C811yescharacteristic
187C23×C19C2×M1611yescharacteristic
188C23×C19#13111yescharacteristic
189C23×C19#13111yescharacteristic
190C22×D19—21no—
191C22×D19—21no—
192C22×D19—21no—
193C22×D19—21no—
194C22×D19—21no—
195C22×D19—21no—
196C22×D19—21no—
197C22×D19—21no—
198C22×D19—21no—
199C22×D19—21no—
200C22×D19—22no—
201C22×D19—22no—
202C22×D19—22no—
203C22×D19—22no—
204C22×D19—24no—
205C22×D19—24no—
206C22×D19—42no—
207C22×D19—42no—
208C22×D19—42no—
209C22×D19—42no—
210C22×D19—42no—
211C22×D19—42no—
212C22×D19—42no—
213C22×D19—42no—
214C22×D19—42no—
215C22×D19—42no—
216C22×D19C22⋊C812yes—
217C22×D19C22⋊C812yes—
218C22×D19#9912yes—
219C22×D19#10112yes—
220C2×C4×C19—21no—
221C2×C4×C19—21no—
222C2×C4×C19—21no—
223C2×C4×C19—21no—
224C2×C4×C19—22no—
225C2×C4×C19—22no—
226C2×C4×C19—22no—
227C2×C4×C19—41no—
228C2×C4×C19—41no—
229C2×C4×C19—41no—
230C2×C4×C19—41no—
231C2×C4×C19—41no—
232C2×C4×C19—41no—
233C2×C4×C19—41no—
234C2×C4×C19—41no—
235C2×C4×C19—41no—
236C2×C4×C19—41no—
237C2×C4×C19—41no—
238C2×C4×C19—81no—
239C2×C4×C19—81no—
240C2×C4×C19#12011yescharacteristic
241C2×C4×C19#12111yescharacteristic
242C2×C4×C19#12111yescharacteristic
243C2×C4×C19#12311yescharacteristic
244C2×Dic19—21no—
245C2×Dic19—21no—
246C2×Dic19—21no—
247C2×Dic19—22no—
248C2×Dic19—21no—
249C2×Dic19—21no—
250C2×Dic19—42no—
251C2×Dic19—42no—
252C2×Dic19—42no—
253C2×Dic19—41no—
254C2×Dic19—41no—
255C2×Dic19—42no—
256C2×Dic19—41no—
257C2×Dic19—41no—
258C2×Dic19—41no—
259C2×Dic19—81no—
260C2×Dic19—81no—
261C2×Dic19#9912yes—
262C4×D19—24no—
263C4×D19—24no—
264C4×D19—42no—
265C4×D19—42no—
266C4×D19—42no—
267C4×D19—42no—
268C4×D19—42no—
269C4×D19—42no—
270C8×C19—42no—
271C8×C19—81no—
272C19⋊C8—42no—
273C19⋊C8—81no—
274C22×C22⋊C8—191no—
275C2×#385—191no—
276#1779—191no—
277C2×#324—191no—
278C2×#324D1911yescharacteristic, complemented
279#1280—191no—
280#1280—191no—
281C22×C19—21no—
282C22×C19—21no—
283C22×C19—21no—
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#38611yescharacteristic
294C22×C19C2×C22⋊C811yescharacteristic
295C22×C19#40811yescharacteristic
296C22×C19C2×#9911yescharacteristic
297C22×C19C2×#9911yescharacteristic
298C22×C19C2×#10111yescharacteristic
299C22×C19#41311yescharacteristic
300C22×C19C8×D411yescharacteristic
301C22×C19C8×D411yescharacteristic
302C22×C19#43511yescharacteristic
303C22×C19#43511yescharacteristic
304C2×D19—22no—
305C2×D19—22no—
306C2×D19—22no—
307C2×D19—22no—
308C2×D19—22no—
309C2×D19—22no—
310C2×D19—22no—
311C2×D19—22no—
312C2×D19—22no—
313C2×D19—44no—
314C2×D19—44no—
315C2×D19—44no—
316C2×D19—44no—
317C2×D19—41no—
318C2×D19—41no—
319C2×D19—41no—
320C2×D19—41no—
321C2×D19#32414yescomplemented
322C4×C19—21no—
323C4×C19—21no—
324C4×C19—21no—
325C4×C19—21no—
326C4×C19—42no—
327C4×C19—81no—
328Dic19—22no—
329Dic19—41no—
330Dic19—42no—
331Dic19—81no—
332C24×C4—191no—
333C23×C8—381no—
334C22×C4⋊C4—191no—
335C22×C4⋊C4C2×D1911yescharacteristic
336C22×C22⋊C4—191no—
337C22×C22⋊C4—191no—
338C2×C22⋊C8—191no—
339C2×C22⋊C8—191no—
340C2×C22⋊C8—382no—
341C2×C22⋊C8—381no—
342C2×C22⋊C8—382no—
343C2×C22⋊C8—381no—
344C2×C22⋊C8—381no—
345C2×C22⋊C8C2×D1911yescharacteristic
346C2×C22⋊C8C2×D1911yescharacteristic
347#385—381no—
348#385—381no—
349#385—381no—
350#385—381no—
351C2×#95—191no—
352C2×#95—191no—
353#324—22no—
354#324—382no—
355C2×C19—21no—
356C2×C19—21no—
357C2×C19—21no—
358C2×C19—21no—
359C2×C19C2×#32411yescharacteristic
360C2×C19#145911yescharacteristic
361C2×C19#146811yescharacteristic
362C2×C19#147211yescharacteristic
363C2×C19#186911yescharacteristic
364C2×C19#189811yescharacteristic
365C2×C19#190111yescharacteristic
366D19—24no—
367D19—42no—
368C25—191no—
369C23×C4—191no—
370C23×C4—191no—
371C23×C4—191no—
372C23×C4—191no—
373C23×C4—191no—
374C23×C4—191no—
375C23×C4—191no—
376C23×C4—381no—
377C23×C4—381no—
378C23×C4—381no—
379C23×C4—381no—
380C23×C4—762no—
381C23×C4—762no—
382C23×C4C4×D1911yescharacteristic
383C23×C4C4×D1911yescharacteristic
384C23×C4C22×D1911yescharacteristic
385C22×C8—21no—
386C22×C8—21no—
387C22×C8—384no—
388C22×C8—381no—
389C22×C8—381no—
390C22×C8—762no—
391C22×C8—762no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—381no—
399C2×C4⋊C4—381no—
400C2×C4⋊C4—762no—
401C2×C22⋊C4—194no—
402C2×C22⋊C4—381no—
403C2×C22⋊C4—381no—
404C2×C22⋊C4—382no—
405C2×C22⋊C4—381no—
406C2×C22⋊C4—381no—
407C2×C22⋊C4—762no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—192no—
412C22⋊C8—384no—
413C22⋊C8—381no—
414C22⋊C8—381no—
415C22⋊C8—381no—
416C22⋊C8—762no—
417C22⋊C8—762no—
418C22⋊C8C22⋊D1912yes—
419#95—381no—
420#95—381no—
421#95—381no—
422#95—381no—
423C19#908111yescharacteristic, complemented, Sylow
424C24—191no—
425C24—191no—
426C24—192no—
427C24—192no—
428C24—382no—
429C24—382no—
430C24—381no—
431C24—381no—
432C24—381no—
433C24—381no—
434C24—761no—
435C24—761no—
436C24C2×C4×D1911yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—191no—
451C22×C4—191no—
452C22×C4—192no—
453C22×C4—382no—
454C22×C4—382no—
455C22×C4—382no—
456C22×C4—382no—
457C22×C4—382no—
458C22×C4—381no—
459C22×C4—381no—
460C22×C4—381no—
461C22×C4—381no—
462C22×C4—381no—
463C22×C4—381no—
464C22×C4—381no—
465C22×C4—381no—
466C22×C4—381no—
467C22×C4—381no—
468C22×C4—381no—
469C22×C4—381no—
470C22×C4—381no—
471C22×C4—381no—
472C22×C4—381no—
473C22×C4—761no—
474C22×C4—761no—
475C22×C4—761no—
476C22×C4—761no—
477C22×C4—764no—
478C22×C4—764no—
479C22×C4—764no—
480C22×C4—764no—
481C22×C4—761no—
482C22×C4—761no—
483C22×C4—761no—
484C22×C4—761no—
485C22×C4—761no—
486C22×C4C8×D1912yescomplemented
487C22×C4#6454111yescharacteristic
488C22×C4D4×D1911yescharacteristic
489C22×C4D4×D1911yescharacteristic
490C22×C4D4×D1911yescharacteristic
491C22×C4#6454311yescharacteristic
492C22×C4C2×C22⋊D1911yescharacteristic
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—382no—
500C2×C8—768no—
501C2×C8—761no—
502C2×C8—761no—
503C2×C8—761no—
504C2×C8—761no—
505C2×C8—761no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—762no—
511C4⋊C4—762no—
512C22⋊C4—384no—
513C22⋊C4—384no—
514C22⋊C4—762no—
515C22⋊C4—762no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—192no—
521C23—192no—
522C23—192no—
523C23—192no—
524C23—384no—
525C23—384no—
526C23—381no—
527C23—381no—
528C23—381no—
529C23—381no—
530C23—382no—
531C23—382no—
532C23—382no—
533C23—382no—
534C23—381no—
535C23—381no—
536C23—381no—
537C23—381no—
538C23—381no—
539C23—381no—
540C23—762no—
541C23—762no—
542C23—762no—
543C23—762no—
544C23—762no—
545C23—762no—
546C23—762no—
547C23—762no—
548C23—762no—
549C23—762no—
550C23C22⋊C4×D1911yescharacteristic
551C23(C22⋊D19)⋊C411yescharacteristic
552C23C2×C8×D1911yescharacteristic
553C23#1059734711yescharacteristic
554C23M16×D1911yescharacteristic
555C23#1059735311yescharacteristic
556C23C4×C22⋊D1911yescharacteristic
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—192no—
578C2×C4—384no—
579C2×C4—384no—
580C2×C4—381no—
581C2×C4—381no—
582C2×C4—381no—
583C2×C4—382no—
584C2×C4—381no—
585C2×C4—381no—
586C2×C4—762no—
587C2×C4—762no—
588C2×C4—762no—
589C2×C4—762no—
590C2×C4—762no—
591C2×C4—762no—
592C2×C4—762no—
593C2×C4—762no—
594C2×C4—762no—
595C2×C4—761no—
596C2×C4—761no—
597C2×C4—762no—
598C2×C4—761no—
599C2×C4—761no—
600C2×C4—761no—
601C2×C4—1521no—
602C2×C4—1521no—
603C2×C4#1059732911yescharacteristic
604C2×C4#1059733011yescharacteristic
605C2×C4#1059738311yescharacteristic
606C2×C4#1059738411yescharacteristic
607C8—42no—
608C8—81no—
609C8—762no—
610C8—1521no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—194no—
624C22—382no—
625C22—382no—
626C22—382no—
627C22—382no—
628C22—382no—
629C22—382no—
630C22—382no—
631C22—382no—
632C22—382no—
633C22—764no—
634C22—764no—
635C22—764no—
636C22—764no—
637C22—761no—
638C22—761no—
639C22—761no—
640C22—761no—
641C22#1192642011yescharacteristic
642C22C22⋊C8×D1911yescharacteristic
643C22#1192650911yescharacteristic
644C22#99×D1911yescharacteristic
645C22#99×D1911yescharacteristic
646C22#101×D1911yescharacteristic
647C22#1192652711yescharacteristic
648C22(C22⋊D19)⋊C811yescharacteristic
649C22C8×C22⋊D1911yescharacteristic
650C22#1192661311yescharacteristic
651C22#1192661811yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—81no—
658C4—382no—
659C4—762no—
660C4—761no—
661C4—1521no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—384no—
667C2—762no—
668C2D19×#32411yescharacteristic
669C2#1456195211yescharacteristic
670C2#1456198211yescharacteristic
671C2#1456199711yescharacteristic
672C2#1456392411yescharacteristic
673C2#1456408511yescharacteristic
674C2#1456410011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC23×C19C22×C8
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#9081
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. C2×#11926270C2semidirect
5. #14561477C2semidirect
6. #14561477C2semidirect
7. C2×C19×#324C2semidirect
62. C2×(C2×D19)⋊C4C8semidirect
112. C22×C4×C19C2×C8semidirect
134. C22×Dic19C2×C8semidirect
278. C2×#324D19semidirect
321. C2×D19#324semidirect
423. C19#9081semidirect
486. C22×C4C8×D19semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D192
C2×#119264152
#145635442
C2×#119262702
#145614772
C2×C19×#3242
#908119