Finite Group Databasebeta

← #35326985

Subgroups — #35326985

Order 21248.

1846 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581751C211yesmaximal, characteristic
2C2×#19127586C212yesmaximal, complemented
3#24905732C212yesmaximal, complemented
4#24905706C212yesmaximal
5#24905700C212yesmaximal
6Dic83⋊#95C211yesmaximal, characteristic, complemented
7#24905689C211yesmaximal, characteristic, complemented
8#24905688C211yesmaximal, characteristic, complemented
9#24905686C211yesmaximal, characteristic
10#95×Dic83C211yesmaximal, characteristic, complemented
11C83×C22⋊#95C211yesmaximal, characteristic
12C2×#14581751—28no—
13C2×#14581751C418yescomplemented
14C22×C4⋊Dic83C2211yescharacteristic
15C22×C4⋊Dic83C2211yescharacteristic
16C22×Dic83⋊C4C2212yes—
17C22×C22⋊Dic83C2212yes—
18C22×C22⋊Dic83C2211yescharacteristic
19C22×C22⋊Dic83C2211yescharacteristic
20C22×C4×Dic83C2212yes—
21C22×C4×Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23#19127586—28no—
24C2×C83⋊#95C2212yes—
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C24×C4×C83C2211yescharacteristic
34C22×C22⋊C4×C83C2212yes—
35C2×#95×C83C2212yes—
36C2×#95×C83C2211yescharacteristic
37C2×#95×C83C2211yescharacteristic
38C23×Dic83C2312yes—
39C23×Dic83C2311yescharacteristic
40C23×Dic83C2311yescharacteristic
41C23×Dic83C2312yes—
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2311yescharacteristic
44#14581751—232no—
45C2×C4⋊Dic83—24no—
46C2×C4⋊Dic83C2×C414yes—
47C2×C4⋊Dic83C2×C414yes—
48C2×C4⋊Dic83D418yes—
49C2×Dic83⋊C4—24no—
50C2×Dic83⋊C4—24no—
51C2×Dic83⋊C4—42no—
52C2×C22⋊Dic83—24no—
53C2×C22⋊Dic83—24no—
54C2×C22⋊Dic83—24no—
55C2×C22⋊Dic83—24no—
56C2×C22⋊Dic83—42no—
57C2×C22⋊Dic83C2×C414yes—
58C2×C22⋊Dic83C2×C414yes—
59C2×C4×Dic83—24no—
60C2×C4×Dic83—24no—
61C2×C4×Dic83—24no—
62C2×C4×Dic83—24no—
63C2×C4×Dic83—42no—
64C2×C4×Dic83C2×C414yes—
65C2×C4×Dic83C2×C414yes—
66C83⋊#95—24no—
67C83⋊#95—24no—
68C83⋊#95—24no—
69C83⋊#95—24no—
70C83⋊#95—24no—
71C83⋊#95—22no—
72C83⋊#95—22no—
73C83⋊#95—42no—
74C83⋊#95—42no—
75C25×C83C2311yescharacteristic
76C23×C4×C83—24no—
77C23×C4×C83—24no—
78C23×C4×C83—22no—
79C23×C4×C83—22no—
80C23×C4×C83C2×C414yes—
81C23×C4×C83C2312yes—
82C23×C4×C83C2312yes—
83C23×C4×C83C2311yescharacteristic
84C23×C4×C83C2311yescharacteristic
85C2×C22⋊C4×C83—24no—
86C2×C22⋊C4×C83—24no—
87C2×C22⋊C4×C83—42no—
88#95×C83—24no—
89#95×C83—22no—
90#95×C83—22no—
91C22×Dic83—22no—
92C22×Dic83—22no—
93C22×Dic83—21no—
94C22×Dic83—21no—
95C22×Dic83—21no—
96C22×Dic83—21no—
97C22×Dic83—22no—
98C22×Dic83—22no—
99C22×Dic83—22no—
100C22×Dic83—22no—
101C22×Dic83—22no—
102C22×Dic83—22no—
103C22×Dic83—22no—
104C22×Dic83—22no—
105C22×Dic83—21no—
106C22×Dic83—21no—
107C22×Dic83—22no—
108C22×Dic83—21no—
109C22×Dic83—21no—
110C22×Dic83—22no—
111C22×Dic83—22no—
112C22×Dic83—22no—
113C22×Dic83—22no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—22no—
118C22×Dic83C22×C412yes—
119C22×Dic83C22×C412yes—
120C22×Dic83C22×C412yes—
121C22×Dic83C22×C412yes—
122C22×Dic83C2×D414yes—
123C22×Dic83C2×D414yes—
124C22×Dic83#4114yes—
125C4⋊Dic83—28no—
126C4⋊Dic83C22⋊C4116yescomplemented
127Dic83⋊C4—48no—
128C22⋊Dic83—28no—
129C22⋊Dic83—28no—
130C22⋊Dic83—48no—
131C4×Dic83—28no—
132C4×Dic83—28no—
133C4×Dic83—48no—
134C24×C83—22no—
135C24×C83—22no—
136C24×C83—21no—
137C24×C83—21no—
138C24×C83—22no—
139C24×C83—21no—
140C24×C83—21no—
141C24×C83—21no—
142C24×C83—21no—
143C24×C83C22×C412yes—
144C24×C83#4114yes—
145C24×C83C2411yescharacteristic
146C22×C4×C83—216no—
147C22×C4×C83—216no—
148C22×C4×C83—28no—
149C22×C4×C83—22no—
150C22×C4×C83—21no—
151C22×C4×C83—21no—
152C22×C4×C83—22no—
153C22×C4×C83—22no—
154C22×C4×C83—28no—
155C22×C4×C83—28no—
156C22×C4×C83—22no—
157C22×C4×C83—22no—
158C22×C4×C83—22no—
159C22×C4×C83—22no—
160C22×C4×C83—22no—
161C22×C4×C83—22no—
162C22×C4×C83—22no—
163C22×C4×C83—22no—
164C22×C4×C83—22no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83C22×C412yes—
170C22×C4×C83C22×C412yes—
171C22×C4×C83C2×D414yes—
172C22×C4×C83#4112yes—
173C22×C4×C83#4112yes—
174C22×C4×C83#4114yes—
175C22⋊C4×C83—48no—
176C23×C83—22no—
177C23×C83—22no—
178C23×C83—22no—
179C23×C83—22no—
180C23×C83—22no—
181C23×C83—22no—
182C23×C83—24no—
183C23×C83—24no—
184C23×C83—24no—
185C23×C83—24no—
186C23×C83—24no—
187C23×C83—24no—
188C23×C83—42no—
189C23×C83—42no—
190C23×C83—41no—
191C23×C83—41no—
192C23×C83—41no—
193C23×C83—41no—
194C23×C83—42no—
195C23×C83—42no—
196C23×C83—42no—
197C23×C83—42no—
198C23×C83#11714yes—
199C23×C83C23×C411yescharacteristic
200C23×C83C22×D412yes—
201C23×C83C2×#4112yes—
202C23×C83C2×#4111yescharacteristic
203C23×C83C2×#4111yescharacteristic
204C23×C83C2×#4112yes—
205C23×C83C2×#4112yes—
206C23×C83H(5,𝔽2)11yescharacteristic
207C23×C83H(5,𝔽2)11yescharacteristic
208C23×C832−1+411yescharacteristic
209C23×C832−1+411yescharacteristic
210C2×C4×C83—232no—
211C2×C4×C83—22no—
212C2×C4×C83—22no—
213C2×C4×C83—22no—
214C2×C4×C83—22no—
215C2×C4×C83—24no—
216C2×C4×C83—24no—
217C2×C4×C83—24no—
218C2×C4×C83—24no—
219C2×C4×C83—24no—
220C2×C4×C83—24no—
221C2×C4×C83—24no—
222C2×C4×C83—42no—
223C2×C4×C83—42no—
224C2×C4×C83—42no—
225C2×C4×C83—42no—
226C2×C4×C83—42no—
227C2×C4×C83—42no—
228C2×C4×C83—42no—
229C2×C4×C83—42no—
230C2×C4×C83—42no—
231C2×C4×C83—42no—
232C2×C4×C83—42no—
233C2×C4×C83C2×C22⋊C414yes—
234C2×C4×C83#11714yes—
235C2×Dic83—22no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—22no—
239C2×Dic83—24no—
240C2×Dic83—24no—
241C2×Dic83—24no—
242C2×Dic83—24no—
243C2×Dic83—22no—
244C2×Dic83—22no—
245C2×Dic83—22no—
246C2×Dic83—22no—
247C2×Dic83—22no—
248C2×Dic83—22no—
249C2×Dic83—24no—
250C2×Dic83—24no—
251C2×Dic83—24no—
252C2×Dic83—42no—
253C2×Dic83—42no—
254C2×Dic83—42no—
255C2×Dic83—42no—
256C2×Dic83—42no—
257C2×Dic83—42no—
258C2×Dic83—42no—
259C2×Dic83—42no—
260C2×Dic83—42no—
261C2×Dic83—42no—
262C2×Dic83—42no—
263C2×Dic83—42no—
264C2×Dic83—42no—
265C2×Dic83—42no—
266C2×Dic83—42no—
267C2×Dic83C2×C22⋊C414yes—
268C2×Dic83C2×C22⋊C414yes—
269C22×C83—24no—
270C22×C83—24no—
271C22×C83—24no—
272C22×C83—42no—
273C22×C83—42no—
274C22×C83—42no—
275C22×C83—44no—
276C22×C83—44no—
277C22×C83—44no—
278C22×C83—44no—
279C22×C83—42no—
280C22×C83C22×C22⋊C411yescharacteristic
281C22×C83C2×#11711yescharacteristic
282C22×C83C2×#11711yescharacteristic
283C22×C83C4×#4111yescharacteristic
284C22×C83C4×#4111yescharacteristic
285C22×C83#52011yescharacteristic
286C22×C83#52011yescharacteristic
287C22×C83#52512yes—
288C22×C83#52512yes—
289C22×C83#52912yes—
290C22×C83#52912yes—
291C22×C83#54011yescharacteristic
292C22×C83#54111yescharacteristic
293C22×C83#54211yescharacteristic
294C22×C83#54211yescharacteristic
295C22×C83#54612yes—
296C22×C83#54712yes—
297C22×C83#54812yes—
298C22×C83#55012yes—
299C22×C83#55112yes—
300C22×C83#55112yes—
301C22×C83#55212yes—
302C22×C83#55212yes—
303C4×C83—24no—
304C4×C83—24no—
305C4×C83—44no—
306C4×C83—82no—
307Dic83—24no—
308Dic83—24no—
309Dic83—42no—
310Dic83—42no—
311Dic83—44no—
312Dic83—82no—
313#13944—831nomaximal, Sylow
314C2×C83—44no—
315C2×C83#228011yescharacteristic
316C2×C83#229811yescharacteristic
317C2×C83#231411yescharacteristic
318C2×C83#233911yescharacteristic
319C2×C83#234111yescharacteristic
320C2×C83#234311yescharacteristic
321C2×C83#234311yescharacteristic
322C2×C83#247112yes—
323C2×C83#247512yes—
324C2×C83#247712yes—
325C2×C83#247912yes—
326C22×#117—831no—
327C2×#387—832no—
328#1445—832no—
329#1439—832no—
330#1437—832no—
331C4⋊#95—831no—
332#1434—831no—
333#1434—831no—
334C22⋊#95—831no—
335C22⋊#95D8311yescharacteristic
336C4×#95—831no—
337C83#1394411yescharacteristic, complemented, Sylow
338C24×C4C2×D8311yescharacteristic
339C2×#117—838no—
340C2×#117—1668no—
341C22×C4⋊C4—832no—
342C22×C4⋊C4—831no—
343C22×C4⋊C4—831no—
344C22×C22⋊C4—832no—
345C22×C22⋊C4—831no—
346C22×C22⋊C4—831no—
347C22×C22⋊C4C2×D8312yes—
348C22×C42—832no—
349C22×C42—831no—
350C22×C42—831no—
351#387—1668no—
352C2×#95—832no—
353C2×#95—832no—
354C2×#95—831no—
355C2×#95—832no—
356C2×#95—831no—
357C2×#95—832no—
358C2×#95—832no—
359C2×#95—832no—
360C2×#95—832no—
361C2×#95C2×D8311yescharacteristic
362C2×#95C2×D8311yescharacteristic
363C2×#95C2×D8312yes—
364C25C22×D8311yescharacteristic
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—831no—
370C23×C4—831no—
371C23×C4—831no—
372C23×C4—831no—
373C23×C4—832no—
374C23×C4—832no—
375C23×C4C4×D8314yes—
376C23×C4C22×D8312yes—
377C23×C4C22×D8312yes—
378C23×C4C22×D8311yescharacteristic
379C23×C4C22×D8311yescharacteristic
380#117—16632no—
381C2×C4⋊C4—3322no—
382C2×C4⋊C4—834no—
383C2×C4⋊C4—838no—
384C2×C4⋊C4—834no—
385C2×C4⋊C4—1664no—
386C2×C4⋊C4—1664no—
387C2×C4⋊C4—1664no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—3322no—
392C2×C22⋊C4—834no—
393C2×C22⋊C4—834no—
394C2×C22⋊C4—1664no—
395C2×C22⋊C4—1664no—
396C2×C22⋊C4—1664no—
397C2×C22⋊C4—1664no—
398C2×C42—3322no—
399C2×C42—834no—
400C2×C42—834no—
401C2×C42—1664no—
402C2×C42—1664no—
403C2×C42—1664no—
404C2×C42—1664no—
405#95—24no—
406#95—22no—
407#95—22no—
408#95—3322no—
409#95—3322no—
410#95—1664no—
411#95—1664no—
412#95—1664no—
413#95—1664no—
414#95—1664no—
415#95—1662no—
416#95—1662no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24C2×C4×D8312yes—
427C24#1305058914yes—
428C24C23×D8311yescharacteristic
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—832no—
453C22×C4—832no—
454C22×C4—834no—
455C22×C4—834no—
456C22×C4—832no—
457C22×C4—832no—
458C22×C4—834no—
459C22×C4—1662no—
460C22×C4—1662no—
461C22×C4—1662no—
462C22×C4—1662no—
463C22×C4—1662no—
464C22×C4—1662no—
465C22×C4—1662no—
466C22×C4—1662no—
467C22×C4—1662no—
468C22×C4—1662no—
469C22×C4—1662no—
470C22×C4—1662no—
471C22×C4—1662no—
472C22×C4—1662no—
473C22×C4—1662no—
474C22×C4—1661no—
475C22×C4—1661no—
476C22×C4—1662no—
477C22×C4—1662no—
478C22×C4—1661no—
479C22×C4—1661no—
480C22×C4—1662no—
481C22×C4—1662no—
482C22×C4—1661no—
483C22×C4—1661no—
484C22×C4—1661no—
485C22×C4—1661no—
486C22×C4C2×C4×D8312yes—
487C22×C4C2×C4×D8312yes—
488C22×C4D4×D8314yes—
489C22×C4#1305058912yes—
490C22×C4#1305058912yes—
491C22×C4#1305059014yes—
492C4⋊C4—3328no—
493C4⋊C4—8316no—
494C4⋊C4—1668no—
495C22⋊C4—48no—
496C22⋊C4—3328no—
497C22⋊C4—1668no—
498C22⋊C4—1668no—
499C42—3328no—
500C42—1668no—
501C42—1668no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—24no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23#1458174814yes—
525C23C22×C4×D8311yescharacteristic
526C23C2×D4×D8312yes—
527C23#41×D8312yes—
528C23C2×#1305058911yescharacteristic
529C23C2×#1305058912yes—
530C23C2×#1305058911yescharacteristic
531C23C2×#1305059012yes—
532C23#1458183711yescharacteristic
533C23#1458183811yescharacteristic
534C23#1458183911yescharacteristic
535C23#1458184011yescharacteristic
536C2×C4—232no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—3322no—
560C2×C4—3322no—
561C2×C4—3322no—
562C2×C4—3322no—
563C2×C4—3322no—
564C2×C4—3322no—
565C2×C4—3322no—
566C2×C4—3322no—
567C2×C4—3322no—
568C2×C4—3322no—
569C2×C4—3322no—
570C2×C4—3322no—
571C2×C4—3322no—
572C2×C4—3322no—
573C2×C4—3322no—
574C2×C4—834no—
575C2×C4—834no—
576C2×C4—1664no—
577C2×C4—1664no—
578C2×C4—1662no—
579C2×C4—1662no—
580C2×C4—1662no—
581C2×C4—1662no—
582C2×C4—1662no—
583C2×C4—1662no—
584C2×C4—1664no—
585C2×C4—1664no—
586C2×C4—1664no—
587C2×C4—1664no—
588C2×C4—1664no—
589C2×C4—1662no—
590C2×C4—1662no—
591C2×C4—1662no—
592C2×C4—1662no—
593C2×C4C22⋊C4×D8314yes—
594C2×C4#1458174814yes—
595C22—24no—
596C22—24no—
597C22—24no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—42no—
602C22—44no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22C2×C22⋊C4×D8311yescharacteristic
607C22C2×#1458174811yescharacteristic
608C22C2×#1458174811yescharacteristic
609C22#1912816911yescharacteristic
610C22C4×#1305059011yescharacteristic
611C22#1912818111yescharacteristic
612C22#1912818211yescharacteristic
613C22#1912820712yes—
614C22#1912820712yes—
615C22#1912823112yes—
616C22#1912823312yes—
617C22#1912830411yescharacteristic
618C22#1912831111yescharacteristic
619C22#1912831811yescharacteristic
620C22#1912832411yescharacteristic
621C22#1912834712yes—
622C22#1912835612yes—
623C22#1912836112yes—
624C22#1912836912yes—
625C22#1912837412yes—
626C22#1912837712yes—
627C22#1912838612yes—
628C22#1912838812yes—
629C4—24no—
630C4—24no—
631C4—44no—
632C4—82no—
633C4—3324no—
634C4—3322no—
635C4—3322no—
636C4—6642no—
637C4—1664no—
638C4—1664no—
639C2—44no—
640C2#2490984111yescharacteristic
641C2#2490995911yescharacteristic
642C2#2491007011yescharacteristic
643C2#2491029411yescharacteristic
644C2#2491030011yescharacteristic
645C2#2491031911yescharacteristic
646C2#2491032511yescharacteristic
647C2#2491157112yes—
648C2#2491163112yes—
649C2#2491166312yes—
650C2#2491169312yes—
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×C22⋊#95C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC22⋊#95D83
hypocenterC83#13944
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#19127586C2semidirect
3. #24905732C2semidirect
6. Dic83⋊#95C2semidirect
7. #24905689C2semidirect
8. #24905688C2semidirect
10. #95×Dic83C2semidirect
13. C2×#14581751C4semidirect
126. C4⋊Dic83C22⋊C4semidirect
337. C83#13944semidirect

Maximal subgroups

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

subgroupindex
C22×#145817512
C2×#191275862
#249057322
#249057062
#249057002
Dic83⋊#952
#249056892
#249056882
#249056862
#95×Dic832
C83×C22⋊#952
#1394483