Finite Group Databasebeta

← #35325733

Subgroups — #35325733

Order 21248.

1710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127590C212yesmaximal
2C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
3#24905701C212yesmaximal
4#24905696C212yesmaximal, complemented
5Dic83⋊#95C211yesmaximal, characteristic, complemented
6#24905689C211yesmaximal, characteristic, complemented
7#24905688C212yesmaximal, complemented
8(C2×D83)⋊#95C211yesmaximal, characteristic
9(C2×D83)⋊#95C211yesmaximal, characteristic
10C4×C83⋊#95C211yesmaximal, characteristic, complemented
11C4×#95×C83C211yesmaximal, characteristic, complemented
12C23×C4×D83C2211yescharacteristic
13C22×Dic83⋊C4C2212yes—
14C22×(C2×D83)⋊C4C2211yescharacteristic
15C22×(C2×D83)⋊C4C2212yes—
16C22×(C2×D83)⋊C4C2212yes—
17C22×(C2×D83)⋊C4C2211yescharacteristic
18C22×C4×Dic83C2211yescharacteristic
19C22×C4×Dic83C2212yes—
20#19127590C4116yescomplemented
21C4×(C2×D83)⋊C4C418yescomplemented
22C2×C83⋊#95C2211yescharacteristic
23C2×C83⋊#95C2211yescharacteristic
24C2×C83⋊#95C2212yes—
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2212yes—
32C22×C42×C83C2212yes—
33C22×C42×C83C2211yescharacteristic
34C2×#95×C83C2211yescharacteristic
35C2×#95×C83C2211yescharacteristic
36C2×#95×C83C2212yes—
37C24×D83C2311yescharacteristic
38C23×Dic83C2312yes—
39C23×Dic83C2312yes—
40C23×Dic83C2311yescharacteristic
41C23×Dic83C2311yescharacteristic
42C23×Dic83C2311yescharacteristic
43C22×C4×D83—22no—
44C22×C4×D83—22no—
45C22×C4×D83—42no—
46C22×C4×D83—42no—
47C22×C4×D83C2×C414yes—
48C2×Dic83⋊C4—42no—
49C2×Dic83⋊C4—42no—
50C2×Dic83⋊C4C2×C418yescomplemented
51C2×(C2×D83)⋊C4—24no—
52C2×(C2×D83)⋊C4—42no—
53C2×(C2×D83)⋊C4—42no—
54C2×(C2×D83)⋊C4—42no—
55C2×(C2×D83)⋊C4—42no—
56C2×(C2×D83)⋊C4C2×C414yes—
57C2×(C2×D83)⋊C4C2×C418yes—
58C2×(C2×D83)⋊C4C2×C418yes—
59C2×(C2×D83)⋊C4C2×C418yes—
60C2×(C2×D83)⋊C4C2×C414yes—
61C2×C4×Dic83—42no—
62C2×C4×Dic83—42no—
63C2×C4×Dic83—42no—
64C2×C4×Dic83C2×C414yes—
65C2×C4×Dic83C2×C418yescomplemented
66C83⋊#95—22no—
67C83⋊#95—22no—
68C83⋊#95—24no—
69C83⋊#95—42no—
70C83⋊#95—42no—
71C83⋊#95—42no—
72C83⋊#95—42no—
73C83⋊#95C2×C414yes—
74C83⋊#95C2×C414yes—
75C83⋊#95C2×C418yescomplemented
76C23×C4×C83C2312yes—
77C23×C4×C83C2312yes—
78C23×C4×C83C2311yescharacteristic
79C23×C4×C83C2311yescharacteristic
80C23×C4×C83C2311yescharacteristic
81C2×C42×C83—24no—
82C2×C42×C83—42no—
83C2×C42×C83—42no—
84C2×C42×C83—42no—
85C2×C42×C83C2×C414yes—
86#95×C83—22no—
87#95×C83—22no—
88#95×C83C2×C418yescomplemented
89C23×D83—21no—
90C23×D83—21no—
91C23×D83—22no—
92C23×D83—22no—
93C23×D83—22no—
94C23×D83—21no—
95C23×D83—21no—
96C23×D83—21no—
97C23×D83—21no—
98C23×D83C22×C412yes—
99C23×D83C22×C414yes—
100C22×Dic83—22no—
101C22×Dic83—21no—
102C22×Dic83—21no—
103C22×Dic83—21no—
104C22×Dic83—21no—
105C22×Dic83—22no—
106C22×Dic83—22no—
107C22×Dic83—22no—
108C22×Dic83—22no—
109C22×Dic83—22no—
110C22×Dic83—22no—
111C22×Dic83—22no—
112C22×Dic83—22no—
113C22×Dic83—21no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—22no—
118C22×Dic83—22no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—21no—
122C22×Dic83—22no—
123C22×Dic83C22×C412yes—
124C22×Dic83C22×C412yes—
125C22×Dic83C22×C414yes—
126C22×Dic83C22×C414yes—
127C22×Dic83C22×C412yes—
128C22×Dic83C22×C414yes—
129C2×C4×D83—28no—
130C2×C4×D83—44no—
131C2×C4×D83—44no—
132C2×C4×D83—48no—
133C2×C4×D83—48no—
134Dic83⋊C4—48no—
135(C2×D83)⋊C4—28no—
136(C2×D83)⋊C4—48no—
137(C2×D83)⋊C4—48no—
138(C2×D83)⋊C4C42116yescomplemented
139C4×Dic83—44no—
140C4×Dic83—48no—
141C24×C83C2411yescharacteristic
142C22×C4×C83—22no—
143C22×C4×C83—22no—
144C22×C4×C83—22no—
145C22×C4×C83—21no—
146C22×C4×C83—22no—
147C22×C4×C83—21no—
148C22×C4×C83—21no—
149C22×C4×C83—21no—
150C22×C4×C83—22no—
151C22×C4×C83—22no—
152C22×C4×C83—22no—
153C22×C4×C83—22no—
154C22×C4×C83—22no—
155C22×C4×C83—22no—
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×C83C22×C414yes—
163C22×C4×C83C22×C414yes—
164C22×C4×C83C22×C414yes—
165C22×C4×C83C22×C412yes—
166C22×C4×C83C22×C412yes—
167C22×C4×C83C22×C412yes—
168C22×C4×C83#4112yes—
169C22×C4×C83#4112yes—
170C22×C4×C83#4114yes—
171C42×C83—44no—
172C42×C83—48no—
173C23×C83C23×C411yescharacteristic
174C23×C83C23×C412yes—
175C23×C83C2×#4111yescharacteristic
176C23×C83C2×#4111yescharacteristic
177C23×C83C2×#4112yes—
178C23×C83H(5,𝔽2)12yes—
179C23×C83H(5,𝔽2)11yescharacteristic
180C23×C83H(5,𝔽2)12yes—
181C23×C83H(5,𝔽2)11yescharacteristic
182C23×C832−1+411yescharacteristic
183C23×C832−1+411yescharacteristic
184C22×D83—22no—
185C22×D83—22no—
186C22×D83—24no—
187C22×D83—24no—
188C22×D83—24no—
189C22×D83—24no—
190C22×D83—22no—
191C22×D83—22no—
192C22×D83—24no—
193C22×D83—22no—
194C22×D83—22no—
195C22×D83—24no—
196C22×D83—42no—
197C22×D83—42no—
198C22×D83—42no—
199C22×D83—42no—
200C22×D83—41no—
201C22×D83—42no—
202C22×D83—41no—
203C22×D83—42no—
204C22×D83—41no—
205C22×D83—41no—
206C22×D83C2×C4214yes—
207C2×C4×C83—22no—
208C2×C4×C83—22no—
209C2×C4×C83—22no—
210C2×C4×C83—24no—
211C2×C4×C83—22no—
212C2×C4×C83—24no—
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—24no—
223C2×C4×C83—24no—
224C2×C4×C83—24no—
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×C4214yes—
234C2×C4×C83#11714yes—
235C2×C4×C83#11714yes—
236C2×Dic83—22no—
237C2×Dic83—24no—
238C2×Dic83—22no—
239C2×Dic83—24no—
240C2×Dic83—22no—
241C2×Dic83—22no—
242C2×Dic83—24no—
243C2×Dic83—24no—
244C2×Dic83—24no—
245C2×Dic83—24no—
246C2×Dic83—22no—
247C2×Dic83—24no—
248C2×Dic83—22no—
249C2×Dic83—22no—
250C2×Dic83—22no—
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×Dic83C2×C4214yes—
265C4×D83—416no—
266C22×C83C22×C4211yescharacteristic
267C22×C83C2×#11711yescharacteristic
268C22×C83C2×#11711yescharacteristic
269C22×C83C4×#4112yes—
270C22×C83C4×#4112yes—
271C22×C83#51812yes—
272C22×C83#51812yes—
273C22×C83#51811yescharacteristic
274C22×C83#51811yescharacteristic
275C22×C83#52012yes—
276C22×C83#52011yescharacteristic
277C22×C83#52011yescharacteristic
278C22×C83#52012yes—
279C22×C83#53812yes—
280C22×C83#53812yes—
281C22×C83#53812yes—
282C22×C83#53912yes—
283C22×C83#54011yescharacteristic
284C22×C83#54012yes—
285C22×C83#54111yescharacteristic
286C22×C83#54212yes—
287C22×C83#54211yescharacteristic
288C22×C83#54211yescharacteristic
289C2×D83—24no—
290C2×D83—24no—
291C2×D83—24no—
292C2×D83—42no—
293C2×D83—42no—
294C2×D83—42no—
295C2×D83—42no—
296C2×D83—44no—
297C2×D83—44no—
298C2×D83—44no—
299C2×D83—44no—
300C4×C83—24no—
301C4×C83—24no—
302C4×C83—24no—
303C4×C83—44no—
304C4×C83—44no—
305Dic83—24no—
306Dic83—42no—
307Dic83—42no—
308Dic83—44no—
309Dic83—44no—
310#13788—831nomaximal, Sylow
311C2×C83C4×#11711yescharacteristic
312C2×C83#227511yescharacteristic
313C2×C83#227511yescharacteristic
314C2×C83#231211yescharacteristic
315C2×C83#231411yescharacteristic
316C2×C83#231811yescharacteristic
317C2×C83#231911yescharacteristic
318C2×C83#233312yes—
319C2×C83#233412yes—
320C2×C83#233512yes—
321C2×C83#233712yes—
322D83—44no—
323C2×#388—832no—
324C2×C4×C22⋊C4—831no—
325#1437—832no—
326#1436—832no—
327C4⋊#95—831no—
328#1434—832no—
329#1434—831no—
330C22⋊#95—831no—
331C22⋊#95—831no—
332C4×#95—831no—
333C4×#95D8311yescharacteristic, complemented
334C83#1378811yescharacteristic, complemented, Sylow
335C24×C4—831no—
336C22×C4⋊C4—832no—
337C22×C22⋊C4—832no—
338C22×C22⋊C4—832no—
339C22×C22⋊C4—831no—
340C22×C22⋊C4—831no—
341C22×C42—832no—
342C22×C42—831no—
343C22×C42C2×D8312yes—
344C22×C42C2×D8311yescharacteristic
345#388—8316no—
346C4×C22⋊C4—838no—
347C2×#95—832no—
348C2×#95—832no—
349C2×#95—832no—
350C2×#95—832no—
351C2×#95—831no—
352C2×#95—832no—
353C2×#95—831no—
354C2×#95—831no—
355C2×#95—831no—
356C2×#95—832no—
357C2×#95C2×D8311yescharacteristic
358C2×#95C2×D8311yescharacteristic
359C2×#95C2×D8312yes—
360C25—831no—
361C23×C4—3322no—
362C23×C4—3322no—
363C23×C4—834no—
364C23×C4—831no—
365C23×C4—832no—
366C23×C4—832no—
367C23×C4—831no—
368C23×C4—831no—
369C23×C4—1662no—
370C23×C4—1662no—
371C23×C4C22×D8312yes—
372C23×C4C22×D8312yes—
373C23×C4C22×D8311yescharacteristic
374C23×C4C22×D8311yescharacteristic
375C23×C4C22×D8311yescharacteristic
376C2×C4⋊C4—3322no—
377C2×C4⋊C4—3322no—
378C2×C4⋊C4—838no—
379C2×C22⋊C4—3322no—
380C2×C22⋊C4—3322no—
381C2×C22⋊C4—3322no—
382C2×C22⋊C4—3322no—
383C2×C22⋊C4—838no—
384C2×C22⋊C4—838no—
385C2×C22⋊C4—834no—
386C2×C22⋊C4—838no—
387C2×C22⋊C4—834no—
388C2×C22⋊C4—1664no—
389C2×C42—24no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—3322no—
394C2×C42—3322no—
395C2×C42—3322no—
396C2×C42—834no—
397C2×C42—838no—
398C2×C42C4×D8314yes—
399#95—22no—
400#95—22no—
401#95—3322no—
402#95—3322no—
403#95—3322no—
404#95—3322no—
405#95—834no—
406#95—834no—
407#95—838no—
408#95—1662no—
409#95—1662no—
410#95—1664no—
411#95C4×D8318yescomplemented
412C24—834no—
413C24—832no—
414C24—1662no—
415C24—1661no—
416C24—1661no—
417C24—1661no—
418C24—1662no—
419C24—1661no—
420C24—1662no—
421C24—1661no—
422C24—1661no—
423C24C23×D8311yescharacteristic
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—3328no—
445C22×C4—3328no—
446C22×C4—3324no—
447C22×C4—3324no—
448C22×C4—832no—
449C22×C4—834no—
450C22×C4—832no—
451C22×C4—832no—
452C22×C4—834no—
453C22×C4—834no—
454C22×C4—1662no—
455C22×C4—1662no—
456C22×C4—1662no—
457C22×C4—1662no—
458C22×C4—1662no—
459C22×C4—1661no—
460C22×C4—1661no—
461C22×C4—1662no—
462C22×C4—1662no—
463C22×C4—1662no—
464C22×C4—1662no—
465C22×C4—1662no—
466C22×C4—1661no—
467C22×C4—1662no—
468C22×C4—1662no—
469C22×C4—1662no—
470C22×C4—1662no—
471C22×C4—1662no—
472C22×C4—1661no—
473C22×C4—1662no—
474C22×C4—1668no—
475C22×C4—1661no—
476C22×C4—1662no—
477C22×C4—1661no—
478C22×C4C2×C4×D8314yes—
479C22×C4C2×C4×D8314yes—
480C22×C4C2×C4×D8312yes—
481C22×C4C2×C4×D8314yes—
482C22×C4C2×C4×D8312yes—
483C22×C4C2×C4×D8312yes—
484C22×C4#1305059012yes—
485C22×C4#1305059012yes—
486C22×C4#1305059014yes—
487C4⋊C4—3328no—
488C22⋊C4—3328no—
489C22⋊C4—3328no—
490C22⋊C4—8316no—
491C22⋊C4—1668no—
492C42—44no—
493C42—48no—
494C42—3328no—
495C42—3324no—
496C23—3322no—
497C23—3321no—
498C23—3322no—
499C23—3322no—
500C23—3322no—
501C23—3322no—
502C23—3321no—
503C23—3322no—
504C23—3321no—
505C23—3321no—
506C23—834no—
507C23—1662no—
508C23—1662no—
509C23—1664no—
510C23—1664no—
511C23—1664no—
512C23—1664no—
513C23—1662no—
514C23—1662no—
515C23—1664no—
516C23—1662no—
517C23—1662no—
518C23—1664no—
519C23C22×C4×D8311yescharacteristic
520C23C22×C4×D8312yes—
521C23C2×#1305059012yes—
522C23C2×#1305059011yescharacteristic
523C23C2×#1305059011yescharacteristic
524C23#1458183711yescharacteristic
525C23#1458183712yes—
526C23#1458183812yes—
527C23#1458183811yescharacteristic
528C23#1458183911yescharacteristic
529C23#1458184011yescharacteristic
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
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—33216no—
557C2×C4—3322no—
558C2×C4—3322no—
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—834no—
570C2×C4—1662no—
571C2×C4—1662no—
572C2×C4—1664no—
573C2×C4—1664no—
574C2×C4—1664no—
575C2×C4—1664no—
576C2×C4—1664no—
577C2×C4—1662no—
578C2×C4—1662no—
579C2×C4—1662no—
580C2×C4—1662no—
581C2×C4—1664no—
582C2×C4—1664no—
583C2×C4—1662no—
584C2×C4—1662no—
585C2×C4—1664no—
586C2×C4C42×D8314yes—
587C2×C4#1458174914yes—
588C2×C4#1458174914yes—
589C22—3322no—
590C22—3322no—
591C22—3324no—
592C22—3324no—
593C22—3324no—
594C22—3324no—
595C22—3322no—
596C22—3322no—
597C22—1664no—
598C22—1664no—
599C22—1664no—
600C22C2×C42×D8311yescharacteristic
601C22C2×#1458174911yescharacteristic
602C22C2×#1458174911yescharacteristic
603C22C4×#1305059012yes—
604C22C4×#1305059012yes—
605C22#1912817312yes—
606C22#1912817312yes—
607C22#1912817411yescharacteristic
608C22#1912817511yescharacteristic
609C22#1912818012yes—
610C22#1912818111yescharacteristic
611C22#1912818211yescharacteristic
612C22#1912818312yes—
613C22#1912828412yes—
614C22#1912828412yes—
615C22#1912828912yes—
616C22#1912829812yes—
617C22#1912830211yescharacteristic
618C22#1912830612yes—
619C22#1912830911yescharacteristic
620C22#1912831611yescharacteristic
621C22#1912832212yes—
622C22#1912832311yescharacteristic
623C4—24no—
624C4—24no—
625C4—24no—
626C4—44no—
627C4—44no—
628C4—3322no—
629C4—3324no—
630C4—3324no—
631C4—3322no—
632C4—1664no—
633C2—3324no—
634C2C4×#1458174911yescharacteristic
635C2#2490982211yescharacteristic
636C2#2490982311yescharacteristic
637C2#2491005811yescharacteristic
638C2#2491006811yescharacteristic
639C2#2491009711yescharacteristic
640C2#2491010711yescharacteristic
641C2#2491022312yes—
642C2#2491023212yes—
643C2#2491024712yes—
644C2#2491027112yes—
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC4×#95×C83C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenterC4×#95D83
hypocenterC83#13788
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
4. #24905696C2semidirect
5. Dic83⋊#95C2semidirect
6. #24905689C2semidirect
7. #24905688C2semidirect
10. C4×C83⋊#95C2semidirect
11. C4×#95×C83C2semidirect
20. #19127590C4semidirect
21. C4×(C2×D83)⋊C4C4semidirect
50. C2×Dic83⋊C4C2×C4semidirect
65. C2×C4×Dic83C2×C4semidirect
75. C83⋊#95C2×C4semidirect
88. #95×C83C2×C4semidirect
138. (C2×D83)⋊C4C42semidirect
333. C4×#95D83semidirect
334. C83#13788semidirect
411. #95C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275902
C2×C4×(C2×D83)⋊C42
#249057012
#249056962
Dic83⋊#952
#249056892
#249056882
(C2×D83)⋊#952
C4×C83⋊#952
C4×#95×C832
#1378883