Finite Group Databasebeta

← C83×#14734 #35242558

Subgroups — C83×#14734 #35242558

Order 21248.

3494 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C83C211yesmaximal, characteristic
2C2×#399×C83C212yesmaximal, complemented
3C2×#385×C83C212yesmaximal, complemented
4C2×#380×C83C211yesmaximal, characteristic, complemented
5C2×#379×C83C212yesmaximal
6C83×#1439C214yesmaximal, complemented
7C83×#1439C212yesmaximal, complemented
8C83×C22⋊#95C211yesmaximal, characteristic, complemented
9C26×C83C2211yescharacteristic
10C24×C4×C83C2211yescharacteristic
11C24×C4×C83C2211yescharacteristic
12C22×C4⋊C4×C83C2211yescharacteristic, complemented
13C22×C4⋊C4×C83C2214yescomplemented
14C22×C4⋊C4×C83C2211yescharacteristic, complemented
15C22×C22⋊C4×C83—24no—
16C22×C22⋊C4×C83—28no—
17C22×C22⋊C4×C83C2212yes—
18C22×C22⋊C4×C83C2212yes—
19C22×C22⋊C4×C83C2214yes—
20C22×C22⋊C4×C83C2214yes—
21C22×C22⋊C4×C83C2212yes—
22C22×C22⋊C4×C83C2212yes—
23#399×C83—28no—
24#385×C83—28no—
25#380×C83—24no—
26#379×C83—28no—
27C2×#95×C83C2212yescomplemented
28C2×#95×C83C2214yescomplemented
29C2×#95×C83C2212yescomplemented
30C2×#95×C83C2212yescomplemented
31C25×C83—24no—
32C25×C83—22no—
33C25×C83—24no—
34C25×C83—22no—
35C25×C83—24no—
36C25×C83—24no—
37C25×C83—42no—
38C25×C83—42no—
39C25×C83Q814yes—
40C25×C83C2312yes—
41C25×C83C2311yescharacteristic
42C23×C4×C83—22no—
43C23×C4×C83—24no—
44C23×C4×C83—24no—
45C23×C4×C83—24no—
46C23×C4×C83—24no—
47C23×C4×C83—42no—
48C23×C4×C83—42no—
49C23×C4×C83D414yes—
50C23×C4×C83C2312yes—
51C23×C4×C83C2312yes—
52C23×C4×C83C2314yes—
53C23×C4×C83C2312yes—
54C23×C4×C83C2311yescharacteristic
55C23×C4×C83C2311yescharacteristic
56C2×C4⋊C4×C83—22no—
57C2×C4⋊C4×C83—22no—
58C2×C4⋊C4×C83—28no—
59C2×C4⋊C4×C83—28no—
60C2×C4⋊C4×C83—24no—
61C2×C4⋊C4×C83—44no—
62C2×C4⋊C4×C83—42no—
63C2×C22⋊C4×C83—232no—
64C2×C22⋊C4×C83—24no—
65C2×C22⋊C4×C83—24no—
66C2×C22⋊C4×C83—24no—
67C2×C22⋊C4×C83—24no—
68C2×C22⋊C4×C83—24no—
69C2×C22⋊C4×C83—24no—
70C2×C22⋊C4×C83—24no—
71C2×C22⋊C4×C83—24no—
72C2×C22⋊C4×C83—24no—
73C2×C22⋊C4×C83—24no—
74C2×C22⋊C4×C83—28no—
75C2×C22⋊C4×C83—28no—
76C2×C22⋊C4×C83—28no—
77C2×C22⋊C4×C83—28no—
78C2×C22⋊C4×C83—44no—
79C2×C22⋊C4×C83—44no—
80C2×C22⋊C4×C83D418yes—
81C2×C22⋊C4×C83D418yes—
82#95×C83—24no—
83#95×C83—28no—
84#95×C83—24no—
85#95×C83—42no—
86C24×C83—22no—
87C24×C83—22no—
88C24×C83—22no—
89C24×C83—22no—
90C24×C83—28no—
91C24×C83—28no—
92C24×C83—216no—
93C24×C83—216no—
94C24×C83—28no—
95C24×C83—22no—
96C24×C83—22no—
97C24×C83—24no—
98C24×C83—22no—
99C24×C83—22no—
100C24×C83—24no—
101C24×C83—24no—
102C24×C83—24no—
103C24×C83—216no—
104C24×C83—48no—
105C24×C83—416no—
106C24×C83—416no—
107C24×C83—416no—
108C24×C83—416no—
109C24×C83—44no—
110C24×C83—44no—
111C24×C83—48no—
112C24×C83—48no—
113C24×C83—44no—
114C24×C83—44no—
115C24×C83C2×D414yes—
116C24×C83C2×D414yes—
117C24×C83C2×D412yes—
118C24×C83C2×Q814yes—
119C24×C83C2×Q812yes—
120C24×C83#4114yes—
121C24×C83#4112yes—
122C24×C83#4114yes—
123C24×C83C2411yescharacteristic
124C22×C4×C83—22no—
125C22×C4×C83—22no—
126C22×C4×C83—28no—
127C22×C4×C83—28no—
128C22×C4×C83—24no—
129C22×C4×C83—24no—
130C22×C4×C83—22no—
131C22×C4×C83—22no—
132C22×C4×C83—22no—
133C22×C4×C83—24no—
134C22×C4×C83—24no—
135C22×C4×C83—24no—
136C22×C4×C83—22no—
137C22×C4×C83—24no—
138C22×C4×C83—22no—
139C22×C4×C83—24no—
140C22×C4×C83—24no—
141C22×C4×C83—28no—
142C22×C4×C83—22no—
143C22×C4×C83—22no—
144C22×C4×C83—22no—
145C22×C4×C83—22no—
146C22×C4×C83—22no—
147C22×C4×C83—24no—
148C22×C4×C83—22no—
149C22×C4×C83—24no—
150C22×C4×C83—24no—
151C22×C4×C83—24no—
152C22×C4×C83—44no—
153C22×C4×C83—416no—
154C22×C4×C83—416no—
155C22×C4×C83—44no—
156C22×C4×C83—44no—
157C22×C4×C83C2×D412yes—
158C22×C4×C83C2×D418yes—
159C22×C4×C83C2×D414yes—
160C22×C4×C83C2×D414yes—
161C22×C4×C83C2×D412yes—
162C4⋊C4×C83—416no—
163C4⋊C4×C83—44no—
164C4⋊C4×C83—44no—
165C22⋊C4×C83—216no—
166C22⋊C4×C83—216no—
167C22⋊C4×C83—216no—
168C22⋊C4×C83—416no—
169C22⋊C4×C83—416no—
170C22⋊C4×C83—48no—
171C23×C83—22no—
172C23×C83—24no—
173C23×C83—22no—
174C23×C83—24no—
175C23×C83—22no—
176C23×C83—22no—
177C23×C83—24no—
178C23×C83—24no—
179C23×C83—28no—
180C23×C83—28no—
181C23×C83—28no—
182C23×C83—28no—
183C23×C83—232no—
184C23×C83—24no—
185C23×C83—24no—
186C23×C83—24no—
187C23×C83—28no—
188C23×C83—24no—
189C23×C83—24no—
190C23×C83—24no—
191C23×C83—28no—
192C23×C83—28no—
193C23×C83—28no—
194C23×C83—28no—
195C23×C83—28no—
196C23×C83—464no—
197C23×C83—416no—
198C23×C83—416no—
199C23×C83—464no—
200C23×C83—416no—
201C23×C83—416no—
202C23×C83—416no—
203C23×C83—42no—
204C23×C83—44no—
205C23×C83—42no—
206C23×C83—42no—
207C23×C83—42no—
208C23×C83—44no—
209C23×C83—44no—
210C23×C83—44no—
211C23×C83—44no—
212C23×C83—44no—
213C23×C83—416no—
214C23×C83C22⋊Q818yes—
215C23×C83C22⋊Q814yes—
216C23×C83C22⋊Q818yes—
217C23×C83#12318yes—
218C23×C83#12314yes—
219C23×C83#12714yes—
220C23×C83C22×D411yescharacteristic
221C23×C83C22×D412yes—
222C23×C83C22×D412yes—
223C23×C83C22×Q811yescharacteristic
224C23×C83C2×#4111yescharacteristic
225C23×C83C2×#4112yes—
226C23×C83C2×#4112yes—
227C23×C83H(5,𝔽2)12yes—
228C23×C83H(5,𝔽2)12yes—
229C2×C4×C83—22no—
230C2×C4×C83—22no—
231C2×C4×C83—28no—
232C2×C4×C83—22no—
233C2×C4×C83—24no—
234C2×C4×C83—28no—
235C2×C4×C83—22no—
236C2×C4×C83—22no—
237C2×C4×C83—28no—
238C2×C4×C83—28no—
239C2×C4×C83—28no—
240C2×C4×C83—416no—
241C2×C4×C83—416no—
242C2×C4×C83—44no—
243C2×C4×C83—42no—
244C2×C4×C83—42no—
245C2×C4×C83—44no—
246C2×C4×C83—44no—
247C2×C4×C83—44no—
248C2×C4×C83—44no—
249C2×C4×C83—44no—
250C2×C4×C83—42no—
251C2×C4×C83—42no—
252C2×C4×C83—42no—
253C2×C4×C83—42no—
254C2×C4×C83—42no—
255C2×C4×C83—42no—
256C2×C4×C83—44no—
257C2×C4×C83—44no—
258C2×C4×C83—44no—
259C2×C4×C83—44no—
260C2×C4×C83#12014yes—
261C22×C83—24no—
262C22×C83—24no—
263C22×C83—24no—
264C22×C83—216no—
265C22×C83—24no—
266C22×C83—216no—
267C22×C83—24no—
268C22×C83—24no—
269C22×C83—28no—
270C22×C83—216no—
271C22×C83—464no—
272C22×C83—44no—
273C22×C83—44no—
274C22×C83—44no—
275C22×C83—48no—
276C22×C83—48no—
277C22×C83—44no—
278C22×C83—48no—
279C22×C83—44no—
280C22×C83—44no—
281C22×C83#39918yescomplemented
282C22×C83C2×#12011yescharacteristic
283C22×C83C2×C22⋊Q811yescharacteristic
284C22×C83C2×C22⋊Q812yes—
285C22×C83C2×C22⋊Q812yes—
286C22×C83C2×#12311yescharacteristic
287C22×C83C2×#12312yes—
288C22×C83#52512yes—
289C22×C83#52511yescharacteristic
290C22×C83C2×#12711yescharacteristic
291C22×C83#53411yescharacteristic
292C22×C83#53511yescharacteristic
293C22×C83#53812yes—
294C22×C83#54312yes—
295C22×C83D4214yes—
296C22×C83#54614yes—
297C22×C83#54614yes—
298C22×C83#55114yes—
299C4×C83—24no—
300C4×C83—42no—
301C4×C83—48no—
302C4×C83—44no—
303C4×C83—82no—
304C4×C83—82no—
305#14734C8311yesmaximal, characteristic, direct product factor, Sylow
306C2×C83—28no—
307C2×C83—48no—
308C2×C83C2×#39911yescharacteristic
309C2×C83#240511yescharacteristic
310C2×C83#241814yes—
311C2×C83#243311yescharacteristic
312C2×C83#243714yes—
313C2×C83#248211yescharacteristic
314C2×C83#253911yescharacteristic
315C2×C83#262611yescharacteristic
316C2×C83#284811yescharacteristic
317C23×C22⋊C4C2×C8311yescharacteristic
318C2×#399C2×C8312yescomplemented
319C2×#385C2×C8312yescomplemented
320C2×#380C2×C8311yescharacteristic, complemented
321C2×#379C2×C8312yes—
322#1439C2×C8314yescomplemented
323#1439C2×C8312yescomplemented
324C22⋊#95C2×C8311yescharacteristic, complemented
325C83#1473411yescharacteristic, direct product factor, Sylow
326C26C22×C8311yescharacteristic
327C24×C4C22×C8311yescharacteristic
328C24×C4C22×C8311yescharacteristic
329C22×C4⋊C4C22×C8311yescharacteristic, complemented
330C22×C4⋊C4C22×C8314yescomplemented
331C22×C4⋊C4C22×C8311yescharacteristic, complemented
332C22×C22⋊C4—24no—
333C22×C22⋊C4—28no—
334C22×C22⋊C4C22×C8312yes—
335C22×C22⋊C4C22×C8312yes—
336C22×C22⋊C4C22×C8314yes—
337C22×C22⋊C4C22×C8314yes—
338C22×C22⋊C4C22×C8312yes—
339C22×C22⋊C4C22×C8312yes—
340#399—28no—
341#385—28no—
342#380—24no—
343#379—28no—
344C2×#95C22×C8312yescomplemented
345C2×#95C22×C8312yescomplemented
346C2×#95C22×C8314yescomplemented
347C2×#95C22×C8312yescomplemented
348C25—24no—
349C25—22no—
350C25—24no—
351C25—22no—
352C25—24no—
353C25—24no—
354C25—42no—
355C25—42no—
356C25Q8×C8314yes—
357C25C23×C8312yes—
358C25C23×C8311yescharacteristic
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4D4×C8314yes—
367C23×C4C23×C8312yes—
368C23×C4C23×C8312yes—
369C23×C4C23×C8314yes—
370C23×C4C23×C8312yes—
371C23×C4C23×C8311yescharacteristic
372C23×C4C23×C8311yescharacteristic
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—42no—
380C2×C22⋊C4—232no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4D4×C8318yes—
398C2×C22⋊C4D4×C8318yes—
399#95—24no—
400#95—28no—
401#95—24no—
402#95—42no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—28no—
408C24—28no—
409C24—216no—
410C24—216no—
411C24—28no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—216no—
421C24—48no—
422C24—416no—
423C24—416no—
424C24—416no—
425C24—416no—
426C24—44no—
427C24—44no—
428C24—48no—
429C24—48no—
430C24—44no—
431C24—44no—
432C24C2×D4×C8314yes—
433C24C2×D4×C8314yes—
434C24C2×D4×C8312yes—
435C24C2×Q8×C8314yes—
436C24C2×Q8×C8312yes—
437C24#41×C8314yes—
438C24#41×C8312yes—
439C24#41×C8314yes—
440C24C24×C8311yescharacteristic
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—28no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—44no—
470C22×C4—416no—
471C22×C4—416no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4C2×D4×C8312yes—
475C22×C4C2×D4×C8318yes—
476C22×C4C2×D4×C8314yes—
477C22×C4C2×D4×C8314yes—
478C22×C4C2×D4×C8312yes—
479C4⋊C4—416no—
480C4⋊C4—44no—
481C4⋊C4—44no—
482C22⋊C4—216no—
483C22⋊C4—216no—
484C22⋊C4—216no—
485C22⋊C4—416no—
486C22⋊C4—416no—
487C22⋊C4—48no—
488C23—22no—
489C23—24no—
490C23—22no—
491C23—24no—
492C23—22no—
493C23—22no—
494C23—24no—
495C23—24no—
496C23—28no—
497C23—28no—
498C23—28no—
499C23—28no—
500C23—232no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—28no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—28no—
509C23—28no—
510C23—28no—
511C23—28no—
512C23—28no—
513C23—464no—
514C23—416no—
515C23—416no—
516C23—416no—
517C23—464no—
518C23—416no—
519C23—416no—
520C23—42no—
521C23—44no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—416no—
531C23C22⋊Q8×C8318yes—
532C23C22⋊Q8×C8314yes—
533C23C22⋊Q8×C8318yes—
534C23#123×C8318yes—
535C23#123×C8314yes—
536C23#127×C8314yes—
537C23C22×D4×C8311yescharacteristic
538C23C22×D4×C8312yes—
539C23C22×D4×C8312yes—
540C23C22×Q8×C8311yescharacteristic
541C23C2×#41×C8311yescharacteristic
542C23C2×#41×C8312yes—
543C23C2×#41×C8312yes—
544C23H(5,𝔽2)×C8312yes—
545C23H(5,𝔽2)×C8312yes—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—28no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—416no—
558C2×C4—416no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4#120×C8314yes—
578C22—24no—
579C22—24no—
580C22—24no—
581C22—24no—
582C22—216no—
583C22—24no—
584C22—216no—
585C22—24no—
586C22—28no—
587C22—216no—
588C22—464no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—48no—
594C22—48no—
595C22—44no—
596C22—48no—
597C22—44no—
598C22#399×C8318yescomplemented
599C22C2×#120×C8311yescharacteristic
600C22C2×C22⋊Q8×C8311yescharacteristic
601C22C2×C22⋊Q8×C8312yes—
602C22C2×C22⋊Q8×C8312yes—
603C22C2×#123×C8311yescharacteristic
604C22C2×#123×C8312yes—
605C22#525×C8311yescharacteristic
606C22#525×C8312yes—
607C22C2×#127×C8311yescharacteristic
608C22#534×C8311yescharacteristic
609C22#535×C8311yescharacteristic
610C22#538×C8312yes—
611C22#543×C8312yes—
612C22D42×C8314yes—
613C22#546×C8314yes—
614C22#546×C8314yes—
615C22#551×C8314yes—
616C4—24no—
617C4—42no—
618C4—48no—
619C4—44no—
620C4—82no—
621C4—82no—
622C2—28no—
623C2—48no—
624C2C2×#399×C8311yescharacteristic
625C2C83×#240511yescharacteristic
626C2C83×#241814yes—
627C2C83×#243311yescharacteristic
628C2C83×#243714yes—
629C2C83×#248211yescharacteristic
630C2C83×#253911yescharacteristic
631C2C83×#262611yescharacteristic
632C2C83×#284811yescharacteristic
subgroupG/H
center, socleC24×C83C24
commutator, Frattini, cosocleC24C24×C83
prime radicalC26×C83C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#399×C83C2semidirect
3. C2×#385×C83C2semidirect
4. C2×#380×C83C2semidirect
6. C83×#1439C2semidirect
7. C83×#1439C2semidirect
8. C83×C22⋊#95C2semidirect
12. C22×C4⋊C4×C83C22semidirect
13. C22×C4⋊C4×C83C22semidirect
14. C22×C4⋊C4×C83C22semidirect
27. C2×#95×C83C22semidirect
28. C2×#95×C83C22semidirect
29. C2×#95×C83C22semidirect
30. C2×#95×C83C22semidirect
281. C22×C83#399semidirect
305. #14734C83direct (N × H)
318. C2×#399C2×C83semidirect
319. C2×#385C2×C83semidirect
320. C2×#380C2×C83semidirect
322. #1439C2×C83semidirect
323. #1439C2×C83semidirect
324. C22⋊#95C2×C83semidirect
325. C83#14734direct (N × H)
329. C22×C4⋊C4C22×C83semidirect
330. C22×C4⋊C4C22×C83semidirect
331. C22×C4⋊C4C22×C83semidirect
344. C2×#95C22×C83semidirect
345. C2×#95C22×C83semidirect
346. C2×#95C22×C83semidirect
347. C2×#95C22×C83semidirect
598. C22#399×C83semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C832
C2×#399×C832
C2×#385×C832
C2×#380×C832
C2×#379×C832
C83×#14392
C83×C22⋊#952
#1473483