Finite Group Databasebeta

← C83×#26329 #35254153

Subgroups — C83×#26329 #35254153

Order 21248.

674 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#2592C211yesmaximal, characteristic
2C83×#2355C211yesmaximal, characteristic, complemented
3C83×#2097C211yesmaximal, characteristic, complemented
4C83×#2092C211yesmaximal, characteristic
5C83×#2074C211yesmaximal, characteristic, complemented
6C83×#2073C211yesmaximal, characteristic
7C83×#1985C211yesmaximal, characteristic, complemented
8C83×#1983C211yesmaximal, characteristic
9C83×#1959C211yesmaximal, characteristic
10C83×#1947C211yesmaximal, characteristic, complemented
11C83×#1928C211yesmaximal, characteristic, complemented
12C83×#1928C211yesmaximal, characteristic, complemented
13C83×#1925C211yesmaximal, characteristic
14C83×#1925C211yesmaximal, characteristic
15C83×#1776C211yesmaximal, characteristic, complemented
16C2×#124×C83C2211yescharacteristic
17C2×C4×Q8×C83C2211yescharacteristic
18C2×#107×C83C2211yescharacteristic
19C2×#107×C83C2211yescharacteristic
20C2×#107×C83C2211yescharacteristic
21C2×#106×C83C2211yescharacteristic
22C2×C4⋊C8×C83C2211yescharacteristic
23C2×#103×C83C2211yescharacteristic
24C2×#103×C83C2211yescharacteristic
25C2×#103×C83C2211yescharacteristic
26C2×#103×C83C2211yescharacteristic
27C2×#102×C83C2211yescharacteristic
28C2×#102×C83C2211yescharacteristic
29C2×#102×C83C2211yescharacteristic
30C2×#102×C83C2211yescharacteristic
31C2×#97×C83C2211yescharacteristic
32#397×C83—21no—
33#393×C83—21no—
34#391×C83—21no—
35#391×C83C2211yescharacteristic
36#391×C83C2211yescharacteristic
37#390×C83C2211yescharacteristic
38#390×C83C2211yescharacteristic
39#388×C83—21no—
40#388×C83—21no—
41#387×C83—21no—
42#387×C83—21no—
43#384×C83C2211yescharacteristic
44#382×C83C2211yescharacteristic
45#382×C83C2211yescharacteristic
46C4×C4⋊C4×C83—21no—
47C4×C4⋊C4×C83C2211yescharacteristic
48C4×C4⋊C4×C83C2211yescharacteristic
49C4×C4⋊C4×C83C2211yescharacteristic
50C4×C4⋊C4×C83C2211yescharacteristic
51#340×C83C2211yescharacteristic
52#340×C83C2211yescharacteristic
53#340×C83C2211yescharacteristic
54#340×C83C2211yescharacteristic
55#336×C83C2211yescharacteristic
56#336×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59C22×Q8×C83D411yescharacteristic
60C22×Q8×C83C2311yescharacteristic
61C22×D4×C83C2311yescharacteristic
62C22×C8×C83C2311yescharacteristic
63C22×C8×C83C2311yescharacteristic
64C22×C8×C83C2311yescharacteristic
65C22×C8×C83C2311yescharacteristic
66#124×C83—22no—
67#124×C83—22no—
68C4×Q8×C83—22no—
69C4×Q8×C83—22no—
70C2×C4⋊C4×C83—21no—
71C2×C4⋊C4×C83—21no—
72C2×C4⋊C4×C83D411yescharacteristic
73C2×C4⋊C4×C83D411yescharacteristic
74C2×C4⋊C4×C83D411yescharacteristic
75C2×C4⋊C4×C83C2311yescharacteristic
76C2×C4⋊C4×C83C2311yescharacteristic
77C2×C4⋊C4×C83C2311yescharacteristic
78C2×C4⋊C4×C83C2311yescharacteristic
79C2×C4⋊C4×C83C2311yescharacteristic
80C2×C4⋊C4×C83C2311yescharacteristic
81C2×C22⋊C4×C83—21no—
82C2×C22⋊C4×C83—21no—
83C2×C22⋊C4×C83—21no—
84C2×C22⋊C4×C83—21no—
85C2×C22⋊C4×C83—21no—
86C2×C22⋊C4×C83—21no—
87C2×C42×C83—21no—
88C2×C42×C83—21no—
89C2×C42×C83—21no—
90C2×C42×C83—21no—
91C2×C42×C83C2311yescharacteristic
92C2×C42×C83C2311yescharacteristic
93C2×C42×C83C2311yescharacteristic
94#107×C83—22no—
95#107×C83—41no—
96#107×C83—41no—
97#106×C83—22no—
98C4⋊C8×C83—22no—
99#103×C83—22no—
100#103×C83—22no—
101#103×C83—41no—
102#103×C83—41no—
103#102×C83—22no—
104#102×C83—22no—
105#102×C83—41no—
106#102×C83—41no—
107#97×C83—22no—
108#95×C83—21no—
109#95×C83—21no—
110#95×C83—21no—
111#95×C83—21no—
112#95×C83—21no—
113#95×C83—21no—
114#95×C83—21no—
115#95×C83—21no—
116#95×C83—21no—
117#95×C83—21no—
118#95×C83—21no—
119#95×C83—21no—
120C24×C83—21no—
121C2×Q8×C83—22no—
122C2×Q8×C83—21no—
123C2×Q8×C83—21no—
124C2×Q8×C83—21no—
125C2×Q8×C83—21no—
126C2×Q8×C83—21no—
127C2×Q8×C83—21no—
128C2×Q8×C83—41no—
129C2×Q8×C83—41no—
130C2×D4×C83—21no—
131C2×D4×C83—21no—
132C2×D4×C83—21no—
133C2×D4×C83—21no—
134C2×D4×C83—21no—
135C2×D4×C83—21no—
136C22×C4×C83—21no—
137C22×C4×C83—21no—
138C22×C4×C83—21no—
139C22×C4×C83—21no—
140C22×C4×C83—21no—
141C22×C4×C83—21no—
142C22×C4×C83—21no—
143C22×C4×C83C2×D411yescharacteristic
144C22×C4×C83C2×D411yescharacteristic
145C22×C4×C83C2×D411yescharacteristic
146C22×C4×C83C2×D411yescharacteristic
147C22×C4×C83C2×D411yescharacteristic
148C22×C4×C83C2×D411yescharacteristic
149C22×C4×C83C2411yescharacteristic
150C2×C8×C83—21no—
151C2×C8×C83—21no—
152C2×C8×C83—21no—
153C2×C8×C83—21no—
154C2×C8×C83—21no—
155C2×C8×C83—21no—
156C2×C8×C83—21no—
157C2×C8×C83—21no—
158C2×C8×C83—21no—
159C2×C8×C83—21no—
160C2×C8×C83—21no—
161C2×C8×C83#4112yes—
162C4⋊C4×C83—22no—
163C4⋊C4×C83—22no—
164C4⋊C4×C83—22no—
165C4⋊C4×C83—21no—
166C4⋊C4×C83—21no—
167C4⋊C4×C83—21no—
168C4⋊C4×C83—21no—
169C4⋊C4×C83—21no—
170C4⋊C4×C83—21no—
171C4⋊C4×C83—21no—
172C4⋊C4×C83—21no—
173C4⋊C4×C83—21no—
174C4⋊C4×C83—21no—
175C4⋊C4×C83—21no—
176C4⋊C4×C83—42no—
177C4⋊C4×C83—81no—
178C4⋊C4×C83#4112yes—
179C22⋊C4×C83—42no—
180C22⋊C4×C83—42no—
181C22⋊C4×C83—42no—
182C22⋊C4×C83—42no—
183C22⋊C4×C83—81no—
184C22⋊C4×C83—81no—
185C42×C83—21no—
186C42×C83—21no—
187C42×C83—21no—
188C42×C83—21no—
189C42×C83—42no—
190C42×C83—81no—
191C42×C83—81no—
192C42×C83—81no—
193C42×C83#4112yes—
194C42×C83#4112yes—
195C23×C83—41no—
196C23×C83—41no—
197C23×C83—41no—
198C23×C83—41no—
199C23×C83—41no—
200C23×C83—41no—
201C23×C83—41no—
202C23×C83C22×D411yescharacteristic
203Q8×C83—44no—
204Q8×C83—41no—
205Q8×C83—41no—
206Q8×C83—41no—
207Q8×C83—41no—
208D4×C83—41no—
209D4×C83—41no—
210D4×C83—41no—
211D4×C83—41no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—22no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83—41no—
246C2×C4×C83—41no—
247C2×C4×C83—41no—
248C2×C4×C83—41no—
249C2×C4×C83#12312yes—
250C2×C4×C83#12312yes—
251C2×C4×C83C2×#4111yescharacteristic
252C2×C4×C83C2×#4111yescharacteristic
253C2×C4×C83C2×#4111yescharacteristic
254C2×C4×C83C2×#4111yescharacteristic
255C2×C4×C83H(5,𝔽2)11yescharacteristic
256C2×C4×C832−1+411yescharacteristic
257C8×C83—22no—
258C8×C83—41no—
259C8×C83—41no—
260C8×C83—41no—
261C22×C83—81no—
262C22×C83—81no—
263C22×C83—81no—
264C22×C83—81no—
265C22×C83—81no—
266C22×C83—81no—
267C22×C83—81no—
268C22×C83C2×#12311yescharacteristic
269C22×C83#54811yescharacteristic
270C22×C83#55011yescharacteristic
271C22×C83#57511yescharacteristic
272C22×C83#57511yescharacteristic
273C22×C83#57611yescharacteristic
274C22×C83#57811yescharacteristic
275C4×C83—22no—
276C4×C83—22no—
277C4×C83—41no—
278C4×C83—41no—
279C4×C83—41no—
280C4×C83—41no—
281C4×C83—42no—
282C4×C83—81no—
283C4×C83—81no—
284C4×C83—81no—
285C4×C83—81no—
286C4×C83—81no—
287C4×C83—81no—
288C4×C83#52911yescharacteristic
289C4×C83#54211yescharacteristic
290C4×C83#55611yescharacteristic
291C4×C83#55911yescharacteristic
292#26329C8311yesmaximal, characteristic, direct product factor, Sylow
293C2×C83—161no—
294C2×C83#244811yescharacteristic
295C2×C83#309311yescharacteristic
296C2×C83#309811yescharacteristic
297C2×C83#337011yescharacteristic
298C2×C83#337711yescharacteristic
299C2×C83#340211yescharacteristic
300C2×C83#340311yescharacteristic
301#2592C2×C8311yescharacteristic
302#2355C2×C8311yescharacteristic, complemented
303#2097C2×C8311yescharacteristic, complemented
304#2092C2×C8311yescharacteristic
305#2074C2×C8311yescharacteristic, complemented
306#2073C2×C8311yescharacteristic
307#1985C2×C8311yescharacteristic, complemented
308#1983C2×C8311yescharacteristic
309#1959C2×C8311yescharacteristic
310#1947C2×C8311yescharacteristic, complemented
311#1928C2×C8311yescharacteristic, complemented
312#1928C2×C8311yescharacteristic, complemented
313#1925C2×C8311yescharacteristic
314#1925C2×C8311yescharacteristic
315#1776C2×C8311yescharacteristic, complemented
316C83#2632911yescharacteristic, direct product factor, Sylow
317C2×#124C22×C8311yescharacteristic
318C2×C4×Q8C22×C8311yescharacteristic
319C2×#107C22×C8311yescharacteristic
320C2×#107C22×C8311yescharacteristic
321C2×#107C22×C8311yescharacteristic
322C2×#106C22×C8311yescharacteristic
323C2×C4⋊C8C22×C8311yescharacteristic
324C2×#103C22×C8311yescharacteristic
325C2×#103C22×C8311yescharacteristic
326C2×#103C22×C8311yescharacteristic
327C2×#103C22×C8311yescharacteristic
328C2×#102C22×C8311yescharacteristic
329C2×#102C22×C8311yescharacteristic
330C2×#102C22×C8311yescharacteristic
331C2×#102C22×C8311yescharacteristic
332C2×#97C22×C8311yescharacteristic
333#397—21no—
334#393—21no—
335#391—21no—
336#391C22×C8311yescharacteristic
337#391C22×C8311yescharacteristic
338#390C22×C8311yescharacteristic
339#390C22×C8311yescharacteristic
340#388—21no—
341#388—21no—
342#387—21no—
343#387—21no—
344#384C22×C8311yescharacteristic
345#382C22×C8311yescharacteristic
346#382C22×C8311yescharacteristic
347C4×C4⋊C4—21no—
348C4×C4⋊C4C22×C8311yescharacteristic
349C4×C4⋊C4C22×C8311yescharacteristic
350C4×C4⋊C4C22×C8311yescharacteristic
351C4×C4⋊C4C22×C8311yescharacteristic
352#340C22×C8311yescharacteristic
353#340C22×C8311yescharacteristic
354#340C22×C8311yescharacteristic
355#340C22×C8311yescharacteristic
356#336C22×C8311yescharacteristic
357#336C22×C8311yescharacteristic
358#336C22×C8311yescharacteristic
359#336C22×C8311yescharacteristic
360C22×Q8D4×C8311yescharacteristic
361C22×Q8C23×C8311yescharacteristic
362C22×D4C23×C8311yescharacteristic
363C22×C8C23×C8311yescharacteristic
364C22×C8C23×C8311yescharacteristic
365C22×C8C23×C8311yescharacteristic
366C22×C8C23×C8311yescharacteristic
367#124—22no—
368#124—22no—
369C4×Q8—22no—
370C4×Q8—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C8311yescharacteristic
374C2×C4⋊C4D4×C8311yescharacteristic
375C2×C4⋊C4D4×C8311yescharacteristic
376C2×C4⋊C4C23×C8311yescharacteristic
377C2×C4⋊C4C23×C8311yescharacteristic
378C2×C4⋊C4C23×C8311yescharacteristic
379C2×C4⋊C4C23×C8311yescharacteristic
380C2×C4⋊C4C23×C8311yescharacteristic
381C2×C4⋊C4C23×C8311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C23×C8311yescharacteristic
393C2×C42C23×C8311yescharacteristic
394C2×C42C23×C8311yescharacteristic
395#107—22no—
396#107—41no—
397#107—41no—
398#106—22no—
399C4⋊C8—22no—
400#103—22no—
401#103—22no—
402#103—41no—
403#103—41no—
404#102—22no—
405#102—22no—
406#102—41no—
407#102—41no—
408#97—22no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421C24—21no—
422C2×Q8—22no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4C2×D4×C8311yescharacteristic
445C22×C4C2×D4×C8311yescharacteristic
446C22×C4C2×D4×C8311yescharacteristic
447C22×C4C2×D4×C8311yescharacteristic
448C22×C4C2×D4×C8311yescharacteristic
449C22×C4C2×D4×C8311yescharacteristic
450C22×C4C24×C8311yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8#41×C8312yes—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4#41×C8312yes—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—81no—
492C42—81no—
493C42—81no—
494C42#41×C8312yes—
495C42#41×C8312yes—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C22×D4×C8311yescharacteristic
504Q8—44no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
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—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4#123×C8312yes—
551C2×C4#123×C8312yes—
552C2×C4C2×#41×C8311yescharacteristic
553C2×C4C2×#41×C8311yescharacteristic
554C2×C4C2×#41×C8311yescharacteristic
555C2×C4C2×#41×C8311yescharacteristic
556C2×C4H(5,𝔽2)×C8311yescharacteristic
557C2×C42−1+4×C8311yescharacteristic
558C8—22no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C2×#123×C8311yescharacteristic
570C22#548×C8311yescharacteristic
571C22#550×C8311yescharacteristic
572C22#575×C8311yescharacteristic
573C22#575×C8311yescharacteristic
574C22#576×C8311yescharacteristic
575C22#578×C8311yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4#529×C8311yescharacteristic
590C4#542×C8311yescharacteristic
591C4#556×C8311yescharacteristic
592C4#559×C8311yescharacteristic
593C2—161no—
594C2C83×#244811yescharacteristic
595C2C83×#309311yescharacteristic
596C2C83×#309811yescharacteristic
597C2C83×#337011yescharacteristic
598C2C83×#337711yescharacteristic
599C2C83×#340211yescharacteristic
600C2C83×#340311yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC22×D4×C83C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×C4×Q8×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#2355C2semidirect
3. C83×#2097C2semidirect
5. C83×#2074C2semidirect
7. C83×#1985C2semidirect
10. C83×#1947C2semidirect
11. C83×#1928C2semidirect
12. C83×#1928C2semidirect
15. C83×#1776C2semidirect
292. #26329C83direct (N × H)
302. #2355C2×C83semidirect
303. #2097C2×C83semidirect
305. #2074C2×C83semidirect
307. #1985C2×C83semidirect
310. #1947C2×C83semidirect
311. #1928C2×C83semidirect
312. #1928C2×C83semidirect
315. #1776C2×C83semidirect
316. C83#26329direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#25922
C83×#23552
C83×#20972
C83×#20922
C83×#20742
C83×#20732
C83×#19852
C83×#19832
C83×#19592
C83×#19472
C83×#19282
C83×#19252
C83×#17762
#2632983