Finite Group Databasebeta

← C83×#10941 #35238765

Subgroups — C83×#10941 #35238765

Order 21248.

904 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
1C2×#413×C83C211yesmaximal, characteristic
2C2×#410×C83C211yesmaximal, characteristic
3C83×#2879C211yesmaximal, characteristic
4C83×#2873C211yesmaximal, characteristic, complemented
5C2×#344×C83C211yesmaximal, characteristic, complemented
6C2×#344×C83C211yesmaximal, characteristic, complemented
7C83×#1742C211yesmaximal, characteristic, complemented
8C22×#41×C83C2211yescharacteristic
9C22×M16×C83C2211yescharacteristic
10C22×M16×C83C2211yescharacteristic
11C22×M16×C83C2211yescharacteristic
12C22×M16×C83C2211yescharacteristic
13C2×#117×C83C2211yescharacteristic
14C2×#117×C83C2211yescharacteristic
15#413×C83—22no—
16#413×C83—22no—
17C2×#101×C83C412yescomplemented
18C2×#100×C83C412yescomplemented
19#410×C83—22no—
20#410×C83—22no—
21C2×#99×C83C414yes—
22#408×C83—22no—
23#408×C83—22no—
24#407×C83C414yescomplemented
25#405×C83—22no—
26#405×C83—22no—
27C4×M16×C83—22no—
28#344×C83—22no—
29#344×C83—22no—
30#343×C83—22no—
31C2×#41×C83—21no—
32C2×#41×C83—21no—
33C2×#41×C83—21no—
34C2×#41×C83—21no—
35C2×#41×C83—21no—
36C2×#41×C83—21no—
37C2×#41×C83—21no—
38C2×#41×C83—21no—
39C2×#41×C83—21no—
40C2×#41×C83—21no—
41C2×#41×C83—21no—
42C2×#41×C83—21no—
43C22×Q8×C83C2×C411yescharacteristic
44C22×D4×C83C2×C412yes—
45C22×D4×C83C2×C411yescharacteristic
46C23×C4×C83C2×C412yes—
47C23×C4×C83C2311yescharacteristic
48C2×M16×C83—21no—
49C2×M16×C83—21no—
50C2×M16×C83—21no—
51C2×M16×C83—21no—
52C2×M16×C83—21no—
53C2×M16×C83—21no—
54C2×M16×C83—21no—
55C2×M16×C83—21no—
56C2×M16×C83—21no—
57C2×M16×C83—21no—
58C2×M16×C83—21no—
59C2×M16×C83—21no—
60C2×M16×C83—21no—
61C2×M16×C83—21no—
62C2×M16×C83—21no—
63C2×M16×C83—21no—
64C2×M16×C83—21no—
65C2×M16×C83C2×C412yes—
66C2×M16×C83C2×C412yes—
67C2×M16×C83C2×C412yes—
68C2×M16×C83C2×C412yes—
69C2×M16×C83D412yes—
70C2×M16×C83D412yes—
71C2×M16×C83D412yes—
72C22×C8×C83—21no—
73C22×C8×C83—21no—
74C22×C8×C83—21no—
75C22×C8×C83D412yes—
76#117×C83—21no—
77#117×C83—21no—
78#117×C83—21no—
79#117×C83—21no—
80#117×C83—21no—
81#117×C83—21no—
82#117×C83D412yes—
83#117×C83D412yes—
84C2×C4⋊C4×C83—21no—
85C2×C4⋊C4×C83—21no—
86C2×C22⋊C4×C83C2×C412yes—
87C2×C22⋊C4×C83C2×C412yes—
88C2×C42×C83—21no—
89C2×C42×C83—21no—
90#101×C83—24no—
91#100×C83—24no—
92#99×C83—28no—
93C22⋊C8×C83—28no—
94#97×C83—24no—
95C4×C8×C83—24no—
96C24×C83C4212yes—
97C24×C83C22×C411yescharacteristic
98#41×C83—41no—
99#41×C83—41no—
100#41×C83—41no—
101#41×C83—41no—
102#41×C83—41no—
103#41×C83—41no—
104#41×C83—41no—
105#41×C83—41no—
106#41×C83—41no—
107#41×C83—41no—
108#41×C83—41no—
109#41×C83—41no—
110#41×C83—41no—
111#41×C83—41no—
112#41×C83—41no—
113#41×C83—41no—
114C2×Q8×C83—21no—
115C2×Q8×C83—21no—
116C2×Q8×C83—21no—
117C2×Q8×C83—21no—
118C2×Q8×C83—21no—
119C2×Q8×C83—21no—
120C2×D4×C83—22no—
121C2×D4×C83—22no—
122C2×D4×C83—22no—
123C2×D4×C83—22no—
124C2×D4×C83—22no—
125C2×D4×C83—22no—
126C2×D4×C83—21no—
127C2×D4×C83—21no—
128C2×D4×C83—21no—
129C2×D4×C83—21no—
130C2×D4×C83—21no—
131C2×D4×C83—21no—
132C22×C4×C83—22no—
133C22×C4×C83—22no—
134C22×C4×C83—22no—
135C22×C4×C83—22no—
136C22×C4×C83—22no—
137C22×C4×C83—22no—
138C22×C4×C83—22no—
139C22×C4×C83—22no—
140C22×C4×C83C4212yes—
141C22×C4×C83C22×C411yescharacteristic
142C22×C4×C83C22×C411yescharacteristic
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×C83#4111yescharacteristic
150C22×C4×C83#4111yescharacteristic
151C22×C4×C83#4111yescharacteristic
152C22×C4×C83#4111yescharacteristic
153C22×C4×C83#4111yescharacteristic
154C22×C4×C83#4111yescharacteristic
155M16×C83—22no—
156M16×C83—22no—
157M16×C83—22no—
158M16×C83—22no—
159M16×C83—22no—
160M16×C83—22no—
161M16×C83—22no—
162M16×C83—22no—
163M16×C83—22no—
164M16×C83—22no—
165M16×C83—22no—
166M16×C83—41no—
167M16×C83—41no—
168M16×C83—41no—
169M16×C83—41no—
170M16×C83C22⋊C414yes—
171C2×C8×C83—22no—
172C2×C8×C83—22no—
173C2×C8×C83—22no—
174C2×C8×C83—22no—
175C2×C8×C83—22no—
176C2×C8×C83—22no—
177C2×C8×C83—22no—
178C2×C8×C83—41no—
179C2×C8×C83—41no—
180C2×C8×C83—41no—
181C2×C8×C83—41no—
182C2×C8×C83C22⋊C414yes—
183C4⋊C4×C83—22no—
184C4⋊C4×C83—22no—
185C4⋊C4×C83—41no—
186C4⋊C4×C83—41no—
187C22⋊C4×C83—22no—
188C22⋊C4×C83—22no—
189C22⋊C4×C83—22no—
190C22⋊C4×C83C22⋊C414yes—
191C42×C83—22no—
192C42×C83—22no—
193C42×C83—41no—
194C42×C83—41no—
195C23×C83—22no—
196C23×C83—22no—
197C23×C83—22no—
198C23×C83—81no—
199C23×C83—82no—
200C23×C83C2×C4211yescharacteristic
201C23×C83C2×C22⋊C411yescharacteristic
202C23×C83#11711yescharacteristic
203C23×C83C4×D411yescharacteristic
204C23×C83C4×D411yescharacteristic
205C23×C83C4×D411yescharacteristic
206C23×C83C4×D411yescharacteristic
207Q8×C83—41no—
208Q8×C83—41no—
209Q8×C83—41no—
210Q8×C83—41no—
211D4×C83—42no—
212D4×C83—42no—
213D4×C83—42no—
214D4×C83—42no—
215D4×C83—41no—
216D4×C83—41no—
217D4×C83—41no—
218D4×C83—41no—
219C2×C4×C83—22no—
220C2×C4×C83—22no—
221C2×C4×C83—22no—
222C2×C4×C83—24no—
223C2×C4×C83—42no—
224C2×C4×C83—42no—
225C2×C4×C83—42no—
226C2×C4×C83—42no—
227C2×C4×C83—42no—
228C2×C4×C83—82no—
229C2×C4×C83—82no—
230C2×C4×C83C2×C22⋊C411yescharacteristic
231C2×C4×C83C2×C22⋊C411yescharacteristic
232C2×C4×C83#11711yescharacteristic
233C2×C4×C83#11711yescharacteristic
234C2×C4×C83C4×D411yescharacteristic
235C2×C4×C83C4×D411yescharacteristic
236C2×C4×C83C4×D411yescharacteristic
237C2×C4×C83C4×D411yescharacteristic
238C2×C4×C83C4×D411yescharacteristic
239C2×C4×C83C4×D411yescharacteristic
240C2×C4×C83C4×D411yescharacteristic
241C2×C4×C83C4×D411yescharacteristic
242C2×C4×C83#12011yescharacteristic
243C2×C4×C83#12111yescharacteristic
244C2×C4×C83#12111yescharacteristic
245C2×C4×C83#12111yescharacteristic
246C2×C4×C83#12111yescharacteristic
247C2×C4×C83#12111yescharacteristic
248C2×C4×C83#12111yescharacteristic
249C2×C4×C83#12311yescharacteristic
250C2×C4×C83#12311yescharacteristic
251C2×C4×C83#12311yescharacteristic
252C2×C4×C83#12411yescharacteristic
253C2×C4×C83#12411yescharacteristic
254C2×C4×C83#12411yescharacteristic
255C2×C4×C83#12611yescharacteristic
256C2×C4×C83#12611yescharacteristic
257C2×C4×C83#12711yescharacteristic
258C8×C83—24no—
259C8×C83—24no—
260C8×C83—42no—
261C8×C83—42no—
262C22×C83—41no—
263C22×C83—41no—
264C22×C83—41no—
265C22×C83—41no—
266C22×C83—41no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83—44no—
270C22×C83—42no—
271C22×C83—82no—
272C22×C83—82no—
273C22×C83C4×C22⋊C411yescharacteristic
274C22×C83C4×C22⋊C411yescharacteristic
275C22×C83C4×C22⋊C411yescharacteristic
276C22×C83#38611yescharacteristic
277C22×C83#38811yescharacteristic
278C22×C83#38811yescharacteristic
279C22×C83#39011yescharacteristic
280C4×C83—44no—
281C4×C83—42no—
282C4×C83—82no—
283C4×C83#38611yescharacteristic
284C4×C83#38611yescharacteristic
285C4×C83#38811yescharacteristic
286C4×C83#38811yescharacteristic
287C4×C83#38811yescharacteristic
288C4×C83#38811yescharacteristic
289C4×C83#39011yescharacteristic
290C4×C83#39011yescharacteristic
291#10941C8311yesmaximal, characteristic, direct product factor, Sylow
292C2×C83—21no—
293C2×C83—21no—
294C2×C83—21no—
295C2×C83—21no—
296C2×C83—21no—
297C2×C83—21no—
298C2×C83—21no—
299C2×C83—82no—
300C2×C83#143711yescharacteristic
301C2×#413C2×C8311yescharacteristic
302C2×#410C2×C8311yescharacteristic
303#2879C2×C8311yescharacteristic
304#2873C2×C8311yescharacteristic, complemented
305C2×#344C2×C8311yescharacteristic, complemented
306C2×#344C2×C8311yescharacteristic, complemented
307#1742C2×C8311yescharacteristic, complemented
308C83#1094111yescharacteristic, direct product factor, Sylow
309C22×#41C22×C8311yescharacteristic
310C22×M16C22×C8311yescharacteristic
311C22×M16C22×C8311yescharacteristic
312C22×M16C22×C8311yescharacteristic
313C22×M16C22×C8311yescharacteristic
314C2×#117C22×C8311yescharacteristic
315C2×#117C22×C8311yescharacteristic
316#413—22no—
317#413—22no—
318C2×#101C4×C8312yescomplemented
319C2×#100C4×C8312yescomplemented
320#410—22no—
321#410—22no—
322C2×#99C4×C8314yes—
323#408—22no—
324#408—22no—
325#407C4×C8314yescomplemented
326#405—22no—
327#405—22no—
328C4×M16—22no—
329#344—22no—
330#344—22no—
331#343—22no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C22×Q8C2×C4×C8311yescharacteristic
345C22×D4C2×C4×C8312yes—
346C22×D4C2×C4×C8311yescharacteristic
347C23×C4C2×C4×C8312yes—
348C23×C4C23×C8311yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16C2×C4×C8312yes—
367C2×M16C2×C4×C8312yes—
368C2×M16C2×C4×C8312yes—
369C2×M16C2×C4×C8312yes—
370C2×M16D4×C8312yes—
371C2×M16D4×C8312yes—
372C2×M16D4×C8312yes—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8D4×C8312yes—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117D4×C8312yes—
384#117D4×C8312yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C22⋊C4C2×C4×C8312yes—
388C2×C22⋊C4C2×C4×C8312yes—
389C2×C42—21no—
390C2×C42—21no—
391#101—24no—
392#100—24no—
393#99—28no—
394C22⋊C8—28no—
395#97—24no—
396C4×C8—24no—
397C24C42×C8312yes—
398C24C22×C4×C8311yescharacteristic
399#41—41no—
400#41—41no—
401#41—41no—
402#41—41no—
403#41—41no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
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×C4C42×C8312yes—
442C22×C4C22×C4×C8311yescharacteristic
443C22×C4C22×C4×C8311yescharacteristic
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×C4#41×C8311yescharacteristic
451C22×C4#41×C8311yescharacteristic
452C22×C4#41×C8311yescharacteristic
453C22×C4#41×C8311yescharacteristic
454C22×C4#41×C8311yescharacteristic
455C22×C4#41×C8311yescharacteristic
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16C22⋊C4×C8314yes—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8C22⋊C4×C8314yes—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4C22⋊C4×C8314yes—
492C42—22no—
493C42—22no—
494C42—41no—
495C42—41no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—81no—
500C23—82no—
501C23C2×C42×C8311yescharacteristic
502C23C2×C22⋊C4×C8311yescharacteristic
503C23#117×C8311yescharacteristic
504C23C4×D4×C8311yescharacteristic
505C23C4×D4×C8311yescharacteristic
506C23C4×D4×C8311yescharacteristic
507C23C4×D4×C8311yescharacteristic
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4C2×C22⋊C4×C8311yescharacteristic
532C2×C4C2×C22⋊C4×C8311yescharacteristic
533C2×C4#117×C8311yescharacteristic
534C2×C4#117×C8311yescharacteristic
535C2×C4C4×D4×C8311yescharacteristic
536C2×C4C4×D4×C8311yescharacteristic
537C2×C4C4×D4×C8311yescharacteristic
538C2×C4C4×D4×C8311yescharacteristic
539C2×C4C4×D4×C8311yescharacteristic
540C2×C4C4×D4×C8311yescharacteristic
541C2×C4C4×D4×C8311yescharacteristic
542C2×C4C4×D4×C8311yescharacteristic
543C2×C4#120×C8311yescharacteristic
544C2×C4#121×C8311yescharacteristic
545C2×C4#121×C8311yescharacteristic
546C2×C4#121×C8311yescharacteristic
547C2×C4#121×C8311yescharacteristic
548C2×C4#121×C8311yescharacteristic
549C2×C4#121×C8311yescharacteristic
550C2×C4#123×C8311yescharacteristic
551C2×C4#123×C8311yescharacteristic
552C2×C4#123×C8311yescharacteristic
553C2×C4#124×C8311yescharacteristic
554C2×C4#124×C8311yescharacteristic
555C2×C4#124×C8311yescharacteristic
556C2×C4#126×C8311yescharacteristic
557C2×C4#126×C8311yescharacteristic
558C2×C4#127×C8311yescharacteristic
559C8—24no—
560C8—24no—
561C8—42no—
562C8—42no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—44no—
571C22—42no—
572C22—82no—
573C22—82no—
574C22C4×C22⋊C4×C8311yescharacteristic
575C22C4×C22⋊C4×C8311yescharacteristic
576C22C4×C22⋊C4×C8311yescharacteristic
577C22#386×C8311yescharacteristic
578C22#388×C8311yescharacteristic
579C22#388×C8311yescharacteristic
580C22#390×C8311yescharacteristic
581C4—44no—
582C4—42no—
583C4—82no—
584C4#386×C8311yescharacteristic
585C4#386×C8311yescharacteristic
586C4#388×C8311yescharacteristic
587C4#388×C8311yescharacteristic
588C4#388×C8311yescharacteristic
589C4#388×C8311yescharacteristic
590C4#390×C8311yescharacteristic
591C4#390×C8311yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—82no—
600C2C83×#143711yescharacteristic
subgroupG/H
centerC4×C83#386
commutatorC23C2×C42×C83
Frattini, cosocleC23×C4C23×C83
socleC2×C83#1437
prime radicalC22×#41×C83C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C4×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
4. C83×#2873C2semidirect
5. C2×#344×C83C2semidirect
6. C2×#344×C83C2semidirect
7. C83×#1742C2semidirect
17. C2×#101×C83C4semidirect
18. C2×#100×C83C4semidirect
24. #407×C83C4semidirect
291. #10941C83direct (N × H)
304. #2873C2×C83semidirect
305. C2×#344C2×C83semidirect
306. C2×#344C2×C83semidirect
307. #1742C2×C83semidirect
308. C83#10941direct (N × H)
318. C2×#101C4×C83semidirect
319. C2×#100C4×C83semidirect
325. #407C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#413×C832
C2×#410×C832
C83×#28792
C83×#28732
C2×#344×C832
C83×#17422
#1094183