Finite Group Databasebeta

← C83×#25192 #35253016

Subgroups — C83×#25192 #35253016

Order 21248.

1054 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3062C211yesmaximal, characteristic, complemented
2C83×#3045C211yesmaximal, characteristic, complemented
3C2×#453×C83C211yesmaximal, characteristic, complemented
4C83×#3012C211yesmaximal, characteristic, complemented
5C2×#444×C83C211yesmaximal, characteristic, complemented
6C83×#2897C211yesmaximal, characteristic, complemented
7C83×#2063C211yesmaximal, characteristic, complemented
8C83×#2051C211yesmaximal, characteristic, complemented
9C83×#2040C211yesmaximal, characteristic, complemented
10C83×#2002C211yesmaximal, characteristic, complemented
11C83×#1961C211yesmaximal, characteristic, complemented
12C83×#1938C211yesmaximal, characteristic, complemented
13C83×#1907C211yesmaximal, characteristic, complemented
14C83×#1907C211yesmaximal, characteristic, complemented
15C83×#1860C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C83C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C83C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C83C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C83C2211yescharacteristic
20C2×#135×C83C2211yescharacteristic
21C2×#131×C83C2211yescharacteristic
22C2×#131×C83C2211yescharacteristic, complemented
23#537×C83C2211yescharacteristic
24#535×C83C2211yescharacteristic, complemented
25C2×#127×C83C2211yescharacteristic
26#520×C83C2211yescharacteristic
27#469×C83—21no—
28#468×C83—21no—
29#466×C83—21no—
30#465×C83—21no—
31#464×C83—21no—
32#463×C83—21no—
33#460×C83—21no—
34#459×C83—21no—
35#453×C83—24no—
36#452×C83—21no—
37#450×C83—21no—
38#449×C83—21no—
39#447×C83—21no—
40#444×C83—24no—
41C2×#108×C83C2211yescharacteristic, complemented
42#428×C83C2211yescharacteristic, complemented
43#424×C83C2211yescharacteristic, complemented
44C2×#104×C83C2211yescharacteristic
45C2×#104×C83C2211yescharacteristic
46C2×#104×C83C2211yescharacteristic, complemented
47#418×C83—21no—
48#418×C83C2211yescharacteristic
49#417×C83—21no—
50#417×C83C2211yescharacteristic
51#417×C83C2211yescharacteristic
52#417×C83C2211yescharacteristic, complemented
53#416×C83—21no—
54#416×C83C2211yescharacteristic
55C2×#102×C83—21no—
56C2×#102×C83C2211yescharacteristic
57C2×#102×C83C2211yescharacteristic
58C2×#102×C83C2211yescharacteristic, complemented
59C2×#102×C83C2211yescharacteristic, complemented
60C2×#100×C83C2211yescharacteristic
61C2×#100×C83C2211yescharacteristic, complemented
62#408×C83C2211yescharacteristic
63C2×#97×C83C2211yescharacteristic, complemented
64#382×C83C2211yescharacteristic, complemented
65#343×C83C2211yescharacteristic, complemented
66#343×C83C2211yescharacteristic, complemented
67#341×C83C2211yescharacteristic, complemented
68#339×C83C2211yescharacteristic, complemented
69H(5,𝔽2)×C83—22no—
70H(5,𝔽2)×C83—22no—
71H(5,𝔽2)×C83—22no—
72H(5,𝔽2)×C83—41no—
73C2×#41×C83—21no—
74C2×#41×C83—21no—
75C2×#41×C83C2311yescharacteristic
76C2×#41×C83C2311yescharacteristic
77C2×#41×C83C2311yescharacteristic
78C22×D4×C83—21no—
79C22×D4×C83—21no—
80C22×D4×C83—41no—
81C22×D4×C83—41no—
82C22×D4×C83C2311yescharacteristic
83C22×D4×C83C2311yescharacteristic
84AGL(1,ℤ/8)×C83—22no—
85AGL(1,ℤ/8)×C83—22no—
86AGL(1,ℤ/8)×C83—22no—
87AGL(1,ℤ/8)×C83—22no—
88AGL(1,ℤ/8)×C83—41no—
89AGL(1,ℤ/8)×C83—41no—
90#135×C83—22no—
91#135×C83—22no—
92C2×Q16×C83D411yescharacteristic, complemented
93C2×SD16×C83—21no—
94C2×SD16×C83—21no—
95C2×SD16×C83—21no—
96C2×SD16×C83D411yescharacteristic, complemented
97C2×SD16×C83D411yescharacteristic, complemented
98C2×D8×C83—21no—
99C2×D8×C83—21no—
100C2×D8×C83—21no—
101C2×D8×C83D411yescharacteristic, complemented
102#131×C83—22no—
103#131×C83—22no—
104#131×C83—41no—
105#131×C83—41no—
106C2×M16×C83—21no—
107C2×M16×C83—21no—
108C2×M16×C83C2311yescharacteristic
109C2×M16×C83C2311yescharacteristic
110C2×M16×C83C2311yescharacteristic
111C2×M16×C83C2311yescharacteristic
112C22×C8×C83—21no—
113C22×C8×C83—21no—
114C22×C8×C83C2311yescharacteristic
115C22×C8×C83C2311yescharacteristic
116#127×C83—21no—
117#127×C83—22no—
118#127×C83—22no—
119#124×C83—21no—
120C22⋊Q8×C83—21no—
121C22⋊Q8×C83—21no—
122#121×C83—21no—
123#121×C83—21no—
124#121×C83—21no—
125#121×C83—21no—
126#121×C83—41no—
127#120×C83—41no—
128C4×Q8×C83—21no—
129C4×D4×C83—21no—
130C4×D4×C83—41no—
131#117×C83—21no—
132#117×C83C2311yescharacteristic
133C2×C4⋊C4×C83—21no—
134C2×C4⋊C4×C83C2311yescharacteristic
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C42×C83C2311yescharacteristic
137#108×C83—22no—
138#107×C83—21no—
139#106×C83—21no—
140C4⋊C8×C83—21no—
141C4⋊C8×C83—21no—
142#104×C83—22no—
143#104×C83—22no—
144#104×C83D414yescomplemented
145#103×C83—21no—
146#103×C83—21no—
147#103×C83—21no—
148#103×C83D411yescharacteristic, complemented
149#103×C83D411yescharacteristic, complemented
150#102×C83—21no—
151#102×C83—21no—
152#102×C83—21no—
153#102×C83—21no—
154#102×C83—21no—
155#102×C83—21no—
156#102×C83—21no—
157#102×C83—21no—
158#102×C83—21no—
159#102×C83—21no—
160#102×C83—21no—
161#102×C83—21no—
162#102×C83—21no—
163#102×C83D411yescharacteristic, complemented
164#102×C83D411yescharacteristic, complemented
165#100×C83—22no—
166#100×C83—41no—
167C22⋊C8×C83—21no—
168C22⋊C8×C83—21no—
169#97×C83—22no—
170#95×C83—41no—
171C24×C83—21no—
172C24×C83—21no—
173C24×C83—41no—
174#41×C83—21no—
175#41×C83—21no—
176#41×C83—24no—
177#41×C83—21no—
178#41×C83—21no—
179#41×C83—21no—
180#41×C83—21no—
181#41×C83—21no—
182#41×C83—21no—
183#41×C83—21no—
184#41×C83—21no—
185#41×C83—42no—
186#41×C83—42no—
187#41×C83—42no—
188#41×C83C2×D412yes—
189#41×C83#4112yes—
190C2×Q8×C83C2×D411yescharacteristic
191C2×Q8×C83C2×D411yescharacteristic
192C2×Q8×C83C2×D411yescharacteristic
193C2×D4×C83—21no—
194C2×D4×C83—24no—
195C2×D4×C83—21no—
196C2×D4×C83—21no—
197C2×D4×C83—21no—
198C2×D4×C83—21no—
199C2×D4×C83—21no—
200C2×D4×C83—21no—
201C2×D4×C83—21no—
202C2×D4×C83—21no—
203C2×D4×C83—21no—
204C2×D4×C83—21no—
205C2×D4×C83—21no—
206C2×D4×C83—21no—
207C2×D4×C83—21no—
208C2×D4×C83—42no—
209C2×D4×C83—41no—
210C2×D4×C83—41no—
211C2×D4×C83—44no—
212C2×D4×C83—41no—
213C2×D4×C83—41no—
214C2×D4×C83—42no—
215C2×D4×C83—44no—
216C2×D4×C83—44no—
217C2×D4×C83—42no—
218C2×D4×C83—41no—
219C2×D4×C83—82no—
220C2×D4×C83—82no—
221C2×D4×C83C2×D411yescharacteristic
222C2×D4×C83C2×D411yescharacteristic
223C2×D4×C83C2×D411yescharacteristic
224C2×D4×C83#4112yes—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—41no—
232C22×C4×C83—41no—
233C22×C4×C83C2411yescharacteristic
234Q16×C83—22no—
235SD16×C83—22no—
236SD16×C83—22no—
237SD16×C83—42no—
238SD16×C83—42no—
239SD16×C83—42no—
240D8×C83—22no—
241D8×C83—42no—
242D8×C83—42no—
243D8×C83—42no—
244M16×C83—21no—
245M16×C83—21no—
246M16×C83—21no—
247M16×C83—21no—
248M16×C83—21no—
249M16×C83—21no—
250M16×C83—21no—
251M16×C83—42no—
252M16×C83—42no—
253M16×C83C2×D412yes—
254C2×C8×C83—21no—
255C2×C8×C83—21no—
256C2×C8×C83—21no—
257C2×C8×C83—21no—
258C2×C8×C83—21no—
259C2×C8×C83—21no—
260C2×C8×C83—21no—
261C2×C8×C83—21no—
262C2×C8×C83—42no—
263C2×C8×C83—42no—
264C2×C8×C83C2×D411yescharacteristic
265C2×C8×C83C2×D411yescharacteristic
266C2×C8×C83C2×D411yescharacteristic
267C2×C8×C83C2×D411yescharacteristic
268C4⋊C4×C83—21no—
269C4⋊C4×C83—21no—
270C4⋊C4×C83—21no—
271C4⋊C4×C83—21no—
272C4⋊C4×C83—41no—
273C4⋊C4×C83—41no—
274C4⋊C4×C83C2×D411yescharacteristic
275C4⋊C4×C83C2×D411yescharacteristic
276C22⋊C4×C83—21no—
277C22⋊C4×C83—41no—
278C22⋊C4×C83—41no—
279C22⋊C4×C83—41no—
280C22⋊C4×C83—41no—
281C22⋊C4×C83—41no—
282C42×C83—21no—
283C42×C83—21no—
284C42×C83—41no—
285C42×C83C2×D412yes—
286C23×C83—21no—
287C23×C83—21no—
288C23×C83—21no—
289C23×C83—22no—
290C23×C83—44no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83—41no—
295C23×C83—41no—
296C23×C83—81no—
297C23×C83—81no—
298C23×C83—81no—
299C23×C83—81no—
300C23×C83—161no—
301C23×C83—161no—
302C23×C83H(5,𝔽2)11yescharacteristic
303Q8×C83—21no—
304Q8×C83—21no—
305Q8×C83—21no—
306Q8×C83—21no—
307Q8×C83—21no—
308Q8×C83#12112yes—
309D4×C83—22no—
310D4×C83—22no—
311D4×C83—21no—
312D4×C83—21no—
313D4×C83—22no—
314D4×C83—21no—
315D4×C83—21no—
316D4×C83—21no—
317D4×C83—22no—
318D4×C83—44no—
319D4×C83—44no—
320D4×C83—41no—
321D4×C83—41no—
322D4×C83—41no—
323D4×C83—41no—
324D4×C83—41no—
325D4×C83—41no—
326D4×C83—41no—
327D4×C83—41no—
328D4×C83—41no—
329D4×C83—41no—
330D4×C83—88no—
331D4×C83—161no—
332D4×C83—161no—
333D4×C83—161no—
334D4×C83#12112yes—
335C2×C4×C83—21no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—21no—
339C2×C4×C83—21no—
340C2×C4×C83—21no—
341C2×C4×C83—21no—
342C2×C4×C83—22no—
343C2×C4×C83—44no—
344C2×C4×C83—41no—
345C2×C4×C83—41no—
346C2×C4×C83—41no—
347C2×C4×C83—41no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—41no—
351C2×C4×C83—41no—
352C2×C4×C83—81no—
353C2×C4×C83—81no—
354C2×C4×C83—161no—
355C2×C4×C83C22×D411yescharacteristic
356C2×C4×C83C22×D411yescharacteristic
357C2×C4×C83C22×D411yescharacteristic
358C2×C4×C83C2×#4111yescharacteristic
359C2×C4×C83C2×#4111yescharacteristic
360C2×C4×C83H(5,𝔽2)11yescharacteristic
361C8×C83—21no—
362C8×C83—21no—
363C8×C83—21no—
364C8×C83—21no—
365C8×C83—22no—
366C8×C83—41no—
367C8×C83—41no—
368C8×C83—41no—
369C22×C83—21no—
370C22×C83—21no—
371C22×C83—22no—
372C22×C83—41no—
373C22×C83—41no—
374C22×C83—41no—
375C22×C83—42no—
376C22×C83—41no—
377C22×C83—41no—
378C22×C83—41no—
379C22×C83—41no—
380C22×C83—41no—
381C22×C83—82no—
382C22×C83—82no—
383C22×C83—81no—
384C22×C83—81no—
385C22×C83—81no—
386C22×C83—81no—
387C22×C83—81no—
388C22×C83—161no—
389C22×C83—161no—
390C22×C83—164no—
391C22×C83#53811yescharacteristic
392C22×C83D4211yescharacteristic
393C22×C83#54611yescharacteristic
394C4×C83—22no—
395C4×C83—42no—
396C4×C83—41no—
397C4×C83—41no—
398C4×C83—41no—
399C4×C83—41no—
400C4×C83—81no—
401C4×C83—81no—
402C4×C83C2×#12111yescharacteristic
403C4×C83#52511yescharacteristic
404C4×C83D4211yescharacteristic
405C4×C83#54611yescharacteristic
406#25192C8311yesmaximal, characteristic, direct product factor, Sylow
407C2×C83—21no—
408C2×C83—21no—
409C2×C83—42no—
410C2×C83—81no—
411C2×C83—81no—
412C2×C83—82no—
413C2×C83—161no—
414C2×C83#242411yescharacteristic
415C2×C83#328811yescharacteristic
416C2×C83#328811yescharacteristic
417#3062C2×C8311yescharacteristic, complemented
418#3045C2×C8311yescharacteristic, complemented
419C2×#453C2×C8311yescharacteristic, complemented
420#3012C2×C8311yescharacteristic, complemented
421C2×#444C2×C8311yescharacteristic, complemented
422#2897C2×C8311yescharacteristic, complemented
423#2063C2×C8311yescharacteristic, complemented
424#2051C2×C8311yescharacteristic, complemented
425#2040C2×C8311yescharacteristic, complemented
426#2002C2×C8311yescharacteristic, complemented
427#1961C2×C8311yescharacteristic, complemented
428#1938C2×C8311yescharacteristic, complemented
429#1907C2×C8311yescharacteristic, complemented
430#1907C2×C8311yescharacteristic, complemented
431#1860C2×C8311yescharacteristic, complemented
432C83#2519211yescharacteristic, direct product factor, Sylow
433C2×H(5,𝔽2)C22×C8311yescharacteristic
434C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
435C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
436C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
437C2×#135C22×C8311yescharacteristic
438C2×#131C22×C8311yescharacteristic
439C2×#131C22×C8311yescharacteristic, complemented
440#537C22×C8311yescharacteristic
441#535C22×C8311yescharacteristic, complemented
442C2×#127C22×C8311yescharacteristic
443#520C22×C8311yescharacteristic
444#469—21no—
445#468—21no—
446#466—21no—
447#465—21no—
448#464—21no—
449#463—21no—
450#460—21no—
451#459—21no—
452#453—24no—
453#452—21no—
454#450—21no—
455#449—21no—
456#447—21no—
457#444—24no—
458C2×#108C22×C8311yescharacteristic, complemented
459#428C22×C8311yescharacteristic, complemented
460#424C22×C8311yescharacteristic, complemented
461C2×#104C22×C8311yescharacteristic
462C2×#104C22×C8311yescharacteristic
463C2×#104C22×C8311yescharacteristic, complemented
464#418—21no—
465#418C22×C8311yescharacteristic
466#417—21no—
467#417C22×C8311yescharacteristic
468#417C22×C8311yescharacteristic
469#417C22×C8311yescharacteristic, complemented
470#416—21no—
471#416C22×C8311yescharacteristic
472C2×#102—21no—
473C2×#102C22×C8311yescharacteristic
474C2×#102C22×C8311yescharacteristic
475C2×#102C22×C8311yescharacteristic, complemented
476C2×#102C22×C8311yescharacteristic, complemented
477C2×#100C22×C8311yescharacteristic
478C2×#100C22×C8311yescharacteristic, complemented
479#408C22×C8311yescharacteristic
480C2×#97C22×C8311yescharacteristic, complemented
481#382C22×C8311yescharacteristic, complemented
482#343C22×C8311yescharacteristic, complemented
483#343C22×C8311yescharacteristic, complemented
484#341C22×C8311yescharacteristic, complemented
485#339C22×C8311yescharacteristic, complemented
486H(5,𝔽2)—22no—
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—41no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41C23×C8311yescharacteristic
493C2×#41C23×C8311yescharacteristic
494C2×#41C23×C8311yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C8311yescharacteristic
500C22×D4C23×C8311yescharacteristic
501AGL(1,ℤ/8)—22no—
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—41no—
506AGL(1,ℤ/8)—41no—
507#135—22no—
508#135—22no—
509C2×Q16D4×C8311yescharacteristic, complemented
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16D4×C8311yescharacteristic, complemented
514C2×SD16D4×C8311yescharacteristic, complemented
515C2×D8—21no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8D4×C8311yescharacteristic, complemented
519#131—22no—
520#131—22no—
521#131—41no—
522#131—41no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16C23×C8311yescharacteristic
526C2×M16C23×C8311yescharacteristic
527C2×M16C23×C8311yescharacteristic
528C2×M16C23×C8311yescharacteristic
529C22×C8—21no—
530C22×C8—21no—
531C22×C8C23×C8311yescharacteristic
532C22×C8C23×C8311yescharacteristic
533#127—21no—
534#127—22no—
535#127—22no—
536#124—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—41no—
544#120—41no—
545C4×Q8—21no—
546C4×D4—21no—
547C4×D4—41no—
548#117—21no—
549#117C23×C8311yescharacteristic
550C2×C4⋊C4—21no—
551C2×C4⋊C4C23×C8311yescharacteristic
552C2×C4⋊C4C23×C8311yescharacteristic
553C2×C42C23×C8311yescharacteristic
554#108—22no—
555#107—21no—
556#106—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559#104—22no—
560#104—22no—
561#104D4×C8314yescomplemented
562#103—21no—
563#103—21no—
564#103—21no—
565#103D4×C8311yescharacteristic, complemented
566#103D4×C8311yescharacteristic, complemented
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102D4×C8311yescharacteristic, complemented
581#102D4×C8311yescharacteristic, complemented
582#100—22no—
583#100—41no—
584C22⋊C8—21no—
585C22⋊C8—21no—
586#97—22no—
587#95—41no—
588C24—21no—
589C24—21no—
590C24—41no—
591#41—21no—
592#41—21no—
593#41—24no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41C2×D4×C8312yes—
606#41#41×C8312yes—
607C2×Q8C2×D4×C8311yescharacteristic
608C2×Q8C2×D4×C8311yescharacteristic
609C2×Q8C2×D4×C8311yescharacteristic
610C2×D4—21no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—44no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—41no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C8311yescharacteristic
639C2×D4C2×D4×C8311yescharacteristic
640C2×D4C2×D4×C8311yescharacteristic
641C2×D4#41×C8312yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C8311yescharacteristic
651Q16—22no—
652SD16—22no—
653SD16—22no—
654SD16—42no—
655SD16—42no—
656SD16—42no—
657D8—22no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16—42no—
670M16C2×D4×C8312yes—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—42no—
681C2×C8C2×D4×C8311yescharacteristic
682C2×C8C2×D4×C8311yescharacteristic
683C2×C8C2×D4×C8311yescharacteristic
684C2×C8C2×D4×C8311yescharacteristic
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4C2×D4×C8311yescharacteristic
692C4⋊C4C2×D4×C8311yescharacteristic
693C22⋊C4—21no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C42—21no—
700C42—21no—
701C42—41no—
702C42C2×D4×C8312yes—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—161no—
718C23—161no—
719C23H(5,𝔽2)×C8311yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8#121×C8312yes—
726D4—22no—
727D4—22no—
728D4—21no—
729D4—21no—
730D4—22no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—22no—
735D4—44no—
736D4—44no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—88no—
748D4—161no—
749D4—161no—
750D4—161no—
751D4#121×C8312yes—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—161no—
772C2×C4C22×D4×C8311yescharacteristic
773C2×C4C22×D4×C8311yescharacteristic
774C2×C4C22×D4×C8311yescharacteristic
775C2×C4C2×#41×C8311yescharacteristic
776C2×C4C2×#41×C8311yescharacteristic
777C2×C4H(5,𝔽2)×C8311yescharacteristic
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—161no—
806C22—161no—
807C22—164no—
808C22#538×C8311yescharacteristic
809C22D42×C8311yescharacteristic
810C22#546×C8311yescharacteristic
811C4—22no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4C2×#121×C8311yescharacteristic
820C4#525×C8311yescharacteristic
821C4D42×C8311yescharacteristic
822C4#546×C8311yescharacteristic
823C2—21no—
824C2—21no—
825C2—42no—
826C2—81no—
827C2—81no—
828C2—82no—
829C2—161no—
830C2C83×#242411yescharacteristic
831C2C83×#328811yescharacteristic
832C2C83×#328811yescharacteristic
subgroupG/H
center, socleC22×C83D42
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C22×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3062C2semidirect
2. C83×#3045C2semidirect
3. C2×#453×C83C2semidirect
4. C83×#3012C2semidirect
5. C2×#444×C83C2semidirect
6. C83×#2897C2semidirect
7. C83×#2063C2semidirect
8. C83×#2051C2semidirect
9. C83×#2040C2semidirect
10. C83×#2002C2semidirect
11. C83×#1961C2semidirect
12. C83×#1938C2semidirect
13. C83×#1907C2semidirect
14. C83×#1907C2semidirect
15. C83×#1860C2semidirect
22. C2×#131×C83C22semidirect
24. #535×C83C22semidirect
41. C2×#108×C83C22semidirect
42. #428×C83C22semidirect
43. #424×C83C22semidirect
46. C2×#104×C83C22semidirect
52. #417×C83C22semidirect
58. C2×#102×C83C22semidirect
59. C2×#102×C83C22semidirect
61. C2×#100×C83C22semidirect
63. C2×#97×C83C22semidirect
64. #382×C83C22semidirect
65. #343×C83C22semidirect
66. #343×C83C22semidirect
67. #341×C83C22semidirect
68. #339×C83C22semidirect
92. C2×Q16×C83D4semidirect
96. C2×SD16×C83D4semidirect
97. C2×SD16×C83D4semidirect
101. C2×D8×C83D4semidirect
144. #104×C83D4semidirect
148. #103×C83D4semidirect
149. #103×C83D4semidirect
163. #102×C83D4semidirect
164. #102×C83D4semidirect
406. #25192C83direct (N × H)
417. #3062C2×C83semidirect
418. #3045C2×C83semidirect
419. C2×#453C2×C83semidirect
420. #3012C2×C83semidirect
421. C2×#444C2×C83semidirect
422. #2897C2×C83semidirect
423. #2063C2×C83semidirect
424. #2051C2×C83semidirect
425. #2040C2×C83semidirect
426. #2002C2×C83semidirect
427. #1961C2×C83semidirect
428. #1938C2×C83semidirect
429. #1907C2×C83semidirect
430. #1907C2×C83semidirect
431. #1860C2×C83semidirect
432. C83#25192direct (N × H)
439. C2×#131C22×C83semidirect
441. #535C22×C83semidirect
458. C2×#108C22×C83semidirect
459. #428C22×C83semidirect
460. #424C22×C83semidirect
463. C2×#104C22×C83semidirect
469. #417C22×C83semidirect
475. C2×#102C22×C83semidirect
476. C2×#102C22×C83semidirect
478. C2×#100C22×C83semidirect
480. C2×#97C22×C83semidirect
481. #382C22×C83semidirect
482. #343C22×C83semidirect
483. #343C22×C83semidirect
484. #341C22×C83semidirect
485. #339C22×C83semidirect
509. C2×Q16D4×C83semidirect
513. C2×SD16D4×C83semidirect
514. C2×SD16D4×C83semidirect
518. C2×D8D4×C83semidirect
561. #104D4×C83semidirect
565. #103D4×C83semidirect
566. #103D4×C83semidirect
580. #102D4×C83semidirect
581. #102D4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#30622
C83×#30452
C2×#453×C832
C83×#30122
C2×#444×C832
C83×#28972
C83×#20632
C83×#20512
C83×#20402
C83×#20022
C83×#19612
C83×#19382
C83×#19072
C83×#18602
#2519283