Finite Group Databasebeta

← C83×#25196 #35253020

Subgroups — C83×#25196 #35253020

Order 21248.

1032 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3068C211yesmaximal, characteristic, complemented
2C83×#3068C211yesmaximal, characteristic, complemented
3C83×#3019C211yesmaximal, characteristic, complemented
4C2×#453×C83C211yesmaximal, characteristic, complemented
5C83×#2956C211yesmaximal, characteristic, complemented
6C83×#2888C211yesmaximal, characteristic, complemented
7C83×#2069C211yesmaximal, characteristic, complemented
8C83×#2050C211yesmaximal, characteristic, complemented
9C83×#2048C211yesmaximal, characteristic, complemented
10C83×#2002C211yesmaximal, characteristic, complemented
11C83×#1965C211yesmaximal, characteristic, complemented
12C83×#1932C211yesmaximal, characteristic, complemented
13C83×#1914C211yesmaximal, characteristic, complemented
14C83×#1903C211yesmaximal, characteristic, complemented
15C83×#1861C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C83C2211yescharacteristic
17#575×C83C2211yescharacteristic
18#575×C83C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C83C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C83C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C83C2211yescharacteristic, complemented
22#568×C83C2211yescharacteristic
23#568×C83C2211yescharacteristic
24#568×C83C2211yescharacteristic, complemented
25#535×C83C2211yescharacteristic
26C2×#127×C83C2211yescharacteristic
27#472×C83—22no—
28#472×C83—22no—
29#471×C83—22no—
30#471×C83—22no—
31#455×C83—22no—
32#453×C83—22no—
33#453×C83—22no—
34#453×C83—22no—
35#444×C83—22no—
36#443×C83—22no—
37#430×C83C2211yescharacteristic, complemented
38#430×C83C2211yescharacteristic, complemented
39#430×C83C2211yescharacteristic, complemented
40#423×C83C2211yescharacteristic, complemented
41#421×C83C2211yescharacteristic
42#421×C83C2211yescharacteristic
43C2×#104×C83C2211yescharacteristic
44C2×#104×C83C2211yescharacteristic
45C2×#104×C83C2211yescharacteristic, complemented
46#418×C83C2211yescharacteristic, complemented
47#413×C83—22no—
48#413×C83C2211yescharacteristic
49#413×C83C2211yescharacteristic
50#413×C83C2211yescharacteristic, complemented
51C2×#100×C83—22no—
52C2×#100×C83C2211yescharacteristic
53C2×#100×C83C2211yescharacteristic
54C2×#100×C83C2211yescharacteristic
55C2×#100×C83C2211yescharacteristic
56C2×#100×C83C2211yescharacteristic, complemented
57C2×#100×C83C2211yescharacteristic, complemented
58C4×M16×C83C2211yescharacteristic, complemented
59#344×C83C2211yescharacteristic, complemented
60#344×C83C2211yescharacteristic, complemented
61#339×C83C2211yescharacteristic, complemented
62#338×C83C2211yescharacteristic, complemented
63H(5,𝔽2)×C83—22no—
64H(5,𝔽2)×C83—22no—
65H(5,𝔽2)×C83—41no—
66H(5,𝔽2)×C83—41no—
67C2×#41×C83—21no—
68C2×#41×C83—21no—
69C2×#41×C83C2311yescharacteristic
70C2×#41×C83C2311yescharacteristic
71C2×#41×C83C2311yescharacteristic
72C22×D4×C83—22no—
73C22×D4×C83—21no—
74C22×D4×C83—21no—
75C22×D4×C83—22no—
76C22×D4×C83C2311yescharacteristic
77C22×D4×C83C2311yescharacteristic
78#137×C83—21no—
79#137×C83—21no—
80#137×C83—21no—
81#137×C83D412yescomplemented
82AGL(1,ℤ/8)×C83—21no—
83AGL(1,ℤ/8)×C83—22no—
84AGL(1,ℤ/8)×C83—22no—
85AGL(1,ℤ/8)×C83—21no—
86AGL(1,ℤ/8)×C83—21no—
87AGL(1,ℤ/8)×C83—22no—
88AGL(1,ℤ/8)×C83—22no—
89AGL(1,ℤ/8)×C83—41no—
90AGL(1,ℤ/8)×C83—41no—
91AGL(1,ℤ/8)×C83D412yescomplemented
92#135×C83—22no—
93#135×C83—41no—
94C2×SD16×C83—21no—
95C2×SD16×C83—21no—
96C2×SD16×C83—21no—
97C2×D8×C83—21no—
98C2×D8×C83—21no—
99C2×D8×C83—21no—
100#131×C83—22no—
101#131×C83—22no—
102#131×C83—22no—
103#131×C83—22no—
104#131×C83—41no—
105#131×C83—41no—
106C2×M16×C83—22no—
107C2×M16×C83—22no—
108C2×M16×C83—41no—
109C2×M16×C83C2311yescharacteristic
110C2×M16×C83C2311yescharacteristic
111C2×M16×C83C2311yescharacteristic
112C2×M16×C83C2311yescharacteristic
113C2×M16×C83C2311yescharacteristic
114C2×M16×C83C2311yescharacteristic
115C2×M16×C83C2311yescharacteristic
116C2×M16×C83C2311yescharacteristic
117#127×C83—21no—
118#127×C83—21no—
119#127×C83—21no—
120#127×C83—41no—
121#124×C83—21no—
122#121×C83—41no—
123#120×C83—22no—
124#117×C83C2311yescharacteristic
125C2×C42×C83C2311yescharacteristic
126#108×C83—22no—
127#108×C83—22no—
128#108×C83—22no—
129C4⋊C8×C83—41no—
130#104×C83—22no—
131#104×C83—22no—
132#104×C83—21no—
133#104×C83—21no—
134#104×C83—21no—
135#104×C83—21no—
136#104×C83D412yescomplemented
137#104×C83D412yescomplemented
138#102×C83—41no—
139#101×C83—21no—
140#101×C83—21no—
141#101×C83D412yescomplemented
142#100×C83—21no—
143#100×C83—21no—
144#100×C83—22no—
145#100×C83—22no—
146#100×C83—22no—
147#100×C83—22no—
148#100×C83—22no—
149#100×C83—22no—
150#100×C83D412yescomplemented
151#97×C83—21no—
152C4×C8×C83—21no—
153C24×C83—22no—
154C24×C83—21no—
155C24×C83#4112yes—
156#41×C83—21no—
157#41×C83—21no—
158#41×C83—21no—
159#41×C83—21no—
160#41×C83—21no—
161#41×C83—21no—
162#41×C83—21no—
163#41×C83—21no—
164#41×C83—21no—
165#41×C83—21no—
166#41×C83—42no—
167#41×C83—42no—
168#41×C83—42no—
169#41×C83—42no—
170#41×C83C2×D412yes—
171#41×C83C2×D412yes—
172C2×Q8×C83C2×D411yescharacteristic
173C2×Q8×C83C2×D411yescharacteristic
174C2×Q8×C83#4111yescharacteristic
175C2×D4×C83—21no—
176C2×D4×C83—22no—
177C2×D4×C83—22no—
178C2×D4×C83—21no—
179C2×D4×C83—21no—
180C2×D4×C83—21no—
181C2×D4×C83—21no—
182C2×D4×C83—21no—
183C2×D4×C83—21no—
184C2×D4×C83—21no—
185C2×D4×C83—21no—
186C2×D4×C83—21no—
187C2×D4×C83—21no—
188C2×D4×C83—21no—
189C2×D4×C83—21no—
190C2×D4×C83—21no—
191C2×D4×C83—21no—
192C2×D4×C83—42no—
193C2×D4×C83—42no—
194C2×D4×C83—42no—
195C2×D4×C83—42no—
196C2×D4×C83—44no—
197C2×D4×C83—44no—
198C2×D4×C83—42no—
199C2×D4×C83—42no—
200C2×D4×C83—42no—
201C2×D4×C83—84no—
202C2×D4×C83C2×D411yescharacteristic
203C2×D4×C83C2×D411yescharacteristic
204C2×D4×C83#4111yescharacteristic
205C22×C4×C83—21no—
206C22×C4×C83—22no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83C2411yescharacteristic
211Q16×C83—22no—
212Q16×C83—41no—
213SD16×C83—22no—
214SD16×C83—22no—
215SD16×C83—42no—
216SD16×C83—42no—
217SD16×C83—41no—
218SD16×C83—41no—
219SD16×C83—42no—
220D8×C83—22no—
221D8×C83—42no—
222D8×C83—42no—
223D8×C83—41no—
224D8×C83—42no—
225M16×C83—21no—
226M16×C83—21no—
227M16×C83—21no—
228M16×C83—21no—
229M16×C83—21no—
230M16×C83—21no—
231M16×C83—21no—
232M16×C83—21no—
233M16×C83—21no—
234M16×C83—21no—
235M16×C83—21no—
236M16×C83—21no—
237M16×C83—42no—
238M16×C83—42no—
239M16×C83—42no—
240M16×C83C2×D412yes—
241M16×C83C2×D412yes—
242M16×C83C2×D412yes—
243M16×C83C2×D412yes—
244C2×C8×C83—21no—
245C2×C8×C83—21no—
246C2×C8×C83—21no—
247C2×C8×C83—21no—
248C2×C8×C83—21no—
249C2×C8×C83—21no—
250C2×C8×C83—21no—
251C2×C8×C83—21no—
252C2×C8×C83—42no—
253C2×C8×C83—42no—
254C2×C8×C83—42no—
255C4⋊C4×C83—21no—
256C22⋊C4×C83—21no—
257C22⋊C4×C83—42no—
258C42×C83—21no—
259C42×C83—21no—
260C42×C83C2×D411yescharacteristic
261C42×C83C2×D411yescharacteristic
262C23×C83—21no—
263C23×C83—22no—
264C23×C83—21no—
265C23×C83—22no—
266C23×C83—21no—
267C23×C83—22no—
268C23×C83—44no—
269C23×C83—41no—
270C23×C83—41no—
271C23×C83—41no—
272C23×C83—82no—
273C23×C83—82no—
274C23×C83—162no—
275C23×C83C2×#4111yescharacteristic
276Q8×C83—21no—
277Q8×C83—21no—
278Q8×C83—21no—
279Q8×C83—21no—
280Q8×C83—21no—
281Q8×C83#12112yes—
282D4×C83—22no—
283D4×C83—22no—
284D4×C83—21no—
285D4×C83—21no—
286D4×C83—21no—
287D4×C83—21no—
288D4×C83—21no—
289D4×C83—44no—
290D4×C83—44no—
291D4×C83—41no—
292D4×C83—41no—
293D4×C83—41no—
294D4×C83—41no—
295D4×C83—41no—
296D4×C83—41no—
297D4×C83—41no—
298D4×C83—41no—
299D4×C83—41no—
300D4×C83—41no—
301D4×C83—41no—
302D4×C83—41no—
303D4×C83—84no—
304D4×C83—84no—
305D4×C83—162no—
306D4×C83#12112yes—
307C2×C4×C83—21no—
308C2×C4×C83—21no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—21no—
312C2×C4×C83—21no—
313C2×C4×C83—21no—
314C2×C4×C83—44no—
315C2×C4×C83—42no—
316C2×C4×C83—41no—
317C2×C4×C83—41no—
318C2×C4×C83—41no—
319C2×C4×C83—41no—
320C2×C4×C83—41no—
321C2×C4×C83C22×D411yescharacteristic
322C2×C4×C83C22×D411yescharacteristic
323C2×C4×C83C22×D411yescharacteristic
324C2×C4×C83C2×#4111yescharacteristic
325C2×C4×C83H(5,𝔽2)11yescharacteristic
326C2×C4×C83H(5,𝔽2)11yescharacteristic
327C8×C83—22no—
328C8×C83—22no—
329C8×C83—22no—
330C8×C83—22no—
331C8×C83—41no—
332C8×C83—41no—
333C8×C83—41no—
334C8×C83—41no—
335C22×C83—22no—
336C22×C83—41no—
337C22×C83—41no—
338C22×C83—41no—
339C22×C83—42no—
340C22×C83—81no—
341C22×C83—82no—
342C22×C83—81no—
343C22×C83—82no—
344C22×C83—82no—
345C22×C83—81no—
346C22×C83—82no—
347C22×C83—81no—
348C22×C83—161no—
349C22×C83—161no—
350C22×C83—164no—
351C22×C83#52511yescharacteristic
352C22×C83#54611yescharacteristic
353C22×C83#54611yescharacteristic
354C4×C83—22no—
355C4×C83—22no—
356C4×C83—41no—
357C4×C83—41no—
358C4×C83—41no—
359C4×C83—81no—
360C4×C83C2×#12111yescharacteristic
361C4×C83#53811yescharacteristic
362C4×C83D4211yescharacteristic
363C4×C83D4211yescharacteristic
364#25196C8311yesmaximal, characteristic, direct product factor, Sylow
365C2×C83—21no—
366C2×C83—21no—
367C2×C83—21no—
368C2×C83—42no—
369C2×C83—81no—
370C2×C83—82no—
371C2×C83—81no—
372C2×C83—161no—
373C2×C83#242411yescharacteristic
374#3068C2×C8311yescharacteristic, complemented
375#3068C2×C8311yescharacteristic, complemented
376#3019C2×C8311yescharacteristic, complemented
377C2×#453C2×C8311yescharacteristic, complemented
378#2956C2×C8311yescharacteristic, complemented
379#2888C2×C8311yescharacteristic, complemented
380#2069C2×C8311yescharacteristic, complemented
381#2050C2×C8311yescharacteristic, complemented
382#2048C2×C8311yescharacteristic, complemented
383#2002C2×C8311yescharacteristic, complemented
384#1965C2×C8311yescharacteristic, complemented
385#1932C2×C8311yescharacteristic, complemented
386#1914C2×C8311yescharacteristic, complemented
387#1903C2×C8311yescharacteristic, complemented
388#1861C2×C8311yescharacteristic, complemented
389C83#2519611yescharacteristic, direct product factor, Sylow
390C2×H(5,𝔽2)C22×C8311yescharacteristic
391#575C22×C8311yescharacteristic
392#575C22×C8311yescharacteristic
393C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
394C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
395C2×AGL(1,ℤ/8)C22×C8311yescharacteristic, complemented
396#568C22×C8311yescharacteristic
397#568C22×C8311yescharacteristic
398#568C22×C8311yescharacteristic, complemented
399#535C22×C8311yescharacteristic
400C2×#127C22×C8311yescharacteristic
401#472—22no—
402#472—22no—
403#471—22no—
404#471—22no—
405#455—22no—
406#453—22no—
407#453—22no—
408#453—22no—
409#444—22no—
410#443—22no—
411#430C22×C8311yescharacteristic, complemented
412#430C22×C8311yescharacteristic, complemented
413#430C22×C8311yescharacteristic, complemented
414#423C22×C8311yescharacteristic, complemented
415#421C22×C8311yescharacteristic
416#421C22×C8311yescharacteristic
417C2×#104C22×C8311yescharacteristic
418C2×#104C22×C8311yescharacteristic
419C2×#104C22×C8311yescharacteristic, complemented
420#418C22×C8311yescharacteristic, complemented
421#413—22no—
422#413C22×C8311yescharacteristic
423#413C22×C8311yescharacteristic
424#413C22×C8311yescharacteristic, complemented
425C2×#100—22no—
426C2×#100C22×C8311yescharacteristic
427C2×#100C22×C8311yescharacteristic
428C2×#100C22×C8311yescharacteristic
429C2×#100C22×C8311yescharacteristic
430C2×#100C22×C8311yescharacteristic, complemented
431C2×#100C22×C8311yescharacteristic, complemented
432C4×M16C22×C8311yescharacteristic, complemented
433#344C22×C8311yescharacteristic, complemented
434#344C22×C8311yescharacteristic, complemented
435#339C22×C8311yescharacteristic, complemented
436#338C22×C8311yescharacteristic, complemented
437H(5,𝔽2)—22no—
438H(5,𝔽2)—22no—
439H(5,𝔽2)—41no—
440H(5,𝔽2)—41no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41C23×C8311yescharacteristic
444C2×#41C23×C8311yescharacteristic
445C2×#41C23×C8311yescharacteristic
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4C23×C8311yescharacteristic
451C22×D4C23×C8311yescharacteristic
452#137—21no—
453#137—21no—
454#137—21no—
455#137D4×C8312yescomplemented
456AGL(1,ℤ/8)—21no—
457AGL(1,ℤ/8)—22no—
458AGL(1,ℤ/8)—22no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—22no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—41no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)D4×C8312yescomplemented
466#135—22no—
467#135—41no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×D8—21no—
472C2×D8—21no—
473C2×D8—21no—
474#131—22no—
475#131—22no—
476#131—22no—
477#131—22no—
478#131—41no—
479#131—41no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16—41no—
483C2×M16C23×C8311yescharacteristic
484C2×M16C23×C8311yescharacteristic
485C2×M16C23×C8311yescharacteristic
486C2×M16C23×C8311yescharacteristic
487C2×M16C23×C8311yescharacteristic
488C2×M16C23×C8311yescharacteristic
489C2×M16C23×C8311yescharacteristic
490C2×M16C23×C8311yescharacteristic
491#127—21no—
492#127—21no—
493#127—21no—
494#127—41no—
495#124—21no—
496#121—41no—
497#120—22no—
498#117C23×C8311yescharacteristic
499C2×C42C23×C8311yescharacteristic
500#108—22no—
501#108—22no—
502#108—22no—
503C4⋊C8—41no—
504#104—22no—
505#104—22no—
506#104—21no—
507#104—21no—
508#104—21no—
509#104—21no—
510#104D4×C8312yescomplemented
511#104D4×C8312yescomplemented
512#102—41no—
513#101—21no—
514#101—21no—
515#101D4×C8312yescomplemented
516#100—21no—
517#100—21no—
518#100—22no—
519#100—22no—
520#100—22no—
521#100—22no—
522#100—22no—
523#100—22no—
524#100D4×C8312yescomplemented
525#97—21no—
526C4×C8—21no—
527C24—22no—
528C24—21no—
529C24#41×C8312yes—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41C2×D4×C8312yes—
545#41C2×D4×C8312yes—
546C2×Q8C2×D4×C8311yescharacteristic
547C2×Q8C2×D4×C8311yescharacteristic
548C2×Q8#41×C8311yescharacteristic
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—84no—
576C2×D4C2×D4×C8311yescharacteristic
577C2×D4C2×D4×C8311yescharacteristic
578C2×D4#41×C8311yescharacteristic
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C8311yescharacteristic
585Q16—22no—
586Q16—41no—
587SD16—22no—
588SD16—22no—
589SD16—42no—
590SD16—42no—
591SD16—41no—
592SD16—41no—
593SD16—42no—
594D8—22no—
595D8—42no—
596D8—42no—
597D8—41no—
598D8—42no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16C2×D4×C8312yes—
615M16C2×D4×C8312yes—
616M16C2×D4×C8312yes—
617M16C2×D4×C8312yes—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—42no—
627C2×C8—42no—
628C2×C8—42no—
629C4⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42C2×D4×C8311yescharacteristic
635C42C2×D4×C8311yescharacteristic
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—44no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—82no—
647C23—82no—
648C23—162no—
649C23C2×#41×C8311yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8#121×C8312yes—
656D4—22no—
657D4—22no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—44no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—162no—
680D4#121×C8312yes—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4C22×D4×C8311yescharacteristic
696C2×C4C22×D4×C8311yescharacteristic
697C2×C4C22×D4×C8311yescharacteristic
698C2×C4C2×#41×C8311yescharacteristic
699C2×C4H(5,𝔽2)×C8311yescharacteristic
700C2×C4H(5,𝔽2)×C8311yescharacteristic
701C8—22no—
702C8—22no—
703C8—22no—
704C8—22no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—81no—
715C22—82no—
716C22—81no—
717C22—82no—
718C22—82no—
719C22—81no—
720C22—82no—
721C22—81no—
722C22—161no—
723C22—161no—
724C22—164no—
725C22#525×C8311yescharacteristic
726C22#546×C8311yescharacteristic
727C22#546×C8311yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4C2×#121×C8311yescharacteristic
735C4#538×C8311yescharacteristic
736C4D42×C8311yescharacteristic
737C4D42×C8311yescharacteristic
738C2—21no—
739C2—21no—
740C2—21no—
741C2—42no—
742C2—82no—
743C2—81no—
744C2—81no—
745C2—161no—
746C2C83×#242411yescharacteristic
subgroupG/H
center, socleC2×C83#2424
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C83 ◁ C22×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3068C2semidirect
2. C83×#3068C2semidirect
3. C83×#3019C2semidirect
4. C2×#453×C83C2semidirect
5. C83×#2956C2semidirect
6. C83×#2888C2semidirect
7. C83×#2069C2semidirect
8. C83×#2050C2semidirect
9. C83×#2048C2semidirect
10. C83×#2002C2semidirect
11. C83×#1965C2semidirect
12. C83×#1932C2semidirect
13. C83×#1914C2semidirect
14. C83×#1903C2semidirect
15. C83×#1861C2semidirect
21. C2×AGL(1,ℤ/8)×C83C22semidirect
24. #568×C83C22semidirect
37. #430×C83C22semidirect
38. #430×C83C22semidirect
39. #430×C83C22semidirect
40. #423×C83C22semidirect
45. C2×#104×C83C22semidirect
46. #418×C83C22semidirect
50. #413×C83C22semidirect
56. C2×#100×C83C22semidirect
57. C2×#100×C83C22semidirect
58. C4×M16×C83C22semidirect
59. #344×C83C22semidirect
60. #344×C83C22semidirect
61. #339×C83C22semidirect
62. #338×C83C22semidirect
81. #137×C83D4semidirect
91. AGL(1,ℤ/8)×C83D4semidirect
136. #104×C83D4semidirect
137. #104×C83D4semidirect
141. #101×C83D4semidirect
150. #100×C83D4semidirect
364. #25196C83direct (N × H)
374. #3068C2×C83semidirect
375. #3068C2×C83semidirect
376. #3019C2×C83semidirect
377. C2×#453C2×C83semidirect
378. #2956C2×C83semidirect
379. #2888C2×C83semidirect
380. #2069C2×C83semidirect
381. #2050C2×C83semidirect
382. #2048C2×C83semidirect
383. #2002C2×C83semidirect
384. #1965C2×C83semidirect
385. #1932C2×C83semidirect
386. #1914C2×C83semidirect
387. #1903C2×C83semidirect
388. #1861C2×C83semidirect
389. C83#25196direct (N × H)
395. C2×AGL(1,ℤ/8)C22×C83semidirect
398. #568C22×C83semidirect
411. #430C22×C83semidirect
412. #430C22×C83semidirect
413. #430C22×C83semidirect
414. #423C22×C83semidirect
419. C2×#104C22×C83semidirect
420. #418C22×C83semidirect
424. #413C22×C83semidirect
430. C2×#100C22×C83semidirect
431. C2×#100C22×C83semidirect
432. C4×M16C22×C83semidirect
433. #344C22×C83semidirect
434. #344C22×C83semidirect
435. #339C22×C83semidirect
436. #338C22×C83semidirect
455. #137D4×C83semidirect
465. AGL(1,ℤ/8)D4×C83semidirect
510. #104D4×C83semidirect
511. #104D4×C83semidirect
515. #101D4×C83semidirect
524. #100D4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#30682
C83×#30192
C2×#453×C832
C83×#29562
C83×#28882
C83×#20692
C83×#20502
C83×#20482
C83×#20022
C83×#19652
C83×#19322
C83×#19142
C83×#19032
C83×#18612
#2519683