Finite Group Databasebeta

← C83×#25180 #35253004

Subgroups — C83×#25180 #35253004

Order 21248.

1074 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C83C211yesmaximal, characteristic, complemented
2C83×#3041C211yesmaximal, characteristic, complemented
3C2×#453×C83C211yesmaximal, characteristic, complemented
4C83×#3008C211yesmaximal, characteristic, complemented
5C83×#2946C211yesmaximal, characteristic, complemented
6C83×#2897C211yesmaximal, characteristic, complemented
7C83×#2063C211yesmaximal, characteristic, complemented
8C83×#2051C211yesmaximal, characteristic, complemented
9C83×#2037C211yesmaximal, characteristic, complemented
10C83×#2011C211yesmaximal, characteristic, complemented
11C83×#1978C211yesmaximal, characteristic, complemented
12C83×#1929C211yesmaximal, characteristic, complemented
13C83×#1887C211yesmaximal, characteristic, complemented
14C83×#1883C211yesmaximal, characteristic, complemented
15C83×#1866C211yesmaximal, 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
20C22×D8×C83C2211yescharacteristic
21C22×D8×C83C2211yescharacteristic, complemented
22C2×#131×C83C2211yescharacteristic
23#535×C83C2211yescharacteristic
24C2×#127×C83C2211yescharacteristic
25#520×C83C2211yescharacteristic
26#518×C83C2211yescharacteristic, complemented
27#472×C83—24no—
28#463×C83—21no—
29#463×C83—21no—
30#459×C83—21no—
31#459×C83—21no—
32#453×C83—24no—
33#449×C83—21no—
34#449×C83—21no—
35#447×C83—21no—
36#447×C83—21no—
37#442×C83—21no—
38#440×C83—21no—
39C4×SD16×C83—21no—
40C4×D8×C83—21no—
41C2×#108×C83C2211yescharacteristic, complemented
42C2×#108×C83C2211yescharacteristic, complemented
43#428×C83C2211yescharacteristic, complemented
44#424×C83C2211yescharacteristic, complemented
45C2×#104×C83C2211yescharacteristic
46C2×#104×C83C2211yescharacteristic
47#418×C83—21no—
48#418×C83C2211yescharacteristic
49#418×C83C2211yescharacteristic
50#418×C83C2211yescharacteristic, complemented
51#417×C83—21no—
52#417×C83C2211yescharacteristic
53#416×C83—21no—
54#416×C83C2211yescharacteristic
55#416×C83C2211yescharacteristic
56C2×#102×C83—21no—
57C2×#102×C83C2211yescharacteristic
58C2×#102×C83C2211yescharacteristic, complemented
59C2×#100×C83C2211yescharacteristic
60C2×#100×C83C2211yescharacteristic, complemented
61C2×#100×C83C2211yescharacteristic, complemented
62#408×C83C2211yescharacteristic
63#405×C83C2211yescharacteristic, complemented
64#390×C83C2211yescharacteristic, complemented
65#343×C83C2211yescharacteristic, complemented
66#339×C83C2211yescharacteristic, complemented
67#339×C83C2211yescharacteristic, complemented
68#336×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
77C22×D4×C83—21no—
78C22×D4×C83—21no—
79C22×D4×C83—41no—
80C22×D4×C83—41no—
81C22×D4×C83C2311yescharacteristic
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)×C83D414yescomplemented
90C2×SD16×C83—21no—
91C2×SD16×C83—21no—
92C2×SD16×C83—21no—
93C2×D8×C83—21no—
94C2×D8×C83—22no—
95C2×D8×C83—21no—
96C2×D8×C83—21no—
97C2×D8×C83—22no—
98C2×D8×C83—21no—
99C2×D8×C83—21no—
100C2×D8×C83—21no—
101C2×D8×C83—21no—
102C2×D8×C83—41no—
103C2×D8×C83—41no—
104#131×C83—22no—
105#131×C83—41no—
106C2×M16×C83—21no—
107C2×M16×C83C2311yescharacteristic
108C2×M16×C83C2311yescharacteristic
109C2×M16×C83C2311yescharacteristic
110C2×M16×C83C2311yescharacteristic
111C22×C8×C83—21no—
112C22×C8×C83C2311yescharacteristic
113C22×C8×C83C2311yescharacteristic
114#127×C83—22no—
115#127×C83—21no—
116#127×C83—22no—
117#124×C83—21no—
118#121×C83—21no—
119#121×C83—21no—
120#120×C83—41no—
121C4×Q8×C83—21no—
122C4×D4×C83—21no—
123C4×D4×C83—21no—
124C4×D4×C83—21no—
125C4×D4×C83—21no—
126C4×D4×C83—21no—
127C4×D4×C83—41no—
128#117×C83—21no—
129#117×C83C2311yescharacteristic
130#117×C83C2311yescharacteristic
131C2×C4⋊C4×C83—21no—
132C2×C4⋊C4×C83C2311yescharacteristic
133C2×C22⋊C4×C83—41no—
134C2×C22⋊C4×C83—41no—
135C2×C42×C83C2311yescharacteristic
136#108×C83—22no—
137#108×C83—41no—
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#103×C83—21no—
145#103×C83D411yescharacteristic, complemented
146#103×C83D411yescharacteristic, complemented
147#103×C83D411yescharacteristic, complemented
148#103×C83D411yescharacteristic, complemented
149#102×C83—21no—
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×C83D411yescharacteristic, complemented
161#102×C83D411yescharacteristic, complemented
162#102×C83D411yescharacteristic, complemented
163#102×C83D411yescharacteristic, complemented
164#100×C83—22no—
165#100×C83—22no—
166#100×C83—22no—
167C22⋊C8×C83—21no—
168C22⋊C8×C83—21no—
169#97×C83—21no—
170C4×C8×C83—21no—
171C24×C83—21no—
172C24×C83—21no—
173C24×C83—21no—
174C24×C83—41no—
175#41×C83—21no—
176#41×C83—21no—
177#41×C83—24no—
178#41×C83—21no—
179#41×C83—21no—
180#41×C83—21no—
181#41×C83—21no—
182#41×C83—42no—
183#41×C83—42no—
184#41×C83—42no—
185#41×C83C2×D412yes—
186#41×C83#4112yes—
187C2×Q8×C83C2×D411yescharacteristic
188C2×Q8×C83C2×D411yescharacteristic
189C2×D4×C83—21no—
190C2×D4×C83—24no—
191C2×D4×C83—21no—
192C2×D4×C83—21no—
193C2×D4×C83—21no—
194C2×D4×C83—21no—
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—41no—
212C2×D4×C83—41no—
213C2×D4×C83—42no—
214C2×D4×C83—44no—
215C2×D4×C83—44no—
216C2×D4×C83—42no—
217C2×D4×C83—44no—
218C2×D4×C83—82no—
219C2×D4×C83—82no—
220C2×D4×C83C2×D412yes—
221C2×D4×C83C2×D411yescharacteristic
222C2×D4×C83C2×D411yescharacteristic
223C2×D4×C83#4112yes—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—41no—
229C22×C4×C83—41no—
230C22×C4×C83—41no—
231C22×C4×C83—41no—
232C22×C4×C83C2411yescharacteristic
233SD16×C83—24no—
234SD16×C83—42no—
235SD16×C83—42no—
236D8×C83—24no—
237D8×C83—42no—
238D8×C83—42no—
239D8×C83—42no—
240D8×C83—42no—
241D8×C83—42no—
242D8×C83—42no—
243M16×C83—21no—
244M16×C83—21no—
245M16×C83—21no—
246M16×C83—21no—
247M16×C83—21no—
248M16×C83—21no—
249M16×C83—21no—
250M16×C83—42no—
251M16×C83C2×D412yes—
252C2×C8×C83—21no—
253C2×C8×C83—21no—
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—42no—
261C2×C8×C83C2×D411yescharacteristic
262C2×C8×C83C2×D411yescharacteristic
263C2×C8×C83C2×D411yescharacteristic
264C2×C8×C83C2×D411yescharacteristic
265C4⋊C4×C83—21no—
266C4⋊C4×C83—21no—
267C4⋊C4×C83—41no—
268C4⋊C4×C83C2×D411yescharacteristic
269C4⋊C4×C83C2×D411yescharacteristic
270C4⋊C4×C83C2×D411yescharacteristic
271C4⋊C4×C83C2×D411yescharacteristic
272C22⋊C4×C83—21no—
273C22⋊C4×C83—21no—
274C22⋊C4×C83—41no—
275C22⋊C4×C83—41no—
276C22⋊C4×C83—41no—
277C22⋊C4×C83—41no—
278C22⋊C4×C83—41no—
279C22⋊C4×C83—82no—
280C42×C83—21no—
281C42×C83—21no—
282C42×C83—21no—
283C42×C83—21no—
284C42×C83—41no—
285C23×C83—21no—
286C23×C83—21no—
287C23×C83—22no—
288C23×C83—22no—
289C23×C83—44no—
290C23×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83—41no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—81no—
298C23×C83—81no—
299C23×C83—81no—
300C23×C83—81no—
301C23×C83—81no—
302C23×C83—81no—
303C23×C83—161no—
304C23×C83—161no—
305C23×C83H(5,𝔽2)11yescharacteristic
306Q8×C83—21no—
307Q8×C83—21no—
308Q8×C83—21no—
309Q8×C83#12112yes—
310D4×C83—22no—
311D4×C83—22no—
312D4×C83—22no—
313D4×C83—21no—
314D4×C83—22no—
315D4×C83—22no—
316D4×C83—21no—
317D4×C83—21no—
318D4×C83—22no—
319D4×C83—44no—
320D4×C83—44no—
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—41no—
331D4×C83—88no—
332D4×C83—161no—
333D4×C83—161no—
334D4×C83#12112yes—
335C2×C4×C83—21no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—22no—
339C2×C4×C83—21no—
340C2×C4×C83—21no—
341C2×C4×C83—21no—
342C2×C4×C83—21no—
343C2×C4×C83—21no—
344C2×C4×C83—44no—
345C2×C4×C83—41no—
346C2×C4×C83—41no—
347C2×C4×C83—41no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—81no—
351C2×C4×C83—161no—
352C2×C4×C83—161no—
353C2×C4×C83—161no—
354C2×C4×C83C22×D411yescharacteristic
355C2×C4×C83C22×D411yescharacteristic
356C2×C4×C83C22×D411yescharacteristic
357C2×C4×C83C2×#4111yescharacteristic
358C2×C4×C83C2×#4111yescharacteristic
359C2×C4×C83H(5,𝔽2)11yescharacteristic
360C8×C83—22no—
361C8×C83—21no—
362C8×C83—21no—
363C8×C83—21no—
364C8×C83—21no—
365C8×C83—41no—
366C8×C83—41no—
367C8×C83—41no—
368C22×C83—21no—
369C22×C83—21no—
370C22×C83—22no—
371C22×C83—41no—
372C22×C83—41no—
373C22×C83—41no—
374C22×C83—42no—
375C22×C83—42no—
376C22×C83—41no—
377C22×C83—41no—
378C22×C83—82no—
379C22×C83—82no—
380C22×C83—82no—
381C22×C83—81no—
382C22×C83—81no—
383C22×C83—81no—
384C22×C83—81no—
385C22×C83—81no—
386C22×C83—81no—
387C22×C83—81no—
388C22×C83—161no—
389C22×C83—161no—
390C22×C83—161no—
391C22×C83—164no—
392C22×C83#53811yescharacteristic
393C22×C83D4211yescharacteristic
394C22×C83#54611yescharacteristic
395C4×C83—22no—
396C4×C83—42no—
397C4×C83—41no—
398C4×C83—41no—
399C4×C83—41no—
400C4×C83—41no—
401C4×C83—41no—
402C4×C83—81no—
403C4×C83C2×#12111yescharacteristic
404C4×C83#52511yescharacteristic
405C4×C83D4211yescharacteristic
406C4×C83#54611yescharacteristic
407#25180C8311yesmaximal, characteristic, direct product factor, Sylow
408C2×C83—21no—
409C2×C83—21no—
410C2×C83—42no—
411C2×C83—81no—
412C2×C83—82no—
413C2×C83—82no—
414C2×C83—161no—
415C2×C83#242411yescharacteristic
416C2×C83#328811yescharacteristic
417C2×C83#329211yescharacteristic
418C2×#472C2×C8311yescharacteristic, complemented
419#3041C2×C8311yescharacteristic, complemented
420C2×#453C2×C8311yescharacteristic, complemented
421#3008C2×C8311yescharacteristic, complemented
422#2946C2×C8311yescharacteristic, complemented
423#2897C2×C8311yescharacteristic, complemented
424#2063C2×C8311yescharacteristic, complemented
425#2051C2×C8311yescharacteristic, complemented
426#2037C2×C8311yescharacteristic, complemented
427#2011C2×C8311yescharacteristic, complemented
428#1978C2×C8311yescharacteristic, complemented
429#1929C2×C8311yescharacteristic, complemented
430#1887C2×C8311yescharacteristic, complemented
431#1883C2×C8311yescharacteristic, complemented
432#1866C2×C8311yescharacteristic, complemented
433C83#2518011yescharacteristic, direct product factor, Sylow
434C2×H(5,𝔽2)C22×C8311yescharacteristic
435C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
436C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
437C2×AGL(1,ℤ/8)C22×C8311yescharacteristic
438C22×D8C22×C8311yescharacteristic
439C22×D8C22×C8311yescharacteristic, complemented
440C2×#131C22×C8311yescharacteristic
441#535C22×C8311yescharacteristic
442C2×#127C22×C8311yescharacteristic
443#520C22×C8311yescharacteristic
444#518C22×C8311yescharacteristic, complemented
445#472—24no—
446#463—21no—
447#463—21no—
448#459—21no—
449#459—21no—
450#453—24no—
451#449—21no—
452#449—21no—
453#447—21no—
454#447—21no—
455#442—21no—
456#440—21no—
457C4×SD16—21no—
458C4×D8—21no—
459C2×#108C22×C8311yescharacteristic, complemented
460C2×#108C22×C8311yescharacteristic, complemented
461#428C22×C8311yescharacteristic, complemented
462#424C22×C8311yescharacteristic, complemented
463C2×#104C22×C8311yescharacteristic
464C2×#104C22×C8311yescharacteristic
465#418—21no—
466#418C22×C8311yescharacteristic
467#418C22×C8311yescharacteristic
468#418C22×C8311yescharacteristic, complemented
469#417—21no—
470#417C22×C8311yescharacteristic
471#416—21no—
472#416C22×C8311yescharacteristic
473#416C22×C8311yescharacteristic
474C2×#102—21no—
475C2×#102C22×C8311yescharacteristic
476C2×#102C22×C8311yescharacteristic, complemented
477C2×#100C22×C8311yescharacteristic
478C2×#100C22×C8311yescharacteristic, complemented
479C2×#100C22×C8311yescharacteristic, complemented
480#408C22×C8311yescharacteristic
481#405C22×C8311yescharacteristic, complemented
482#390C22×C8311yescharacteristic, complemented
483#343C22×C8311yescharacteristic, complemented
484#339C22×C8311yescharacteristic, complemented
485#339C22×C8311yescharacteristic, complemented
486#336C22×C8311yescharacteristic, complemented
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C8311yescharacteristic
494C2×#41C23×C8311yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C8311yescharacteristic
500C22×D4C23×C8311yescharacteristic
501C22×D4C23×C8311yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)D4×C8314yescomplemented
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×D8—21no—
512C2×D8—22no—
513C2×D8—21no—
514C2×D8—21no—
515C2×D8—22no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8—21no—
520C2×D8—41no—
521C2×D8—41no—
522#131—22no—
523#131—41no—
524C2×M16—21no—
525C2×M16C23×C8311yescharacteristic
526C2×M16C23×C8311yescharacteristic
527C2×M16C23×C8311yescharacteristic
528C2×M16C23×C8311yescharacteristic
529C22×C8—21no—
530C22×C8C23×C8311yescharacteristic
531C22×C8C23×C8311yescharacteristic
532#127—22no—
533#127—21no—
534#127—22no—
535#124—21no—
536#121—21no—
537#121—21no—
538#120—41no—
539C4×Q8—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—41no—
546#117—21no—
547#117C23×C8311yescharacteristic
548#117C23×C8311yescharacteristic
549C2×C4⋊C4—21no—
550C2×C4⋊C4C23×C8311yescharacteristic
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C42C23×C8311yescharacteristic
554#108—22no—
555#108—41no—
556#107—21no—
557#106—21no—
558C4⋊C8—21no—
559C4⋊C8—21no—
560#104—22no—
561#104—22no—
562#103—21no—
563#103D4×C8311yescharacteristic, complemented
564#103D4×C8311yescharacteristic, complemented
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#102D4×C8311yescharacteristic, complemented
579#102D4×C8311yescharacteristic, complemented
580#102D4×C8311yescharacteristic, complemented
581#102D4×C8311yescharacteristic, complemented
582#100—22no—
583#100—22no—
584#100—22no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587#97—21no—
588C4×C8—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24—41no—
593#41—21no—
594#41—21no—
595#41—24no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41C2×D4×C8312yes—
604#41#41×C8312yes—
605C2×Q8C2×D4×C8311yescharacteristic
606C2×Q8C2×D4×C8311yescharacteristic
607C2×D4—21no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
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—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—44no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C8312yes—
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—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C8311yescharacteristic
651SD16—24no—
652SD16—42no—
653SD16—42no—
654D8—24no—
655D8—42no—
656D8—42no—
657D8—42no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16C2×D4×C8312yes—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—42no—
679C2×C8C2×D4×C8311yescharacteristic
680C2×C8C2×D4×C8311yescharacteristic
681C2×C8C2×D4×C8311yescharacteristic
682C2×C8C2×D4×C8311yescharacteristic
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—41no—
686C4⋊C4C2×D4×C8311yescharacteristic
687C4⋊C4C2×D4×C8311yescharacteristic
688C4⋊C4C2×D4×C8311yescharacteristic
689C4⋊C4C2×D4×C8311yescharacteristic
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—82no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—41no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—161no—
722C23—161no—
723C23H(5,𝔽2)×C8311yescharacteristic
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C8312yes—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—21no—
732D4—22no—
733D4—22no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4#121×C8312yes—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—44no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—81no—
769C2×C4—161no—
770C2×C4—161no—
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—22no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—21no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—161no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22#538×C8311yescharacteristic
811C22D42×C8311yescharacteristic
812C22#546×C8311yescharacteristic
813C4—22no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—81no—
821C4C2×#121×C8311yescharacteristic
822C4#525×C8311yescharacteristic
823C4D42×C8311yescharacteristic
824C4#546×C8311yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C83×#242411yescharacteristic
833C2C83×#328811yescharacteristic
834C2C83×#329211yescharacteristic
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. C2×#472×C83C2semidirect
2. C83×#3041C2semidirect
3. C2×#453×C83C2semidirect
4. C83×#3008C2semidirect
5. C83×#2946C2semidirect
6. C83×#2897C2semidirect
7. C83×#2063C2semidirect
8. C83×#2051C2semidirect
9. C83×#2037C2semidirect
10. C83×#2011C2semidirect
11. C83×#1978C2semidirect
12. C83×#1929C2semidirect
13. C83×#1887C2semidirect
14. C83×#1883C2semidirect
15. C83×#1866C2semidirect
21. C22×D8×C83C22semidirect
26. #518×C83C22semidirect
41. C2×#108×C83C22semidirect
42. C2×#108×C83C22semidirect
43. #428×C83C22semidirect
44. #424×C83C22semidirect
50. #418×C83C22semidirect
58. C2×#102×C83C22semidirect
60. C2×#100×C83C22semidirect
61. C2×#100×C83C22semidirect
63. #405×C83C22semidirect
64. #390×C83C22semidirect
65. #343×C83C22semidirect
66. #339×C83C22semidirect
67. #339×C83C22semidirect
68. #336×C83C22semidirect
89. AGL(1,ℤ/8)×C83D4semidirect
145. #103×C83D4semidirect
146. #103×C83D4semidirect
147. #103×C83D4semidirect
148. #103×C83D4semidirect
160. #102×C83D4semidirect
161. #102×C83D4semidirect
162. #102×C83D4semidirect
163. #102×C83D4semidirect
407. #25180C83direct (N × H)
418. C2×#472C2×C83semidirect
419. #3041C2×C83semidirect
420. C2×#453C2×C83semidirect
421. #3008C2×C83semidirect
422. #2946C2×C83semidirect
423. #2897C2×C83semidirect
424. #2063C2×C83semidirect
425. #2051C2×C83semidirect
426. #2037C2×C83semidirect
427. #2011C2×C83semidirect
428. #1978C2×C83semidirect
429. #1929C2×C83semidirect
430. #1887C2×C83semidirect
431. #1883C2×C83semidirect
432. #1866C2×C83semidirect
433. C83#25180direct (N × H)
439. C22×D8C22×C83semidirect
444. #518C22×C83semidirect
459. C2×#108C22×C83semidirect
460. C2×#108C22×C83semidirect
461. #428C22×C83semidirect
462. #424C22×C83semidirect
468. #418C22×C83semidirect
476. C2×#102C22×C83semidirect
478. C2×#100C22×C83semidirect
479. C2×#100C22×C83semidirect
481. #405C22×C83semidirect
482. #390C22×C83semidirect
483. #343C22×C83semidirect
484. #339C22×C83semidirect
485. #339C22×C83semidirect
486. #336C22×C83semidirect
507. AGL(1,ℤ/8)D4×C83semidirect
563. #103D4×C83semidirect
564. #103D4×C83semidirect
565. #103D4×C83semidirect
566. #103D4×C83semidirect
578. #102D4×C83semidirect
579. #102D4×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
C2×#472×C832
C83×#30412
C2×#453×C832
C83×#30082
C83×#29462
C83×#28972
C83×#20632
C83×#20512
C83×#20372
C83×#20112
C83×#19782
C83×#19292
C83×#18872
C83×#18832
C83×#18662
#2518083