Finite Group Databasebeta

← C83×#26619 #35254443

Subgroups — C83×#26619 #35254443

Order 21248.

1040 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C83C211yesmaximal, characteristic, complemented
2C2×C4×D8×C83C211yesmaximal, characteristic, complemented
3C83×#2428C211yesmaximal, characteristic, complemented
4C83×#2363C211yesmaximal, characteristic, complemented
5C83×#2065C211yesmaximal, characteristic, complemented
6C83×#2011C211yesmaximal, characteristic, complemented
7C83×#1999C211yesmaximal, characteristic, complemented
8C83×#1999C211yesmaximal, characteristic, complemented
9C83×#1982C211yesmaximal, characteristic, complemented
10C83×#1934C211yesmaximal, characteristic, complemented
11C83×#1923C211yesmaximal, characteristic, complemented
12C83×#1921C211yesmaximal, characteristic, complemented
13C83×#1879C211yesmaximal, characteristic, complemented
14C83×#1875C211yesmaximal, characteristic, complemented
15C83×#1864C211yesmaximal, characteristic, complemented
16C22×D8×C83C2211yescharacteristic
17C22×D8×C83C2211yescharacteristic
18C2×#127×C83C2211yescharacteristic
19C2×#121×C83—21no—
20C2×#121×C83C2211yescharacteristic
21C2×#121×C83C2211yescharacteristic
22C2×#121×C83C2211yescharacteristic
23C2×C4×D4×C83C2211yescharacteristic
24C2×C4×D4×C83C2211yescharacteristic
25C2×#117×C83C2211yescharacteristic
26#482×C83—24no—
27C4×D8×C83—24no—
28C2×#107×C83C2211yescharacteristic
29C2×#106×C83C2211yescharacteristic
30C2×C4⋊C8×C83C2211yescharacteristic
31C2×#102×C83C2211yescharacteristic
32C2×#102×C83C2211yescharacteristic
33C2×#102×C83C2211yescharacteristic
34C2×#102×C83C2211yescharacteristic
35C2×#102×C83C2211yescharacteristic
36C2×#102×C83C2211yescharacteristic
37C2×#102×C83C2211yescharacteristic
38C2×#102×C83C2211yescharacteristic
39C2×C22⋊C8×C83C2211yescharacteristic
40C2×C22⋊C8×C83C2211yescharacteristic
41C2×C4×C8×C83C2211yescharacteristic
42#394×C83—21no—
43#392×C83—21no—
44#390×C83—21no—
45#390×C83C2211yescharacteristic
46#390×C83C2211yescharacteristic
47#389×C83C2211yescharacteristic
48#389×C83C2211yescharacteristic
49#388×C83—21no—
50#386×C83—21no—
51#386×C83—21no—
52C4×C4⋊C4×C83C2211yescharacteristic
53C4×C22⋊C4×C83—21no—
54C4×C22⋊C4×C83C2211yescharacteristic
55#340×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#340×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61C22×D4×C83—21no—
62C22×D4×C83—21no—
63C22×D4×C83—21no—
64C22×D4×C83—21no—
65C22×D4×C83—21no—
66C22×D4×C83C2311yescharacteristic
67C22×D4×C83C2311yescharacteristic
68C22×D4×C83C2311yescharacteristic
69C23×C4×C83—21no—
70C23×C4×C83—21no—
71C23×C4×C83C2311yescharacteristic
72C2×D8×C83—22no—
73C2×D8×C83—22no—
74C2×D8×C83—22no—
75C2×D8×C83—22no—
76C2×D8×C83—41no—
77C2×D8×C83—41no—
78C22×C8×C83C2311yescharacteristic
79C22×C8×C83C2311yescharacteristic
80C22×C8×C83C2311yescharacteristic
81C22×C8×C83C2311yescharacteristic
82#127×C83—22no—
83#127×C83—41no—
84#121×C83—22no—
85#121×C83—22no—
86#121×C83—22no—
87#121×C83—22no—
88#121×C83—44no—
89#121×C83—41no—
90#121×C83—41no—
91C4×D4×C83—22no—
92C4×D4×C83—22no—
93C4×D4×C83—41no—
94C4×D4×C83—41no—
95#117×C83—22no—
96#117×C83—41no—
97C2×C4⋊C4×C83—21no—
98C2×C4⋊C4×C83—21no—
99C2×C4⋊C4×C83C2311yescharacteristic
100C2×C4⋊C4×C83C2311yescharacteristic
101C2×C4⋊C4×C83C2311yescharacteristic
102C2×C4⋊C4×C83C2311yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C22⋊C4×C83—21no—
105C2×C22⋊C4×C83—21no—
106C2×C22⋊C4×C83—21no—
107C2×C22⋊C4×C83—21no—
108C2×C22⋊C4×C83—21no—
109C2×C22⋊C4×C83—21no—
110C2×C22⋊C4×C83—21no—
111C2×C22⋊C4×C83—21no—
112C2×C22⋊C4×C83—21no—
113C2×C22⋊C4×C83—21no—
114C2×C22⋊C4×C83D411yescharacteristic
115C2×C22⋊C4×C83D411yescharacteristic
116C2×C42×C83—21no—
117C2×C42×C83—21no—
118C2×C42×C83C2311yescharacteristic
119C2×C42×C83C2311yescharacteristic
120#107×C83D414yescomplemented
121#106×C83—22no—
122C4⋊C8×C83—41no—
123#102×C83—22no—
124#102×C83—22no—
125#102×C83—22no—
126#102×C83—22no—
127#102×C83—22no—
128#102×C83—22no—
129#102×C83—41no—
130#102×C83—41no—
131C22⋊C8×C83—22no—
132C22⋊C8×C83—41no—
133C4×C8×C83—22no—
134#95×C83—21no—
135#95×C83—21no—
136#95×C83—21no—
137#95×C83D411yescharacteristic
138#95×C83D411yescharacteristic
139C24×C83—21no—
140C24×C83—21no—
141C24×C83—21no—
142C24×C83C2×D411yescharacteristic
143C2×D4×C83—24no—
144C2×D4×C83—21no—
145C2×D4×C83—21no—
146C2×D4×C83—21no—
147C2×D4×C83—21no—
148C2×D4×C83—21no—
149C2×D4×C83—21no—
150C2×D4×C83—21no—
151C2×D4×C83—21no—
152C2×D4×C83—21no—
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—21no—
157C2×D4×C83—21no—
158C2×D4×C83—21no—
159C2×D4×C83—21no—
160C2×D4×C83—42no—
161C2×D4×C83—42no—
162C2×D4×C83—42no—
163C2×D4×C83—42no—
164C2×D4×C83—42no—
165C2×D4×C83—42no—
166C2×D4×C83—42no—
167C2×D4×C83—42no—
168C2×D4×C83—81no—
169C2×D4×C83—81no—
170C2×D4×C83—81no—
171C2×D4×C83—81no—
172C2×D4×C83—81no—
173C2×D4×C83—81no—
174C2×D4×C83#4112yes—
175C2×D4×C83#4112yes—
176C22×C4×C83—21no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—42no—
188C22×C4×C83—42no—
189C22×C4×C83—42no—
190C22×C4×C83—42no—
191C22×C4×C83—81no—
192C22×C4×C83—81no—
193C22×C4×C83C2×D411yescharacteristic
194C22×C4×C83C2×D411yescharacteristic
195C22×C4×C83C2×D411yescharacteristic
196C22×C4×C83C2×D411yescharacteristic
197C22×C4×C83C2×D411yescharacteristic
198C22×C4×C83C2411yescharacteristic
199D8×C83—28no—
200D8×C83—44no—
201C2×C8×C83—21no—
202C2×C8×C83—21no—
203C2×C8×C83—21no—
204C2×C8×C83—21no—
205C2×C8×C83—21no—
206C2×C8×C83—21no—
207C2×C8×C83—21no—
208C2×C8×C83—21no—
209C2×C8×C83—21no—
210C2×C8×C83—21no—
211C2×C8×C83—21no—
212C2×C8×C83C2×D412yes—
213C4⋊C4×C83—21no—
214C4⋊C4×C83—21no—
215C4⋊C4×C83—21no—
216C4⋊C4×C83—21no—
217C4⋊C4×C83—21no—
218C4⋊C4×C83—21no—
219C4⋊C4×C83—21no—
220C4⋊C4×C83—42no—
221C4⋊C4×C83—81no—
222C4⋊C4×C83C2×D412yes—
223C4⋊C4×C83C2×D412yes—
224C4⋊C4×C83#4112yes—
225C22⋊C4×C83—24no—
226C22⋊C4×C83—22no—
227C22⋊C4×C83—22no—
228C22⋊C4×C83—42no—
229C22⋊C4×C83—42no—
230C22⋊C4×C83—42no—
231C22⋊C4×C83—42no—
232C22⋊C4×C83—42no—
233C22⋊C4×C83—42no—
234C22⋊C4×C83—42no—
235C22⋊C4×C83—81no—
236C22⋊C4×C83—81no—
237C42×C83—21no—
238C42×C83—21no—
239C42×C83—21no—
240C42×C83—21no—
241C42×C83—42no—
242C42×C83—81no—
243C23×C83—22no—
244C23×C83—21no—
245C23×C83—21no—
246C23×C83—22no—
247C23×C83—21no—
248C23×C83—21no—
249C23×C83—21no—
250C23×C83—21no—
251C23×C83—21no—
252C23×C83—41no—
253C23×C83—41no—
254C23×C83—41no—
255C23×C83—41no—
256C23×C83—41no—
257C23×C83—41no—
258C23×C83—41no—
259C23×C83—41no—
260C23×C83—41no—
261C23×C83—41no—
262C23×C83—41no—
263C23×C83—41no—
264C23×C83—41no—
265C23×C83—41no—
266C23×C83—41no—
267C23×C83—41no—
268C23×C83—41no—
269C23×C83—41no—
270C23×C83—41no—
271C23×C83C22×D411yescharacteristic
272D4×C83—22no—
273D4×C83—22no—
274D4×C83—22no—
275D4×C83—22no—
276D4×C83—41no—
277D4×C83—41no—
278D4×C83—41no—
279D4×C83—41no—
280D4×C83—41no—
281D4×C83—41no—
282D4×C83—41no—
283D4×C83—41no—
284D4×C83—84no—
285D4×C83—84no—
286D4×C83—84no—
287D4×C83—84no—
288D4×C83—84no—
289C2×C4×C83—21no—
290C2×C4×C83—21no—
291C2×C4×C83—21no—
292C2×C4×C83—21no—
293C2×C4×C83—21no—
294C2×C4×C83—22no—
295C2×C4×C83—21no—
296C2×C4×C83—21no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—21no—
300C2×C4×C83—21no—
301C2×C4×C83—21no—
302C2×C4×C83—21no—
303C2×C4×C83—21no—
304C2×C4×C83—21no—
305C2×C4×C83—41no—
306C2×C4×C83—41no—
307C2×C4×C83—41no—
308C2×C4×C83—41no—
309C2×C4×C83—41no—
310C2×C4×C83—41no—
311C2×C4×C83—41no—
312C2×C4×C83—41no—
313C2×C4×C83—41no—
314C2×C4×C83—41no—
315C2×C4×C83—41no—
316C2×C4×C83—41no—
317C2×C4×C83—41no—
318C2×C4×C83—41no—
319C2×C4×C83—41no—
320C2×C4×C83—41no—
321C2×C4×C83—84no—
322C2×C4×C83—84no—
323C2×C4×C83#13512yes—
324C2×C4×C83AGL(1,ℤ/8)12yes—
325C2×C4×C83C22×D411yescharacteristic
326C2×C4×C83C2×#4111yescharacteristic
327C2×C4×C83C2×#4111yescharacteristic
328C2×C4×C83C2×#4111yescharacteristic
329C2×C4×C83H(5,𝔽2)11yescharacteristic
330C2×C4×C83H(5,𝔽2)11yescharacteristic
331C8×C83—22no—
332C8×C83—41no—
333C8×C83—41no—
334C8×C83—41no—
335C22×C83—41no—
336C22×C83—42no—
337C22×C83—41no—
338C22×C83—42no—
339C22×C83—41no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83—41no—
343C22×C83—41no—
344C22×C83—42no—
345C22×C83—41no—
346C22×C83—41no—
347C22×C83—42no—
348C22×C83—81no—
349C22×C83—81no—
350C22×C83—81no—
351C22×C83—81no—
352C22×C83—81no—
353C22×C83—81no—
354C22×C83—81no—
355C22×C83—81no—
356C22×C83—81no—
357C22×C83—81no—
358C22×C83—81no—
359C22×C83—81no—
360C22×C83—81no—
361C22×C83—81no—
362C22×C83—81no—
363C22×C83#52511yescharacteristic
364C22×C83D4211yescharacteristic
365C22×C83#54611yescharacteristic
366C22×C83C2×#13511yescharacteristic
367C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C83#57611yescharacteristic
369C22×C83#57611yescharacteristic
370C4×C83—22no—
371C4×C83—22no—
372C4×C83—42no—
373C4×C83—41no—
374C4×C83—42no—
375C4×C83—42no—
376C4×C83—41no—
377C4×C83—41no—
378C4×C83—81no—
379C4×C83—81no—
380C4×C83#52511yescharacteristic
381C4×C83#53811yescharacteristic
382C4×C83#55011yescharacteristic
383C4×C83#55311yescharacteristic
384#26619C8311yesmaximal, characteristic, direct product factor, Sylow
385C2×C83—81no—
386C2×C83—82no—
387C2×C83—82no—
388C2×C83—161no—
389C2×C83#245611yescharacteristic
390C2×C83#310611yescharacteristic
391C2×C83#312211yescharacteristic
392C2×C83#326411yescharacteristic
393C2×C83#328711yescharacteristic
394C2×C83#329711yescharacteristic
395C2×C83#332511yescharacteristic
396C2×#482C2×C8311yescharacteristic, complemented
397C2×C4×D8C2×C8311yescharacteristic, complemented
398#2428C2×C8311yescharacteristic, complemented
399#2363C2×C8311yescharacteristic, complemented
400#2065C2×C8311yescharacteristic, complemented
401#2011C2×C8311yescharacteristic, complemented
402#1999C2×C8311yescharacteristic, complemented
403#1999C2×C8311yescharacteristic, complemented
404#1982C2×C8311yescharacteristic, complemented
405#1934C2×C8311yescharacteristic, complemented
406#1923C2×C8311yescharacteristic, complemented
407#1921C2×C8311yescharacteristic, complemented
408#1879C2×C8311yescharacteristic, complemented
409#1875C2×C8311yescharacteristic, complemented
410#1864C2×C8311yescharacteristic, complemented
411C83#2661911yescharacteristic, direct product factor, Sylow
412C22×D8C22×C8311yescharacteristic
413C22×D8C22×C8311yescharacteristic
414C2×#127C22×C8311yescharacteristic
415C2×#121—21no—
416C2×#121C22×C8311yescharacteristic
417C2×#121C22×C8311yescharacteristic
418C2×#121C22×C8311yescharacteristic
419C2×C4×D4C22×C8311yescharacteristic
420C2×C4×D4C22×C8311yescharacteristic
421C2×#117C22×C8311yescharacteristic
422#482—24no—
423C4×D8—24no—
424C2×#107C22×C8311yescharacteristic
425C2×#106C22×C8311yescharacteristic
426C2×C4⋊C8C22×C8311yescharacteristic
427C2×#102C22×C8311yescharacteristic
428C2×#102C22×C8311yescharacteristic
429C2×#102C22×C8311yescharacteristic
430C2×#102C22×C8311yescharacteristic
431C2×#102C22×C8311yescharacteristic
432C2×#102C22×C8311yescharacteristic
433C2×#102C22×C8311yescharacteristic
434C2×#102C22×C8311yescharacteristic
435C2×C22⋊C8C22×C8311yescharacteristic
436C2×C22⋊C8C22×C8311yescharacteristic
437C2×C4×C8C22×C8311yescharacteristic
438#394—21no—
439#392—21no—
440#390—21no—
441#390C22×C8311yescharacteristic
442#390C22×C8311yescharacteristic
443#389C22×C8311yescharacteristic
444#389C22×C8311yescharacteristic
445#388—21no—
446#386—21no—
447#386—21no—
448C4×C4⋊C4C22×C8311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4C22×C8311yescharacteristic
451#340C22×C8311yescharacteristic
452#340C22×C8311yescharacteristic
453#340C22×C8311yescharacteristic
454#340C22×C8311yescharacteristic
455#336C22×C8311yescharacteristic
456#336C22×C8311yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C23×C8311yescharacteristic
463C22×D4C23×C8311yescharacteristic
464C22×D4C23×C8311yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C23×C8311yescharacteristic
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C2×D8—41no—
474C22×C8C23×C8311yescharacteristic
475C22×C8C23×C8311yescharacteristic
476C22×C8C23×C8311yescharacteristic
477C22×C8C23×C8311yescharacteristic
478#127—22no—
479#127—41no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—44no—
485#121—41no—
486#121—41no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491#117—22no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C8311yescharacteristic
496C2×C4⋊C4C23×C8311yescharacteristic
497C2×C4⋊C4C23×C8311yescharacteristic
498C2×C4⋊C4C23×C8311yescharacteristic
499C2×C4⋊C4C23×C8311yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C8311yescharacteristic
511C2×C22⋊C4D4×C8311yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C23×C8311yescharacteristic
515C2×C42C23×C8311yescharacteristic
516#107D4×C8314yescomplemented
517#106—22no—
518C4⋊C8—41no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—41no—
529C4×C8—22no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95D4×C8311yescharacteristic
534#95D4×C8311yescharacteristic
535C24—21no—
536C24—21no—
537C24—21no—
538C24C2×D4×C8311yescharacteristic
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4#41×C8312yes—
571C2×D4#41×C8312yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4C2×D4×C8311yescharacteristic
590C22×C4C2×D4×C8311yescharacteristic
591C22×C4C2×D4×C8311yescharacteristic
592C22×C4C2×D4×C8311yescharacteristic
593C22×C4C2×D4×C8311yescharacteristic
594C22×C4C24×C8311yescharacteristic
595D8—28no—
596D8—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8C2×D4×C8312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4C2×D4×C8312yes—
619C4⋊C4C2×D4×C8312yes—
620C4⋊C4#41×C8312yes—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—42no—
638C42—81no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C22×D4×C8311yescharacteristic
668D4—22no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—84no—
681D4—84no—
682D4—84no—
683D4—84no—
684D4—84no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4#135×C8312yes—
720C2×C4AGL(1,ℤ/8)×C8312yes—
721C2×C4C22×D4×C8311yescharacteristic
722C2×C4C2×#41×C8311yescharacteristic
723C2×C4C2×#41×C8311yescharacteristic
724C2×C4C2×#41×C8311yescharacteristic
725C2×C4H(5,𝔽2)×C8311yescharacteristic
726C2×C4H(5,𝔽2)×C8311yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22#525×C8311yescharacteristic
760C22D42×C8311yescharacteristic
761C22#546×C8311yescharacteristic
762C22C2×#135×C8311yescharacteristic
763C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
764C22#576×C8311yescharacteristic
765C22#576×C8311yescharacteristic
766C4—22no—
767C4—22no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—42no—
773C4—42no—
774C4—81no—
775C4—81no—
776C4#525×C8311yescharacteristic
777C4#538×C8311yescharacteristic
778C4#550×C8311yescharacteristic
779C4#553×C8311yescharacteristic
780C2—81no—
781C2—82no—
782C2—82no—
783C2—161no—
784C2C83×#245611yescharacteristic
785C2C83×#310611yescharacteristic
786C2C83×#312211yescharacteristic
787C2C83×#326411yescharacteristic
788C2C83×#328711yescharacteristic
789C2C83×#329711yescharacteristic
790C2C83×#332511yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C4×C22⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C83C2semidirect
2. C2×C4×D8×C83C2semidirect
3. C83×#2428C2semidirect
4. C83×#2363C2semidirect
5. C83×#2065C2semidirect
6. C83×#2011C2semidirect
7. C83×#1999C2semidirect
8. C83×#1999C2semidirect
9. C83×#1982C2semidirect
10. C83×#1934C2semidirect
11. C83×#1923C2semidirect
12. C83×#1921C2semidirect
13. C83×#1879C2semidirect
14. C83×#1875C2semidirect
15. C83×#1864C2semidirect
120. #107×C83D4semidirect
384. #26619C83direct (N × H)
396. C2×#482C2×C83semidirect
397. C2×C4×D8C2×C83semidirect
398. #2428C2×C83semidirect
399. #2363C2×C83semidirect
400. #2065C2×C83semidirect
401. #2011C2×C83semidirect
402. #1999C2×C83semidirect
403. #1999C2×C83semidirect
404. #1982C2×C83semidirect
405. #1934C2×C83semidirect
406. #1923C2×C83semidirect
407. #1921C2×C83semidirect
408. #1879C2×C83semidirect
409. #1875C2×C83semidirect
410. #1864C2×C83semidirect
411. C83#26619direct (N × H)
516. #107D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C832
C2×C4×D8×C832
C83×#24282
C83×#23632
C83×#20652
C83×#20112
C83×#19992
C83×#19822
C83×#19342
C83×#19232
C83×#19212
C83×#18792
C83×#18752
C83×#18642
#2661983