Finite Group Databasebeta

← C83×#29467 #35257291

Subgroups — C83×#29467 #35257291

Order 21248.

828 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#2854C211yesmaximal, characteristic
2C4×C22⋊Q8×C83C211yesmaximal, characteristic, complemented
3C83×#2077C211yesmaximal, characteristic, complemented
4C83×#2036C211yesmaximal, characteristic, complemented
5C83×#2033C211yesmaximal, characteristic
6C83×#2000C211yesmaximal, characteristic
7C83×#1968C211yesmaximal, characteristic, complemented
8C83×#1942C211yesmaximal, characteristic, complemented
9C83×#1934C211yesmaximal, characteristic, complemented
10C83×#1933C211yesmaximal, characteristic, complemented
11C83×#1925C211yesmaximal, characteristic, complemented
12C83×#1920C211yesmaximal, characteristic, complemented
13C83×#1880C211yesmaximal, characteristic, complemented
14C83×#1863C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C83C211yesmaximal, characteristic, complemented
16C22×SD16×C83C2211yescharacteristic
17C2×#123×C83—21no—
18C2×C22⋊Q8×C83C2211yescharacteristic
19C2×#121×C83C2211yescharacteristic
20C2×C4×Q8×C83C2211yescharacteristic
21C22×C42×C83C2211yescharacteristic
22C2×#107×C83C2211yescharacteristic
23C2×#107×C83C2211yescharacteristic
24C2×#106×C83C2211yescharacteristic
25C2×#103×C83C2211yescharacteristic
26C2×#103×C83C2211yescharacteristic
27C2×#103×C83C2211yescharacteristic
28C2×#102×C83C2211yescharacteristic
29C2×#102×C83C2211yescharacteristic
30C2×#102×C83C2211yescharacteristic
31C2×C22⋊C8×C83C2211yescharacteristic
32C2×C22⋊C8×C83C2211yescharacteristic
33C2×C4×C8×C83C2211yescharacteristic
34C2×C4×C8×C83C2211yescharacteristic
35#391×C83C2211yescharacteristic
36#390×C83C2211yescharacteristic
37#390×C83C2211yescharacteristic
38#389×C83C2211yescharacteristic
39#389×C83C2211yescharacteristic
40#389×C83C2211yescharacteristic
41#388×C83—21no—
42#388×C83—21no—
43#387×C83—21no—
44#386×C83—21no—
45#385×C83—21no—
46#380×C83C2211yescharacteristic
47#380×C83C2211yescharacteristic
48C4×C4⋊C4×C83—21no—
49C4×C4⋊C4×C83C2211yescharacteristic
50C4×C22⋊C4×C83—21no—
51#340×C83C2211yescharacteristic
52#340×C83C2211yescharacteristic
53#340×C83C2211yescharacteristic
54#340×C83C2211yescharacteristic
55#340×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59C22×Q8×C83C2311yescharacteristic
60C22×D4×C83—21no—
61C22×D4×C83C2311yescharacteristic
62C23×C4×C83D411yescharacteristic
63C23×C4×C83D411yescharacteristic
64C23×C4×C83C2311yescharacteristic
65C2×SD16×C83—22no—
66C2×SD16×C83—22no—
67C2×SD16×C83—41no—
68C22×C8×C83C2311yescharacteristic
69C22×C8×C83C2311yescharacteristic
70C22×C8×C83C2311yescharacteristic
71C22×C8×C83C2311yescharacteristic
72#123×C83—44no—
73C22⋊Q8×C83—22no—
74C22⋊Q8×C83—22no—
75#121×C83—41no—
76#121×C83—41no—
77C4×Q8×C83—41no—
78C4×Q8×C83—41no—
79C2×C4⋊C4×C83—21no—
80C2×C4⋊C4×C83—21no—
81C2×C4⋊C4×C83—21no—
82C2×C4⋊C4×C83—21no—
83C2×C4⋊C4×C83—21no—
84C2×C4⋊C4×C83C2311yescharacteristic
85C2×C4⋊C4×C83C2311yescharacteristic
86C2×C4⋊C4×C83C2311yescharacteristic
87C2×C4⋊C4×C83C2311yescharacteristic
88C2×C4⋊C4×C83C2311yescharacteristic
89C2×C4⋊C4×C83C2311yescharacteristic
90C2×C22⋊C4×C83—21no—
91C2×C22⋊C4×C83—21no—
92C2×C22⋊C4×C83—21no—
93C2×C22⋊C4×C83—21no—
94C2×C22⋊C4×C83—21no—
95C2×C22⋊C4×C83—21no—
96C2×C22⋊C4×C83—21no—
97C2×C22⋊C4×C83—21no—
98C2×C42×C83—21no—
99C2×C42×C83—21no—
100C2×C42×C83—41no—
101C2×C42×C83—41no—
102C2×C42×C83D411yescharacteristic
103C2×C42×C83D411yescharacteristic
104C2×C42×C83C2311yescharacteristic
105C2×C42×C83C2311yescharacteristic
106#107×C83—22no—
107#107×C83—41no—
108#106×C83—22no—
109#103×C83—22no—
110#103×C83—22no—
111#103×C83—41no—
112#102×C83—22no—
113#102×C83—22no—
114#102×C83—41no—
115C22⋊C8×C83—22no—
116C22⋊C8×C83—22no—
117C4×C8×C83—41no—
118C4×C8×C83—41no—
119#95×C83—21no—
120#95×C83—21no—
121#95×C83—21no—
122#95×C83—21no—
123#95×C83—21no—
124#95×C83—21no—
125#95×C83—21no—
126#95×C83—21no—
127C24×C83—21no—
128C24×C83C2×D411yescharacteristic
129C2×Q8×C83—21no—
130C2×Q8×C83—21no—
131C2×Q8×C83—21no—
132C2×Q8×C83—21no—
133C2×Q8×C83—21no—
134C2×Q8×C83#4112yes—
135C2×D4×C83—21no—
136C2×D4×C83—21no—
137C2×D4×C83—21no—
138C2×D4×C83—21no—
139C2×D4×C83—21no—
140C2×D4×C83—21no—
141C2×D4×C83—42no—
142C2×D4×C83—42no—
143C2×D4×C83—42no—
144C22×C4×C83—22no—
145C22×C4×C83—21no—
146C22×C4×C83—21no—
147C22×C4×C83—22no—
148C22×C4×C83—22no—
149C22×C4×C83—22no—
150C22×C4×C83—21no—
151C22×C4×C83—21no—
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—41no—
162C22×C4×C83—41no—
163C22×C4×C83C2×D411yescharacteristic
164C22×C4×C83C2×D411yescharacteristic
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83C2411yescharacteristic
169SD16×C83—44no—
170C2×C8×C83—21no—
171C2×C8×C83—21no—
172C2×C8×C83—21no—
173C2×C8×C83—21no—
174C2×C8×C83—21no—
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83#4112yes—
181C2×C8×C83#4112yes—
182C4⋊C4×C83—24no—
183C4⋊C4×C83—21no—
184C4⋊C4×C83—21no—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—42no—
195C4⋊C4×C83—42no—
196C4⋊C4×C83—42no—
197C4⋊C4×C83—42no—
198C4⋊C4×C83#4112yes—
199C22⋊C4×C83—24no—
200C22⋊C4×C83—42no—
201C22⋊C4×C83—42no—
202C22⋊C4×C83—42no—
203C22⋊C4×C83—42no—
204C22⋊C4×C83—42no—
205C22⋊C4×C83—42no—
206C22⋊C4×C83—42no—
207C42×C83—21no—
208C42×C83—21no—
209C42×C83—21no—
210C42×C83—21no—
211C42×C83—41no—
212C42×C83—41no—
213C42×C83—42no—
214C42×C83—42no—
215C23×C83—21no—
216C23×C83—21no—
217C23×C83—21no—
218C23×C83—21no—
219C23×C83—21no—
220C23×C83—21no—
221C23×C83—41no—
222C23×C83—41no—
223C23×C83—41no—
224C23×C83—41no—
225C23×C83—41no—
226C23×C83—41no—
227C23×C83—41no—
228C23×C83#13512yes—
229C23×C83C22×D411yescharacteristic
230Q8×C83—22no—
231Q8×C83—22no—
232Q8×C83—41no—
233Q8×C83—41no—
234D4×C83—41no—
235D4×C83—41no—
236D4×C83—41no—
237D4×C83—41no—
238D4×C83—84no—
239C2×C4×C83—21no—
240C2×C4×C83—21no—
241C2×C4×C83—21no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—22no—
246C2×C4×C83—22no—
247C2×C4×C83—21no—
248C2×C4×C83—21no—
249C2×C4×C83—21no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—44no—
254C2×C4×C83—44no—
255C2×C4×C83—41no—
256C2×C4×C83—41no—
257C2×C4×C83—41no—
258C2×C4×C83—41no—
259C2×C4×C83—41no—
260C2×C4×C83—41no—
261C2×C4×C83—41no—
262C2×C4×C83—41no—
263C2×C4×C83—41no—
264C2×C4×C83—41no—
265C2×C4×C83—41no—
266C2×C4×C83—41no—
267C2×C4×C83—41no—
268C2×C4×C83—41no—
269C2×C4×C83—41no—
270C2×C4×C83—41no—
271C2×C4×C83—41no—
272C2×C4×C83—41no—
273C2×C4×C83—41no—
274C2×C4×C83—41no—
275C2×C4×C83—41no—
276C2×C4×C83—41no—
277C2×C4×C83—41no—
278C2×C4×C83#13512yes—
279C2×C4×C83AGL(1,ℤ/8)12yes—
280C2×C4×C83#13712yes—
281C2×C4×C83C2×#4111yescharacteristic
282C2×C4×C83C2×#4111yescharacteristic
283C2×C4×C83C2×#4111yescharacteristic
284C2×C4×C83C2×#4111yescharacteristic
285C2×C4×C83H(5,𝔽2)11yescharacteristic
286C2×C4×C83H(5,𝔽2)11yescharacteristic
287C8×C83—22no—
288C8×C83—22no—
289C8×C83—41no—
290C8×C83—41no—
291C22×C83—22no—
292C22×C83—22no—
293C22×C83—22no—
294C22×C83—41no—
295C22×C83—41no—
296C22×C83—41no—
297C22×C83—41no—
298C22×C83—81no—
299C22×C83—81no—
300C22×C83—81no—
301C22×C83—81no—
302C22×C83—81no—
303C22×C83—81no—
304C22×C83—81no—
305C22×C83#52511yescharacteristic
306C22×C83#53211yescharacteristic
307C22×C83#53411yescharacteristic
308C22×C83C2×#13511yescharacteristic
309C22×C83C2×#13511yescharacteristic
310C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C83C2×#13711yescharacteristic
312C4×C83—22no—
313C4×C83—22no—
314C4×C83—22no—
315C4×C83—42no—
316C4×C83—41no—
317C4×C83—42no—
318C4×C83—41no—
319C4×C83—81no—
320C4×C83—81no—
321C4×C83—81no—
322C4×C83—81no—
323C4×C83—81no—
324C4×C83#55111yescharacteristic
325C4×C83#55311yescharacteristic
326C4×C83#55311yescharacteristic
327C4×C83#55911yescharacteristic
328#29467C8311yesmaximal, characteristic, direct product factor, Sylow
329C2×C83—42no—
330C2×C83—161no—
331C2×C83#260211yescharacteristic
332C2×C83#310611yescharacteristic
333C2×C83#310811yescharacteristic
334C2×C83#316811yescharacteristic
335C2×C83#318211yescharacteristic
336C2×C83#318811yescharacteristic
337C2×C83#319011yescharacteristic
338#2854C2×C8311yescharacteristic
339C4×C22⋊Q8C2×C8311yescharacteristic, complemented
340#2077C2×C8311yescharacteristic, complemented
341#2036C2×C8311yescharacteristic, complemented
342#2033C2×C8311yescharacteristic
343#2000C2×C8311yescharacteristic
344#1968C2×C8311yescharacteristic, complemented
345#1942C2×C8311yescharacteristic, complemented
346#1934C2×C8311yescharacteristic, complemented
347#1933C2×C8311yescharacteristic, complemented
348#1925C2×C8311yescharacteristic, complemented
349#1920C2×C8311yescharacteristic, complemented
350#1880C2×C8311yescharacteristic, complemented
351#1863C2×C8311yescharacteristic, complemented
352C4×C22⋊C8C2×C8311yescharacteristic, complemented
353C83#2946711yescharacteristic, direct product factor, Sylow
354C22×SD16C22×C8311yescharacteristic
355C2×#123—21no—
356C2×C22⋊Q8C22×C8311yescharacteristic
357C2×#121C22×C8311yescharacteristic
358C2×C4×Q8C22×C8311yescharacteristic
359C22×C42C22×C8311yescharacteristic
360C2×#107C22×C8311yescharacteristic
361C2×#107C22×C8311yescharacteristic
362C2×#106C22×C8311yescharacteristic
363C2×#103C22×C8311yescharacteristic
364C2×#103C22×C8311yescharacteristic
365C2×#103C22×C8311yescharacteristic
366C2×#102C22×C8311yescharacteristic
367C2×#102C22×C8311yescharacteristic
368C2×#102C22×C8311yescharacteristic
369C2×C22⋊C8C22×C8311yescharacteristic
370C2×C22⋊C8C22×C8311yescharacteristic
371C2×C4×C8C22×C8311yescharacteristic
372C2×C4×C8C22×C8311yescharacteristic
373#391C22×C8311yescharacteristic
374#390C22×C8311yescharacteristic
375#390C22×C8311yescharacteristic
376#389C22×C8311yescharacteristic
377#389C22×C8311yescharacteristic
378#389C22×C8311yescharacteristic
379#388—21no—
380#388—21no—
381#387—21no—
382#386—21no—
383#385—21no—
384#380C22×C8311yescharacteristic
385#380C22×C8311yescharacteristic
386C4×C4⋊C4—21no—
387C4×C4⋊C4C22×C8311yescharacteristic
388C4×C22⋊C4—21no—
389#340C22×C8311yescharacteristic
390#340C22×C8311yescharacteristic
391#340C22×C8311yescharacteristic
392#340C22×C8311yescharacteristic
393#340C22×C8311yescharacteristic
394#340C22×C8311yescharacteristic
395#336C22×C8311yescharacteristic
396#336C22×C8311yescharacteristic
397C22×Q8C23×C8311yescharacteristic
398C22×D4—21no—
399C22×D4C23×C8311yescharacteristic
400C23×C4D4×C8311yescharacteristic
401C23×C4D4×C8311yescharacteristic
402C23×C4C23×C8311yescharacteristic
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16—41no—
406C22×C8C23×C8311yescharacteristic
407C22×C8C23×C8311yescharacteristic
408C22×C8C23×C8311yescharacteristic
409C22×C8C23×C8311yescharacteristic
410#123—44no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413#121—41no—
414#121—41no—
415C4×Q8—41no—
416C4×Q8—41no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4C23×C8311yescharacteristic
423C2×C4⋊C4C23×C8311yescharacteristic
424C2×C4⋊C4C23×C8311yescharacteristic
425C2×C4⋊C4C23×C8311yescharacteristic
426C2×C4⋊C4C23×C8311yescharacteristic
427C2×C4⋊C4C23×C8311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—41no—
439C2×C42—41no—
440C2×C42D4×C8311yescharacteristic
441C2×C42D4×C8311yescharacteristic
442C2×C42C23×C8311yescharacteristic
443C2×C42C23×C8311yescharacteristic
444#107—22no—
445#107—41no—
446#106—22no—
447#103—22no—
448#103—22no—
449#103—41no—
450#102—22no—
451#102—22no—
452#102—41no—
453C22⋊C8—22no—
454C22⋊C8—22no—
455C4×C8—41no—
456C4×C8—41no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465C24—21no—
466C24C2×D4×C8311yescharacteristic
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8#41×C8312yes—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4C2×D4×C8311yescharacteristic
502C22×C4C2×D4×C8311yescharacteristic
503C22×C4C2×D4×C8311yescharacteristic
504C22×C4C2×D4×C8311yescharacteristic
505C22×C4C2×D4×C8311yescharacteristic
506C22×C4C24×C8311yescharacteristic
507SD16—44no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8#41×C8312yes—
519C2×C8#41×C8312yes—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4#41×C8312yes—
537C22⋊C4—24no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—41no—
550C42—41no—
551C42—42no—
552C42—42no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23#135×C8312yes—
567C23C22×D4×C8311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—84no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4#135×C8312yes—
617C2×C4AGL(1,ℤ/8)×C8312yes—
618C2×C4#137×C8312yes—
619C2×C4C2×#41×C8311yescharacteristic
620C2×C4C2×#41×C8311yescharacteristic
621C2×C4C2×#41×C8311yescharacteristic
622C2×C4C2×#41×C8311yescharacteristic
623C2×C4H(5,𝔽2)×C8311yescharacteristic
624C2×C4H(5,𝔽2)×C8311yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22#525×C8311yescharacteristic
644C22#532×C8311yescharacteristic
645C22#534×C8311yescharacteristic
646C22C2×#135×C8311yescharacteristic
647C22C2×#135×C8311yescharacteristic
648C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
649C22C2×#137×C8311yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4#551×C8311yescharacteristic
663C4#553×C8311yescharacteristic
664C4#553×C8311yescharacteristic
665C4#559×C8311yescharacteristic
666C2—42no—
667C2—161no—
668C2C83×#260211yescharacteristic
669C2C83×#310611yescharacteristic
670C2C83×#310811yescharacteristic
671C2C83×#316811yescharacteristic
672C2C83×#318211yescharacteristic
673C2C83×#318811yescharacteristic
674C2C83×#319011yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×#121×C83C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C22×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Q8×C83C2semidirect
3. C83×#2077C2semidirect
4. C83×#2036C2semidirect
7. C83×#1968C2semidirect
8. C83×#1942C2semidirect
9. C83×#1934C2semidirect
10. C83×#1933C2semidirect
11. C83×#1925C2semidirect
12. C83×#1920C2semidirect
13. C83×#1880C2semidirect
14. C83×#1863C2semidirect
15. C4×C22⋊C8×C83C2semidirect
328. #29467C83direct (N × H)
339. C4×C22⋊Q8C2×C83semidirect
340. #2077C2×C83semidirect
341. #2036C2×C83semidirect
344. #1968C2×C83semidirect
345. #1942C2×C83semidirect
346. #1934C2×C83semidirect
347. #1933C2×C83semidirect
348. #1925C2×C83semidirect
349. #1920C2×C83semidirect
350. #1880C2×C83semidirect
351. #1863C2×C83semidirect
352. C4×C22⋊C8C2×C83semidirect
353. C83#29467direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#28542
C4×C22⋊Q8×C832
C83×#20772
C83×#20362
C83×#20332
C83×#20002
C83×#19682
C83×#19422
C83×#19342
C83×#19332
C83×#19252
C83×#19202
C83×#18802
C83×#18632
C4×C22⋊C8×C832
#2946783