Finite Group Databasebeta

← C83×#24434 #35252258

Subgroups — C83×#24434 #35252258

Order 21248.

1674 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C83C211yesmaximal, characteristic, complemented
2C2×#465×C83C211yesmaximal, characteristic, complemented
3C2×#449×C83C211yesmaximal, characteristic, complemented
4C2×#447×C83C211yesmaximal, characteristic, complemented
5C22×#102×C83C211yesmaximal, characteristic, complemented
6C83×#2416C211yesmaximal, characteristic, complemented
7C83×#2042C211yesmaximal, characteristic, complemented
8C83×#2034C211yesmaximal, characteristic, complemented
9C83×#2012C211yesmaximal, characteristic, complemented
10C83×#1999C211yesmaximal, characteristic, complemented
11C83×#1879C211yesmaximal, characteristic, complemented
12C83×#1872C211yesmaximal, characteristic, complemented
13C83×#1869C211yesmaximal, characteristic, complemented
14C83×#1864C211yesmaximal, characteristic, complemented
15C83×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic, complemented
19C22×D8×C83C2211yescharacteristic
20C22×D8×C83C2211yescharacteristic
21C23×C8×C83C2211yescharacteristic
22#546×C83—24no—
23#546×C83—24no—
24C2×#124×C83C2211yescharacteristic
25C2×#123×C83—21no—
26C2×C22⋊Q8×C83C2211yescharacteristic
27C2×#121×C83—21no—
28C2×#121×C83—21no—
29C2×#121×C83C2211yescharacteristic
30C2×#121×C83C2211yescharacteristic
31C2×#121×C83C2211yescharacteristic, complemented
32C2×#120×C83—21no—
33C2×C4×D4×C83C2211yescharacteristic
34C2×C4×D4×C83C2211yescharacteristic
35C22×C4⋊C4×C83C2211yescharacteristic
36C22×C22⋊C4×C83—21no—
37#465×C83—24no—
38#449×C83—24no—
39#447×C83—24no—
40C2×#106×C83C2211yescharacteristic, complemented
41C2×#103×C83C2211yescharacteristic, complemented
42C2×#103×C83C2211yescharacteristic, complemented
43C2×#103×C83C2211yescharacteristic, complemented
44C2×#102×C83—24no—
45C2×#102×C83C2211yescharacteristic
46C2×#102×C83C2211yescharacteristic
47C2×#102×C83C2211yescharacteristic
48C2×#102×C83C2211yescharacteristic
49C2×#102×C83C2211yescharacteristic
50C2×#102×C83C2211yescharacteristic
51C2×#102×C83C2211yescharacteristic, complemented
52C2×C22⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic, complemented
54C2×C22⋊C8×C83C2211yescharacteristic, complemented
55#396×C83—21no—
56#394×C83—21no—
57#390×C83C2211yescharacteristic, complemented
58#389×C83C2211yescharacteristic, complemented
59#386×C83—21no—
60#380×C83C2211yescharacteristic, complemented
61#340×C83C2211yescharacteristic, complemented
62#340×C83C2211yescharacteristic, complemented
63#336×C83C2211yescharacteristic, complemented
64#336×C83C2211yescharacteristic, complemented
65C25×C83—21no—
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—22no—
69C2×#41×C83—22no—
70C2×#41×C83—41no—
71C2×#41×C83—41no—
72C22×Q8×C83C2311yescharacteristic
73C22×D4×C83—22no—
74C22×D4×C83—22no—
75C22×D4×C83—21no—
76C22×D4×C83—21no—
77C22×D4×C83—21no—
78C22×D4×C83—21no—
79C22×D4×C83—21no—
80C22×D4×C83—22no—
81C22×D4×C83—41no—
82C22×D4×C83—41no—
83C22×D4×C83D411yescharacteristic
84C22×D4×C83D414yescomplemented
85C22×D4×C83C2311yescharacteristic
86C22×D4×C83C2311yescharacteristic
87C22×D4×C83C2311yescharacteristic
88C23×C4×C83—21no—
89C23×C4×C83—21no—
90C23×C4×C83—21no—
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C2×SD16×C83—22no—
94C2×SD16×C83—22no—
95C2×SD16×C83—41no—
96C2×D8×C83—22no—
97C2×D8×C83—22no—
98C2×D8×C83—22no—
99C2×D8×C83—22no—
100C2×D8×C83—41no—
101C2×D8×C83—41no—
102C22×C8×C83—22no—
103C22×C8×C83—22no—
104C22×C8×C83—41no—
105C22×C8×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109#124×C83—22no—
110#124×C83—22no—
111#123×C83—28no—
112C22⋊Q8×C83—22no—
113C22⋊Q8×C83D414yescomplemented
114#121×C83—28no—
115#121×C83—22no—
116#121×C83—22no—
117#121×C83—22no—
118#121×C83—22no—
119#121×C83—22no—
120#121×C83—41no—
121#121×C83—44no—
122#120×C83—28no—
123C4×D4×C83—22no—
124C4×D4×C83—22no—
125C4×D4×C83—22no—
126C4×D4×C83—22no—
127C2×C4⋊C4×C83—21no—
128C2×C4⋊C4×C83—22no—
129C2×C4⋊C4×C83—21no—
130C2×C4⋊C4×C83—21no—
131C2×C4⋊C4×C83—41no—
132C2×C4⋊C4×C83D411yescharacteristic
133C2×C4⋊C4×C83C2311yescharacteristic
134C2×C4⋊C4×C83C2311yescharacteristic
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83C2311yescharacteristic
137C2×C22⋊C4×C83—28no—
138C2×C22⋊C4×C83—21no—
139C2×C22⋊C4×C83—21no—
140C2×C22⋊C4×C83—21no—
141C2×C22⋊C4×C83—21no—
142C2×C22⋊C4×C83—21no—
143C2×C22⋊C4×C83—21no—
144C2×C22⋊C4×C83—21no—
145C2×C22⋊C4×C83—21no—
146C2×C22⋊C4×C83—21no—
147C2×C22⋊C4×C83—21no—
148C2×C22⋊C4×C83D411yescharacteristic
149C2×C22⋊C4×C83D411yescharacteristic
150C2×C42×C83C2311yescharacteristic
151#106×C83—22no—
152#103×C83—22no—
153#103×C83—22no—
154#103×C83—41no—
155#102×C83—22no—
156#102×C83—22no—
157#102×C83—22no—
158#102×C83—22no—
159#102×C83—22no—
160#102×C83—22no—
161#102×C83D414yescomplemented
162C22⋊C8×C83—22no—
163C22⋊C8×C83—22no—
164C22⋊C8×C83—41no—
165#95×C83—21no—
166#95×C83—21no—
167C24×C83—21no—
168C24×C83—21no—
169C24×C83—24no—
170C24×C83—21no—
171C24×C83—42no—
172C24×C83—42no—
173C24×C83—42no—
174C24×C83—42no—
175C24×C83—81no—
176C24×C83—81no—
177C24×C83C2×D411yescharacteristic
178C24×C83C2×D411yescharacteristic
179#41×C83—44no—
180#41×C83—44no—
181#41×C83—44no—
182#41×C83—44no—
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83—21no—
186C2×Q8×C83—21no—
187C2×Q8×C83—21no—
188C2×Q8×C83C2×D412yes—
189C2×D4×C83—28no—
190C2×D4×C83—24no—
191C2×D4×C83—22no—
192C2×D4×C83—22no—
193C2×D4×C83—22no—
194C2×D4×C83—24no—
195C2×D4×C83—24no—
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—21no—
209C2×D4×C83—21no—
210C2×D4×C83—44no—
211C2×D4×C83—44no—
212C2×D4×C83—44no—
213C2×D4×C83—42no—
214C2×D4×C83—42no—
215C2×D4×C83—42no—
216C2×D4×C83—42no—
217C2×D4×C83—42no—
218C2×D4×C83—42no—
219C2×D4×C83—42no—
220C2×D4×C83—42no—
221C2×D4×C83—42no—
222C2×D4×C83—81no—
223C2×D4×C83—81no—
224C2×D4×C83—81no—
225C2×D4×C83C2×D412yes—
226C2×D4×C83C2×D412yes—
227C2×D4×C83C2×D412yes—
228C2×D4×C83#4112yes—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—24no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
237C22×C4×C83—24no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—42no—
247C22×C4×C83—42no—
248C22×C4×C83—42no—
249C22×C4×C83—42no—
250C22×C4×C83—81no—
251C22×C4×C83—81no—
252C22×C4×C83—81no—
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2×D412yes—
258C22×C4×C83C2×D412yes—
259C22×C4×C83C2411yescharacteristic
260SD16×C83—44no—
261D8×C83—44no—
262D8×C83—44no—
263C2×C8×C83—21no—
264C2×C8×C83—21no—
265C2×C8×C83—21no—
266C2×C8×C83—21no—
267C2×C8×C83—21no—
268C2×C8×C83—21no—
269C2×C8×C83—21no—
270C2×C8×C83—21no—
271C2×C8×C83—21no—
272C2×C8×C83—21no—
273C2×C8×C83—21no—
274C2×C8×C83—44no—
275C2×C8×C83C2×D412yes—
276C4⋊C4×C83—24no—
277C4⋊C4×C83—22no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83—21no—
280C4⋊C4×C83—21no—
281C4⋊C4×C83—21no—
282C4⋊C4×C83—21no—
283C4⋊C4×C83—21no—
284C4⋊C4×C83—42no—
285C4⋊C4×C83—42no—
286C4⋊C4×C83C2×D412yes—
287C4⋊C4×C83C2×D412yes—
288C22⋊C4×C83—24no—
289C22⋊C4×C83—24no—
290C22⋊C4×C83—24no—
291C22⋊C4×C83—24no—
292C22⋊C4×C83—22no—
293C22⋊C4×C83—24no—
294C22⋊C4×C83—22no—
295C22⋊C4×C83—42no—
296C22⋊C4×C83—42no—
297C22⋊C4×C83—42no—
298C22⋊C4×C83—42no—
299C22⋊C4×C83—81no—
300C42×C83—21no—
301C42×C83—21no—
302C23×C83—21no—
303C23×C83—21no—
304C23×C83—21no—
305C23×C83—21no—
306C23×C83—22no—
307C23×C83—22no—
308C23×C83—22no—
309C23×C83—22no—
310C23×C83—21no—
311C23×C83—21no—
312C23×C83—21no—
313C23×C83—21no—
314C23×C83—21no—
315C23×C83—21no—
316C23×C83—21no—
317C23×C83—48no—
318C23×C83—41no—
319C23×C83—41no—
320C23×C83—41no—
321C23×C83—41no—
322C23×C83—41no—
323C23×C83—41no—
324C23×C83—41no—
325C23×C83—41no—
326C23×C83—41no—
327C23×C83—41no—
328C23×C83—48no—
329C23×C83—41no—
330C23×C83—41no—
331C23×C83—41no—
332C23×C83—41no—
333C23×C83—41no—
334C23×C83—41no—
335C23×C83—41no—
336C23×C83—84no—
337C23×C83—84no—
338C23×C83—84no—
339C23×C83—84no—
340C23×C83—84no—
341C23×C83#12012yes—
342C23×C83#13512yes—
343C23×C83AGL(1,ℤ/8)12yes—
344C23×C83C22×D411yescharacteristic
345Q8×C83—22no—
346Q8×C83—22no—
347Q8×C83—41no—
348Q8×C83—41no—
349D4×C83—22no—
350D4×C83—22no—
351D4×C83—22no—
352D4×C83—22no—
353D4×C83—22no—
354D4×C83—48no—
355D4×C83—48no—
356D4×C83—44no—
357D4×C83—41no—
358D4×C83—41no—
359D4×C83—41no—
360D4×C83—41no—
361D4×C83—41no—
362D4×C83—41no—
363D4×C83—84no—
364D4×C83—84no—
365D4×C83—84no—
366D4×C83#12114yescomplemented
367C2×C4×C83—21no—
368C2×C4×C83—21no—
369C2×C4×C83—22no—
370C2×C4×C83—22no—
371C2×C4×C83—22no—
372C2×C4×C83—22no—
373C2×C4×C83—21no—
374C2×C4×C83—21no—
375C2×C4×C83—22no—
376C2×C4×C83—21no—
377C2×C4×C83—22no—
378C2×C4×C83—21no—
379C2×C4×C83—22no—
380C2×C4×C83—21no—
381C2×C4×C83—21no—
382C2×C4×C83—21no—
383C2×C4×C83—21no—
384C2×C4×C83—21no—
385C2×C4×C83—48no—
386C2×C4×C83—41no—
387C2×C4×C83—41no—
388C2×C4×C83—41no—
389C2×C4×C83—41no—
390C2×C4×C83—41no—
391C2×C4×C83—41no—
392C2×C4×C83—41no—
393C2×C4×C83—41no—
394C2×C4×C83—41no—
395C2×C4×C83—41no—
396C2×C4×C83—41no—
397C2×C4×C83—41no—
398C2×C4×C83—41no—
399C2×C4×C83—41no—
400C2×C4×C83—41no—
401C2×C4×C83—41no—
402C2×C4×C83—84no—
403C2×C4×C83—84no—
404C2×C4×C83#12012yes—
405C2×C4×C83C22×D411yescharacteristic
406C2×C4×C83C22×D411yescharacteristic
407C2×C4×C83C22×D411yescharacteristic
408C2×C4×C83C2×#4111yescharacteristic
409C2×C4×C83H(5,𝔽2)11yescharacteristic
410C2×C4×C83H(5,𝔽2)11yescharacteristic
411C8×C83—22no—
412C8×C83—41no—
413C8×C83—41no—
414C8×C83—41no—
415C22×C83—22no—
416C22×C83—22no—
417C22×C83—22no—
418C22×C83—22no—
419C22×C83—22no—
420C22×C83—22no—
421C22×C83—24no—
422C22×C83—42no—
423C22×C83—42no—
424C22×C83—42no—
425C22×C83—42no—
426C22×C83—42no—
427C22×C83—42no—
428C22×C83—41no—
429C22×C83—42no—
430C22×C83—41no—
431C22×C83—42no—
432C22×C83—41no—
433C22×C83—41no—
434C22×C83—42no—
435C22×C83—41no—
436C22×C83—41no—
437C22×C83—41no—
438C22×C83—816no—
439C22×C83—81no—
440C22×C83—81no—
441C22×C83—81no—
442C22×C83—81no—
443C22×C83—81no—
444C22×C83—81no—
445C22×C83—81no—
446C22×C83—81no—
447C22×C83—81no—
448C22×C83—81no—
449C22×C83—81no—
450C22×C83#44914yescomplemented
451C22×C83C2×#12011yescharacteristic
452C22×C83D4211yescharacteristic
453C22×C83#54611yescharacteristic
454C22×C83C2×#13511yescharacteristic
455C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C83#57611yescharacteristic
457C22×C83#57711yescharacteristic
458C4×C83—22no—
459C4×C83—41no—
460C4×C83—42no—
461C4×C83—41no—
462C4×C83—42no—
463C4×C83—41no—
464C4×C83—42no—
465C4×C83—81no—
466C4×C83—81no—
467C4×C83C2×#12111yescharacteristic
468C4×C83#53411yescharacteristic
469C4×C83D4211yescharacteristic
470C4×C83#54611yescharacteristic
471#24434C8311yesmaximal, characteristic, direct product factor, Sylow
472C2×C83—24no—
473C2×C83—44no—
474C2×C83—81no—
475C2×C83—82no—
476C2×C83—161no—
477C2×C83#241011yescharacteristic
478C2×C83C2×#44911yescharacteristic
479C2×C83#301211yescharacteristic
480C2×C83#326411yescharacteristic
481C2×C83#328211yescharacteristic
482C2×C83#329711yescharacteristic
483C2×C83#330611yescharacteristic
484C2×#546C2×C8311yescharacteristic, complemented
485C2×#465C2×C8311yescharacteristic, complemented
486C2×#449C2×C8311yescharacteristic, complemented
487C2×#447C2×C8311yescharacteristic, complemented
488C22×#102C2×C8311yescharacteristic, complemented
489#2416C2×C8311yescharacteristic, complemented
490#2042C2×C8311yescharacteristic, complemented
491#2034C2×C8311yescharacteristic, complemented
492#2012C2×C8311yescharacteristic, complemented
493#1999C2×C8311yescharacteristic, complemented
494#1879C2×C8311yescharacteristic, complemented
495#1872C2×C8311yescharacteristic, complemented
496#1869C2×C8311yescharacteristic, complemented
497#1864C2×C8311yescharacteristic, complemented
498#1788C2×C8311yescharacteristic, complemented
499C83#2443411yescharacteristic, direct product factor, Sylow
500C22×#41C22×C8311yescharacteristic
501C23×D4C22×C8311yescharacteristic
502C22×SD16C22×C8311yescharacteristic, complemented
503C22×D8C22×C8311yescharacteristic
504C22×D8C22×C8311yescharacteristic
505C23×C8C22×C8311yescharacteristic
506#546—24no—
507#546—24no—
508C2×#124C22×C8311yescharacteristic
509C2×#123—21no—
510C2×C22⋊Q8C22×C8311yescharacteristic
511C2×#121—21no—
512C2×#121—21no—
513C2×#121C22×C8311yescharacteristic
514C2×#121C22×C8311yescharacteristic
515C2×#121C22×C8311yescharacteristic, complemented
516C2×#120—21no—
517C2×C4×D4C22×C8311yescharacteristic
518C2×C4×D4C22×C8311yescharacteristic
519C22×C4⋊C4C22×C8311yescharacteristic
520C22×C22⋊C4—21no—
521#465—24no—
522#449—24no—
523#447—24no—
524C2×#106C22×C8311yescharacteristic, complemented
525C2×#103C22×C8311yescharacteristic, complemented
526C2×#103C22×C8311yescharacteristic, complemented
527C2×#103C22×C8311yescharacteristic, complemented
528C2×#102—24no—
529C2×#102C22×C8311yescharacteristic
530C2×#102C22×C8311yescharacteristic
531C2×#102C22×C8311yescharacteristic
532C2×#102C22×C8311yescharacteristic
533C2×#102C22×C8311yescharacteristic
534C2×#102C22×C8311yescharacteristic
535C2×#102C22×C8311yescharacteristic, complemented
536C2×C22⋊C8C22×C8311yescharacteristic
537C2×C22⋊C8C22×C8311yescharacteristic, complemented
538C2×C22⋊C8C22×C8311yescharacteristic, complemented
539#396—21no—
540#394—21no—
541#390C22×C8311yescharacteristic, complemented
542#389C22×C8311yescharacteristic, complemented
543#386—21no—
544#380C22×C8311yescharacteristic, complemented
545#340C22×C8311yescharacteristic, complemented
546#340C22×C8311yescharacteristic, complemented
547#336C22×C8311yescharacteristic, complemented
548#336C22×C8311yescharacteristic, complemented
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—41no—
555C2×#41—41no—
556C22×Q8C23×C8311yescharacteristic
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C8311yescharacteristic
568C22×D4D4×C8314yescomplemented
569C22×D4C23×C8311yescharacteristic
570C22×D4C23×C8311yescharacteristic
571C22×D4C23×C8311yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C8311yescharacteristic
576C23×C4C23×C8311yescharacteristic
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C22×C8—22no—
587C22×C8—22no—
588C22×C8—41no—
589C22×C8C23×C8311yescharacteristic
590C22×C8C23×C8311yescharacteristic
591C22×C8C23×C8311yescharacteristic
592C22×C8C23×C8311yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8D4×C8314yescomplemented
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—41no—
605#121—44no—
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C8311yescharacteristic
617C2×C4⋊C4C23×C8311yescharacteristic
618C2×C4⋊C4C23×C8311yescharacteristic
619C2×C4⋊C4C23×C8311yescharacteristic
620C2×C4⋊C4C23×C8311yescharacteristic
621C2×C22⋊C4—28no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C8311yescharacteristic
633C2×C22⋊C4D4×C8311yescharacteristic
634C2×C42C23×C8311yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—41no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102D4×C8314yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—21no—
653C24—24no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C8311yescharacteristic
662C24C2×D4×C8311yescharacteristic
663#41—44no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C8312yes—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C8312yes—
710C2×D4C2×D4×C8312yes—
711C2×D4C2×D4×C8312yes—
712C2×D4#41×C8312yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C8311yescharacteristic
738C22×C4C2×D4×C8311yescharacteristic
739C22×C4C2×D4×C8311yescharacteristic
740C22×C4C2×D4×C8311yescharacteristic
741C22×C4C2×D4×C8312yes—
742C22×C4C2×D4×C8312yes—
743C22×C4C24×C8311yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—44no—
759C2×C8C2×D4×C8312yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C8312yes—
771C4⋊C4C2×D4×C8312yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—24no—
778C22⋊C4—22no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—48no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—48no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23#120×C8312yes—
826C23#135×C8312yes—
827C23AGL(1,ℤ/8)×C8312yes—
828C23C22×D4×C8311yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—44no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C8314yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C8312yes—
889C2×C4C22×D4×C8311yescharacteristic
890C2×C4C22×D4×C8311yescharacteristic
891C2×C4C22×D4×C8311yescharacteristic
892C2×C4C2×#41×C8311yescharacteristic
893C2×C4H(5,𝔽2)×C8311yescharacteristic
894C2×C4H(5,𝔽2)×C8311yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—24no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22#449×C8314yescomplemented
935C22C2×#120×C8311yescharacteristic
936C22D42×C8311yescharacteristic
937C22#546×C8311yescharacteristic
938C22C2×#135×C8311yescharacteristic
939C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
940C22#576×C8311yescharacteristic
941C22#577×C8311yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C8311yescharacteristic
952C4#534×C8311yescharacteristic
953C4D42×C8311yescharacteristic
954C4#546×C8311yescharacteristic
955C2—24no—
956C2—44no—
957C2—81no—
958C2—82no—
959C2—161no—
960C2C83×#241011yescharacteristic
961C2C2×#449×C8311yescharacteristic
962C2C83×#301211yescharacteristic
963C2C83×#326411yescharacteristic
964C2C83×#328211yescharacteristic
965C2C83×#329711yescharacteristic
966C2C83×#330611yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×C4×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#546×C83C2semidirect
2. C2×#465×C83C2semidirect
3. C2×#449×C83C2semidirect
4. C2×#447×C83C2semidirect
5. C22×#102×C83C2semidirect
6. C83×#2416C2semidirect
7. C83×#2042C2semidirect
8. C83×#2034C2semidirect
9. C83×#2012C2semidirect
10. C83×#1999C2semidirect
11. C83×#1879C2semidirect
12. C83×#1872C2semidirect
13. C83×#1869C2semidirect
14. C83×#1864C2semidirect
15. C83×#1788C2semidirect
18. C22×SD16×C83C22semidirect
31. C2×#121×C83C22semidirect
40. C2×#106×C83C22semidirect
41. C2×#103×C83C22semidirect
42. C2×#103×C83C22semidirect
43. C2×#103×C83C22semidirect
51. C2×#102×C83C22semidirect
53. C2×C22⋊C8×C83C22semidirect
54. C2×C22⋊C8×C83C22semidirect
57. #390×C83C22semidirect
58. #389×C83C22semidirect
60. #380×C83C22semidirect
61. #340×C83C22semidirect
62. #340×C83C22semidirect
63. #336×C83C22semidirect
64. #336×C83C22semidirect
84. C22×D4×C83D4semidirect
113. C22⋊Q8×C83D4semidirect
161. #102×C83D4semidirect
366. D4×C83#121semidirect
450. C22×C83#449semidirect
471. #24434C83direct (N × H)
484. C2×#546C2×C83semidirect
485. C2×#465C2×C83semidirect
486. C2×#449C2×C83semidirect
487. C2×#447C2×C83semidirect
488. C22×#102C2×C83semidirect
489. #2416C2×C83semidirect
490. #2042C2×C83semidirect
491. #2034C2×C83semidirect
492. #2012C2×C83semidirect
493. #1999C2×C83semidirect
494. #1879C2×C83semidirect
495. #1872C2×C83semidirect
496. #1869C2×C83semidirect
497. #1864C2×C83semidirect
498. #1788C2×C83semidirect
499. C83#24434direct (N × H)
502. C22×SD16C22×C83semidirect
515. C2×#121C22×C83semidirect
524. C2×#106C22×C83semidirect
525. C2×#103C22×C83semidirect
526. C2×#103C22×C83semidirect
527. C2×#103C22×C83semidirect
535. C2×#102C22×C83semidirect
537. C2×C22⋊C8C22×C83semidirect
538. C2×C22⋊C8C22×C83semidirect
541. #390C22×C83semidirect
542. #389C22×C83semidirect
544. #380C22×C83semidirect
545. #340C22×C83semidirect
546. #340C22×C83semidirect
547. #336C22×C83semidirect
548. #336C22×C83semidirect
568. C22×D4D4×C83semidirect
597. C22⋊Q8D4×C83semidirect
645. #102D4×C83semidirect
850. D4#121×C83semidirect
934. C22#449×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C832
C2×#465×C832
C2×#449×C832
C2×#447×C832
C22×#102×C832
C83×#24162
C83×#20422
C83×#20342
C83×#20122
C83×#19992
C83×#18792
C83×#18722
C83×#18692
C83×#18642
C83×#17882
#2443483