Finite Group Databasebeta

← C83×#14725 #35242549

Subgroups — C83×#14725 #35242549

Order 21248.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C83C211yesmaximal, characteristic
2C23×C22⋊C4×C83C211yesmaximal, characteristic, complemented
3C2×#394×C83C212yesmaximal, complemented
4C2×#386×C83C211yesmaximal, characteristic, complemented
5C2×#386×C83C211yesmaximal, characteristic, complemented
6C2×#380×C83C211yesmaximal, characteristic, complemented
7C2×#379×C83C211yesmaximal, characteristic, complemented
8C83×#1440C212yesmaximal, complemented
9C83×#1439C212yesmaximal, complemented
10C83×#1438C212yesmaximal, complemented
11C83×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C83C2211yescharacteristic
13C23×D4×C83C2211yescharacteristic
14C23×D4×C83C2212yes—
15C24×C4×C83C2211yescharacteristic
16C24×C4×C83C2211yescharacteristic
17C2×#120×C83—24no—
18C2×#120×C83—24no—
19C2×#120×C83—24no—
20C22×C4⋊C4×C83C2212yescomplemented
21C22×C22⋊C4×C83—24no—
22C22×C22⋊C4×C83—28no—
23C22×C22⋊C4×C83C2211yescharacteristic
24C22×C22⋊C4×C83C2211yescharacteristic
25C22×C22⋊C4×C83C2212yes—
26C22×C22⋊C4×C83C2212yes—
27C22×C22⋊C4×C83C2212yes—
28C22×C22⋊C4×C83C2211yescharacteristic
29C22×C22⋊C4×C83C2212yes—
30C22×C22⋊C4×C83C2212yes—
31C22×C22⋊C4×C83C2211yescharacteristic, complemented
32C22×C22⋊C4×C83C2212yescomplemented
33C22×C22⋊C4×C83C2211yescharacteristic, complemented
34#394×C83—28no—
35#386×C83—24no—
36#386×C83—24no—
37#380×C83—24no—
38#379×C83—24no—
39C2×#95×C83C2212yescomplemented
40C2×#95×C83C2211yescharacteristic, complemented
41C2×#95×C83C2212yescomplemented
42C2×#95×C83C2211yescharacteristic, complemented
43C2×#95×C83C2212yescomplemented
44C2×#95×C83C2212yescomplemented
45C25×C83—24no—
46C25×C83—22no—
47C25×C83—24no—
48C25×C83—22no—
49C25×C83—22no—
50C25×C83—22no—
51C25×C83—22no—
52C25×C83—22no—
53C25×C83—42no—
54C25×C83—42no—
55C25×C83D414yes—
56C25×C83C2311yescharacteristic
57C25×C83C2312yes—
58C25×C83C2311yescharacteristic
59C22×D4×C83—24no—
60C22×D4×C83—24no—
61C22×D4×C83—22no—
62C22×D4×C83—22no—
63C22×D4×C83—22no—
64C22×D4×C83—22no—
65C22×D4×C83—22no—
66C22×D4×C83—22no—
67C22×D4×C83—24no—
68C22×D4×C83—24no—
69C22×D4×C83—24no—
70C22×D4×C83—42no—
71C22×D4×C83—42no—
72C22×D4×C83D414yes—
73C23×C4×C83—22no—
74C23×C4×C83—22no—
75C23×C4×C83—22no—
76C23×C4×C83—24no—
77C23×C4×C83—24no—
78C23×C4×C83—22no—
79C23×C4×C83—22no—
80C23×C4×C83—42no—
81C23×C4×C83—42no—
82C23×C4×C83D414yescomplemented
83C23×C4×C83C2312yes—
84C23×C4×C83C2311yescharacteristic
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2311yescharacteristic
87C23×C4×C83C2312yes—
88C23×C4×C83C2312yes—
89C23×C4×C83C2311yescharacteristic
90C23×C4×C83C2311yescharacteristic
91#120×C83—232no—
92C2×C4⋊C4×C83—24no—
93C2×C4⋊C4×C83—24no—
94C2×C4⋊C4×C83—42no—
95C2×C22⋊C4×C83—232no—
96C2×C22⋊C4×C83—24no—
97C2×C22⋊C4×C83—24no—
98C2×C22⋊C4×C83—22no—
99C2×C22⋊C4×C83—22no—
100C2×C22⋊C4×C83—24no—
101C2×C22⋊C4×C83—24no—
102C2×C22⋊C4×C83—24no—
103C2×C22⋊C4×C83—24no—
104C2×C22⋊C4×C83—24no—
105C2×C22⋊C4×C83—24no—
106C2×C22⋊C4×C83—24no—
107C2×C22⋊C4×C83—22no—
108C2×C22⋊C4×C83—24no—
109C2×C22⋊C4×C83—22no—
110C2×C22⋊C4×C83—22no—
111C2×C22⋊C4×C83—22no—
112C2×C22⋊C4×C83—22no—
113C2×C22⋊C4×C83—24no—
114C2×C22⋊C4×C83—24no—
115C2×C22⋊C4×C83—24no—
116C2×C22⋊C4×C83—22no—
117C2×C22⋊C4×C83—22no—
118C2×C22⋊C4×C83—22no—
119C2×C22⋊C4×C83—24no—
120C2×C22⋊C4×C83—24no—
121C2×C22⋊C4×C83—42no—
122C2×C22⋊C4×C83—42no—
123C2×C22⋊C4×C83—42no—
124C2×C22⋊C4×C83—42no—
125C2×C22⋊C4×C83D414yes—
126C2×C22⋊C4×C83D418yescomplemented
127#95×C83—24no—
128#95×C83—22no—
129#95×C83—22no—
130#95×C83—24no—
131#95×C83—24no—
132#95×C83—42no—
133C24×C83—22no—
134C24×C83—22no—
135C24×C83—22no—
136C24×C83—22no—
137C24×C83—28no—
138C24×C83—28no—
139C24×C83—216no—
140C24×C83—216no—
141C24×C83—28no—
142C24×C83—22no—
143C24×C83—22no—
144C24×C83—22no—
145C24×C83—22no—
146C24×C83—22no—
147C24×C83—22no—
148C24×C83—22no—
149C24×C83—22no—
150C24×C83—22no—
151C24×C83—22no—
152C24×C83—22no—
153C24×C83—22no—
154C24×C83—28no—
155C24×C83—28no—
156C24×C83—21no—
157C24×C83—22no—
158C24×C83—21no—
159C24×C83—21no—
160C24×C83—21no—
161C24×C83—21no—
162C24×C83—21no—
163C24×C83—22no—
164C24×C83—22no—
165C24×C83—22no—
166C24×C83—48no—
167C24×C83—48no—
168C24×C83—48no—
169C24×C83—48no—
170C24×C83—48no—
171C24×C83—48no—
172C24×C83—48no—
173C24×C83—48no—
174C24×C83—48no—
175C24×C83—44no—
176C24×C83—44no—
177C24×C83—48no—
178C24×C83—44no—
179C24×C83—44no—
180C24×C83—44no—
181C24×C83—44no—
182C24×C83C2×D412yes—
183C24×C83C2×D414yes—
184C24×C83C2×D414yes—
185C24×C83C2×D412yes—
186C24×C83C2×D412yes—
187C24×C83C2×D412yes—
188C24×C83C2×D412yes—
189C24×C83#4114yes—
190C24×C83#4112yes—
191C24×C83#4112yes—
192C24×C83#4112yes—
193C24×C83C2411yescharacteristic
194C2×D4×C83—216no—
195C2×D4×C83—28no—
196C2×D4×C83—28no—
197C2×D4×C83—28no—
198C2×D4×C83—48no—
199C2×D4×C83—48no—
200C2×D4×C83—48no—
201C2×D4×C83—48no—
202C2×D4×C83—48no—
203C2×D4×C83—48no—
204C2×D4×C83—44no—
205C2×D4×C83—44no—
206C2×D4×C83—44no—
207C2×D4×C83—44no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—22no—
211C22×C4×C83—28no—
212C22×C4×C83—28no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—21no—
225C22×C4×C83—22no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—28no—
236C22×C4×C83—21no—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—21no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—22no—
245C22×C4×C83—21no—
246C22×C4×C83—22no—
247C22×C4×C83—21no—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83—22no—
252C22×C4×C83—22no—
253C22×C4×C83—44no—
254C22×C4×C83—48no—
255C22×C4×C83—48no—
256C22×C4×C83—48no—
257C22×C4×C83—48no—
258C22×C4×C83—44no—
259C22×C4×C83—44no—
260C22×C4×C83C2×D412yes—
261C22×C4×C83C2×D412yes—
262C22×C4×C83C2×D414yes—
263C22×C4×C83C2×D414yes—
264C22×C4×C83C2×D412yes—
265C22×C4×C83C2×D414yes—
266C4⋊C4×C83—48no—
267C22⋊C4×C83—216no—
268C22⋊C4×C83—216no—
269C22⋊C4×C83—28no—
270C22⋊C4×C83—216no—
271C22⋊C4×C83—48no—
272C22⋊C4×C83—44no—
273C22⋊C4×C83—48no—
274C22⋊C4×C83—44no—
275C22⋊C4×C83—48no—
276C22⋊C4×C83—44no—
277C22⋊C4×C83—44no—
278C23×C83—22no—
279C23×C83—24no—
280C23×C83—22no—
281C23×C83—24no—
282C23×C83—22no—
283C23×C83—24no—
284C23×C83—22no—
285C23×C83—24no—
286C23×C83—24no—
287C23×C83—24no—
288C23×C83—24no—
289C23×C83—24no—
290C23×C83—24no—
291C23×C83—24no—
292C23×C83—24no—
293C23×C83—24no—
294C23×C83—232no—
295C23×C83—24no—
296C23×C83—24no—
297C23×C83—24no—
298C23×C83—24no—
299C23×C83—24no—
300C23×C83—24no—
301C23×C83—24no—
302C23×C83—24no—
303C23×C83—24no—
304C23×C83—24no—
305C23×C83—24no—
306C23×C83—24no—
307C23×C83—24no—
308C23×C83—24no—
309C23×C83—24no—
310C23×C83—24no—
311C23×C83—24no—
312C23×C83—24no—
313C23×C83—22no—
314C23×C83—22no—
315C23×C83—22no—
316C23×C83—24no—
317C23×C83—24no—
318C23×C83—432no—
319C23×C83—432no—
320C23×C83—416no—
321C23×C83—416no—
322C23×C83—416no—
323C23×C83—416no—
324C23×C83—432no—
325C23×C83—432no—
326C23×C83—416no—
327C23×C83—42no—
328C23×C83—42no—
329C23×C83—42no—
330C23×C83—42no—
331C23×C83—42no—
332C23×C83—42no—
333C23×C83—42no—
334C23×C83—42no—
335C23×C83—42no—
336C23×C83—42no—
337C23×C83—42no—
338C23×C83—42no—
339C23×C83—42no—
340C23×C83—42no—
341C23×C83—42no—
342C23×C83—42no—
343C23×C83—416no—
344C23×C83—41no—
345C23×C83—41no—
346C23×C83—41no—
347C23×C83—42no—
348C23×C83—41no—
349C23×C83—42no—
350C23×C83—41no—
351C23×C83—41no—
352C23×C83—41no—
353C23×C83—42no—
354C23×C83—41no—
355C23×C83—42no—
356C23×C83—42no—
357C23×C83—42no—
358C23×C83—42no—
359C23×C83—42no—
360C23×C83—42no—
361C23×C83—42no—
362C23×C83#12014yes—
363C23×C83#12118yes—
364C23×C83#12114yes—
365C23×C83#12114yes—
366C23×C83#12114yes—
367C23×C83#12314yes—
368C23×C83#12314yes—
369C23×C83#12414yes—
370C23×C83C22×D411yescharacteristic
371C23×C83C22×D411yescharacteristic
372C23×C83C22×D411yescharacteristic
373C23×C83C22×D412yes—
374C23×C83C22×D411yescharacteristic
375C23×C83C2×#4111yescharacteristic
376C23×C83C2×#4111yescharacteristic
377C23×C83C2×#4111yescharacteristic
378C23×C83C2×#4112yes—
379C23×C83H(5,𝔽2)12yes—
380C23×C83H(5,𝔽2)12yes—
381D4×C83—432no—
382D4×C83—416no—
383C2×C4×C83—22no—
384C2×C4×C83—22no—
385C2×C4×C83—24no—
386C2×C4×C83—24no—
387C2×C4×C83—24no—
388C2×C4×C83—22no—
389C2×C4×C83—22no—
390C2×C4×C83—24no—
391C2×C4×C83—22no—
392C2×C4×C83—22no—
393C2×C4×C83—22no—
394C2×C4×C83—22no—
395C2×C4×C83—24no—
396C2×C4×C83—24no—
397C2×C4×C83—24no—
398C2×C4×C83—24no—
399C2×C4×C83—416no—
400C2×C4×C83—416no—
401C2×C4×C83—42no—
402C2×C4×C83—41no—
403C2×C4×C83—41no—
404C2×C4×C83—42no—
405C2×C4×C83—41no—
406C2×C4×C83—41no—
407C2×C4×C83—42no—
408C2×C4×C83—42no—
409C2×C4×C83—42no—
410C2×C4×C83—42no—
411C2×C4×C83—42no—
412C2×C4×C83—42no—
413C2×C4×C83—42no—
414C2×C4×C83—42no—
415C2×C4×C83—41no—
416C2×C4×C83—42no—
417C2×C4×C83—41no—
418C2×C4×C83—42no—
419C2×C4×C83—41no—
420C2×C4×C83—42no—
421C2×C4×C83—41no—
422C2×C4×C83—42no—
423C2×C4×C83—42no—
424C2×C4×C83—41no—
425C2×C4×C83—42no—
426C2×C4×C83—41no—
427C2×C4×C83—42no—
428C2×C4×C83—42no—
429C2×C4×C83—42no—
430C2×C4×C83—42no—
431C2×C4×C83—42no—
432C2×C4×C83#12014yescomplemented
433C22×C83—24no—
434C22×C83—24no—
435C22×C83—24no—
436C22×C83—24no—
437C22×C83—28no—
438C22×C83—24no—
439C22×C83—28no—
440C22×C83—28no—
441C22×C83—28no—
442C22×C83—24no—
443C22×C83—28no—
444C22×C83—28no—
445C22×C83—28no—
446C22×C83—464no—
447C22×C83—44no—
448C22×C83—44no—
449C22×C83—44no—
450C22×C83—44no—
451C22×C83—44no—
452C22×C83—44no—
453C22×C83—44no—
454C22×C83—44no—
455C22×C83—44no—
456C22×C83—44no—
457C22×C83—44no—
458C22×C83—44no—
459C22×C83—42no—
460C22×C83—42no—
461C22×C83—44no—
462C22×C83—44no—
463C22×C83—42no—
464C22×C83—81no—
465C22×C83—81no—
466C22×C83—81no—
467C22×C83—81no—
468C22×C83—82no—
469C22×C83—82no—
470C22×C83#39418yescomplemented
471C22×C83C2×#12011yescharacteristic
472C22×C83C2×#12011yescharacteristic
473C22×C83C2×#12111yescharacteristic
474C22×C83C2×#12112yes—
475C22×C83C2×#12111yescharacteristic
476C22×C83C2×#12111yescharacteristic
477C22×C83C2×#12311yescharacteristic
478C22×C83C2×#12311yescharacteristic
479C22×C83#52511yescharacteristic
480C22×C83#52512yes—
481C22×C83C2×#12411yescharacteristic
482C22×C83#53412yes—
483C22×C83#53411yescharacteristic
484C22×C83#53511yescharacteristic
485C22×C83#53812yes—
486C22×C83D4212yes—
487C22×C83D4212yes—
488C22×C83#54612yes—
489C22×C83#54612yes—
490C22×C83#54612yes—
491C22×C83#54612yes—
492C22×C83#55112yes—
493C22×C83#55112yes—
494C4×C83—24no—
495C4×C83—42no—
496C4×C83—44no—
497C4×C83—42no—
498C4×C83—44no—
499C4×C83—81no—
500C4×C83—81no—
501C4×C83—82no—
502#14725C8311yesmaximal, characteristic, direct product factor, Sylow
503C2×C83—28no—
504C2×C83—48no—
505C2×C83—82no—
506C2×C83C2×#39411yescharacteristic
507C2×C83#240811yescharacteristic
508C2×C83#241011yescharacteristic
509C2×C83#241012yes—
510C2×C83#241111yescharacteristic
511C2×C83#241212yes—
512C2×C83#241812yes—
513C2×C83#247212yes—
514C2×C83#253411yescharacteristic
515C2×C83#261711yescharacteristic
516C2×C83#284711yescharacteristic
517C22×#120C2×C8311yescharacteristic
518C23×C22⋊C4C2×C8311yescharacteristic, complemented
519C2×#394C2×C8312yescomplemented
520C2×#386C2×C8311yescharacteristic, complemented
521C2×#386C2×C8311yescharacteristic, complemented
522C2×#380C2×C8311yescharacteristic, complemented
523C2×#379C2×C8311yescharacteristic, complemented
524#1440C2×C8312yescomplemented
525#1439C2×C8312yescomplemented
526#1438C2×C8312yescomplemented
527C22⋊#95C2×C8311yescharacteristic, complemented
528C83#1472511yescharacteristic, direct product factor, Sylow
529C26C22×C8311yescharacteristic
530C23×D4C22×C8311yescharacteristic
531C23×D4C22×C8312yes—
532C24×C4C22×C8311yescharacteristic
533C24×C4C22×C8311yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C8312yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C8312yes—
541C22×C22⋊C4C22×C8312yes—
542C22×C22⋊C4C22×C8312yes—
543C22×C22⋊C4C22×C8311yescharacteristic
544C22×C22⋊C4C22×C8311yescharacteristic
545C22×C22⋊C4C22×C8311yescharacteristic
546C22×C22⋊C4C22×C8312yes—
547C22×C22⋊C4C22×C8312yes—
548C22×C22⋊C4C22×C8311yescharacteristic, complemented
549C22×C22⋊C4C22×C8312yescomplemented
550C22×C22⋊C4C22×C8311yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C8312yescomplemented
557C2×#95C22×C8312yescomplemented
558C2×#95C22×C8311yescharacteristic, complemented
559C2×#95C22×C8312yescomplemented
560C2×#95C22×C8311yescharacteristic, complemented
561C2×#95C22×C8312yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C8314yes—
573C25C23×C8311yescharacteristic
574C25C23×C8312yes—
575C25C23×C8311yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C8314yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C8314yescomplemented
600C23×C4C23×C8312yes—
601C23×C4C23×C8311yescharacteristic
602C23×C4C23×C8311yescharacteristic
603C23×C4C23×C8311yescharacteristic
604C23×C4C23×C8312yes—
605C23×C4C23×C8312yes—
606C23×C4C23×C8311yescharacteristic
607C23×C4C23×C8311yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C8314yes—
643C2×C22⋊C4D4×C8318yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C8312yes—
700C24C2×D4×C8314yes—
701C24C2×D4×C8314yes—
702C24C2×D4×C8312yes—
703C24C2×D4×C8312yes—
704C24C2×D4×C8312yes—
705C24C2×D4×C8312yes—
706C24#41×C8314yes—
707C24#41×C8312yes—
708C24#41×C8312yes—
709C24#41×C8312yes—
710C24C24×C8311yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C8312yes—
778C22×C4C2×D4×C8312yes—
779C22×C4C2×D4×C8314yes—
780C22×C4C2×D4×C8314yes—
781C22×C4C2×D4×C8312yes—
782C22×C4C2×D4×C8314yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C8314yes—
880C23#121×C8318yes—
881C23#121×C8314yes—
882C23#121×C8314yes—
883C23#121×C8314yes—
884C23#123×C8314yes—
885C23#123×C8314yes—
886C23#124×C8314yes—
887C23C22×D4×C8311yescharacteristic
888C23C22×D4×C8311yescharacteristic
889C23C22×D4×C8311yescharacteristic
890C23C22×D4×C8312yes—
891C23C22×D4×C8311yescharacteristic
892C23C2×#41×C8311yescharacteristic
893C23C2×#41×C8311yescharacteristic
894C23C2×#41×C8311yescharacteristic
895C23C2×#41×C8312yes—
896C23H(5,𝔽2)×C8312yes—
897C23H(5,𝔽2)×C8312yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C8314yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22#394×C8318yescomplemented
988C22C2×#120×C8311yescharacteristic
989C22C2×#120×C8311yescharacteristic
990C22C2×#121×C8311yescharacteristic
991C22C2×#121×C8311yescharacteristic
992C22C2×#121×C8312yes—
993C22C2×#121×C8311yescharacteristic
994C22C2×#123×C8311yescharacteristic
995C22C2×#123×C8311yescharacteristic
996C22#525×C8311yescharacteristic
997C22#525×C8312yes—
998C22C2×#124×C8311yescharacteristic
999C22#534×C8311yescharacteristic
1000C22#534×C8312yes—
1001C22#535×C8311yescharacteristic
1002C22#538×C8312yes—
1003C22D42×C8312yes—
1004C22D42×C8312yes—
1005C22#546×C8312yes—
1006C22#546×C8312yes—
1007C22#546×C8312yes—
1008C22#546×C8312yes—
1009C22#551×C8312yes—
1010C22#551×C8312yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C8311yescharacteristic
1023C2C83×#240811yescharacteristic
1024C2C83×#241011yescharacteristic
1025C2C83×#241012yes—
1026C2C83×#241111yescharacteristic
1027C2C83×#241212yes—
1028C2C83×#241812yes—
1029C2C83×#247212yes—
1030C2C83×#253411yescharacteristic
1031C2C83×#261711yescharacteristic
1032C2C83×#284711yescharacteristic
subgroupG/H
center, socleC24×C83C24
commutator, Frattini, cosocleC24C24×C83
prime radicalC22×#120×C83C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C83C2semidirect
3. C2×#394×C83C2semidirect
4. C2×#386×C83C2semidirect
5. C2×#386×C83C2semidirect
6. C2×#380×C83C2semidirect
7. C2×#379×C83C2semidirect
8. C83×#1440C2semidirect
9. C83×#1439C2semidirect
10. C83×#1438C2semidirect
11. C83×C22⋊#95C2semidirect
20. C22×C4⋊C4×C83C22semidirect
31. C22×C22⋊C4×C83C22semidirect
32. C22×C22⋊C4×C83C22semidirect
33. C22×C22⋊C4×C83C22semidirect
39. C2×#95×C83C22semidirect
40. C2×#95×C83C22semidirect
41. C2×#95×C83C22semidirect
42. C2×#95×C83C22semidirect
43. C2×#95×C83C22semidirect
44. C2×#95×C83C22semidirect
82. C23×C4×C83D4semidirect
126. C2×C22⋊C4×C83D4semidirect
432. C2×C4×C83#120semidirect
470. C22×C83#394semidirect
502. #14725C83direct (N × H)
518. C23×C22⋊C4C2×C83semidirect
519. C2×#394C2×C83semidirect
520. C2×#386C2×C83semidirect
521. C2×#386C2×C83semidirect
522. C2×#380C2×C83semidirect
523. C2×#379C2×C83semidirect
524. #1440C2×C83semidirect
525. #1439C2×C83semidirect
526. #1438C2×C83semidirect
527. C22⋊#95C2×C83semidirect
528. C83#14725direct (N × H)
537. C22×C4⋊C4C22×C83semidirect
548. C22×C22⋊C4C22×C83semidirect
549. C22×C22⋊C4C22×C83semidirect
550. C22×C22⋊C4C22×C83semidirect
556. C2×#95C22×C83semidirect
557. C2×#95C22×C83semidirect
558. C2×#95C22×C83semidirect
559. C2×#95C22×C83semidirect
560. C2×#95C22×C83semidirect
561. C2×#95C22×C83semidirect
599. C23×C4D4×C83semidirect
643. C2×C22⋊C4D4×C83semidirect
949. C2×C4#120×C83semidirect
987. C22#394×C83semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C832
C23×C22⋊C4×C832
C2×#394×C832
C2×#386×C832
C2×#380×C832
C2×#379×C832
C83×#14402
C83×#14392
C83×#14382
C83×C22⋊#952
#1472583