Finite Group Databasebeta

← C83×#14722 #35242546

Subgroups — C83×#14722 #35242546

Order 21248.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C83C211yesmaximal, characteristic, complemented
2C22×C4×D4×C83C211yesmaximal, characteristic, complemented
3C2×#394×C83C211yesmaximal, characteristic, complemented
4C2×#392×C83C212yesmaximal, complemented
5C2×#392×C83C211yesmaximal, characteristic, complemented
6C2×#386×C83C212yesmaximal, complemented
7C83×#1441C211yesmaximal, characteristic, complemented
8C83×#1439C211yesmaximal, characteristic, complemented
9C83×#1438C212yesmaximal, complemented
10C83×#1437C212yesmaximal, complemented
11C83×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C83C2211yescharacteristic
13C23×D4×C83C2212yes—
14C23×D4×C83C2211yescharacteristic
15C23×D4×C83C2212yes—
16C24×C4×C83C2211yescharacteristic
17C24×C4×C83C2211yescharacteristic
18C2×#121×C83—24no—
19C2×#121×C83—28no—
20C2×C4×D4×C83—24no—
21C2×C4×D4×C83—24no—
22C2×C4×D4×C83—24no—
23C22×C4⋊C4×C83C2211yescharacteristic
24C22×C4⋊C4×C83C2211yescharacteristic
25C22×C22⋊C4×C83C2212yes—
26C22×C22⋊C4×C83C2211yescharacteristic
27C22×C22⋊C4×C83C2212yes—
28C22×C22⋊C4×C83C2212yes—
29C22×C22⋊C4×C83C2212yes—
30C22×C22⋊C4×C83C2212yes—
31C22×C22⋊C4×C83C2212yes—
32C22×C22⋊C4×C83C2211yescharacteristic
33C22×C42×C83C2211yescharacteristic
34#394×C83—24no—
35#392×C83—28no—
36#392×C83—24no—
37#386×C83—28no—
38C2×#95×C83C2212yes—
39C2×#95×C83C2212yes—
40C2×#95×C83C2211yescharacteristic
41C2×#95×C83C2212yes—
42C2×#95×C83C2211yescharacteristic
43C2×#95×C83C2212yes—
44C25×C83C2312yes—
45C25×C83C2311yescharacteristic
46C25×C83C2311yescharacteristic
47C22×D4×C83—22no—
48C22×D4×C83—22no—
49C22×D4×C83—22no—
50C22×D4×C83—22no—
51C22×D4×C83—24no—
52C22×D4×C83—24no—
53C22×D4×C83—24no—
54C22×D4×C83—24no—
55C22×D4×C83—24no—
56C22×D4×C83—24no—
57C22×D4×C83—24no—
58C22×D4×C83—24no—
59C22×D4×C83—24no—
60C22×D4×C83—22no—
61C22×D4×C83—24no—
62C22×D4×C83—22no—
63C22×D4×C83—22no—
64C22×D4×C83—22no—
65C22×D4×C83—22no—
66C22×D4×C83—24no—
67C22×D4×C83—42no—
68C22×D4×C83—42no—
69C22×D4×C83—42no—
70C22×D4×C83—42no—
71C22×D4×C83—42no—
72C22×D4×C83D414yescomplemented
73C23×C4×C83—22no—
74C23×C4×C83—22no—
75C23×C4×C83—22no—
76C23×C4×C83—22no—
77C23×C4×C83—22no—
78C23×C4×C83—24no—
79C23×C4×C83—24no—
80C23×C4×C83—42no—
81C23×C4×C83—42no—
82C23×C4×C83D414yescomplemented
83C23×C4×C83C2312yes—
84C23×C4×C83C2311yescharacteristic
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2312yes—
87C23×C4×C83C2312yes—
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2311yescharacteristic
90C23×C4×C83C2311yescharacteristic
91#121×C83—232no—
92C4×D4×C83—232no—
93C2×C4⋊C4×C83—22no—
94C2×C4⋊C4×C83—22no—
95C2×C4⋊C4×C83—24no—
96C2×C4⋊C4×C83—22no—
97C2×C4⋊C4×C83D414yescomplemented
98C2×C22⋊C4×C83—22no—
99C2×C22⋊C4×C83—22no—
100C2×C22⋊C4×C83—22no—
101C2×C22⋊C4×C83—22no—
102C2×C22⋊C4×C83—22no—
103C2×C22⋊C4×C83—24no—
104C2×C22⋊C4×C83—24no—
105C2×C22⋊C4×C83—24no—
106C2×C22⋊C4×C83—24no—
107C2×C22⋊C4×C83—24no—
108C2×C22⋊C4×C83—24no—
109C2×C22⋊C4×C83—24no—
110C2×C22⋊C4×C83—24no—
111C2×C22⋊C4×C83—24no—
112C2×C22⋊C4×C83—24no—
113C2×C22⋊C4×C83—24no—
114C2×C22⋊C4×C83—24no—
115C2×C22⋊C4×C83—24no—
116C2×C22⋊C4×C83—42no—
117C2×C22⋊C4×C83—42no—
118C2×C22⋊C4×C83—42no—
119C2×C22⋊C4×C83—42no—
120C2×C22⋊C4×C83D414yescomplemented
121C2×C22⋊C4×C83D418yescomplemented
122C2×C42×C83—22no—
123C2×C42×C83—22no—
124C2×C42×C83—22no—
125#95×C83—24no—
126#95×C83—24no—
127#95×C83—22no—
128#95×C83—24no—
129#95×C83—22no—
130#95×C83—42no—
131C24×C83—21no—
132C24×C83—21no—
133C24×C83—21no—
134C24×C83—21no—
135C24×C83—22no—
136C24×C83—22no—
137C24×C83—22no—
138C24×C83—21no—
139C24×C83—21no—
140C24×C83—21no—
141C24×C83—21no—
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—22no—
155C24×C83—22no—
156C24×C83—22no—
157C24×C83—22no—
158C24×C83—22no—
159C24×C83—22no—
160C24×C83—22no—
161C24×C83C2×D414yes—
162C24×C83C2×D412yes—
163C24×C83C2×D412yes—
164C24×C83C2×D412yes—
165C24×C83C2×D412yes—
166C24×C83#4112yes—
167C24×C83#4112yes—
168C24×C83C2411yescharacteristic
169C2×D4×C83—28no—
170C2×D4×C83—28no—
171C2×D4×C83—28no—
172C2×D4×C83—28no—
173C2×D4×C83—28no—
174C2×D4×C83—28no—
175C2×D4×C83—28no—
176C2×D4×C83—216no—
177C2×D4×C83—216no—
178C2×D4×C83—28no—
179C2×D4×C83—48no—
180C2×D4×C83—48no—
181C2×D4×C83—48no—
182C2×D4×C83—48no—
183C2×D4×C83—48no—
184C2×D4×C83—48no—
185C2×D4×C83—44no—
186C2×D4×C83—48no—
187C2×D4×C83—48no—
188C2×D4×C83—48no—
189C2×D4×C83—48no—
190C2×D4×C83—48no—
191C2×D4×C83—48no—
192C2×D4×C83—48no—
193C2×D4×C83—48no—
194C2×D4×C83—44no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—22no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—22no—
203C22×C4×C83—22no—
204C22×C4×C83—28no—
205C22×C4×C83—22no—
206C22×C4×C83—22no—
207C22×C4×C83—22no—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—28no—
226C22×C4×C83—28no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—44no—
235C22×C4×C83—48no—
236C22×C4×C83—48no—
237C22×C4×C83—48no—
238C22×C4×C83—48no—
239C22×C4×C83—44no—
240C22×C4×C83—44no—
241C22×C4×C83C2×D414yes—
242C22×C4×C83C2×D412yes—
243C22×C4×C83C2×D412yes—
244C22×C4×C83C2×D414yes—
245C22×C4×C83C2×D412yes—
246C22×C4×C83C2×D412yes—
247C22×C4×C83C2×D412yes—
248C22×C4×C83C2×D412yes—
249C22×C4×C83C2×D412yes—
250C22×C4×C83C2×D412yes—
251C22×C4×C83#4114yes—
252C22×C4×C83#4112yes—
253C4⋊C4×C83—28no—
254C4⋊C4×C83—28no—
255C22⋊C4×C83—28no—
256C22⋊C4×C83—28no—
257C22⋊C4×C83—216no—
258C22⋊C4×C83—48no—
259C22⋊C4×C83—48no—
260C22⋊C4×C83—48no—
261C22⋊C4×C83—48no—
262C22⋊C4×C83—48no—
263C42×C83—28no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—24no—
278C23×C83—22no—
279C23×C83—22no—
280C23×C83—22no—
281C23×C83—24no—
282C23×C83—24no—
283C23×C83—24no—
284C23×C83—24no—
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—24no—
295C23×C83—24no—
296C23×C83—24no—
297C23×C83—41no—
298C23×C83—42no—
299C23×C83—42no—
300C23×C83—42no—
301C23×C83—41no—
302C23×C83—41no—
303C23×C83—41no—
304C23×C83—42no—
305C23×C83—42no—
306C23×C83—42no—
307C23×C83—42no—
308C23×C83—42no—
309C23×C83—42no—
310C23×C83—42no—
311C23×C83—42no—
312C23×C83—42no—
313C23×C83—42no—
314C23×C83—42no—
315C23×C83—42no—
316C23×C83—42no—
317C23×C83—42no—
318C23×C83—42no—
319C23×C83—42no—
320C23×C83—42no—
321C23×C83—42no—
322C23×C83—42no—
323C23×C83—42no—
324C23×C83—42no—
325C23×C83—42no—
326C23×C83—42no—
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#12114yes—
344C23×C83#12114yescomplemented
345C23×C83C22×D411yescharacteristic
346C23×C83C22×D411yescharacteristic
347C23×C83C22×D411yescharacteristic
348C23×C83C22×D412yes—
349C23×C83C22×D411yescharacteristic
350C23×C83C2×#4111yescharacteristic
351C23×C83C2×#4111yescharacteristic
352C23×C83C2×#4111yescharacteristic
353C23×C83C2×#4112yes—
354C23×C83H(5,𝔽2)12yes—
355C23×C83H(5,𝔽2)12yes—
356D4×C83—232no—
357D4×C83—416no—
358D4×C83—432no—
359D4×C83—432no—
360C2×C4×C83—22no—
361C2×C4×C83—22no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—22no—
366C2×C4×C83—22no—
367C2×C4×C83—22no—
368C2×C4×C83—22no—
369C2×C4×C83—22no—
370C2×C4×C83—24no—
371C2×C4×C83—24no—
372C2×C4×C83—24no—
373C2×C4×C83—24no—
374C2×C4×C83—22no—
375C2×C4×C83—22no—
376C2×C4×C83—24no—
377C2×C4×C83—24no—
378C2×C4×C83—24no—
379C2×C4×C83—24no—
380C2×C4×C83—24no—
381C2×C4×C83—24no—
382C2×C4×C83—24no—
383C2×C4×C83—24no—
384C2×C4×C83—416no—
385C2×C4×C83—416no—
386C2×C4×C83—41no—
387C2×C4×C83—42no—
388C2×C4×C83—42no—
389C2×C4×C83—41no—
390C2×C4×C83—41no—
391C2×C4×C83—41no—
392C2×C4×C83—42no—
393C2×C4×C83—42no—
394C2×C4×C83—42no—
395C2×C4×C83—42no—
396C2×C4×C83—42no—
397C2×C4×C83—42no—
398C2×C4×C83—42no—
399C2×C4×C83—42no—
400C2×C4×C83—42no—
401C2×C4×C83—42no—
402C2×C4×C83—42no—
403C2×C4×C83—42no—
404C2×C4×C83—42no—
405C2×C4×C83—42no—
406C2×C4×C83—42no—
407C2×C4×C83#12014yes—
408C2×C4×C83#12014yes—
409C2×C4×C83#12114yescomplemented
410C22×C83—24no—
411C22×C83—24no—
412C22×C83—24no—
413C22×C83—28no—
414C22×C83—24no—
415C22×C83—42no—
416C22×C83—42no—
417C22×C83—42no—
418C22×C83—42no—
419C22×C83—42no—
420C22×C83—42no—
421C22×C83—42no—
422C22×C83—44no—
423C22×C83—44no—
424C22×C83—44no—
425C22×C83—42no—
426C22×C83—42no—
427C22×C83—44no—
428C22×C83—44no—
429C22×C83—44no—
430C22×C83—44no—
431C22×C83—42no—
432C22×C83—44no—
433C22×C83—44no—
434C22×C83—44no—
435C22×C83—44no—
436C22×C83—44no—
437C22×C83—44no—
438C22×C83—44no—
439C22×C83—82no—
440C22×C83—82no—
441C22×C83—82no—
442C22×C83—82no—
443C22×C83—82no—
444C22×C83—82no—
445C22×C83—82no—
446C22×C83—82no—
447C22×C83C2×#12011yescharacteristic
448C22×C83C2×#12011yescharacteristic
449C22×C83C2×#12111yescharacteristic
450C22×C83C2×#12111yescharacteristic
451C22×C83C2×#12111yescharacteristic
452C22×C83#52511yescharacteristic
453C22×C83#52511yescharacteristic
454C22×C83#52511yescharacteristic
455C22×C83#52512yes—
456C22×C83#53212yes—
457C22×C83#53211yescharacteristic
458C22×C83#53411yescharacteristic
459C22×C83#53511yescharacteristic
460C22×C83#53812yes—
461C22×C83#54012yes—
462C22×C83D4212yes—
463C22×C83D4212yes—
464C22×C83D4212yes—
465C22×C83#54612yes—
466C22×C83#54612yes—
467C22×C83#54612yes—
468C22×C83#55012yes—
469C22×C83#55312yes—
470C4×C83—24no—
471C4×C83—24no—
472C4×C83—24no—
473C4×C83—42no—
474C4×C83—44no—
475C4×C83—44no—
476C4×C83—42no—
477C4×C83—82no—
478#14722C8311yesmaximal, characteristic, direct product factor, Sylow
479C2×C83—44no—
480C2×C83—44no—
481C2×C83—84no—
482C2×C83#238811yescharacteristic
483C2×C83#240311yescharacteristic
484C2×C83#240811yescharacteristic
485C2×C83#242412yes—
486C2×C83#242812yes—
487C2×C83#243111yescharacteristic
488C2×C83#245612yes—
489C2×C83#246412yes—
490C2×C83#254311yescharacteristic
491C2×C83#263511yescharacteristic
492C2×C83#284711yescharacteristic
493C22×#121C2×C8311yescharacteristic, complemented
494C22×C4×D4C2×C8311yescharacteristic, complemented
495C2×#394C2×C8311yescharacteristic, complemented
496C2×#392C2×C8312yescomplemented
497C2×#392C2×C8311yescharacteristic, complemented
498C2×#386C2×C8312yescomplemented
499#1441C2×C8311yescharacteristic, complemented
500#1439C2×C8311yescharacteristic, complemented
501#1438C2×C8312yescomplemented
502#1437C2×C8312yescomplemented
503C22⋊#95C2×C8311yescharacteristic, complemented
504C83#1472211yescharacteristic, direct product factor, Sylow
505C23×D4C22×C8311yescharacteristic
506C23×D4C22×C8312yes—
507C23×D4C22×C8311yescharacteristic
508C23×D4C22×C8312yes—
509C24×C4C22×C8311yescharacteristic
510C24×C4C22×C8311yescharacteristic
511C2×#121—24no—
512C2×#121—28no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C2×C4×D4—24no—
516C22×C4⋊C4C22×C8311yescharacteristic
517C22×C4⋊C4C22×C8311yescharacteristic
518C22×C22⋊C4C22×C8312yes—
519C22×C22⋊C4C22×C8311yescharacteristic
520C22×C22⋊C4C22×C8312yes—
521C22×C22⋊C4C22×C8312yes—
522C22×C22⋊C4C22×C8312yes—
523C22×C22⋊C4C22×C8312yes—
524C22×C22⋊C4C22×C8311yescharacteristic
525C22×C22⋊C4C22×C8312yes—
526C22×C42C22×C8311yescharacteristic
527#394—24no—
528#392—28no—
529#392—24no—
530#386—28no—
531C2×#95C22×C8311yescharacteristic
532C2×#95C22×C8312yes—
533C2×#95C22×C8311yescharacteristic
534C2×#95C22×C8312yes—
535C2×#95C22×C8312yes—
536C2×#95C22×C8312yes—
537C25C23×C8312yes—
538C25C23×C8311yescharacteristic
539C25C23×C8311yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C8314yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C8314yescomplemented
576C23×C4C23×C8312yes—
577C23×C4C23×C8311yescharacteristic
578C23×C4C23×C8311yescharacteristic
579C23×C4C23×C8312yes—
580C23×C4C23×C8312yes—
581C23×C4C23×C8311yescharacteristic
582C23×C4C23×C8311yescharacteristic
583C23×C4C23×C8311yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C8314yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C8314yescomplemented
614C2×C22⋊C4D4×C8318yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C8314yes—
655C24C2×D4×C8312yes—
656C24C2×D4×C8312yes—
657C24C2×D4×C8312yes—
658C24C2×D4×C8312yes—
659C24#41×C8312yes—
660C24#41×C8312yes—
661C24C24×C8311yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C8314yes—
735C22×C4C2×D4×C8312yes—
736C22×C4C2×D4×C8312yes—
737C22×C4C2×D4×C8314yes—
738C22×C4C2×D4×C8312yes—
739C22×C4C2×D4×C8312yes—
740C22×C4C2×D4×C8312yes—
741C22×C4C2×D4×C8312yes—
742C22×C4C2×D4×C8312yes—
743C22×C4C2×D4×C8312yes—
744C22×C4#41×C8314yes—
745C22×C4#41×C8312yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—41no—
793C23—42no—
794C23—42no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C8314yes—
837C23#121×C8314yescomplemented
838C23C22×D4×C8311yescharacteristic
839C23C22×D4×C8311yescharacteristic
840C23C22×D4×C8311yescharacteristic
841C23C22×D4×C8312yes—
842C23C22×D4×C8311yescharacteristic
843C23C2×#41×C8311yescharacteristic
844C23C2×#41×C8311yescharacteristic
845C23C2×#41×C8311yescharacteristic
846C23C2×#41×C8312yes—
847C23H(5,𝔽2)×C8312yes—
848C23H(5,𝔽2)×C8312yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C8314yes—
901C2×C4#120×C8314yes—
902C2×C4#121×C8314yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C8311yescharacteristic
941C22C2×#120×C8311yescharacteristic
942C22C2×#121×C8311yescharacteristic
943C22C2×#121×C8311yescharacteristic
944C22C2×#121×C8311yescharacteristic
945C22#525×C8311yescharacteristic
946C22#525×C8311yescharacteristic
947C22#525×C8311yescharacteristic
948C22#525×C8312yes—
949C22#532×C8311yescharacteristic
950C22#532×C8312yes—
951C22#534×C8311yescharacteristic
952C22#535×C8311yescharacteristic
953C22#538×C8312yes—
954C22#540×C8312yes—
955C22D42×C8312yes—
956C22D42×C8312yes—
957C22D42×C8312yes—
958C22#546×C8312yes—
959C22#546×C8312yes—
960C22#546×C8312yes—
961C22#550×C8312yes—
962C22#553×C8312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C83×#238811yescharacteristic
975C2C83×#240311yescharacteristic
976C2C83×#240811yescharacteristic
977C2C83×#242412yes—
978C2C83×#242812yes—
979C2C83×#243111yescharacteristic
980C2C83×#245612yes—
981C2C83×#246412yes—
982C2C83×#254311yescharacteristic
983C2C83×#263511yescharacteristic
984C2C83×#284711yescharacteristic
subgroupG/H
center, socleC24×C83C24
commutator, Frattini, cosocleC24C24×C83
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C83C2semidirect
2. C22×C4×D4×C83C2semidirect
3. C2×#394×C83C2semidirect
4. C2×#392×C83C2semidirect
5. C2×#392×C83C2semidirect
6. C2×#386×C83C2semidirect
7. C83×#1441C2semidirect
8. C83×#1439C2semidirect
9. C83×#1438C2semidirect
10. C83×#1437C2semidirect
11. C83×C22⋊#95C2semidirect
72. C22×D4×C83D4semidirect
82. C23×C4×C83D4semidirect
97. C2×C4⋊C4×C83D4semidirect
120. C2×C22⋊C4×C83D4semidirect
121. C2×C22⋊C4×C83D4semidirect
344. C23×C83#121semidirect
409. C2×C4×C83#121semidirect
478. #14722C83direct (N × H)
493. C22×#121C2×C83semidirect
494. C22×C4×D4C2×C83semidirect
495. C2×#394C2×C83semidirect
496. C2×#392C2×C83semidirect
497. C2×#392C2×C83semidirect
498. C2×#386C2×C83semidirect
499. #1441C2×C83semidirect
500. #1439C2×C83semidirect
501. #1438C2×C83semidirect
502. #1437C2×C83semidirect
503. C22⋊#95C2×C83semidirect
504. C83#14722direct (N × H)
565. C22×D4D4×C83semidirect
575. C23×C4D4×C83semidirect
590. C2×C4⋊C4D4×C83semidirect
613. C2×C22⋊C4D4×C83semidirect
614. C2×C22⋊C4D4×C83semidirect
837. C23#121×C83semidirect
902. C2×C4#121×C83semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C832
C22×C4×D4×C832
C2×#394×C832
C2×#392×C832
C2×#386×C832
C83×#14412
C83×#14392
C83×#14382
C83×#14372
C83×C22⋊#952
#1472283