Finite Group Databasebeta

← C83×#24389 #35252213

Subgroups — C83×#24389 #35252213

Order 21248.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C83C211yesmaximal, characteristic
2C2×#470×C83C211yesmaximal, characteristic, complemented
3C2×#468×C83C211yesmaximal, characteristic, complemented
4C2×#452×C83C211yesmaximal, characteristic, complemented
5C2×#407×C83C211yesmaximal, characteristic, complemented
6C83×#2848C211yesmaximal, characteristic, complemented
7C83×#2036C211yesmaximal, characteristic, complemented
8C83×#2034C211yesmaximal, characteristic, complemented
9C83×#2001C211yesmaximal, characteristic, complemented
10C83×#2000C211yesmaximal, characteristic, complemented
11C83×#1895C211yesmaximal, characteristic, complemented
12C83×#1894C211yesmaximal, characteristic, complemented
13C83×#1873C211yesmaximal, characteristic, complemented
14C83×#1854C211yesmaximal, characteristic, complemented
15C83×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C24×C4×C83C2211yescharacteristic
18C22×Q16×C83C2211yescharacteristic, complemented
19C22×SD16×C83C2211yescharacteristic, complemented
20C22×M16×C83C2211yescharacteristic
21C22×M16×C83C2211yescharacteristic
22#525×C83—24no—
23#525×C83—24no—
24C2×#123×C83—21no—
25C2×C22⋊Q8×C83C2211yescharacteristic
26C2×C22⋊Q8×C83C2211yescharacteristic
27C2×C22⋊Q8×C83C2211yescharacteristic
28C2×C22⋊Q8×C83C2211yescharacteristic
29C2×C22⋊Q8×C83C2211yescharacteristic
30C2×#121×C83C2211yescharacteristic
31C2×#121×C83C2211yescharacteristic
32C2×#120×C83—21no—
33C2×C4×D4×C83—21no—
34C2×C4×D4×C83—21no—
35C2×#117×C83C2211yescharacteristic
36#470×C83—24no—
37#468×C83—24no—
38#452×C83—24no—
39C2×#107×C83C2211yescharacteristic, complemented
40C2×#106×C83C2211yescharacteristic, complemented
41C2×#103×C83C2211yescharacteristic, complemented
42C2×#103×C83C2211yescharacteristic, complemented
43C2×#103×C83C2211yescharacteristic, complemented
44C2×#103×C83C2211yescharacteristic, complemented
45C2×#103×C83C2211yescharacteristic, complemented
46C2×#102×C83C2211yescharacteristic, complemented
47C2×#102×C83C2211yescharacteristic, complemented
48C2×#102×C83C2211yescharacteristic, complemented
49#407×C83—24no—
50C2×C22⋊C8×C83C2211yescharacteristic
51C2×C22⋊C8×C83C2211yescharacteristic
52C2×C22⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic
54#385×C83—21no—
55#385×C83—21no—
56#385×C83—21no—
57#380×C83C2211yescharacteristic
58#380×C83C2211yescharacteristic
59#380×C83C2211yescharacteristic
60#379×C83—21no—
61#340×C83C2211yescharacteristic, complemented
62#340×C83C2211yescharacteristic, complemented
63#340×C83C2211yescharacteristic, complemented
64#340×C83C2211yescharacteristic, complemented
65C25×C83D411yescharacteristic
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×Q8×C83C2311yescharacteristic
74C22×D4×C83—21no—
75C22×D4×C83—21no—
76C22×D4×C83—21no—
77C22×D4×C83C2311yescharacteristic
78C23×C4×C83—21no—
79C23×C4×C83—22no—
80C23×C4×C83—22no—
81C23×C4×C83—22no—
82C23×C4×C83—22no—
83C23×C4×C83—41no—
84C23×C4×C83—41no—
85C23×C4×C83D411yescharacteristic
86C23×C4×C83D411yescharacteristic
87C23×C4×C83D411yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2311yescharacteristic
90C23×C4×C83C2311yescharacteristic
91C2×Q16×C83—22no—
92C2×Q16×C83—22no—
93C2×Q16×C83—41no—
94C2×SD16×C83—22no—
95C2×SD16×C83—22no—
96C2×SD16×C83—41no—
97C2×M16×C83—22no—
98C2×M16×C83—22no—
99C2×M16×C83—22no—
100C2×M16×C83—22no—
101C2×M16×C83—41no—
102C2×M16×C83—41no—
103C22×C8×C83C2311yescharacteristic
104C22×C8×C83C2311yescharacteristic
105C22×C8×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107#123×C83—28no—
108C22⋊Q8×C83—22no—
109C22⋊Q8×C83—22no—
110C22⋊Q8×C83—22no—
111C22⋊Q8×C83—22no—
112C22⋊Q8×C83—22no—
113C22⋊Q8×C83—22no—
114C22⋊Q8×C83—22no—
115C22⋊Q8×C83—41no—
116C22⋊Q8×C83—41no—
117C22⋊Q8×C83D414yes—
118#121×C83—22no—
119#121×C83—22no—
120#121×C83—22no—
121#121×C83D414yes—
122#120×C83—28no—
123C4×D4×C83—28no—
124C4×D4×C83—28no—
125#117×C83—22no—
126#117×C83—22no—
127C2×C4⋊C4×C83—21no—
128C2×C4⋊C4×C83—21no—
129C2×C4⋊C4×C83—21no—
130C2×C4⋊C4×C83—21no—
131C2×C4⋊C4×C83—21no—
132C2×C4⋊C4×C83C2311yescharacteristic
133C2×C4⋊C4×C83C2311yescharacteristic
134C2×C4⋊C4×C83C2311yescharacteristic
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83C2311yescharacteristic
137C2×C22⋊C4×C83—21no—
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×C42×C83—21no—
149#107×C83—22no—
150#106×C83—22no—
151#103×C83—22no—
152#103×C83—22no—
153#103×C83—22no—
154#103×C83—22no—
155#103×C83—41no—
156#102×C83—22no—
157#102×C83—22no—
158#102×C83—41no—
159C22⋊C8×C83—22no—
160C22⋊C8×C83—22no—
161C22⋊C8×C83—22no—
162C22⋊C8×C83D414yescomplemented
163#95×C83—21no—
164#95×C83—21no—
165#95×C83—21no—
166C24×C83—22no—
167C24×C83—22no—
168C24×C83—22no—
169C24×C83—21no—
170C24×C83—41no—
171C24×C83—41no—
172C24×C83—41no—
173C24×C83—41no—
174C24×C83C2×D411yescharacteristic
175C24×C83C2×D411yescharacteristic
176C24×C83C2×D411yescharacteristic
177#41×C83—44no—
178#41×C83—44no—
179#41×C83—44no—
180#41×C83—44no—
181C2×Q8×C83—21no—
182C2×Q8×C83—21no—
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83—21no—
186C2×Q8×C83—21no—
187C2×Q8×C83—21no—
188C2×Q8×C83—21no—
189C2×Q8×C83—21no—
190C2×Q8×C83—21no—
191C2×Q8×C83—21no—
192C2×Q8×C83C2×D412yes—
193C2×D4×C83—24no—
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—42no—
202C2×D4×C83—42no—
203C2×D4×C83—42no—
204C2×D4×C83—42no—
205C2×D4×C83—42no—
206C2×D4×C83—42no—
207C2×D4×C83C2×D412yes—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83—24no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—21no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—41no—
237C22×C4×C83—41no—
238C22×C4×C83—41no—
239C22×C4×C83—44no—
240C22×C4×C83—44no—
241C22×C4×C83—44no—
242C22×C4×C83—44no—
243C22×C4×C83—42no—
244C22×C4×C83—42no—
245C22×C4×C83C2×D411yescharacteristic
246C22×C4×C83C2×D411yescharacteristic
247C22×C4×C83C2×D412yes—
248C22×C4×C83C2×D412yes—
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2×D412yes—
251C22×C4×C83#4112yes—
252C22×C4×C83C2411yescharacteristic
253Q16×C83—44no—
254SD16×C83—44no—
255M16×C83—44no—
256M16×C83—44no—
257C2×C8×C83—21no—
258C2×C8×C83—21no—
259C2×C8×C83—21no—
260C2×C8×C83—21no—
261C2×C8×C83—21no—
262C2×C8×C83—21no—
263C2×C8×C83—21no—
264C2×C8×C83—21no—
265C2×C8×C83—21no—
266C2×C8×C83—21no—
267C2×C8×C83C2×D412yes—
268C2×C8×C83C2×D412yes—
269C4⋊C4×C83—24no—
270C4⋊C4×C83—24no—
271C4⋊C4×C83—21no—
272C4⋊C4×C83—21no—
273C4⋊C4×C83—21no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—21no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83—21no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83—42no—
280C4⋊C4×C83—42no—
281C4⋊C4×C83—42no—
282C4⋊C4×C83C2×D412yes—
283C4⋊C4×C83C2×D412yes—
284C22⋊C4×C83—24no—
285C22⋊C4×C83—24no—
286C22⋊C4×C83—24no—
287C22⋊C4×C83—24no—
288C22⋊C4×C83—24no—
289C22⋊C4×C83—42no—
290C22⋊C4×C83—42no—
291C22⋊C4×C83—42no—
292C22⋊C4×C83—42no—
293C22⋊C4×C83—42no—
294C22⋊C4×C83—42no—
295C42×C83—24no—
296C23×C83—21no—
297C23×C83—21no—
298C23×C83—21no—
299C23×C83—21no—
300C23×C83—21no—
301C23×C83—21no—
302C23×C83—21no—
303C23×C83—21no—
304C23×C83—21no—
305C23×C83—21no—
306C23×C83—21no—
307C23×C83—21no—
308C23×C83—21no—
309C23×C83—21no—
310C23×C83—21no—
311C23×C83—21no—
312C23×C83—21no—
313C23×C83—21no—
314C23×C83—22no—
315C23×C83—44no—
316C23×C83—44no—
317C23×C83—44no—
318C23×C83—44no—
319C23×C83—44no—
320C23×C83—44no—
321C23×C83—44no—
322C23×C83—41no—
323C23×C83—41no—
324C23×C83—41no—
325C23×C83—41no—
326C23×C83—41no—
327C23×C83—41no—
328C23×C83#12012yes—
329C23×C83#12112yes—
330C23×C83#13712yes—
331C23×C83C22×D411yescharacteristic
332Q8×C83—22no—
333Q8×C83—22no—
334Q8×C83—41no—
335Q8×C83—41no—
336Q8×C83—41no—
337Q8×C83—41no—
338Q8×C83—41no—
339Q8×C83—41no—
340D4×C83—22no—
341D4×C83—22no—
342D4×C83—48no—
343D4×C83—48no—
344D4×C83—48no—
345D4×C83—41no—
346D4×C83—41no—
347C2×C4×C83—21no—
348C2×C4×C83—21no—
349C2×C4×C83—21no—
350C2×C4×C83—21no—
351C2×C4×C83—22no—
352C2×C4×C83—22no—
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
358C2×C4×C83—22no—
359C2×C4×C83—22no—
360C2×C4×C83—22no—
361C2×C4×C83—21no—
362C2×C4×C83—22no—
363C2×C4×C83—21no—
364C2×C4×C83—21no—
365C2×C4×C83—44no—
366C2×C4×C83—44no—
367C2×C4×C83—44no—
368C2×C4×C83—48no—
369C2×C4×C83—41no—
370C2×C4×C83—41no—
371C2×C4×C83—41no—
372C2×C4×C83—41no—
373C2×C4×C83—41no—
374C2×C4×C83—41no—
375C2×C4×C83—41no—
376C2×C4×C83—41no—
377C2×C4×C83—41no—
378C2×C4×C83—41no—
379C2×C4×C83—41no—
380C2×C4×C83—41no—
381C2×C4×C83—41no—
382C2×C4×C83—41no—
383C2×C4×C83—41no—
384C2×C4×C83—41no—
385C2×C4×C83—41no—
386C2×C4×C83—41no—
387C2×C4×C83—41no—
388C2×C4×C83—41no—
389C2×C4×C83—41no—
390C2×C4×C83—41no—
391C2×C4×C83#12012yes—
392C2×C4×C83#12112yes—
393C2×C4×C83C22×D411yescharacteristic
394C2×C4×C83C22×D411yescharacteristic
395C2×C4×C83C22×D411yescharacteristic
396C2×C4×C83C2×#4111yescharacteristic
397C2×C4×C83H(5,𝔽2)11yescharacteristic
398C2×C4×C83H(5,𝔽2)11yescharacteristic
399C8×C83—22no—
400C8×C83—22no—
401C8×C83—41no—
402C8×C83—41no—
403C22×C83—22no—
404C22×C83—22no—
405C22×C83—22no—
406C22×C83—22no—
407C22×C83—22no—
408C22×C83—22no—
409C22×C83—22no—
410C22×C83—22no—
411C22×C83—22no—
412C22×C83—416no—
413C22×C83—41no—
414C22×C83—41no—
415C22×C83—41no—
416C22×C83—41no—
417C22×C83—41no—
418C22×C83—41no—
419C22×C83—41no—
420C22×C83—41no—
421C22×C83—41no—
422C22×C83—41no—
423C22×C83—41no—
424C22×C83—41no—
425C22×C83—42no—
426C22×C83—42no—
427C22×C83—42no—
428C22×C83—81no—
429C22×C83—81no—
430C22×C83—81no—
431C22×C83—81no—
432C22×C83C2×#12011yescharacteristic
433C22×C83C2×#12111yescharacteristic
434C22×C83#53411yescharacteristic
435C22×C83C2×#13711yescharacteristic
436C22×C83#57511yescharacteristic
437C22×C83#57511yescharacteristic
438C22×C83#57511yescharacteristic
439C4×C83—22no—
440C4×C83—22no—
441C4×C83—41no—
442C4×C83—42no—
443C4×C83—42no—
444C4×C83—42no—
445C4×C83—81no—
446C4×C83—81no—
447C4×C83—81no—
448C4×C83—81no—
449C4×C83D4211yescharacteristic
450C4×C83D4211yescharacteristic
451C4×C83#54611yescharacteristic
452C4×C83#54611yescharacteristic
453#24389C8311yesmaximal, characteristic, direct product factor, Sylow
454C2×C83—42no—
455C2×C83—42no—
456C2×C83—42no—
457C2×C83—82no—
458C2×C83#241011yescharacteristic
459C2×C83#300511yescharacteristic
460C2×C83#300711yescharacteristic
461C2×C83#305411yescharacteristic
462C2×C83#305611yescharacteristic
463C2×C83#319611yescharacteristic
464C2×C83#319711yescharacteristic
465C2×#525C2×C8311yescharacteristic
466C2×#470C2×C8311yescharacteristic, complemented
467C2×#468C2×C8311yescharacteristic, complemented
468C2×#452C2×C8311yescharacteristic, complemented
469C2×#407C2×C8311yescharacteristic, complemented
470#2848C2×C8311yescharacteristic, complemented
471#2036C2×C8311yescharacteristic, complemented
472#2034C2×C8311yescharacteristic, complemented
473#2001C2×C8311yescharacteristic, complemented
474#2000C2×C8311yescharacteristic, complemented
475#1895C2×C8311yescharacteristic, complemented
476#1894C2×C8311yescharacteristic, complemented
477#1873C2×C8311yescharacteristic, complemented
478#1854C2×C8311yescharacteristic, complemented
479#1788C2×C8311yescharacteristic, complemented
480C83#2438911yescharacteristic, direct product factor, Sylow
481C22×#41C22×C8311yescharacteristic
482C24×C4C22×C8311yescharacteristic
483C22×Q16C22×C8311yescharacteristic, complemented
484C22×SD16C22×C8311yescharacteristic, complemented
485C22×M16C22×C8311yescharacteristic
486C22×M16C22×C8311yescharacteristic
487#525—24no—
488#525—24no—
489C2×#123—21no—
490C2×C22⋊Q8C22×C8311yescharacteristic
491C2×C22⋊Q8C22×C8311yescharacteristic
492C2×C22⋊Q8C22×C8311yescharacteristic
493C2×C22⋊Q8C22×C8311yescharacteristic
494C2×C22⋊Q8C22×C8311yescharacteristic
495C2×#121C22×C8311yescharacteristic
496C2×#121C22×C8311yescharacteristic
497C2×#120—21no—
498C2×C4×D4—21no—
499C2×C4×D4—21no—
500C2×#117C22×C8311yescharacteristic
501#470—24no—
502#468—24no—
503#452—24no—
504C2×#107C22×C8311yescharacteristic, complemented
505C2×#106C22×C8311yescharacteristic, complemented
506C2×#103C22×C8311yescharacteristic, complemented
507C2×#103C22×C8311yescharacteristic, complemented
508C2×#103C22×C8311yescharacteristic, complemented
509C2×#103C22×C8311yescharacteristic, complemented
510C2×#103C22×C8311yescharacteristic, complemented
511C2×#102C22×C8311yescharacteristic, complemented
512C2×#102C22×C8311yescharacteristic, complemented
513C2×#102C22×C8311yescharacteristic, complemented
514#407—24no—
515C2×C22⋊C8C22×C8311yescharacteristic
516C2×C22⋊C8C22×C8311yescharacteristic
517C2×C22⋊C8C22×C8311yescharacteristic
518C2×C22⋊C8C22×C8311yescharacteristic
519#385—21no—
520#385—21no—
521#385—21no—
522#380C22×C8311yescharacteristic
523#380C22×C8311yescharacteristic
524#380C22×C8311yescharacteristic
525#379—21no—
526#340C22×C8311yescharacteristic, complemented
527#340C22×C8311yescharacteristic, complemented
528#340C22×C8311yescharacteristic, complemented
529#340C22×C8311yescharacteristic, complemented
530C25D4×C8311yescharacteristic
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—41no—
536C2×#41—41no—
537C22×Q8C23×C8311yescharacteristic
538C22×Q8C23×C8311yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4C23×C8311yescharacteristic
543C23×C4—21no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4D4×C8311yescharacteristic
551C23×C4D4×C8311yescharacteristic
552C23×C4D4×C8311yescharacteristic
553C23×C4C23×C8311yescharacteristic
554C23×C4C23×C8311yescharacteristic
555C23×C4C23×C8311yescharacteristic
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C23×C8311yescharacteristic
569C22×C8C23×C8311yescharacteristic
570C22×C8C23×C8311yescharacteristic
571C22×C8C23×C8311yescharacteristic
572#123—28no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8D4×C8314yes—
583#121—22no—
584#121—22no—
585#121—22no—
586#121D4×C8314yes—
587#120—28no—
588C4×D4—28no—
589C4×D4—28no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4C23×C8311yescharacteristic
598C2×C4⋊C4C23×C8311yescharacteristic
599C2×C4⋊C4C23×C8311yescharacteristic
600C2×C4⋊C4C23×C8311yescharacteristic
601C2×C4⋊C4C23×C8311yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614#107—22no—
615#106—22no—
616#103—22no—
617#103—22no—
618#103—22no—
619#103—22no—
620#103—41no—
621#102—22no—
622#102—22no—
623#102—41no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8—22no—
627C22⋊C8D4×C8314yescomplemented
628#95—21no—
629#95—21no—
630#95—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24C2×D4×C8311yescharacteristic
640C24C2×D4×C8311yescharacteristic
641C24C2×D4×C8311yescharacteristic
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C8312yes—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C8312yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4C2×D4×C8311yescharacteristic
711C22×C4C2×D4×C8311yescharacteristic
712C22×C4C2×D4×C8312yes—
713C22×C4C2×D4×C8312yes—
714C22×C4C2×D4×C8311yescharacteristic
715C22×C4C2×D4×C8312yes—
716C22×C4#41×C8312yes—
717C22×C4C24×C8311yescharacteristic
718Q16—44no—
719SD16—44no—
720M16—44no—
721M16—44no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C8312yes—
733C2×C8C2×D4×C8312yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4C2×D4×C8312yes—
748C4⋊C4C2×D4×C8312yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—24no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23#120×C8312yes—
794C23#121×C8312yes—
795C23#137×C8312yes—
796C23C22×D4×C8311yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4#120×C8312yes—
857C2×C4#121×C8312yes—
858C2×C4C22×D4×C8311yescharacteristic
859C2×C4C22×D4×C8311yescharacteristic
860C2×C4C22×D4×C8311yescharacteristic
861C2×C4C2×#41×C8311yescharacteristic
862C2×C4H(5,𝔽2)×C8311yescharacteristic
863C2×C4H(5,𝔽2)×C8311yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×#120×C8311yescharacteristic
898C22C2×#121×C8311yescharacteristic
899C22#534×C8311yescharacteristic
900C22C2×#137×C8311yescharacteristic
901C22#575×C8311yescharacteristic
902C22#575×C8311yescharacteristic
903C22#575×C8311yescharacteristic
904C4—22no—
905C4—22no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C8311yescharacteristic
915C4D42×C8311yescharacteristic
916C4#546×C8311yescharacteristic
917C4#546×C8311yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2C83×#241011yescharacteristic
923C2C83×#300511yescharacteristic
924C2C83×#300711yescharacteristic
925C2C83×#305411yescharacteristic
926C2C83×#305611yescharacteristic
927C2C83×#319611yescharacteristic
928C2C83×#319711yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×#525×C83C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C24×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#470×C83C2semidirect
3. C2×#468×C83C2semidirect
4. C2×#452×C83C2semidirect
5. C2×#407×C83C2semidirect
6. C83×#2848C2semidirect
7. C83×#2036C2semidirect
8. C83×#2034C2semidirect
9. C83×#2001C2semidirect
10. C83×#2000C2semidirect
11. C83×#1895C2semidirect
12. C83×#1894C2semidirect
13. C83×#1873C2semidirect
14. C83×#1854C2semidirect
15. C83×#1788C2semidirect
18. C22×Q16×C83C22semidirect
19. C22×SD16×C83C22semidirect
39. C2×#107×C83C22semidirect
40. C2×#106×C83C22semidirect
41. C2×#103×C83C22semidirect
42. C2×#103×C83C22semidirect
43. C2×#103×C83C22semidirect
44. C2×#103×C83C22semidirect
45. C2×#103×C83C22semidirect
46. C2×#102×C83C22semidirect
47. C2×#102×C83C22semidirect
48. C2×#102×C83C22semidirect
61. #340×C83C22semidirect
62. #340×C83C22semidirect
63. #340×C83C22semidirect
64. #340×C83C22semidirect
162. C22⋊C8×C83D4semidirect
453. #24389C83direct (N × H)
466. C2×#470C2×C83semidirect
467. C2×#468C2×C83semidirect
468. C2×#452C2×C83semidirect
469. C2×#407C2×C83semidirect
470. #2848C2×C83semidirect
471. #2036C2×C83semidirect
472. #2034C2×C83semidirect
473. #2001C2×C83semidirect
474. #2000C2×C83semidirect
475. #1895C2×C83semidirect
476. #1894C2×C83semidirect
477. #1873C2×C83semidirect
478. #1854C2×C83semidirect
479. #1788C2×C83semidirect
480. C83#24389direct (N × H)
483. C22×Q16C22×C83semidirect
484. C22×SD16C22×C83semidirect
504. C2×#107C22×C83semidirect
505. C2×#106C22×C83semidirect
506. C2×#103C22×C83semidirect
507. C2×#103C22×C83semidirect
508. C2×#103C22×C83semidirect
509. C2×#103C22×C83semidirect
510. C2×#103C22×C83semidirect
511. C2×#102C22×C83semidirect
512. C2×#102C22×C83semidirect
513. C2×#102C22×C83semidirect
526. #340C22×C83semidirect
527. #340C22×C83semidirect
528. #340C22×C83semidirect
529. #340C22×C83semidirect
627. C22⋊C8D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C832
C2×#470×C832
C2×#468×C832
C2×#452×C832
C2×#407×C832
C83×#28482
C83×#20362
C83×#20342
C83×#20012
C83×#20002
C83×#18952
C83×#18942
C83×#18732
C83×#18542
C83×#17882
#2438983