Finite Group Databasebeta

← C83×#24396 #35252220

Subgroups — C83×#24396 #35252220

Order 21248.

1444 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#536×C83C211yesmaximal, characteristic, complemented
2C2×#468×C83C211yesmaximal, characteristic, complemented
3C2×#465×C83C211yesmaximal, characteristic, complemented
4C2×#448×C83C211yesmaximal, characteristic, complemented
5C2×#408×C83C211yesmaximal, characteristic, complemented
6C83×#2615C211yesmaximal, characteristic
7C83×#2036C211yesmaximal, characteristic, complemented
8C83×#2035C211yesmaximal, characteristic, complemented
9C83×#2000C211yesmaximal, characteristic, complemented
10C83×#2000C211yesmaximal, characteristic, complemented
11C83×#1894C211yesmaximal, characteristic, complemented
12C83×#1892C211yesmaximal, characteristic, complemented
13C83×#1875C211yesmaximal, characteristic, complemented
14C83×#1854C211yesmaximal, characteristic, complemented
15C83×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C23×Q8×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic
19C22×SD16×C83C2211yescharacteristic
20C22×M16×C83C2211yescharacteristic
21C23×C8×C83C2211yescharacteristic
22#536×C83—24no—
23#536×C83—24no—
24C2×C4⋊Q8×C83—21no—
25C2×#124×C83—21no—
26C2×#123×C83—21no—
27C2×#123×C83—21no—
28C2×C22⋊Q8×C83C2211yescharacteristic
29C2×C22⋊Q8×C83C2211yescharacteristic
30C2×C22⋊Q8×C83C2211yescharacteristic
31C2×C22⋊Q8×C83C2211yescharacteristic
32C2×#121×C83C2211yescharacteristic
33C2×#121×C83C2211yescharacteristic
34C2×#121×C83C2211yescharacteristic
35C2×#117×C83C2211yescharacteristic
36#468×C83—24no—
37#465×C83—24no—
38#448×C83—24no—
39C2×#107×C83C2211yescharacteristic
40C2×#106×C83C2211yescharacteristic
41C2×#103×C83C2211yescharacteristic
42C2×#103×C83C2211yescharacteristic
43C2×#103×C83C2211yescharacteristic
44C2×#103×C83C2211yescharacteristic
45C2×#103×C83C2211yescharacteristic
46C2×#103×C83C2211yescharacteristic
47C2×#102×C83C2211yescharacteristic
48C2×#102×C83C2211yescharacteristic
49#408×C83—24no—
50C2×C22⋊C8×C83C2211yescharacteristic
51C2×C22⋊C8×C83C2211yescharacteristic
52C2×C22⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic
54#393×C83—21no—
55#392×C83—21no—
56#392×C83—21no—
57#392×C83—21no—
58#380×C83C2211yescharacteristic
59#380×C83C2211yescharacteristic
60#380×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic
62#340×C83C2211yescharacteristic
63#340×C83C2211yescharacteristic
64#340×C83C2211yescharacteristic
65C2×#41×C83—22no—
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—22no—
69C2×#41×C83—41no—
70C2×#41×C83—41no—
71C22×Q8×C83—22no—
72C22×Q8×C83—22no—
73C22×Q8×C83—21no—
74C22×Q8×C83—22no—
75C22×Q8×C83—22no—
76C22×Q8×C83—41no—
77C22×Q8×C83—41no—
78C22×Q8×C83D411yescharacteristic
79C22×Q8×C83C2311yescharacteristic
80C22×Q8×C83C2311yescharacteristic
81C22×D4×C83—21no—
82C22×D4×C83—21no—
83C22×D4×C83—21no—
84C22×D4×C83D411yescharacteristic
85C22×D4×C83D411yescharacteristic
86C22×D4×C83D411yescharacteristic
87C22×D4×C83C2311yescharacteristic
88C23×C4×C83—21no—
89C23×C4×C83C2311yescharacteristic
90C23×C4×C83C2311yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C2×SD16×C83—22no—
93C2×SD16×C83—22no—
94C2×SD16×C83—22no—
95C2×SD16×C83—22no—
96C2×SD16×C83—41no—
97C2×SD16×C83—41no—
98C2×M16×C83—22no—
99C2×M16×C83—22no—
100C2×M16×C83—41no—
101C22×C8×C83—22no—
102C22×C8×C83—22no—
103C22×C8×C83—41no—
104C22×C8×C83C2311yescharacteristic
105C22×C8×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108C4⋊Q8×C83—28no—
109#124×C83—28no—
110#123×C83—28no—
111#123×C83—28no—
112C22⋊Q8×C83—22no—
113C22⋊Q8×C83—22no—
114C22⋊Q8×C83—22no—
115C22⋊Q8×C83—22no—
116C22⋊Q8×C83—22no—
117C22⋊Q8×C83—22no—
118C22⋊Q8×C83D414yescomplemented
119C22⋊Q8×C83D414yescomplemented
120#121×C83—22no—
121#121×C83—22no—
122#121×C83—22no—
123#121×C83—22no—
124#121×C83—41no—
125#121×C83—41no—
126#117×C83—22no—
127#117×C83—22no—
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#103×C83—41no—
157#102×C83—22no—
158#102×C83—22no—
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—21no—
167C24×C83C2×D411yescharacteristic
168C24×C83C2×D411yescharacteristic
169C24×C83C2×D411yescharacteristic
170#41×C83—44no—
171#41×C83—44no—
172#41×C83—44no—
173#41×C83—44no—
174C2×Q8×C83—24no—
175C2×Q8×C83—22no—
176C2×Q8×C83—22no—
177C2×Q8×C83—21no—
178C2×Q8×C83—21no—
179C2×Q8×C83—21no—
180C2×Q8×C83—21no—
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—41no—
188C2×Q8×C83—44no—
189C2×Q8×C83—44no—
190C2×Q8×C83—44no—
191C2×Q8×C83—44no—
192C2×Q8×C83—42no—
193C2×Q8×C83—42no—
194C2×Q8×C83C2×D412yes—
195C2×Q8×C83C2×D412yes—
196C2×D4×C83—22no—
197C2×D4×C83—22no—
198C2×D4×C83—22no—
199C2×D4×C83—22no—
200C2×D4×C83—22no—
201C2×D4×C83—22no—
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—41no—
209C2×D4×C83—41no—
210C2×D4×C83—41no—
211C2×D4×C83—42no—
212C2×D4×C83—42no—
213C2×D4×C83—42no—
214C2×D4×C83—81no—
215C2×D4×C83—81no—
216C2×D4×C83—81no—
217C2×D4×C83—81no—
218C2×D4×C83—81no—
219C2×D4×C83—81no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—21no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—24no—
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—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—42no—
243C22×C4×C83—42no—
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2×D411yescharacteristic
246C22×C4×C83C2×D412yes—
247C22×C4×C83C2×D412yes—
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2×D412yes—
250C22×C4×C83#4112yes—
251C22×C4×C83C2411yescharacteristic
252SD16×C83—44no—
253SD16×C83—44no—
254M16×C83—44no—
255C2×C8×C83—21no—
256C2×C8×C83—21no—
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—44no—
266C2×C8×C83C2×D412yes—
267C2×C8×C83C2×D412yes—
268C4⋊C4×C83—24no—
269C4⋊C4×C83—24no—
270C4⋊C4×C83—24no—
271C4⋊C4×C83—24no—
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—21no—
280C4⋊C4×C83C2×D412yes—
281C4⋊C4×C83C2×D412yes—
282C22⋊C4×C83—24no—
283C22⋊C4×C83—24no—
284C22⋊C4×C83—24no—
285C22⋊C4×C83—24no—
286C22⋊C4×C83—24no—
287C22⋊C4×C83—42no—
288C22⋊C4×C83—42no—
289C22⋊C4×C83—42no—
290C22⋊C4×C83—81no—
291C22⋊C4×C83—81no—
292C22⋊C4×C83—81no—
293C42×C83—24no—
294C23×C83—21no—
295C23×C83—21no—
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—41no—
314C23×C83—41no—
315C23×C83—41no—
316C23×C83—41no—
317C23×C83—41no—
318C23×C83—41no—
319C23×C83—41no—
320C23×C83#12012yes—
321C23×C83#12112yes—
322C23×C83C22×D411yescharacteristic
323Q8×C83—22no—
324Q8×C83—22no—
325Q8×C83—22no—
326Q8×C83—22no—
327Q8×C83—44no—
328Q8×C83—48no—
329Q8×C83—41no—
330Q8×C83—41no—
331Q8×C83—41no—
332Q8×C83—41no—
333D4×C83—44no—
334D4×C83—44no—
335D4×C83—44no—
336D4×C83—41no—
337D4×C83—41no—
338D4×C83—41no—
339D4×C83—41no—
340D4×C83—84no—
341D4×C83—84no—
342D4×C83—84no—
343C2×C4×C83—21no—
344C2×C4×C83—21no—
345C2×C4×C83—21no—
346C2×C4×C83—21no—
347C2×C4×C83—22no—
348C2×C4×C83—22no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
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—21no—
360C2×C4×C83—21no—
361C2×C4×C83—21no—
362C2×C4×C83—48no—
363C2×C4×C83—41no—
364C2×C4×C83—41no—
365C2×C4×C83—41no—
366C2×C4×C83—41no—
367C2×C4×C83—41no—
368C2×C4×C83—41no—
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#12012yes—
385C2×C4×C83#12112yes—
386C2×C4×C83C22×D411yescharacteristic
387C2×C4×C83C22×D411yescharacteristic
388C2×C4×C83C22×D411yescharacteristic
389C2×C4×C83C2×#4111yescharacteristic
390C2×C4×C83H(5,𝔽2)11yescharacteristic
391C2×C4×C83H(5,𝔽2)11yescharacteristic
392C8×C83—22no—
393C8×C83—22no—
394C8×C83—41no—
395C8×C83—41no—
396C22×C83—22no—
397C22×C83—22no—
398C22×C83—22no—
399C22×C83—22no—
400C22×C83—22no—
401C22×C83—22no—
402C22×C83—41no—
403C22×C83—41no—
404C22×C83—41no—
405C22×C83—41no—
406C22×C83—41no—
407C22×C83—41no—
408C22×C83—41no—
409C22×C83—41no—
410C22×C83—41no—
411C22×C83—41no—
412C22×C83—41no—
413C22×C83—41no—
414C22×C83—41no—
415C22×C83—41no—
416C22×C83—41no—
417C22×C83—81no—
418C22×C83—81no—
419C22×C83—81no—
420C22×C83—81no—
421C22×C83—81no—
422C22×C83—81no—
423C22×C83—81no—
424C22×C83C2×#12011yescharacteristic
425C22×C83C2×#12111yescharacteristic
426C22×C83#53411yescharacteristic
427C22×C83#57711yescharacteristic
428C22×C83#57711yescharacteristic
429C22×C83#57711yescharacteristic
430C22×C83#57811yescharacteristic
431C4×C83—22no—
432C4×C83—22no—
433C4×C83—41no—
434C4×C83—42no—
435C4×C83—42no—
436C4×C83—42no—
437C4×C83—42no—
438C4×C83—81no—
439C4×C83—81no—
440C4×C83—81no—
441C4×C83D4211yescharacteristic
442C4×C83D4211yescharacteristic
443C4×C83#54611yescharacteristic
444C4×C83#54611yescharacteristic
445#24396C8311yesmaximal, characteristic, direct product factor, Sylow
446C2×C83—42no—
447C2×C83—42no—
448C2×C83—81no—
449C2×C83—161no—
450C2×C83#241011yescharacteristic
451C2×C83#301011yescharacteristic
452C2×C83#301311yescharacteristic
453C2×C83#305711yescharacteristic
454C2×C83#306311yescharacteristic
455C2×C83#320011yescharacteristic
456C2×C83#320111yescharacteristic
457C2×#536C2×C8311yescharacteristic, complemented
458C2×#468C2×C8311yescharacteristic, complemented
459C2×#465C2×C8311yescharacteristic, complemented
460C2×#448C2×C8311yescharacteristic, complemented
461C2×#408C2×C8311yescharacteristic, complemented
462#2615C2×C8311yescharacteristic
463#2036C2×C8311yescharacteristic, complemented
464#2035C2×C8311yescharacteristic, complemented
465#2000C2×C8311yescharacteristic, complemented
466#2000C2×C8311yescharacteristic, complemented
467#1894C2×C8311yescharacteristic, complemented
468#1892C2×C8311yescharacteristic, complemented
469#1875C2×C8311yescharacteristic, complemented
470#1854C2×C8311yescharacteristic, complemented
471#1787C2×C8311yescharacteristic, complemented
472C83#2439611yescharacteristic, direct product factor, Sylow
473C22×#41C22×C8311yescharacteristic
474C23×Q8C22×C8311yescharacteristic
475C22×SD16C22×C8311yescharacteristic
476C22×SD16C22×C8311yescharacteristic
477C22×M16C22×C8311yescharacteristic
478C23×C8C22×C8311yescharacteristic
479#536—24no—
480#536—24no—
481C2×C4⋊Q8—21no—
482C2×#124—21no—
483C2×#123—21no—
484C2×#123—21no—
485C2×C22⋊Q8C22×C8311yescharacteristic
486C2×C22⋊Q8C22×C8311yescharacteristic
487C2×C22⋊Q8C22×C8311yescharacteristic
488C2×C22⋊Q8C22×C8311yescharacteristic
489C2×#121C22×C8311yescharacteristic
490C2×#121C22×C8311yescharacteristic
491C2×#121C22×C8311yescharacteristic
492C2×#117C22×C8311yescharacteristic
493#468—24no—
494#465—24no—
495#448—24no—
496C2×#107C22×C8311yescharacteristic
497C2×#106C22×C8311yescharacteristic
498C2×#103C22×C8311yescharacteristic
499C2×#103C22×C8311yescharacteristic
500C2×#103C22×C8311yescharacteristic
501C2×#103C22×C8311yescharacteristic
502C2×#103C22×C8311yescharacteristic
503C2×#103C22×C8311yescharacteristic
504C2×#102C22×C8311yescharacteristic
505C2×#102C22×C8311yescharacteristic
506#408—24no—
507C2×C22⋊C8C22×C8311yescharacteristic
508C2×C22⋊C8C22×C8311yescharacteristic
509C2×C22⋊C8C22×C8311yescharacteristic
510C2×C22⋊C8C22×C8311yescharacteristic
511#393—21no—
512#392—21no—
513#392—21no—
514#392—21no—
515#380C22×C8311yescharacteristic
516#380C22×C8311yescharacteristic
517#380C22×C8311yescharacteristic
518#340C22×C8311yescharacteristic
519#340C22×C8311yescharacteristic
520#340C22×C8311yescharacteristic
521#340C22×C8311yescharacteristic
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—41no—
527C2×#41—41no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—21no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—41no—
534C22×Q8—41no—
535C22×Q8D4×C8311yescharacteristic
536C22×Q8C23×C8311yescharacteristic
537C22×Q8C23×C8311yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4D4×C8311yescharacteristic
542C22×D4D4×C8311yescharacteristic
543C22×D4D4×C8311yescharacteristic
544C22×D4C23×C8311yescharacteristic
545C23×C4—21no—
546C23×C4C23×C8311yescharacteristic
547C23×C4C23×C8311yescharacteristic
548C23×C4C23×C8311yescharacteristic
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8C23×C8311yescharacteristic
562C22×C8C23×C8311yescharacteristic
563C22×C8C23×C8311yescharacteristic
564C22×C8C23×C8311yescharacteristic
565C4⋊Q8—28no—
566#124—28no—
567#123—28no—
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8D4×C8314yescomplemented
576C22⋊Q8D4×C8314yescomplemented
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—41no—
582#121—41no—
583#117—22no—
584#117—22no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4C23×C8311yescharacteristic
590C2×C4⋊C4C23×C8311yescharacteristic
591C2×C4⋊C4C23×C8311yescharacteristic
592C2×C4⋊C4C23×C8311yescharacteristic
593C2×C4⋊C4C23×C8311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C42—21no—
606#107—22no—
607#106—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#103—41no—
614#102—22no—
615#102—22no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8D4×C8314yescomplemented
620#95—21no—
621#95—21no—
622#95—21no—
623C24—21no—
624C24C2×D4×C8311yescharacteristic
625C24C2×D4×C8311yescharacteristic
626C24C2×D4×C8311yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631C2×Q8—24no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—41no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—42no—
650C2×Q8—42no—
651C2×Q8C2×D4×C8312yes—
652C2×Q8C2×D4×C8312yes—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
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—42no—
700C22×C4—42no—
701C22×C4C2×D4×C8311yescharacteristic
702C22×C4C2×D4×C8311yescharacteristic
703C22×C4C2×D4×C8312yes—
704C22×C4C2×D4×C8312yes—
705C22×C4C2×D4×C8311yescharacteristic
706C22×C4C2×D4×C8312yes—
707C22×C4#41×C8312yes—
708C22×C4C24×C8311yescharacteristic
709SD16—44no—
710SD16—44no—
711M16—44no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C8312yes—
724C2×C8C2×D4×C8312yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4C2×D4×C8312yes—
738C4⋊C4C2×D4×C8312yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—81no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C42—24no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C8312yes—
778C23#121×C8312yes—
779C23C22×D4×C8311yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—48no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790D4—44no—
791D4—44no—
792D4—44no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4#120×C8312yes—
842C2×C4#121×C8312yes—
843C2×C4C22×D4×C8311yescharacteristic
844C2×C4C22×D4×C8311yescharacteristic
845C2×C4C22×D4×C8311yescharacteristic
846C2×C4C2×#41×C8311yescharacteristic
847C2×C4H(5,𝔽2)×C8311yescharacteristic
848C2×C4H(5,𝔽2)×C8311yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C8311yescharacteristic
882C22C2×#121×C8311yescharacteristic
883C22#534×C8311yescharacteristic
884C22#577×C8311yescharacteristic
885C22#577×C8311yescharacteristic
886C22#577×C8311yescharacteristic
887C22#578×C8311yescharacteristic
888C4—22no—
889C4—22no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C8311yescharacteristic
899C4D42×C8311yescharacteristic
900C4#546×C8311yescharacteristic
901C4#546×C8311yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—161no—
906C2C83×#241011yescharacteristic
907C2C83×#301011yescharacteristic
908C2C83×#301311yescharacteristic
909C2C83×#305711yescharacteristic
910C2C83×#306311yescharacteristic
911C2C83×#320011yescharacteristic
912C2C83×#320111yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC83×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C22×#41×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#536×C83C2semidirect
2. C2×#468×C83C2semidirect
3. C2×#465×C83C2semidirect
4. C2×#448×C83C2semidirect
5. C2×#408×C83C2semidirect
7. C83×#2036C2semidirect
8. C83×#2035C2semidirect
9. C83×#2000C2semidirect
10. C83×#2000C2semidirect
11. C83×#1894C2semidirect
12. C83×#1892C2semidirect
13. C83×#1875C2semidirect
14. C83×#1854C2semidirect
15. C83×#1787C2semidirect
118. C22⋊Q8×C83D4semidirect
119. C22⋊Q8×C83D4semidirect
162. C22⋊C8×C83D4semidirect
445. #24396C83direct (N × H)
457. C2×#536C2×C83semidirect
458. C2×#468C2×C83semidirect
459. C2×#465C2×C83semidirect
460. C2×#448C2×C83semidirect
461. C2×#408C2×C83semidirect
463. #2036C2×C83semidirect
464. #2035C2×C83semidirect
465. #2000C2×C83semidirect
466. #2000C2×C83semidirect
467. #1894C2×C83semidirect
468. #1892C2×C83semidirect
469. #1875C2×C83semidirect
470. #1854C2×C83semidirect
471. #1787C2×C83semidirect
472. C83#24396direct (N × H)
575. C22⋊Q8D4×C83semidirect
576. C22⋊Q8D4×C83semidirect
619. C22⋊C8D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#536×C832
C2×#468×C832
C2×#465×C832
C2×#448×C832
C2×#408×C832
C83×#26152
C83×#20362
C83×#20352
C83×#20002
C83×#18942
C83×#18922
C83×#18752
C83×#18542
C83×#17872
#2439683