Finite Group Databasebeta

← C83×#24366 #35252190

Subgroups — C83×#24366 #35252190

Order 21248.

1662 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C83C211yesmaximal, characteristic, complemented
2C2×#463×C83C211yesmaximal, characteristic, complemented
3C2×#459×C83C211yesmaximal, characteristic, complemented
4C2×#447×C83C211yesmaximal, characteristic, complemented
5C83×#2431C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
7C83×#2055C211yesmaximal, characteristic, complemented
8C83×#2054C211yesmaximal, characteristic, complemented
9C83×#2012C211yesmaximal, characteristic, complemented
10C83×#2011C211yesmaximal, characteristic, complemented
11C83×#1895C211yesmaximal, characteristic, complemented
12C83×#1879C211yesmaximal, characteristic, complemented
13C83×#1877C211yesmaximal, characteristic, complemented
14C83×#1851C211yesmaximal, characteristic, complemented
15C83×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C83—24no—
19C2×AGL(1,ℤ/8)×C83—24no—
20C2×AGL(1,ℤ/8)×C83—24no—
21C22×SD16×C83C2211yescharacteristic
22C22×SD16×C83C2211yescharacteristic
23C22×D8×C83C2211yescharacteristic
24C22×D8×C83C2211yescharacteristic
25C22×D8×C83C2211yescharacteristic
26C22×D8×C83C2211yescharacteristic
27C22×M16×C83C2211yescharacteristic
28C2×#127×C83C2211yescharacteristic, complemented
29C2×#124×C83C2211yescharacteristic, complemented
30C2×#121×C83C2211yescharacteristic
31C2×C4×D4×C83C2211yescharacteristic
32C2×C4×D4×C83C2211yescharacteristic
33C22×C22⋊C4×C83—21no—
34#463×C83—24no—
35#459×C83—24no—
36#447×C83—24no—
37C2×C4⋊C8×C83C2211yescharacteristic, complemented
38C2×C4⋊C8×C83C2211yescharacteristic, complemented
39C2×#103×C83C2211yescharacteristic, complemented
40C2×#103×C83C2211yescharacteristic, complemented
41C2×#102×C83C2211yescharacteristic
42C2×#102×C83C2211yescharacteristic
43C2×#102×C83C2211yescharacteristic, complemented
44C2×#102×C83C2211yescharacteristic, complemented
45C2×#102×C83C2211yescharacteristic, complemented
46C2×#102×C83C2211yescharacteristic, complemented
47C2×C22⋊C8×C83C2211yescharacteristic
48#392×C83—21no—
49#392×C83—21no—
50#391×C83C2211yescharacteristic, complemented
51#390×C83C2211yescharacteristic
52#390×C83C2211yescharacteristic
53#390×C83C2211yescharacteristic, complemented
54#386×C83—21no—
55#386×C83—21no—
56#386×C83—21no—
57#386×C83—21no—
58#380×C83C2211yescharacteristic
59#379×C83—21no—
60C4×C22⋊C4×C83C2211yescharacteristic
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×C83D414yescomplemented
84C22×D4×C83C2311yescharacteristic
85C22×D4×C83C2311yescharacteristic
86C22×D4×C83C2311yescharacteristic
87C22×D4×C83C2311yescharacteristic
88C23×C4×C83—21no—
89C23×C4×C83—21no—
90C23×C4×C83—21no—
91C23×C4×C83C2311yescharacteristic
92AGL(1,ℤ/8)×C83—232no—
93C2×SD16×C83—22no—
94C2×SD16×C83—22no—
95C2×SD16×C83—22no—
96C2×SD16×C83—22no—
97C2×SD16×C83—22no—
98C2×SD16×C83D414yescomplemented
99C2×D8×C83—22no—
100C2×D8×C83—22no—
101C2×D8×C83—22no—
102C2×D8×C83—22no—
103C2×D8×C83—22no—
104C2×D8×C83—22no—
105C2×D8×C83—22no—
106C2×D8×C83—22no—
107C2×D8×C83—22no—
108C2×D8×C83—41no—
109C2×D8×C83—41no—
110C2×D8×C83D414yescomplemented
111C2×M16×C83—22no—
112C2×M16×C83—22no—
113C2×M16×C83—22no—
114C22×C8×C83C2311yescharacteristic
115C22×C8×C83C2311yescharacteristic
116C22×C8×C83C2311yescharacteristic
117C22×C8×C83C2311yescharacteristic
118#127×C83—22no—
119#127×C83—41no—
120#124×C83—22no—
121#124×C83—41no—
122#121×C83—22no—
123#121×C83—22no—
124C4×D4×C83—22no—
125C4×D4×C83—22no—
126C4×D4×C83—41no—
127C4×D4×C83—41no—
128C2×C4⋊C4×C83C2311yescharacteristic
129C2×C4⋊C4×C83C2311yescharacteristic
130C2×C4⋊C4×C83C2311yescharacteristic
131C2×C22⋊C4×C83—21no—
132C2×C22⋊C4×C83—21no—
133C2×C22⋊C4×C83—21no—
134C2×C22⋊C4×C83—21no—
135C2×C22⋊C4×C83—21no—
136C2×C22⋊C4×C83—21no—
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—44no—
144C2×C22⋊C4×C83D411yescharacteristic
145C2×C22⋊C4×C83D411yescharacteristic
146C2×C42×C83C2311yescharacteristic
147C2×C42×C83C2311yescharacteristic
148C4⋊C8×C83—22no—
149C4⋊C8×C83—22no—
150#103×C83—22no—
151#103×C83—41no—
152#102×C83—22no—
153#102×C83—22no—
154#102×C83—22no—
155#102×C83—22no—
156#102×C83—22no—
157#102×C83—41no—
158C22⋊C8×C83—22no—
159#95×C83—21no—
160#95×C83—21no—
161#95×C83—21no—
162#95×C83D411yescharacteristic
163#95×C83D411yescharacteristic
164C24×C83—21no—
165C24×C83—21no—
166C24×C83—21no—
167C24×C83—24no—
168C24×C83—21no—
169C24×C83—42no—
170C24×C83—42no—
171C24×C83—42no—
172C24×C83—42no—
173C24×C83—81no—
174C24×C83—81no—
175C24×C83C2×D411yescharacteristic
176#41×C83—28no—
177#41×C83—44no—
178#41×C83—44no—
179#41×C83—44no—
180C2×Q8×C83—21no—
181C2×Q8×C83—21no—
182C2×Q8×C83—21no—
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83C2×D412yes—
186C2×D4×C83—28no—
187C2×D4×C83—24no—
188C2×D4×C83—21no—
189C2×D4×C83—21no—
190C2×D4×C83—21no—
191C2×D4×C83—21no—
192C2×D4×C83—21no—
193C2×D4×C83—21no—
194C2×D4×C83—21no—
195C2×D4×C83—21no—
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—44no—
208C2×D4×C83—44no—
209C2×D4×C83—44no—
210C2×D4×C83—42no—
211C2×D4×C83—42no—
212C2×D4×C83—42no—
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—81no—
221C2×D4×C83—81no—
222C2×D4×C83—81no—
223C2×D4×C83—81no—
224C2×D4×C83C2×D412yes—
225C2×D4×C83C2×D412yes—
226C2×D4×C83C2×D412yes—
227C2×D4×C83C2×D412yes—
228C2×D4×C83C2×D412yes—
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—42no—
238C22×C4×C83—42no—
239C22×C4×C83—42no—
240C22×C4×C83—42no—
241C22×C4×C83—42no—
242C22×C4×C83—42no—
243C22×C4×C83—42no—
244C22×C4×C83—81no—
245C22×C4×C83—81no—
246C22×C4×C83C2×D411yescharacteristic
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2×D412yes—
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83#4112yes—
253C22×C4×C83C2411yescharacteristic
254SD16×C83—28no—
255SD16×C83—28no—
256D8×C83—28no—
257D8×C83—28no—
258D8×C83—44no—
259D8×C83—44no—
260M16×C83—28no—
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×C83—21no—
268C2×C8×C83—21no—
269C2×C8×C83—21no—
270C2×C8×C83—21no—
271C2×C8×C83C2×D412yes—
272C2×C8×C83C2×D412yes—
273C4⋊C4×C83—21no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—21no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83—21no—
278C4⋊C4×C83—21no—
279C22⋊C4×C83—22no—
280C22⋊C4×C83—41no—
281C22⋊C4×C83—42no—
282C22⋊C4×C83—42no—
283C22⋊C4×C83—42no—
284C22⋊C4×C83—42no—
285C22⋊C4×C83—42no—
286C22⋊C4×C83—42no—
287C22⋊C4×C83—42no—
288C22⋊C4×C83—42no—
289C22⋊C4×C83—81no—
290C22⋊C4×C83—81no—
291C22⋊C4×C83—81no—
292C22⋊C4×C83—81no—
293C42×C83—21no—
294C42×C83—21no—
295C42×C83—21no—
296C42×C83—21no—
297C23×C83—22no—
298C23×C83—22no—
299C23×C83—22no—
300C23×C83—21no—
301C23×C83—21no—
302C23×C83—21no—
303C23×C83—21no—
304C23×C83—21no—
305C23×C83—21no—
306C23×C83—22no—
307C23×C83—22no—
308C23×C83—48no—
309C23×C83—48no—
310C23×C83—41no—
311C23×C83—41no—
312C23×C83—41no—
313C23×C83—41no—
314C23×C83—41no—
315C23×C83—41no—
316C23×C83—41no—
317C23×C83—41no—
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—41no—
329C23×C83—41no—
330C23×C83—41no—
331C23×C83—41no—
332C23×C83—41no—
333C23×C83—84no—
334C23×C83—84no—
335C23×C83—84no—
336C23×C83—84no—
337C23×C83—84no—
338C23×C83#12112yes—
339C23×C83C22×D411yescharacteristic
340Q8×C83—22no—
341Q8×C83—22no—
342Q8×C83—41no—
343Q8×C83—41no—
344D4×C83—22no—
345D4×C83—22no—
346D4×C83—22no—
347D4×C83—22no—
348D4×C83—22no—
349D4×C83—22no—
350D4×C83—22no—
351D4×C83—48no—
352D4×C83—48no—
353D4×C83—41no—
354D4×C83—41no—
355D4×C83—41no—
356D4×C83—41no—
357D4×C83—41no—
358D4×C83—41no—
359D4×C83—41no—
360D4×C83—41no—
361D4×C83—84no—
362D4×C83—84no—
363D4×C83—84no—
364D4×C83#12014yes—
365C2×C4×C83—21no—
366C2×C4×C83—21no—
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—21no—
376C2×C4×C83—22no—
377C2×C4×C83—21no—
378C2×C4×C83—21no—
379C2×C4×C83—21no—
380C2×C4×C83—21no—
381C2×C4×C83—21no—
382C2×C4×C83—21no—
383C2×C4×C83—48no—
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—41no—
392C2×C4×C83—41no—
393C2×C4×C83—41no—
394C2×C4×C83—41no—
395C2×C4×C83—84no—
396C2×C4×C83—84no—
397C2×C4×C83#12112yes—
398C2×C4×C83AGL(1,ℤ/8)12yescomplemented
399C2×C4×C83C22×D411yescharacteristic
400C2×C4×C83C22×D411yescharacteristic
401C2×C4×C83C22×D411yescharacteristic
402C2×C4×C83C2×#4111yescharacteristic
403C2×C4×C83H(5,𝔽2)11yescharacteristic
404C2×C4×C83H(5,𝔽2)11yescharacteristic
405C8×C83—22no—
406C8×C83—22no—
407C8×C83—41no—
408C8×C83—41no—
409C22×C83—22no—
410C22×C83—24no—
411C22×C83—22no—
412C22×C83—22no—
413C22×C83—42no—
414C22×C83—41no—
415C22×C83—41no—
416C22×C83—42no—
417C22×C83—41no—
418C22×C83—42no—
419C22×C83—42no—
420C22×C83—41no—
421C22×C83—42no—
422C22×C83—42no—
423C22×C83—42no—
424C22×C83—42no—
425C22×C83—42no—
426C22×C83—42no—
427C22×C83—42no—
428C22×C83—42no—
429C22×C83—816no—
430C22×C83—81no—
431C22×C83—81no—
432C22×C83—81no—
433C22×C83—81no—
434C22×C83—81no—
435C22×C83—81no—
436C22×C83—81no—
437C22×C83—81no—
438C22×C83—81no—
439C22×C83—81no—
440C22×C83—81no—
441C22×C83—81no—
442C22×C83—81no—
443C22×C83—81no—
444C22×C83—81no—
445C22×C83C2×#12111yescharacteristic
446C22×C83D4211yescharacteristic
447C22×C83D4211yescharacteristic
448C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
449C22×C83#57511yescharacteristic
450C22×C83#57611yescharacteristic
451C22×C83#57611yescharacteristic
452C4×C83—22no—
453C4×C83—22no—
454C4×C83—42no—
455C4×C83—41no—
456C4×C83—41no—
457C4×C83—41no—
458C4×C83—81no—
459C4×C83—81no—
460C4×C83—81no—
461C4×C83C2×#12011yescharacteristic
462C4×C83#53411yescharacteristic
463C4×C83#54611yescharacteristic
464C4×C83#54611yescharacteristic
465#24366C8311yesmaximal, characteristic, direct product factor, Sylow
466C2×C83—42no—
467C2×C83—44no—
468C2×C83—82no—
469C2×C83—82no—
470C2×C83—161no—
471C2×C83#241011yescharacteristic
472C2×C83#303611yescharacteristic
473C2×C83#304111yescharacteristic
474C2×C83#326411yescharacteristic
475C2×C83#326811yescharacteristic
476C2×C83#327311yescharacteristic
477C2×C83#327411yescharacteristic
478C22×AGL(1,ℤ/8)C2×C8311yescharacteristic, complemented
479C2×#463C2×C8311yescharacteristic, complemented
480C2×#459C2×C8311yescharacteristic, complemented
481C2×#447C2×C8311yescharacteristic, complemented
482#2431C2×C8311yescharacteristic, complemented
483D4×C22⋊C4C2×C8311yescharacteristic, complemented
484#2055C2×C8311yescharacteristic, complemented
485#2054C2×C8311yescharacteristic, complemented
486#2012C2×C8311yescharacteristic, complemented
487#2011C2×C8311yescharacteristic, complemented
488#1895C2×C8311yescharacteristic, complemented
489#1879C2×C8311yescharacteristic, complemented
490#1877C2×C8311yescharacteristic, complemented
491#1851C2×C8311yescharacteristic, complemented
492#1788C2×C8311yescharacteristic, complemented
493C83#2436611yescharacteristic, direct product factor, Sylow
494C22×#41C22×C8311yescharacteristic
495C23×D4C22×C8311yescharacteristic
496C2×AGL(1,ℤ/8)—24no—
497C2×AGL(1,ℤ/8)—24no—
498C2×AGL(1,ℤ/8)—24no—
499C22×SD16C22×C8311yescharacteristic
500C22×SD16C22×C8311yescharacteristic
501C22×D8C22×C8311yescharacteristic
502C22×D8C22×C8311yescharacteristic
503C22×D8C22×C8311yescharacteristic
504C22×D8C22×C8311yescharacteristic
505C22×M16C22×C8311yescharacteristic
506C2×#127C22×C8311yescharacteristic, complemented
507C2×#124C22×C8311yescharacteristic, complemented
508C2×#121C22×C8311yescharacteristic
509C2×C4×D4C22×C8311yescharacteristic
510C2×C4×D4C22×C8311yescharacteristic
511C22×C22⋊C4—21no—
512#463—24no—
513#459—24no—
514#447—24no—
515C2×C4⋊C8C22×C8311yescharacteristic, complemented
516C2×C4⋊C8C22×C8311yescharacteristic, complemented
517C2×#103C22×C8311yescharacteristic, complemented
518C2×#103C22×C8311yescharacteristic, complemented
519C2×#102C22×C8311yescharacteristic
520C2×#102C22×C8311yescharacteristic
521C2×#102C22×C8311yescharacteristic, complemented
522C2×#102C22×C8311yescharacteristic, complemented
523C2×#102C22×C8311yescharacteristic, complemented
524C2×#102C22×C8311yescharacteristic, complemented
525C2×C22⋊C8C22×C8311yescharacteristic
526#392—21no—
527#392—21no—
528#391C22×C8311yescharacteristic, complemented
529#390C22×C8311yescharacteristic
530#390C22×C8311yescharacteristic
531#390C22×C8311yescharacteristic, complemented
532#386—21no—
533#386—21no—
534#386—21no—
535#386—21no—
536#380C22×C8311yescharacteristic
537#379—21no—
538C4×C22⋊C4C22×C8311yescharacteristic
539#340C22×C8311yescharacteristic, complemented
540#340C22×C8311yescharacteristic, complemented
541#336C22×C8311yescharacteristic, complemented
542#336C22×C8311yescharacteristic, complemented
543C25—21no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—41no—
549C2×#41—41no—
550C22×Q8C23×C8311yescharacteristic
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4D4×C8314yescomplemented
562C22×D4C23×C8311yescharacteristic
563C22×D4C23×C8311yescharacteristic
564C22×D4C23×C8311yescharacteristic
565C22×D4C23×C8311yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C8311yescharacteristic
570AGL(1,ℤ/8)—232no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16D4×C8314yescomplemented
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8D4×C8314yescomplemented
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C22×C8C23×C8311yescharacteristic
593C22×C8C23×C8311yescharacteristic
594C22×C8C23×C8311yescharacteristic
595C22×C8C23×C8311yescharacteristic
596#127—22no—
597#127—41no—
598#124—22no—
599#124—41no—
600#121—22no—
601#121—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C2×C4⋊C4C23×C8311yescharacteristic
607C2×C4⋊C4C23×C8311yescharacteristic
608C2×C4⋊C4C23×C8311yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4D4×C8311yescharacteristic
623C2×C22⋊C4D4×C8311yescharacteristic
624C2×C42C23×C8311yescharacteristic
625C2×C42C23×C8311yescharacteristic
626C4⋊C8—22no—
627C4⋊C8—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95D4×C8311yescharacteristic
641#95D4×C8311yescharacteristic
642C24—21no—
643C24—21no—
644C24—21no—
645C24—24no—
646C24—21no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—81no—
652C24—81no—
653C24C2×D4×C8311yescharacteristic
654#41—28no—
655#41—44no—
656#41—44no—
657#41—44no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8C2×D4×C8312yes—
664C2×D4—28no—
665C2×D4—24no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C2×D4×C8312yes—
703C2×D4C2×D4×C8312yes—
704C2×D4C2×D4×C8312yes—
705C2×D4C2×D4×C8312yes—
706C2×D4C2×D4×C8312yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—81no—
724C22×C4C2×D4×C8311yescharacteristic
725C22×C4C2×D4×C8311yescharacteristic
726C22×C4C2×D4×C8311yescharacteristic
727C22×C4C2×D4×C8311yescharacteristic
728C22×C4C2×D4×C8312yes—
729C22×C4C2×D4×C8311yescharacteristic
730C22×C4#41×C8312yes—
731C22×C4C24×C8311yescharacteristic
732SD16—28no—
733SD16—28no—
734D8—28no—
735D8—28no—
736D8—44no—
737D8—44no—
738M16—28no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8C2×D4×C8312yes—
750C2×C8C2×D4×C8312yes—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C22⋊C4—81no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—48no—
787C23—48no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23#121×C8312yes—
817C23C22×D4×C8311yescharacteristic
818Q8—22no—
819Q8—22no—
820Q8—41no—
821Q8—41no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#120×C8314yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4—84no—
875C2×C4#121×C8312yes—
876C2×C4AGL(1,ℤ/8)×C8312yescomplemented
877C2×C4C22×D4×C8311yescharacteristic
878C2×C4C22×D4×C8311yescharacteristic
879C2×C4C22×D4×C8311yescharacteristic
880C2×C4C2×#41×C8311yescharacteristic
881C2×C4H(5,𝔽2)×C8311yescharacteristic
882C2×C4H(5,𝔽2)×C8311yescharacteristic
883C8—22no—
884C8—22no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—24no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#121×C8311yescharacteristic
924C22D42×C8311yescharacteristic
925C22D42×C8311yescharacteristic
926C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
927C22#575×C8311yescharacteristic
928C22#576×C8311yescharacteristic
929C22#576×C8311yescharacteristic
930C4—22no—
931C4—22no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C2×#120×C8311yescharacteristic
940C4#534×C8311yescharacteristic
941C4#546×C8311yescharacteristic
942C4#546×C8311yescharacteristic
943C2—42no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2—161no—
948C2C83×#241011yescharacteristic
949C2C83×#303611yescharacteristic
950C2C83×#304111yescharacteristic
951C2C83×#326411yescharacteristic
952C2C83×#326811yescharacteristic
953C2C83×#327311yescharacteristic
954C2C83×#327411yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C4×C22⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C83C2semidirect
2. C2×#463×C83C2semidirect
3. C2×#459×C83C2semidirect
4. C2×#447×C83C2semidirect
5. C83×#2431C2semidirect
6. D4×C22⋊C4×C83C2semidirect
7. C83×#2055C2semidirect
8. C83×#2054C2semidirect
9. C83×#2012C2semidirect
10. C83×#2011C2semidirect
11. C83×#1895C2semidirect
12. C83×#1879C2semidirect
13. C83×#1877C2semidirect
14. C83×#1851C2semidirect
15. C83×#1788C2semidirect
28. C2×#127×C83C22semidirect
29. C2×#124×C83C22semidirect
37. C2×C4⋊C8×C83C22semidirect
38. C2×C4⋊C8×C83C22semidirect
39. C2×#103×C83C22semidirect
40. C2×#103×C83C22semidirect
43. C2×#102×C83C22semidirect
44. C2×#102×C83C22semidirect
45. C2×#102×C83C22semidirect
46. C2×#102×C83C22semidirect
50. #391×C83C22semidirect
53. #390×C83C22semidirect
61. #340×C83C22semidirect
62. #340×C83C22semidirect
63. #336×C83C22semidirect
64. #336×C83C22semidirect
83. C22×D4×C83D4semidirect
98. C2×SD16×C83D4semidirect
110. C2×D8×C83D4semidirect
398. C2×C4×C83AGL(1,ℤ/8)semidirect
465. #24366C83direct (N × H)
478. C22×AGL(1,ℤ/8)C2×C83semidirect
479. C2×#463C2×C83semidirect
480. C2×#459C2×C83semidirect
481. C2×#447C2×C83semidirect
482. #2431C2×C83semidirect
483. D4×C22⋊C4C2×C83semidirect
484. #2055C2×C83semidirect
485. #2054C2×C83semidirect
486. #2012C2×C83semidirect
487. #2011C2×C83semidirect
488. #1895C2×C83semidirect
489. #1879C2×C83semidirect
490. #1877C2×C83semidirect
491. #1851C2×C83semidirect
492. #1788C2×C83semidirect
493. C83#24366direct (N × H)
506. C2×#127C22×C83semidirect
507. C2×#124C22×C83semidirect
515. C2×C4⋊C8C22×C83semidirect
516. C2×C4⋊C8C22×C83semidirect
517. C2×#103C22×C83semidirect
518. C2×#103C22×C83semidirect
521. C2×#102C22×C83semidirect
522. C2×#102C22×C83semidirect
523. C2×#102C22×C83semidirect
524. C2×#102C22×C83semidirect
528. #391C22×C83semidirect
531. #390C22×C83semidirect
539. #340C22×C83semidirect
540. #340C22×C83semidirect
541. #336C22×C83semidirect
542. #336C22×C83semidirect
561. C22×D4D4×C83semidirect
576. C2×SD16D4×C83semidirect
588. C2×D8D4×C83semidirect
876. C2×C4AGL(1,ℤ/8)×C83semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C832
C2×#463×C832
C2×#459×C832
C2×#447×C832
C83×#24312
D4×C22⋊C4×C832
C83×#20552
C83×#20542
C83×#20122
C83×#20112
C83×#18952
C83×#18792
C83×#18772
C83×#18512
C83×#17882
#2436683