Finite Group Databasebeta

← C83×#25172 #35252996

Subgroups — C83×#25172 #35252996

Order 21248.

1310 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C83C211yesmaximal, characteristic, complemented
2C2×#450×C83C211yesmaximal, characteristic, complemented
3C2×#447×C83C211yesmaximal, characteristic
4C2×#442×C83C211yesmaximal, characteristic, complemented
5C83×#2427C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
7C83×#2065C211yesmaximal, characteristic, complemented
8C83×#2035C211yesmaximal, characteristic, complemented
9C83×#2033C211yesmaximal, characteristic, complemented
10C83×#2012C211yesmaximal, characteristic, complemented
11C83×#1973C211yesmaximal, characteristic, complemented
12C83×#1924C211yesmaximal, characteristic, complemented
13C83×#1879C211yesmaximal, characteristic, complemented
14C83×#1877C211yesmaximal, characteristic, complemented
15C83×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C83C2211yescharacteristic
17C22×SD16×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic
19C22×D8×C83C2211yescharacteristic
20C22×D8×C83C2211yescharacteristic
21C2×#124×C83C2211yescharacteristic, complemented
22C2×C22⋊Q8×C83C2211yescharacteristic
23C2×#121×C83C2211yescharacteristic
24C2×C4×D4×C83C2211yescharacteristic
25C2×C4×D4×C83C2211yescharacteristic
26C2×C4×D4×C83C2211yescharacteristic, complemented
27C22×C22⋊C4×C83—21no—
28#463×C83—24no—
29#450×C83—24no—
30#447×C83—24no—
31#442×C83—24no—
32C2×#107×C83C2211yescharacteristic, complemented
33C2×#106×C83C2211yescharacteristic, complemented
34C2×C4⋊C8×C83C2211yescharacteristic, complemented
35C2×#103×C83C2211yescharacteristic, complemented
36C2×#103×C83C2211yescharacteristic, complemented
37C2×#102×C83C2211yescharacteristic
38C2×#102×C83C2211yescharacteristic
39C2×#102×C83C2211yescharacteristic
40C2×#102×C83C2211yescharacteristic
41C2×#102×C83C2211yescharacteristic, complemented
42C2×#102×C83C2211yescharacteristic, complemented
43C2×C22⋊C8×C83C2211yescharacteristic
44C2×C22⋊C8×C83C2211yescharacteristic
45C2×#97×C83C2211yescharacteristic, complemented
46#397×C83—21no—
47#394×C83—21no—
48#391×C83C2211yescharacteristic, complemented
49#390×C83C2211yescharacteristic
50#390×C83C2211yescharacteristic
51#389×C83C2211yescharacteristic, complemented
52#386×C83—21no—
53#386×C83—21no—
54#386×C83—21no—
55#380×C83—21no—
56#380×C83C2211yescharacteristic
57#379×C83—21no—
58C4×C22⋊C4×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic, complemented
60#340×C83C2211yescharacteristic, complemented
61#336×C83C2211yescharacteristic, complemented
62#336×C83C2211yescharacteristic, complemented
63C25×C83—21no—
64C22×Q8×C83C2311yescharacteristic
65C22×D4×C83—22no—
66C22×D4×C83—22no—
67C22×D4×C83—22no—
68C22×D4×C83—22no—
69C22×D4×C83—21no—
70C22×D4×C83—21no—
71C22×D4×C83—41no—
72C22×D4×C83—41no—
73C22×D4×C83C2311yescharacteristic
74C22×D4×C83C2311yescharacteristic
75C22×D4×C83C2311yescharacteristic
76C23×C4×C83—21no—
77C23×C4×C83—21no—
78C23×C4×C83—21no—
79C23×C4×C83C2311yescharacteristic
80C2×SD16×C83—22no—
81C2×SD16×C83—22no—
82C2×SD16×C83—22no—
83C2×SD16×C83—22no—
84C2×SD16×C83—22no—
85C2×SD16×C83—41no—
86C2×D8×C83—22no—
87C2×D8×C83—22no—
88C2×D8×C83—22no—
89C2×D8×C83—22no—
90C2×D8×C83—41no—
91C2×D8×C83D414yes—
92C22×C8×C83C2311yescharacteristic
93C22×C8×C83C2311yescharacteristic
94C22×C8×C83C2311yescharacteristic
95C22×C8×C83C2311yescharacteristic
96#124×C83—22no—
97#124×C83—41no—
98C22⋊Q8×C83—22no—
99C22⋊Q8×C83—41no—
100#121×C83—22no—
101#121×C83—41no—
102C4×D4×C83—22no—
103C4×D4×C83—22no—
104C4×D4×C83—22no—
105C4×D4×C83—41no—
106C4×D4×C83—41no—
107C4×D4×C83—41no—
108C2×C4⋊C4×C83—21no—
109C2×C4⋊C4×C83—21no—
110C2×C4⋊C4×C83C2311yescharacteristic
111C2×C4⋊C4×C83C2311yescharacteristic
112C2×C4⋊C4×C83C2311yescharacteristic
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C22⋊C4×C83—21no—
115C2×C22⋊C4×C83—21no—
116C2×C22⋊C4×C83—21no—
117C2×C22⋊C4×C83—21no—
118C2×C22⋊C4×C83—21no—
119C2×C22⋊C4×C83—21no—
120C2×C22⋊C4×C83—21no—
121C2×C22⋊C4×C83—21no—
122C2×C22⋊C4×C83—21no—
123C2×C22⋊C4×C83—21no—
124C2×C22⋊C4×C83—21no—
125C2×C22⋊C4×C83—21no—
126C2×C22⋊C4×C83—44no—
127C2×C22⋊C4×C83D411yescharacteristic
128C2×C22⋊C4×C83D411yescharacteristic
129C2×C42×C83C2311yescharacteristic
130C2×C42×C83C2311yescharacteristic
131#107×C83—41no—
132#106×C83—22no—
133C4⋊C8×C83—22no—
134#103×C83—22no—
135#103×C83—41no—
136#102×C83—22no—
137#102×C83—22no—
138#102×C83—22no—
139#102×C83—22no—
140#102×C83—22no—
141#102×C83D414yescomplemented
142C22⋊C8×C83—22no—
143C22⋊C8×C83—22no—
144#97×C83—22no—
145#95×C83—21no—
146#95×C83—21no—
147#95×C83—21no—
148#95×C83—21no—
149#95×C83D411yescharacteristic
150#95×C83D411yescharacteristic
151C24×C83—21no—
152C24×C83—24no—
153C24×C83—21no—
154C24×C83—21no—
155C24×C83—42no—
156C24×C83—42no—
157C24×C83—42no—
158C24×C83—42no—
159C24×C83—81no—
160C24×C83—81no—
161C24×C83C2×D411yescharacteristic
162C2×Q8×C83—21no—
163C2×Q8×C83—21no—
164C2×Q8×C83—21no—
165C2×Q8×C83—21no—
166C2×Q8×C83—21no—
167C2×Q8×C83—21no—
168C2×D4×C83—24no—
169C2×D4×C83—21no—
170C2×D4×C83—21no—
171C2×D4×C83—21no—
172C2×D4×C83—21no—
173C2×D4×C83—21no—
174C2×D4×C83—21no—
175C2×D4×C83—21no—
176C2×D4×C83—21no—
177C2×D4×C83—21no—
178C2×D4×C83—21no—
179C2×D4×C83—21no—
180C2×D4×C83—21no—
181C2×D4×C83—21no—
182C2×D4×C83—42no—
183C2×D4×C83—42no—
184C2×D4×C83—44no—
185C2×D4×C83—44no—
186C2×D4×C83—44no—
187C2×D4×C83—44no—
188C2×D4×C83—42no—
189C2×D4×C83—42no—
190C2×D4×C83—81no—
191C2×D4×C83C2×D412yes—
192C2×D4×C83C2×D412yes—
193C2×D4×C83C2×D412yes—
194C2×D4×C83#4112yes—
195C2×D4×C83#4112yes—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—42no—
208C22×C4×C83—42no—
209C22×C4×C83—42no—
210C22×C4×C83—42no—
211C22×C4×C83—42no—
212C22×C4×C83—42no—
213C22×C4×C83—81no—
214C22×C4×C83—81no—
215C22×C4×C83—81no—
216C22×C4×C83C2×D411yescharacteristic
217C22×C4×C83C2×D411yescharacteristic
218C22×C4×C83C2×D411yescharacteristic
219C22×C4×C83C2×D411yescharacteristic
220C22×C4×C83C2×D411yescharacteristic
221C22×C4×C83C2411yescharacteristic
222SD16×C83—44no—
223SD16×C83—44no—
224D8×C83—28no—
225D8×C83—44no—
226C2×C8×C83—21no—
227C2×C8×C83—21no—
228C2×C8×C83—21no—
229C2×C8×C83—21no—
230C2×C8×C83—21no—
231C2×C8×C83—21no—
232C2×C8×C83—21no—
233C2×C8×C83—21no—
234C2×C8×C83—21no—
235C2×C8×C83—21no—
236C2×C8×C83C2×D412yes—
237C2×C8×C83C2×D412yes—
238C4⋊C4×C83—21no—
239C4⋊C4×C83—21no—
240C4⋊C4×C83—21no—
241C4⋊C4×C83—21no—
242C4⋊C4×C83—21no—
243C4⋊C4×C83—21no—
244C4⋊C4×C83—21no—
245C4⋊C4×C83—42no—
246C4⋊C4×C83—81no—
247C4⋊C4×C83C2×D412yes—
248C22⋊C4×C83—22no—
249C22⋊C4×C83—41no—
250C22⋊C4×C83—42no—
251C22⋊C4×C83—42no—
252C22⋊C4×C83—42no—
253C22⋊C4×C83—42no—
254C22⋊C4×C83—42no—
255C22⋊C4×C83—42no—
256C22⋊C4×C83—42no—
257C22⋊C4×C83—42no—
258C22⋊C4×C83—42no—
259C22⋊C4×C83—42no—
260C22⋊C4×C83—81no—
261C22⋊C4×C83—81no—
262C42×C83—21no—
263C42×C83—21no—
264C42×C83—21no—
265C42×C83—21no—
266C23×C83—21no—
267C23×C83—22no—
268C23×C83—21no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—21no—
272C23×C83—21no—
273C23×C83—21no—
274C23×C83—21no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—48no—
278C23×C83—48no—
279C23×C83—41no—
280C23×C83—41no—
281C23×C83—41no—
282C23×C83—41no—
283C23×C83—41no—
284C23×C83—41no—
285C23×C83—41no—
286C23×C83—41no—
287C23×C83—41no—
288C23×C83—41no—
289C23×C83—41no—
290C23×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83—41no—
295C23×C83—84no—
296C23×C83—84no—
297C23×C83—84no—
298C23×C83—84no—
299C23×C83—84no—
300C23×C83AGL(1,ℤ/8)12yes—
301C23×C83C22×D411yescharacteristic
302Q8×C83—41no—
303Q8×C83—41no—
304Q8×C83—41no—
305Q8×C83—41no—
306D4×C83—22no—
307D4×C83—22no—
308D4×C83—22no—
309D4×C83—22no—
310D4×C83—22no—
311D4×C83—22no—
312D4×C83—22no—
313D4×C83—48no—
314D4×C83—41no—
315D4×C83—41no—
316D4×C83—41no—
317D4×C83—41no—
318D4×C83—84no—
319D4×C83#12114yes—
320C2×C4×C83—21no—
321C2×C4×C83—21no—
322C2×C4×C83—21no—
323C2×C4×C83—21no—
324C2×C4×C83—21no—
325C2×C4×C83—22no—
326C2×C4×C83—21no—
327C2×C4×C83—21no—
328C2×C4×C83—21no—
329C2×C4×C83—21no—
330C2×C4×C83—21no—
331C2×C4×C83—21no—
332C2×C4×C83—21no—
333C2×C4×C83—21no—
334C2×C4×C83—21no—
335C2×C4×C83—21no—
336C2×C4×C83—41no—
337C2×C4×C83—41no—
338C2×C4×C83—41no—
339C2×C4×C83—41no—
340C2×C4×C83—41no—
341C2×C4×C83—41no—
342C2×C4×C83—41no—
343C2×C4×C83—41no—
344C2×C4×C83—41no—
345C2×C4×C83—41no—
346C2×C4×C83—41no—
347C2×C4×C83—41no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—41no—
351C2×C4×C83—41no—
352C2×C4×C83—41no—
353C2×C4×C83—41no—
354C2×C4×C83—84no—
355C2×C4×C83—84no—
356C2×C4×C83—84no—
357C2×C4×C83C22×D411yescharacteristic
358C2×C4×C83C22×D411yescharacteristic
359C2×C4×C83C2×#4111yescharacteristic
360C2×C4×C83C2×#4111yescharacteristic
361C2×C4×C83H(5,𝔽2)11yescharacteristic
362C2×C4×C83H(5,𝔽2)11yescharacteristic
363C8×C83—22no—
364C8×C83—22no—
365C8×C83—41no—
366C8×C83—41no—
367C22×C83—22no—
368C22×C83—24no—
369C22×C83—22no—
370C22×C83—22no—
371C22×C83—42no—
372C22×C83—41no—
373C22×C83—42no—
374C22×C83—41no—
375C22×C83—42no—
376C22×C83—42no—
377C22×C83—41no—
378C22×C83—42no—
379C22×C83—41no—
380C22×C83—42no—
381C22×C83—42no—
382C22×C83—42no—
383C22×C83—42no—
384C22×C83—42no—
385C22×C83—42no—
386C22×C83—42no—
387C22×C83—816no—
388C22×C83—81no—
389C22×C83—81no—
390C22×C83—81no—
391C22×C83—81no—
392C22×C83—81no—
393C22×C83—81no—
394C22×C83—81no—
395C22×C83—81no—
396C22×C83#52511yescharacteristic
397C22×C83D4211yescharacteristic
398C22×C83D4211yescharacteristic
399C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C83#57511yescharacteristic
401C22×C83#57611yescharacteristic
402C22×C83#57711yescharacteristic
403C4×C83—41no—
404C4×C83—41no—
405C4×C83—41no—
406C4×C83—41no—
407C4×C83—41no—
408C4×C83—42no—
409C4×C83—81no—
410C4×C83—81no—
411C4×C83—81no—
412C4×C83—81no—
413C4×C83C2×#12111yescharacteristic
414C4×C83#53811yescharacteristic
415C4×C83#54611yescharacteristic
416C4×C83#54611yescharacteristic
417#25172C8311yesmaximal, characteristic, direct product factor, Sylow
418C2×C83—42no—
419C2×C83—44no—
420C2×C83—82no—
421C2×C83—82no—
422C2×C83#242411yescharacteristic
423C2×C83#311411yescharacteristic
424C2×C83#311811yescharacteristic
425C2×C83#326411yescharacteristic
426C2×C83#326511yescharacteristic
427C2×C83#326711yescharacteristic
428C2×C83#327311yescharacteristic
429C2×#463C2×C8311yescharacteristic, complemented
430C2×#450C2×C8311yescharacteristic, complemented
431C2×#447C2×C8311yescharacteristic
432C2×#442C2×C8311yescharacteristic, complemented
433#2427C2×C8311yescharacteristic, complemented
434D4×C22⋊C4C2×C8311yescharacteristic, complemented
435#2065C2×C8311yescharacteristic, complemented
436#2035C2×C8311yescharacteristic, complemented
437#2033C2×C8311yescharacteristic, complemented
438#2012C2×C8311yescharacteristic, complemented
439#1973C2×C8311yescharacteristic, complemented
440#1924C2×C8311yescharacteristic, complemented
441#1879C2×C8311yescharacteristic, complemented
442#1877C2×C8311yescharacteristic, complemented
443#1862C2×C8311yescharacteristic, complemented
444C83#2517211yescharacteristic, direct product factor, Sylow
445C23×D4C22×C8311yescharacteristic
446C22×SD16C22×C8311yescharacteristic
447C22×SD16C22×C8311yescharacteristic
448C22×D8C22×C8311yescharacteristic
449C22×D8C22×C8311yescharacteristic
450C2×#124C22×C8311yescharacteristic, complemented
451C2×C22⋊Q8C22×C8311yescharacteristic
452C2×#121C22×C8311yescharacteristic
453C2×C4×D4C22×C8311yescharacteristic
454C2×C4×D4C22×C8311yescharacteristic
455C2×C4×D4C22×C8311yescharacteristic, complemented
456C22×C22⋊C4—21no—
457#463—24no—
458#450—24no—
459#447—24no—
460#442—24no—
461C2×#107C22×C8311yescharacteristic, complemented
462C2×#106C22×C8311yescharacteristic, complemented
463C2×C4⋊C8C22×C8311yescharacteristic, complemented
464C2×#103C22×C8311yescharacteristic, complemented
465C2×#103C22×C8311yescharacteristic, complemented
466C2×#102C22×C8311yescharacteristic
467C2×#102C22×C8311yescharacteristic
468C2×#102C22×C8311yescharacteristic
469C2×#102C22×C8311yescharacteristic
470C2×#102C22×C8311yescharacteristic, complemented
471C2×#102C22×C8311yescharacteristic, complemented
472C2×C22⋊C8C22×C8311yescharacteristic
473C2×C22⋊C8C22×C8311yescharacteristic
474C2×#97C22×C8311yescharacteristic, complemented
475#397—21no—
476#394—21no—
477#391C22×C8311yescharacteristic, complemented
478#390C22×C8311yescharacteristic
479#390C22×C8311yescharacteristic
480#389C22×C8311yescharacteristic, complemented
481#386—21no—
482#386—21no—
483#386—21no—
484#380—21no—
485#380C22×C8311yescharacteristic
486#379—21no—
487C4×C22⋊C4C22×C8311yescharacteristic
488#340C22×C8311yescharacteristic, complemented
489#340C22×C8311yescharacteristic, complemented
490#336C22×C8311yescharacteristic, complemented
491#336C22×C8311yescharacteristic, complemented
492C25—21no—
493C22×Q8C23×C8311yescharacteristic
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C23×C8311yescharacteristic
503C22×D4C23×C8311yescharacteristic
504C22×D4C23×C8311yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C23×C8311yescharacteristic
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8D4×C8314yes—
521C22×C8C23×C8311yescharacteristic
522C22×C8C23×C8311yescharacteristic
523C22×C8C23×C8311yescharacteristic
524C22×C8C23×C8311yescharacteristic
525#124—22no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529#121—22no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4C23×C8311yescharacteristic
540C2×C4⋊C4C23×C8311yescharacteristic
541C2×C4⋊C4C23×C8311yescharacteristic
542C2×C4⋊C4C23×C8311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C8311yescharacteristic
557C2×C22⋊C4D4×C8311yescharacteristic
558C2×C42C23×C8311yescharacteristic
559C2×C42C23×C8311yescharacteristic
560#107—41no—
561#106—22no—
562C4⋊C8—22no—
563#103—22no—
564#103—41no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102D4×C8314yescomplemented
571C22⋊C8—22no—
572C22⋊C8—22no—
573#97—22no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95D4×C8311yescharacteristic
579#95D4×C8311yescharacteristic
580C24—21no—
581C24—24no—
582C24—21no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C8311yescharacteristic
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C8312yes—
621C2×D4C2×D4×C8312yes—
622C2×D4C2×D4×C8312yes—
623C2×D4#41×C8312yes—
624C2×D4#41×C8312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4C2×D4×C8311yescharacteristic
646C22×C4C2×D4×C8311yescharacteristic
647C22×C4C2×D4×C8311yescharacteristic
648C22×C4C2×D4×C8311yescharacteristic
649C22×C4C2×D4×C8311yescharacteristic
650C22×C4C24×C8311yescharacteristic
651SD16—44no—
652SD16—44no—
653D8—28no—
654D8—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8C2×D4×C8312yes—
666C2×C8C2×D4×C8312yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—81no—
676C4⋊C4C2×D4×C8312yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—48no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23AGL(1,ℤ/8)×C8312yes—
730C23C22×D4×C8311yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4#121×C8314yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4C22×D4×C8311yescharacteristic
787C2×C4C22×D4×C8311yescharacteristic
788C2×C4C2×#41×C8311yescharacteristic
789C2×C4C2×#41×C8311yescharacteristic
790C2×C4H(5,𝔽2)×C8311yescharacteristic
791C2×C4H(5,𝔽2)×C8311yescharacteristic
792C8—22no—
793C8—22no—
794C8—41no—
795C8—41no—
796C22—22no—
797C22—24no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—816no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22#525×C8311yescharacteristic
826C22D42×C8311yescharacteristic
827C22D42×C8311yescharacteristic
828C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
829C22#575×C8311yescharacteristic
830C22#576×C8311yescharacteristic
831C22#577×C8311yescharacteristic
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—42no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4C2×#121×C8311yescharacteristic
843C4#538×C8311yescharacteristic
844C4#546×C8311yescharacteristic
845C4#546×C8311yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—82no—
850C2C83×#242411yescharacteristic
851C2C83×#311411yescharacteristic
852C2C83×#311811yescharacteristic
853C2C83×#326411yescharacteristic
854C2C83×#326511yescharacteristic
855C2C83×#326711yescharacteristic
856C2C83×#327311yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×#447×C83C2
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. C2×#463×C83C2semidirect
2. C2×#450×C83C2semidirect
4. C2×#442×C83C2semidirect
5. C83×#2427C2semidirect
6. D4×C22⋊C4×C83C2semidirect
7. C83×#2065C2semidirect
8. C83×#2035C2semidirect
9. C83×#2033C2semidirect
10. C83×#2012C2semidirect
11. C83×#1973C2semidirect
12. C83×#1924C2semidirect
13. C83×#1879C2semidirect
14. C83×#1877C2semidirect
15. C83×#1862C2semidirect
21. C2×#124×C83C22semidirect
26. C2×C4×D4×C83C22semidirect
32. C2×#107×C83C22semidirect
33. C2×#106×C83C22semidirect
34. C2×C4⋊C8×C83C22semidirect
35. C2×#103×C83C22semidirect
36. C2×#103×C83C22semidirect
41. C2×#102×C83C22semidirect
42. C2×#102×C83C22semidirect
45. C2×#97×C83C22semidirect
48. #391×C83C22semidirect
51. #389×C83C22semidirect
59. #340×C83C22semidirect
60. #340×C83C22semidirect
61. #336×C83C22semidirect
62. #336×C83C22semidirect
141. #102×C83D4semidirect
417. #25172C83direct (N × H)
429. C2×#463C2×C83semidirect
430. C2×#450C2×C83semidirect
432. C2×#442C2×C83semidirect
433. #2427C2×C83semidirect
434. D4×C22⋊C4C2×C83semidirect
435. #2065C2×C83semidirect
436. #2035C2×C83semidirect
437. #2033C2×C83semidirect
438. #2012C2×C83semidirect
439. #1973C2×C83semidirect
440. #1924C2×C83semidirect
441. #1879C2×C83semidirect
442. #1877C2×C83semidirect
443. #1862C2×C83semidirect
444. C83#25172direct (N × H)
450. C2×#124C22×C83semidirect
455. C2×C4×D4C22×C83semidirect
461. C2×#107C22×C83semidirect
462. C2×#106C22×C83semidirect
463. C2×C4⋊C8C22×C83semidirect
464. C2×#103C22×C83semidirect
465. C2×#103C22×C83semidirect
470. C2×#102C22×C83semidirect
471. C2×#102C22×C83semidirect
474. C2×#97C22×C83semidirect
477. #391C22×C83semidirect
480. #389C22×C83semidirect
488. #340C22×C83semidirect
489. #340C22×C83semidirect
490. #336C22×C83semidirect
491. #336C22×C83semidirect
570. #102D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C832
C2×#450×C832
C2×#447×C832
C2×#442×C832
C83×#24272
D4×C22⋊C4×C832
C83×#20652
C83×#20352
C83×#20332
C83×#20122
C83×#19732
C83×#19242
C83×#18792
C83×#18772
C83×#18622
#2517283