Finite Group Databasebeta

← C83×#25164 #35252988

Subgroups — C83×#25164 #35252988

Order 21248.

1296 conjugacy classes of subgroups.

The subgroup lattice has 856 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×#440×C83C211yesmaximal, characteristic, complemented
5C83×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
7C83×#2067C211yesmaximal, characteristic, complemented
8C83×#2035C211yesmaximal, characteristic, complemented
9C83×#2033C211yesmaximal, characteristic, complemented
10C83×#2012C211yesmaximal, characteristic, complemented
11C83×#1972C211yesmaximal, characteristic, complemented
12C83×#1924C211yesmaximal, characteristic, complemented
13C83×#1880C211yesmaximal, characteristic, complemented
14C83×#1879C211yesmaximal, characteristic, complemented
15C83×#1864C211yesmaximal, 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×Q8×C83C2211yescharacteristic, complemented
25C2×C4×D4×C83C2211yescharacteristic
26C2×C4×D4×C83C2211yescharacteristic
27C22×C22⋊C4×C83—21no—
28#463×C83—24no—
29#450×C83—24no—
30#447×C83—24no—
31#440×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#396×C83—21no—
47#394×C83—21no—
48#390×C83—21no—
49#390×C83C2211yescharacteristic
50#390×C83C2211yescharacteristic
51#390×C83C2211yescharacteristic, complemented
52#389×C83C2211yescharacteristic, complemented
53#388×C83—21no—
54#386×C83—21no—
55#386×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×C83C2311yescharacteristic
79C2×SD16×C83—22no—
80C2×SD16×C83—22no—
81C2×SD16×C83—22no—
82C2×SD16×C83—22no—
83C2×SD16×C83—41no—
84C2×SD16×C83D414yescomplemented
85C2×D8×C83—22no—
86C2×D8×C83—22no—
87C2×D8×C83—22no—
88C2×D8×C83—22no—
89C2×D8×C83—22no—
90C2×D8×C83—41no—
91C22×C8×C83C2311yescharacteristic
92C22×C8×C83C2311yescharacteristic
93C22×C8×C83C2311yescharacteristic
94C22×C8×C83C2311yescharacteristic
95#124×C83—22no—
96#124×C83—41no—
97C22⋊Q8×C83—22no—
98C22⋊Q8×C83—41no—
99#121×C83—22no—
100#121×C83—41no—
101C4×Q8×C83—22no—
102C4×Q8×C83—41no—
103C4×D4×C83—22no—
104C4×D4×C83—22no—
105C4×D4×C83—41no—
106C4×D4×C83—41no—
107C2×C4⋊C4×C83—21no—
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—21no—
127C2×C22⋊C4×C83—44no—
128C2×C22⋊C4×C83D411yescharacteristic
129C2×C22⋊C4×C83D411yescharacteristic
130C2×C42×C83—21no—
131C2×C42×C83C2311yescharacteristic
132C2×C42×C83C2311yescharacteristic
133#107×C83—22no—
134#106×C83—41no—
135C4⋊C8×C83—22no—
136#103×C83—22no—
137#103×C83—22no—
138#102×C83—22no—
139#102×C83—22no—
140#102×C83—22no—
141#102×C83—22no—
142#102×C83—41no—
143#102×C83D414yes—
144C22⋊C8×C83—22no—
145C22⋊C8×C83—22no—
146#97×C83—22no—
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×C83C2×D412yes—
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—21no—
183C2×D4×C83—42no—
184C2×D4×C83—42no—
185C2×D4×C83—42no—
186C2×D4×C83—44no—
187C2×D4×C83—44no—
188C2×D4×C83—44no—
189C2×D4×C83—44no—
190C2×D4×C83—42no—
191C2×D4×C83—81no—
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—81no—
212C22×C4×C83—81no—
213C22×C4×C83C2×D411yescharacteristic
214C22×C4×C83C2×D411yescharacteristic
215C22×C4×C83C2×D411yescharacteristic
216C22×C4×C83C2×D411yescharacteristic
217C22×C4×C83C2×D411yescharacteristic
218C22×C4×C83C2411yescharacteristic
219SD16×C83—28no—
220SD16×C83—44no—
221D8×C83—44no—
222D8×C83—44no—
223C2×C8×C83—21no—
224C2×C8×C83—21no—
225C2×C8×C83—21no—
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×C83C2×D412yes—
234C2×C8×C83C2×D412yes—
235C4⋊C4×C83—21no—
236C4⋊C4×C83—21no—
237C4⋊C4×C83—21no—
238C4⋊C4×C83—21no—
239C4⋊C4×C83—21no—
240C4⋊C4×C83—21no—
241C4⋊C4×C83—21no—
242C4⋊C4×C83—42no—
243C4⋊C4×C83—42no—
244C4⋊C4×C83—81no—
245C4⋊C4×C83C2×D412yes—
246C22⋊C4×C83—22no—
247C22⋊C4×C83—41no—
248C22⋊C4×C83—42no—
249C22⋊C4×C83—42no—
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—81no—
259C22⋊C4×C83—81no—
260C22⋊C4×C83—81no—
261C42×C83—21no—
262C42×C83—21no—
263C42×C83—21no—
264C42×C83—21no—
265C42×C83—42no—
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—48no—
277C23×C83—48no—
278C23×C83—41no—
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—22no—
303Q8×C83—22no—
304Q8×C83—41no—
305Q8×C83—41no—
306D4×C83—22no—
307D4×C83—22no—
308D4×C83—22no—
309D4×C83—22no—
310D4×C83—22no—
311D4×C83—48no—
312D4×C83—41no—
313D4×C83—41no—
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—22no—
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—21no—
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×C83C22×D411yescharacteristic
357C2×C4×C83C22×D411yescharacteristic
358C2×C4×C83C2×#4111yescharacteristic
359C2×C4×C83C2×#4111yescharacteristic
360C2×C4×C83H(5,𝔽2)11yescharacteristic
361C2×C4×C83H(5,𝔽2)11yescharacteristic
362C8×C83—22no—
363C8×C83—22no—
364C8×C83—41no—
365C8×C83—41no—
366C22×C83—22no—
367C22×C83—24no—
368C22×C83—22no—
369C22×C83—22no—
370C22×C83—42no—
371C22×C83—41no—
372C22×C83—42no—
373C22×C83—41no—
374C22×C83—42no—
375C22×C83—42no—
376C22×C83—41no—
377C22×C83—42no—
378C22×C83—41no—
379C22×C83—42no—
380C22×C83—42no—
381C22×C83—42no—
382C22×C83—42no—
383C22×C83—816no—
384C22×C83—81no—
385C22×C83—81no—
386C22×C83—81no—
387C22×C83—81no—
388C22×C83—81no—
389C22×C83—81no—
390C22×C83—81no—
391C22×C83—81no—
392C22×C83—81no—
393C22×C83—81no—
394C22×C83—81no—
395C22×C83#52511yescharacteristic
396C22×C83D4211yescharacteristic
397C22×C83D4211yescharacteristic
398C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C83#57511yescharacteristic
400C22×C83#57611yescharacteristic
401C22×C83#57711yescharacteristic
402C4×C83—41no—
403C4×C83—42no—
404C4×C83—41no—
405C4×C83—42no—
406C4×C83—41no—
407C4×C83—41no—
408C4×C83—41no—
409C4×C83—81no—
410C4×C83—81no—
411C4×C83—81no—
412C4×C83C2×#12111yescharacteristic
413C4×C83#53811yescharacteristic
414C4×C83#54611yescharacteristic
415C4×C83#54611yescharacteristic
416#25164C8311yesmaximal, characteristic, direct product factor, Sylow
417C2×C83—42no—
418C2×C83—44no—
419C2×C83—82no—
420C2×C83—161no—
421C2×C83#242411yescharacteristic
422C2×C83#311411yescharacteristic
423C2×C83#311811yescharacteristic
424C2×C83#326411yescharacteristic
425C2×C83#326511yescharacteristic
426C2×C83#326811yescharacteristic
427C2×C83#327511yescharacteristic
428C2×#463C2×C8311yescharacteristic, complemented
429C2×#450C2×C8311yescharacteristic, complemented
430C2×#447C2×C8311yescharacteristic
431C2×#440C2×C8311yescharacteristic, complemented
432#2426C2×C8311yescharacteristic, complemented
433D4×C22⋊C4C2×C8311yescharacteristic, complemented
434#2067C2×C8311yescharacteristic, complemented
435#2035C2×C8311yescharacteristic, complemented
436#2033C2×C8311yescharacteristic, complemented
437#2012C2×C8311yescharacteristic, complemented
438#1972C2×C8311yescharacteristic, complemented
439#1924C2×C8311yescharacteristic, complemented
440#1880C2×C8311yescharacteristic, complemented
441#1879C2×C8311yescharacteristic, complemented
442#1864C2×C8311yescharacteristic, complemented
443C83#2516411yescharacteristic, direct product factor, Sylow
444C23×D4C22×C8311yescharacteristic
445C22×SD16C22×C8311yescharacteristic
446C22×SD16C22×C8311yescharacteristic
447C22×D8C22×C8311yescharacteristic
448C22×D8C22×C8311yescharacteristic
449C2×#124C22×C8311yescharacteristic, complemented
450C2×C22⋊Q8C22×C8311yescharacteristic
451C2×#121C22×C8311yescharacteristic
452C2×C4×Q8C22×C8311yescharacteristic, complemented
453C2×C4×D4C22×C8311yescharacteristic
454C2×C4×D4C22×C8311yescharacteristic
455C22×C22⋊C4—21no—
456#463—24no—
457#450—24no—
458#447—24no—
459#440—24no—
460C2×#107C22×C8311yescharacteristic, complemented
461C2×#106C22×C8311yescharacteristic, complemented
462C2×C4⋊C8C22×C8311yescharacteristic, complemented
463C2×#103C22×C8311yescharacteristic, complemented
464C2×#103C22×C8311yescharacteristic, complemented
465C2×#102C22×C8311yescharacteristic
466C2×#102C22×C8311yescharacteristic
467C2×#102C22×C8311yescharacteristic
468C2×#102C22×C8311yescharacteristic
469C2×#102C22×C8311yescharacteristic, complemented
470C2×#102C22×C8311yescharacteristic, complemented
471C2×C22⋊C8C22×C8311yescharacteristic
472C2×C22⋊C8C22×C8311yescharacteristic
473C2×#97C22×C8311yescharacteristic, complemented
474#396—21no—
475#394—21no—
476#390—21no—
477#390C22×C8311yescharacteristic
478#390C22×C8311yescharacteristic
479#390C22×C8311yescharacteristic, complemented
480#389C22×C8311yescharacteristic, complemented
481#388—21no—
482#386—21no—
483#386—21no—
484#380C22×C8311yescharacteristic
485#379—21no—
486C4×C22⋊C4C22×C8311yescharacteristic
487#340C22×C8311yescharacteristic, complemented
488#340C22×C8311yescharacteristic, complemented
489#336C22×C8311yescharacteristic, complemented
490#336C22×C8311yescharacteristic, complemented
491C25—21no—
492C22×Q8C23×C8311yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C8311yescharacteristic
502C22×D4C23×C8311yescharacteristic
503C22×D4C23×C8311yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C8311yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C8314yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C8311yescharacteristic
520C22×C8C23×C8311yescharacteristic
521C22×C8C23×C8311yescharacteristic
522C22×C8C23×C8311yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C8311yescharacteristic
539C2×C4⋊C4C23×C8311yescharacteristic
540C2×C4⋊C4C23×C8311yescharacteristic
541C2×C4⋊C4C23×C8311yescharacteristic
542C2×C22⋊C4—21no—
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×C42—21no—
559C2×C42C23×C8311yescharacteristic
560C2×C42C23×C8311yescharacteristic
561#107—22no—
562#106—41no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C8314yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574#97—22no—
575#95—21no—
576#95—21no—
577#95D4×C8311yescharacteristic
578#95D4×C8311yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C8311yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C8312yes—
596C2×D4—24no—
597C2×D4—21no—
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—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C8312yes—
621C2×D4C2×D4×C8312yes—
622C2×D4#41×C8312yes—
623C2×D4#41×C8312yes—
624C22×C4—21no—
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—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C8311yescharacteristic
642C22×C4C2×D4×C8311yescharacteristic
643C22×C4C2×D4×C8311yescharacteristic
644C22×C4C2×D4×C8311yescharacteristic
645C22×C4C2×D4×C8311yescharacteristic
646C22×C4C24×C8311yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C8312yes—
662C2×C8C2×D4×C8312yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C8312yes—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
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—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23AGL(1,ℤ/8)×C8312yes—
729C23C22×D4×C8311yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C8314yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
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—84no—
783C2×C4—84no—
784C2×C4C22×D4×C8311yescharacteristic
785C2×C4C22×D4×C8311yescharacteristic
786C2×C4C2×#41×C8311yescharacteristic
787C2×C4C2×#41×C8311yescharacteristic
788C2×C4H(5,𝔽2)×C8311yescharacteristic
789C2×C4H(5,𝔽2)×C8311yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—41no—
799C22—42no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22#525×C8311yescharacteristic
824C22D42×C8311yescharacteristic
825C22D42×C8311yescharacteristic
826C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
827C22#575×C8311yescharacteristic
828C22#576×C8311yescharacteristic
829C22#577×C8311yescharacteristic
830C4—41no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C8311yescharacteristic
841C4#538×C8311yescharacteristic
842C4#546×C8311yescharacteristic
843C4#546×C8311yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C83×#242411yescharacteristic
849C2C83×#311411yescharacteristic
850C2C83×#311811yescharacteristic
851C2C83×#326411yescharacteristic
852C2C83×#326511yescharacteristic
853C2C83×#326811yescharacteristic
854C2C83×#327511yescharacteristic
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×#440×C83C2semidirect
5. C83×#2426C2semidirect
6. D4×C22⋊C4×C83C2semidirect
7. C83×#2067C2semidirect
8. C83×#2035C2semidirect
9. C83×#2033C2semidirect
10. C83×#2012C2semidirect
11. C83×#1972C2semidirect
12. C83×#1924C2semidirect
13. C83×#1880C2semidirect
14. C83×#1879C2semidirect
15. C83×#1864C2semidirect
21. C2×#124×C83C22semidirect
24. C2×C4×Q8×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
51. #390×C83C22semidirect
52. #389×C83C22semidirect
59. #340×C83C22semidirect
60. #340×C83C22semidirect
61. #336×C83C22semidirect
62. #336×C83C22semidirect
84. C2×SD16×C83D4semidirect
416. #25164C83direct (N × H)
428. C2×#463C2×C83semidirect
429. C2×#450C2×C83semidirect
431. C2×#440C2×C83semidirect
432. #2426C2×C83semidirect
433. D4×C22⋊C4C2×C83semidirect
434. #2067C2×C83semidirect
435. #2035C2×C83semidirect
436. #2033C2×C83semidirect
437. #2012C2×C83semidirect
438. #1972C2×C83semidirect
439. #1924C2×C83semidirect
440. #1880C2×C83semidirect
441. #1879C2×C83semidirect
442. #1864C2×C83semidirect
443. C83#25164direct (N × H)
449. C2×#124C22×C83semidirect
452. C2×C4×Q8C22×C83semidirect
460. C2×#107C22×C83semidirect
461. C2×#106C22×C83semidirect
462. C2×C4⋊C8C22×C83semidirect
463. C2×#103C22×C83semidirect
464. C2×#103C22×C83semidirect
469. C2×#102C22×C83semidirect
470. C2×#102C22×C83semidirect
473. C2×#97C22×C83semidirect
479. #390C22×C83semidirect
480. #389C22×C83semidirect
487. #340C22×C83semidirect
488. #340C22×C83semidirect
489. #336C22×C83semidirect
490. #336C22×C83semidirect
512. C2×SD16D4×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×#440×C832
C83×#24262
D4×C22⋊C4×C832
C83×#20672
C83×#20352
C83×#20332
C83×#20122
C83×#19722
C83×#19242
C83×#18802
C83×#18792
C83×#18642
#2516483