Finite Group Databasebeta

← C83×#21458 #35249282

Subgroups — C83×#21458 #35249282

Order 21248.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C83C211yesmaximal, characteristic, complemented
2C2×#447×C83C211yesmaximal, characteristic
3C2×#442×C83C211yesmaximal, characteristic, complemented
4C2×C4×D8×C83C211yesmaximal, characteristic, complemented
5C83×#2324C211yesmaximal, characteristic, complemented
6C83×#1879C211yesmaximal, characteristic, complemented
7C83×#1879C211yesmaximal, characteristic, complemented
8C83×#1875C211yesmaximal, characteristic, complemented
9C83×#1864C211yesmaximal, characteristic, complemented
10C83×#1862C211yesmaximal, characteristic, complemented
11C83×#1854C211yesmaximal, characteristic, complemented
12C83×#1786C211yesmaximal, characteristic, complemented
13C83×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C83C211yesmaximal, characteristic, complemented
15C83×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C83C2211yescharacteristic
17C22×D8×C83C2211yescharacteristic
18C22×D8×C83C2211yescharacteristic
19C2×#121×C83C2211yescharacteristic
20#518×C83—24no—
21#518×C83—24no—
22C2×C4×D4×C83—21no—
23C2×C4×D4×C83—21no—
24C2×C4×D4×C83C2211yescharacteristic
25C2×C4×D4×C83C2211yescharacteristic
26C2×C4×D4×C83C2211yescharacteristic
27C2×C4×D4×C83C2211yescharacteristic
28C2×C4×D4×C83C2211yescharacteristic, complemented
29C2×#117×C83C2211yescharacteristic
30C2×#117×C83C2211yescharacteristic
31C22×C22⋊C4×C83—21no—
32C22×C22⋊C4×C83—21no—
33#447×C83C418yescomplemented
34#442×C83—24no—
35C4×D8×C83—24no—
36C2×#107×C83C2211yescharacteristic, complemented
37C2×#106×C83C2211yescharacteristic, complemented
38C2×#102×C83C2211yescharacteristic
39C2×#102×C83C2211yescharacteristic
40C2×#102×C83C2211yescharacteristic
41C2×#102×C83C2211yescharacteristic
42C2×#102×C83C2211yescharacteristic
43C2×#102×C83C2211yescharacteristic
44C2×#102×C83C2211yescharacteristic, complemented
45C2×#102×C83C2211yescharacteristic, complemented
46C2×C22⋊C8×C83C2211yescharacteristic
47C2×C22⋊C8×C83C2211yescharacteristic
48C2×#97×C83C2211yescharacteristic, complemented
49C2×C4×C8×C83C2211yescharacteristic, complemented
50#390×C83—21no—
51#390×C83C2211yescharacteristic, complemented
52#389×C83C2211yescharacteristic, complemented
53#388×C83—21no—
54#386×C83—21no—
55#385×C83—21no—
56#380×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic, complemented
58#340×C83C2211yescharacteristic, complemented
59#340×C83C2211yescharacteristic, complemented
60#340×C83C2211yescharacteristic, complemented
61#340×C83C2211yescharacteristic, complemented
62#336×C83C2211yescharacteristic, complemented
63#336×C83C2211yescharacteristic, complemented
64C25×C83—21no—
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—22no—
72C22×D4×C83C2×C414yescomplemented
73C22×D4×C83C2311yescharacteristic
74C22×D4×C83C2311yescharacteristic
75C22×D4×C83C2311yescharacteristic
76C23×C4×C83—21no—
77C23×C4×C83—21no—
78C23×C4×C83—21no—
79C23×C4×C83—21no—
80C23×C4×C83—21no—
81C23×C4×C83C2311yescharacteristic
82C2×D8×C83—22no—
83C2×D8×C83—22no—
84C2×D8×C83—22no—
85C2×D8×C83—22no—
86C2×D8×C83C2×C414yescomplemented
87C2×D8×C83C2×C414yescomplemented
88C22×C8×C83C2311yescharacteristic
89C22×C8×C83C2311yescharacteristic
90C22×C8×C83C2311yescharacteristic
91C22×C8×C83C2311yescharacteristic
92#121×C83—22no—
93#121×C83C2×C414yescomplemented
94C4×D4×C83—28no—
95C4×D4×C83—28no—
96C4×D4×C83—22no—
97C4×D4×C83—22no—
98C4×D4×C83—22no—
99C4×D4×C83—22no—
100C4×D4×C83—22no—
101C4×D4×C83—22no—
102C4×D4×C83—22no—
103C4×D4×C83—22no—
104C4×D4×C83D414yescomplemented
105C4×D4×C83D414yescomplemented
106#117×C83—22no—
107#117×C83—22no—
108#117×C83—22no—
109#117×C83—22no—
110C2×C4⋊C4×C83—21no—
111C2×C4⋊C4×C83D411yescharacteristic
112C2×C4⋊C4×C83D411yescharacteristic
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C4⋊C4×C83C2311yescharacteristic
116C2×C4⋊C4×C83C2311yescharacteristic
117C2×C4⋊C4×C83C2311yescharacteristic
118C2×C22⋊C4×C83—28no—
119C2×C22⋊C4×C83—28no—
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—21no—
128C2×C22⋊C4×C83—21no—
129C2×C22⋊C4×C83—21no—
130C2×C22⋊C4×C83D411yescharacteristic
131C2×C22⋊C4×C83D411yescharacteristic
132C2×C42×C83—21no—
133C2×C42×C83—21no—
134C2×C42×C83C2311yescharacteristic
135C2×C42×C83C2311yescharacteristic
136#107×C83—22no—
137#106×C83—22no—
138#102×C83—22no—
139#102×C83—22no—
140#102×C83—22no—
141#102×C83—22no—
142#102×C83—22no—
143#102×C83—22no—
144#102×C83C2×C414yescomplemented
145#102×C83C2×C414yescomplemented
146C22⋊C8×C83—22no—
147C22⋊C8×C83C2×C414yescomplemented
148#97×C83—22no—
149C4×C8×C83—22no—
150#95×C83—21no—
151#95×C83—21no—
152#95×C83—21no—
153C24×C83—24no—
154C24×C83—24no—
155C24×C83—21no—
156C24×C83—21no—
157C24×C83—24no—
158C24×C83—21no—
159C24×C83—81no—
160C24×C83—81no—
161C24×C83—81no—
162C24×C83—81no—
163C24×C83C2×D411yescharacteristic
164C2×D4×C83—24no—
165C2×D4×C83—24no—
166C2×D4×C83—28no—
167C2×D4×C83—28no—
168C2×D4×C83—28no—
169C2×D4×C83—28no—
170C2×D4×C83—24no—
171C2×D4×C83—24no—
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—81no—
184C2×D4×C83—81no—
185C2×D4×C83C22×C412yes—
186C2×D4×C83C22×C412yes—
187C2×D4×C83C22×C412yes—
188C2×D4×C83C2×D412yes—
189C2×D4×C83C2×D412yes—
190C2×D4×C83#4112yes—
191C2×D4×C83#4112yes—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—24no—
200C22×C4×C83—24no—
201C22×C4×C83—24no—
202C22×C4×C83—24no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—42no—
206C22×C4×C83—81no—
207C22×C4×C83—81no—
208C22×C4×C83—81no—
209C22×C4×C83—81no—
210C22×C4×C83—81no—
211C22×C4×C83—81no—
212C22×C4×C83—81no—
213C22×C4×C83—81no—
214C22×C4×C83—81no—
215C22×C4×C83—81no—
216C22×C4×C83C22×C412yes—
217C22×C4×C83C2×D411yescharacteristic
218C22×C4×C83C2×D411yescharacteristic
219C22×C4×C83C2×D411yescharacteristic
220C22×C4×C83C2×D411yescharacteristic
221C22×C4×C83C2×D411yescharacteristic
222C22×C4×C83#4112yes—
223C22×C4×C83C2411yescharacteristic
224D8×C83—28no—
225D8×C83—28no—
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×C83C22×C412yes—
237C2×C8×C83C22×C412yes—
238C4⋊C4×C83—22no—
239C4⋊C4×C83—22no—
240C4⋊C4×C83—21no—
241C4⋊C4×C83—21no—
242C4⋊C4×C83—21no—
243C4⋊C4×C83—21no—
244C4⋊C4×C83—21no—
245C4⋊C4×C83—21no—
246C4⋊C4×C83—21no—
247C4⋊C4×C83—81no—
248C4⋊C4×C83C22×C412yes—
249C4⋊C4×C83C2×D412yes—
250C4⋊C4×C83C2×D412yes—
251C22⋊C4×C83—24no—
252C22⋊C4×C83—24no—
253C22⋊C4×C83—24no—
254C22⋊C4×C83—24no—
255C22⋊C4×C83—22no—
256C22⋊C4×C83—22no—
257C22⋊C4×C83—24no—
258C22⋊C4×C83—24no—
259C22⋊C4×C83—42no—
260C22⋊C4×C83—81no—
261C22⋊C4×C83—81no—
262C22⋊C4×C83—81no—
263C42×C83—24no—
264C42×C83—21no—
265C42×C83—21no—
266C42×C83—81no—
267C42×C83C2×D412yes—
268C42×C83C2×D412yes—
269C23×C83—216no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—21no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—21no—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83—21no—
279C23×C83—21no—
280C23×C83—21no—
281C23×C83—21no—
282C23×C83—22no—
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—41no—
296C23×C83—41no—
297C23×C83—84no—
298C23×C83—84no—
299C23×C83—84no—
300C23×C83—84no—
301C23×C83—84no—
302C23×C83—84no—
303C23×C83C4×D412yes—
304C23×C83C22×D411yescharacteristic
305D4×C83—216no—
306D4×C83—22no—
307D4×C83—22no—
308D4×C83—22no—
309D4×C83—22no—
310D4×C83—22no—
311D4×C83—22no—
312D4×C83—22no—
313D4×C83—22no—
314D4×C83—41no—
315D4×C83—41no—
316D4×C83—84no—
317D4×C83C4×D414yes—
318D4×C83C4×D414yes—
319C2×C4×C83—21no—
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—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—21no—
331C2×C4×C83—21no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—21no—
335C2×C4×C83—21no—
336C2×C4×C83—21no—
337C2×C4×C83—21no—
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—84no—
351C2×C4×C83—84no—
352C2×C4×C83—84no—
353C2×C4×C83—84no—
354C2×C4×C83—84no—
355C2×C4×C83C4×D412yes—
356C2×C4×C83#12012yes—
357C2×C4×C83#12012yes—
358C2×C4×C83C23×C411yescharacteristic
359C2×C4×C83C22×D411yescharacteristic
360C2×C4×C83C22×D411yescharacteristic
361C2×C4×C83C2×#4111yescharacteristic
362C2×C4×C83C2×#4111yescharacteristic
363C2×C4×C83C2×#4111yescharacteristic
364C8×C83—22no—
365C8×C83—22no—
366C8×C83—41no—
367C8×C83—41no—
368C22×C83—22no—
369C22×C83—22no—
370C22×C83—22no—
371C22×C83—24no—
372C22×C83—24no—
373C22×C83—41no—
374C22×C83—42no—
375C22×C83—42no—
376C22×C83—41no—
377C22×C83—42no—
378C22×C83—42no—
379C22×C83—42no—
380C22×C83—42no—
381C22×C83—42no—
382C22×C83—42no—
383C22×C83—42no—
384C22×C83—42no—
385C22×C83—41no—
386C22×C83—42no—
387C22×C83—42no—
388C22×C83—41no—
389C22×C83—42no—
390C22×C83—42no—
391C22×C83—42no—
392C22×C83—816no—
393C22×C83—81no—
394C22×C83—81no—
395C22×C83—81no—
396C22×C83—81no—
397C22×C83C2×C4×D411yescharacteristic
398C22×C83C2×#12011yescharacteristic
399C22×C83#52511yescharacteristic
400C22×C83#57611yescharacteristic
401C22×C83#57611yescharacteristic
402C22×C83#57611yescharacteristic
403C22×C83#57711yescharacteristic
404C4×C83—22no—
405C4×C83—22no—
406C4×C83—22no—
407C4×C83—42no—
408C4×C83—41no—
409C4×C83—42no—
410C4×C83—41no—
411C4×C83—42no—
412C4×C83—81no—
413C4×C83—81no—
414C4×C83C2×C4×D411yescharacteristic
415C4×C83C2×C4×D411yescharacteristic
416C4×C83#52511yescharacteristic
417C4×C83#52511yescharacteristic
418#21458C8311yesmaximal, characteristic, direct product factor, Sylow
419C2×C83—42no—
420C2×C83—44no—
421C2×C83—44no—
422C2×C83—82no—
423C2×C83C4×#12011yescharacteristic
424C2×C83#294611yescharacteristic
425C2×C83#294811yescharacteristic
426C2×C83#300811yescharacteristic
427C2×C83#301211yescharacteristic
428C2×C83#311811yescharacteristic
429C2×C83#312211yescharacteristic
430C2×#518C2×C8311yescharacteristic, complemented
431C2×#447C2×C8311yescharacteristic
432C2×#442C2×C8311yescharacteristic, complemented
433C2×C4×D8C2×C8311yescharacteristic, complemented
434#2324C2×C8311yescharacteristic, complemented
435#1879C2×C8311yescharacteristic, complemented
436#1879C2×C8311yescharacteristic, complemented
437#1875C2×C8311yescharacteristic, complemented
438#1864C2×C8311yescharacteristic, complemented
439#1862C2×C8311yescharacteristic, complemented
440#1854C2×C8311yescharacteristic, complemented
441#1786C2×C8311yescharacteristic, complemented
442#1762C2×C8311yescharacteristic, complemented
443C4×#102C2×C8311yescharacteristic, complemented
444#1750C2×C8311yescharacteristic, complemented
445C83#2145811yescharacteristic, direct product factor, Sylow
446C23×D4C22×C8311yescharacteristic
447C22×D8C22×C8311yescharacteristic
448C22×D8C22×C8311yescharacteristic
449C2×#121C22×C8311yescharacteristic
450#518—24no—
451#518—24no—
452C2×C4×D4—21no—
453C2×C4×D4—21no—
454C2×C4×D4C22×C8311yescharacteristic
455C2×C4×D4C22×C8311yescharacteristic
456C2×C4×D4C22×C8311yescharacteristic
457C2×C4×D4C22×C8311yescharacteristic
458C2×C4×D4C22×C8311yescharacteristic, complemented
459C2×#117C22×C8311yescharacteristic
460C2×#117C22×C8311yescharacteristic
461C22×C22⋊C4—21no—
462C22×C22⋊C4—21no—
463#447C4×C8318yescomplemented
464#442—24no—
465C4×D8—24no—
466C2×#107C22×C8311yescharacteristic, complemented
467C2×#106C22×C8311yescharacteristic, complemented
468C2×#102C22×C8311yescharacteristic
469C2×#102C22×C8311yescharacteristic
470C2×#102C22×C8311yescharacteristic
471C2×#102C22×C8311yescharacteristic
472C2×#102C22×C8311yescharacteristic
473C2×#102C22×C8311yescharacteristic
474C2×#102C22×C8311yescharacteristic, complemented
475C2×#102C22×C8311yescharacteristic, complemented
476C2×C22⋊C8C22×C8311yescharacteristic
477C2×C22⋊C8C22×C8311yescharacteristic
478C2×#97C22×C8311yescharacteristic, complemented
479C2×C4×C8C22×C8311yescharacteristic, complemented
480#390—21no—
481#390C22×C8311yescharacteristic, complemented
482#389C22×C8311yescharacteristic, complemented
483#388—21no—
484#386—21no—
485#385—21no—
486#380C22×C8311yescharacteristic
487C4×C4⋊C4C22×C8311yescharacteristic, complemented
488#340C22×C8311yescharacteristic, complemented
489#340C22×C8311yescharacteristic, complemented
490#340C22×C8311yescharacteristic, complemented
491#340C22×C8311yescharacteristic, complemented
492#336C22×C8311yescharacteristic, complemented
493#336C22×C8311yescharacteristic, complemented
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4C2×C4×C8314yescomplemented
503C22×D4C23×C8311yescharacteristic
504C22×D4C23×C8311yescharacteristic
505C22×D4C23×C8311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C23×C8311yescharacteristic
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8C2×C4×C8314yescomplemented
517C2×D8C2×C4×C8314yescomplemented
518C22×C8C23×C8311yescharacteristic
519C22×C8C23×C8311yescharacteristic
520C22×C8C23×C8311yescharacteristic
521C22×C8C23×C8311yescharacteristic
522#121—22no—
523#121C2×C4×C8314yescomplemented
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4D4×C8314yescomplemented
535C4×D4D4×C8314yescomplemented
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C8311yescharacteristic
542C2×C4⋊C4D4×C8311yescharacteristic
543C2×C4⋊C4C23×C8311yescharacteristic
544C2×C4⋊C4C23×C8311yescharacteristic
545C2×C4⋊C4C23×C8311yescharacteristic
546C2×C4⋊C4C23×C8311yescharacteristic
547C2×C4⋊C4C23×C8311yescharacteristic
548C2×C22⋊C4—28no—
549C2×C22⋊C4—28no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4D4×C8311yescharacteristic
561C2×C22⋊C4D4×C8311yescharacteristic
562C2×C42—21no—
563C2×C42—21no—
564C2×C42C23×C8311yescharacteristic
565C2×C42C23×C8311yescharacteristic
566#107—22no—
567#106—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102C2×C4×C8314yescomplemented
575#102C2×C4×C8314yescomplemented
576C22⋊C8—22no—
577C22⋊C8C2×C4×C8314yescomplemented
578#97—22no—
579C4×C8—22no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—21no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—81no—
593C24C2×D4×C8311yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—24no—
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—21no—
612C2×D4—21no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C22×C4×C8312yes—
616C2×D4C22×C4×C8312yes—
617C2×D4C22×C4×C8312yes—
618C2×D4C2×D4×C8312yes—
619C2×D4C2×D4×C8312yes—
620C2×D4#41×C8312yes—
621C2×D4#41×C8312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C22×C4×C8312yes—
647C22×C4C2×D4×C8311yescharacteristic
648C22×C4C2×D4×C8311yescharacteristic
649C22×C4C2×D4×C8311yescharacteristic
650C22×C4C2×D4×C8311yescharacteristic
651C22×C4C2×D4×C8311yescharacteristic
652C22×C4#41×C8312yes—
653C22×C4C24×C8311yescharacteristic
654D8—28no—
655D8—28no—
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×C8—21no—
666C2×C8C22×C4×C8312yes—
667C2×C8C22×C4×C8312yes—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—81no—
678C4⋊C4C22×C4×C8312yes—
679C4⋊C4C2×D4×C8312yes—
680C4⋊C4C2×D4×C8312yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—42no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—81no—
697C42C2×D4×C8312yes—
698C42C2×D4×C8312yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23C4×D4×C8312yes—
734C23C22×D4×C8311yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4C4×D4×C8314yes—
748D4C4×D4×C8314yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
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—84no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4C4×D4×C8312yes—
786C2×C4#120×C8312yes—
787C2×C4#120×C8312yes—
788C2×C4C23×C4×C8311yescharacteristic
789C2×C4C22×D4×C8311yescharacteristic
790C2×C4C22×D4×C8311yescharacteristic
791C2×C4C2×#41×C8311yescharacteristic
792C2×C4C2×#41×C8311yescharacteristic
793C2×C4C2×#41×C8311yescharacteristic
794C8—22no—
795C8—22no—
796C8—41no—
797C8—41no—
798C22—22no—
799C22—24no—
800C22—24no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22C2×C4×D4×C8311yescharacteristic
828C22C2×#120×C8311yescharacteristic
829C22#525×C8311yescharacteristic
830C22#576×C8311yescharacteristic
831C22#576×C8311yescharacteristic
832C22#576×C8311yescharacteristic
833C22#577×C8311yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—42no—
838C4—41no—
839C4—42no—
840C4—41no—
841C4—42no—
842C4—81no—
843C4—81no—
844C4C2×C4×D4×C8311yescharacteristic
845C4C2×C4×D4×C8311yescharacteristic
846C4#525×C8311yescharacteristic
847C4#525×C8311yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—82no—
852C2C4×#120×C8311yescharacteristic
853C2C83×#294611yescharacteristic
854C2C83×#294811yescharacteristic
855C2C83×#300811yescharacteristic
856C2C83×#301211yescharacteristic
857C2C83×#311811yescharacteristic
858C2C83×#312211yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC22×C4C24×C83
prime radicalC2×#447×C83C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×#117×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#518×C83C2semidirect
3. C2×#442×C83C2semidirect
4. C2×C4×D8×C83C2semidirect
5. C83×#2324C2semidirect
6. C83×#1879C2semidirect
7. C83×#1879C2semidirect
8. C83×#1875C2semidirect
9. C83×#1864C2semidirect
10. C83×#1862C2semidirect
11. C83×#1854C2semidirect
12. C83×#1786C2semidirect
13. C83×#1762C2semidirect
14. C4×#102×C83C2semidirect
15. C83×#1750C2semidirect
28. C2×C4×D4×C83C22semidirect
33. #447×C83C4semidirect
36. C2×#107×C83C22semidirect
37. C2×#106×C83C22semidirect
44. C2×#102×C83C22semidirect
45. C2×#102×C83C22semidirect
48. C2×#97×C83C22semidirect
49. C2×C4×C8×C83C22semidirect
51. #390×C83C22semidirect
52. #389×C83C22semidirect
57. C4×C4⋊C4×C83C22semidirect
58. #340×C83C22semidirect
59. #340×C83C22semidirect
60. #340×C83C22semidirect
61. #340×C83C22semidirect
62. #336×C83C22semidirect
63. #336×C83C22semidirect
72. C22×D4×C83C2×C4semidirect
86. C2×D8×C83C2×C4semidirect
87. C2×D8×C83C2×C4semidirect
93. #121×C83C2×C4semidirect
104. C4×D4×C83D4semidirect
105. C4×D4×C83D4semidirect
144. #102×C83C2×C4semidirect
145. #102×C83C2×C4semidirect
147. C22⋊C8×C83C2×C4semidirect
418. #21458C83direct (N × H)
430. C2×#518C2×C83semidirect
432. C2×#442C2×C83semidirect
433. C2×C4×D8C2×C83semidirect
434. #2324C2×C83semidirect
435. #1879C2×C83semidirect
436. #1879C2×C83semidirect
437. #1875C2×C83semidirect
438. #1864C2×C83semidirect
439. #1862C2×C83semidirect
440. #1854C2×C83semidirect
441. #1786C2×C83semidirect
442. #1762C2×C83semidirect
443. C4×#102C2×C83semidirect
444. #1750C2×C83semidirect
445. C83#21458direct (N × H)
458. C2×C4×D4C22×C83semidirect
463. #447C4×C83semidirect
466. C2×#107C22×C83semidirect
467. C2×#106C22×C83semidirect
474. C2×#102C22×C83semidirect
475. C2×#102C22×C83semidirect
478. C2×#97C22×C83semidirect
479. C2×C4×C8C22×C83semidirect
481. #390C22×C83semidirect
482. #389C22×C83semidirect
487. C4×C4⋊C4C22×C83semidirect
488. #340C22×C83semidirect
489. #340C22×C83semidirect
490. #340C22×C83semidirect
491. #340C22×C83semidirect
492. #336C22×C83semidirect
493. #336C22×C83semidirect
502. C22×D4C2×C4×C83semidirect
516. C2×D8C2×C4×C83semidirect
517. C2×D8C2×C4×C83semidirect
523. #121C2×C4×C83semidirect
534. C4×D4D4×C83semidirect
535. C4×D4D4×C83semidirect
574. #102C2×C4×C83semidirect
575. #102C2×C4×C83semidirect
577. C22⋊C8C2×C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#518×C832
C2×#447×C832
C2×#442×C832
C2×C4×D8×C832
C83×#23242
C83×#18792
C83×#18752
C83×#18642
C83×#18622
C83×#18542
C83×#17862
C83×#17622
C4×#102×C832
C83×#17502
#2145883