Finite Group Databasebeta

← C83×#25890 #35253714

Subgroups — C83×#25890 #35253714

Order 21248.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C83C211yesmaximal, characteristic
2C2×#488×C83C211yesmaximal, characteristic, complemented
3C2×#478×C83C211yesmaximal, characteristic, complemented
4C83×#2562C211yesmaximal, characteristic, complemented
5C83×#2036C211yesmaximal, characteristic, complemented
6C83×#2035C211yesmaximal, characteristic, complemented
7C83×#2034C211yesmaximal, characteristic, complemented
8C83×#2033C211yesmaximal, characteristic, complemented
9C83×#1983C211yesmaximal, characteristic, complemented
10C83×#1954C211yesmaximal, characteristic, complemented
11C83×#1788C211yesmaximal, characteristic, complemented
12C83×#1788C211yesmaximal, characteristic, complemented
13C83×#1786C211yesmaximal, characteristic, complemented
14C83×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C83C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18#546×C83—24no—
19#546×C83—24no—
20C2×#125×C83C2211yescharacteristic, complemented
21C2×#124×C83C2211yescharacteristic
22C2×#123×C83—21no—
23C2×C22⋊Q8×C83C2211yescharacteristic
24C2×#121×C83—21no—
25C2×#121×C83C2211yescharacteristic
26C2×#120×C83—21no—
27C2×C4×D4×C83C2211yescharacteristic
28C2×C4×D4×C83C2211yescharacteristic
29C22×C22⋊C4×C83—21no—
30#488×C83—24no—
31#478×C83—24no—
32C2×#107×C83C2211yescharacteristic, complemented
33C2×#106×C83C2211yescharacteristic, complemented
34C2×C4⋊C8×C83C2211yescharacteristic, complemented
35C2×#103×C83C2211yescharacteristic, complemented
36C2×#103×C83C2211yescharacteristic, complemented
37C2×#103×C83C2211yescharacteristic, complemented
38C2×#103×C83C2211yescharacteristic, complemented
39C2×#102×C83C2211yescharacteristic
40C2×#102×C83C2211yescharacteristic
41C2×#102×C83C2211yescharacteristic
42C2×#102×C83C2211yescharacteristic
43C2×#102×C83C2211yescharacteristic
44C2×#102×C83C2211yescharacteristic
45C2×#102×C83C2211yescharacteristic
46C2×#102×C83C2211yescharacteristic
47C2×C22⋊C8×C83C2211yescharacteristic
48C2×C22⋊C8×C83C2211yescharacteristic
49C2×C22⋊C8×C83C2211yescharacteristic, complemented
50C2×C22⋊C8×C83C2211yescharacteristic, complemented
51C2×C4×C8×C83C2211yescharacteristic, complemented
52#400×C83—21no—
53#394×C83—21no—
54#388×C83—21no—
55#388×C83—21no—
56#380×C83C2211yescharacteristic
57#380×C83C2211yescharacteristic
58#380×C83C2211yescharacteristic, complemented
59#380×C83C2211yescharacteristic, complemented
60C4×C4⋊C4×C83C2211yescharacteristic, complemented
61#340×C83C2211yescharacteristic, complemented
62#340×C83C2211yescharacteristic, complemented
63C25×C83—21no—
64C2×#41×C83—22no—
65C2×#41×C83—22no—
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—41no—
69C2×#41×C83—41no—
70C22×Q8×C83C2311yescharacteristic
71C22×D4×C83—21no—
72C22×D4×C83—21no—
73C22×D4×C83—22no—
74C22×D4×C83—22no—
75C22×D4×C83—22no—
76C22×D4×C83—22no—
77C22×D4×C83—21no—
78C22×D4×C83—41no—
79C22×D4×C83—41no—
80C22×D4×C83D411yescharacteristic
81C22×D4×C83C2311yescharacteristic
82C22×D4×C83C2311yescharacteristic
83C23×C4×C83—21no—
84C23×C4×C83—21no—
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2311yescharacteristic
87C22×C8×C83C2311yescharacteristic
88C22×C8×C83C2311yescharacteristic
89C22×C8×C83C2311yescharacteristic
90C22×C8×C83C2311yescharacteristic
91#125×C83—22no—
92#125×C83—22no—
93#124×C83—22no—
94#124×C83D414yes—
95#123×C83—28no—
96C22⋊Q8×C83—22no—
97C22⋊Q8×C83—22no—
98#121×C83—28no—
99#121×C83—22no—
100#121×C83—22no—
101#120×C83—28no—
102C4×D4×C83—22no—
103C4×D4×C83—22no—
104C4×D4×C83—22no—
105C4×D4×C83D414yes—
106C2×C4⋊C4×C83—21no—
107C2×C4⋊C4×C83—21no—
108C2×C4⋊C4×C83—21no—
109C2×C4⋊C4×C83D411yescharacteristic
110C2×C4⋊C4×C83C2311yescharacteristic
111C2×C4⋊C4×C83C2311yescharacteristic
112C2×C4⋊C4×C83C2311yescharacteristic
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C22⋊C4×C83—28no—
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×C83D411yescharacteristic
126C2×C22⋊C4×C83D411yescharacteristic
127C2×C42×C83—21no—
128C2×C42×C83C2311yescharacteristic
129#107×C83—22no—
130#106×C83—22no—
131C4⋊C8×C83—22no—
132#103×C83—22no—
133#103×C83—22no—
134#103×C83—41no—
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×C83—22no—
142#102×C83—41no—
143#102×C83—41no—
144C22⋊C8×C83—41no—
145C22⋊C8×C83—41no—
146C22⋊C8×C83—41no—
147C22⋊C8×C83—41no—
148C4×C8×C83—22no—
149#95×C83—21no—
150#95×C83—21no—
151#95×C83—21no—
152#95×C83—21no—
153#95×C83—21no—
154C24×C83—21no—
155C24×C83—24no—
156C24×C83—21no—
157C24×C83—42no—
158C24×C83—42no—
159C24×C83—42no—
160C24×C83—42no—
161C24×C83—81no—
162C24×C83—81no—
163C24×C83C2×D411yescharacteristic
164C24×C83C2×D411yescharacteristic
165#41×C83—44no—
166#41×C83—44no—
167#41×C83—44no—
168#41×C83—44no—
169C2×Q8×C83—21no—
170C2×Q8×C83—21no—
171C2×Q8×C83—21no—
172C2×Q8×C83—21no—
173C2×Q8×C83—21no—
174C2×Q8×C83C2×D412yes—
175C2×D4×C83—24no—
176C2×D4×C83—24no—
177C2×D4×C83—22no—
178C2×D4×C83—24no—
179C2×D4×C83—22no—
180C2×D4×C83—21no—
181C2×D4×C83—21no—
182C2×D4×C83—21no—
183C2×D4×C83—21no—
184C2×D4×C83—21no—
185C2×D4×C83—21no—
186C2×D4×C83—21no—
187C2×D4×C83—21no—
188C2×D4×C83—41no—
189C2×D4×C83—42no—
190C2×D4×C83—42no—
191C2×D4×C83—44no—
192C2×D4×C83—44no—
193C2×D4×C83—44no—
194C2×D4×C83—42no—
195C2×D4×C83—42no—
196C2×D4×C83—44no—
197C2×D4×C83—81no—
198C2×D4×C83—81no—
199C2×D4×C83C2×D412yes—
200C2×D4×C83C2×D412yes—
201C2×D4×C83#4112yes—
202C2×D4×C83#4112yes—
203C22×C4×C83—24no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83—21no—
217C22×C4×C83—21no—
218C22×C4×C83—24no—
219C22×C4×C83—21no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—21no—
223C22×C4×C83—42no—
224C22×C4×C83—42no—
225C22×C4×C83—81no—
226C22×C4×C83—81no—
227C22×C4×C83C2×D411yescharacteristic
228C22×C4×C83C2×D411yescharacteristic
229C22×C4×C83C2×D411yescharacteristic
230C22×C4×C83C2×D411yescharacteristic
231C22×C4×C83C2411yescharacteristic
232C2×C8×C83—21no—
233C2×C8×C83—21no—
234C2×C8×C83—21no—
235C2×C8×C83—21no—
236C2×C8×C83—21no—
237C2×C8×C83—21no—
238C2×C8×C83—21no—
239C2×C8×C83—21no—
240C2×C8×C83—21no—
241C2×C8×C83—21no—
242C2×C8×C83—21no—
243C2×C8×C83—21no—
244C4⋊C4×C83—24no—
245C4⋊C4×C83—22no—
246C4⋊C4×C83—21no—
247C4⋊C4×C83—21no—
248C4⋊C4×C83—21no—
249C4⋊C4×C83—21no—
250C4⋊C4×C83—21no—
251C4⋊C4×C83—21no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83—21no—
254C4⋊C4×C83—21no—
255C4⋊C4×C83—42no—
256C4⋊C4×C83—42no—
257C4⋊C4×C83C2×D412yes—
258C22⋊C4×C83—24no—
259C22⋊C4×C83—24no—
260C22⋊C4×C83—22no—
261C22⋊C4×C83—24no—
262C22⋊C4×C83—24no—
263C22⋊C4×C83—24no—
264C22⋊C4×C83—22no—
265C22⋊C4×C83—42no—
266C22⋊C4×C83—42no—
267C22⋊C4×C83—81no—
268C22⋊C4×C83—81no—
269C42×C83—81no—
270C42×C83C2×D412yes—
271C42×C83C2×D412yes—
272C23×C83—21no—
273C23×C83—22no—
274C23×C83—21no—
275C23×C83—21no—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83—21no—
279C23×C83—21no—
280C23×C83—21no—
281C23×C83—22no—
282C23×C83—21no—
283C23×C83—21no—
284C23×C83—21no—
285C23×C83—21no—
286C23×C83—21no—
287C23×C83—21no—
288C23×C83—21no—
289C23×C83—48no—
290C23×C83—48no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83—41no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—41no—
298C23×C83—41no—
299C23×C83—41no—
300C23×C83—41no—
301C23×C83—84no—
302C23×C83—84no—
303C23×C83—84no—
304C23×C83—84no—
305C23×C83—84no—
306C23×C83#13512yes—
307C23×C83C22×D411yescharacteristic
308Q8×C83—22no—
309Q8×C83—22no—
310Q8×C83—41no—
311Q8×C83—41no—
312D4×C83—22no—
313D4×C83—22no—
314D4×C83—22no—
315D4×C83—22no—
316D4×C83—22no—
317D4×C83—44no—
318D4×C83—48no—
319D4×C83—48no—
320D4×C83—41no—
321D4×C83—41no—
322D4×C83—84no—
323D4×C83#12414yes—
324C2×C4×C83—21no—
325C2×C4×C83—21no—
326C2×C4×C83—21no—
327C2×C4×C83—21no—
328C2×C4×C83—22no—
329C2×C4×C83—21no—
330C2×C4×C83—22no—
331C2×C4×C83—21no—
332C2×C4×C83—21no—
333C2×C4×C83—21no—
334C2×C4×C83—21no—
335C2×C4×C83—21no—
336C2×C4×C83—48no—
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—41no—
355C2×C4×C83—41no—
356C2×C4×C83—41no—
357C2×C4×C83—41no—
358C2×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—41no—
361C2×C4×C83—84no—
362C2×C4×C83#12012yes—
363C2×C4×C83#12012yes—
364C2×C4×C83C22×D411yescharacteristic
365C2×C4×C83C22×D411yescharacteristic
366C2×C4×C83C2×#4111yescharacteristic
367C2×C4×C83C2×#4111yescharacteristic
368C2×C4×C83H(5,𝔽2)11yescharacteristic
369C2×C4×C83H(5,𝔽2)11yescharacteristic
370C8×C83—41no—
371C8×C83—41no—
372C8×C83—41no—
373C8×C83—41no—
374C22×C83—24no—
375C22×C83—22no—
376C22×C83—22no—
377C22×C83—22no—
378C22×C83—41no—
379C22×C83—42no—
380C22×C83—42no—
381C22×C83—41no—
382C22×C83—42no—
383C22×C83—42no—
384C22×C83—41no—
385C22×C83—42no—
386C22×C83—41no—
387C22×C83—42no—
388C22×C83—41no—
389C22×C83—42no—
390C22×C83—41no—
391C22×C83—42no—
392C22×C83—41no—
393C22×C83—42no—
394C22×C83—41no—
395C22×C83—41no—
396C22×C83—41no—
397C22×C83—41no—
398C22×C83—816no—
399C22×C83—81no—
400C22×C83—81no—
401C22×C83—81no—
402C22×C83—81no—
403C22×C83C2×#12011yescharacteristic
404C22×C83#54611yescharacteristic
405C22×C83#54611yescharacteristic
406C22×C83C2×#13511yescharacteristic
407C22×C83#57511yescharacteristic
408C22×C83#57611yescharacteristic
409C22×C83#57711yescharacteristic
410C4×C83—22no—
411C4×C83—22no—
412C4×C83—41no—
413C4×C83—41no—
414C4×C83—42no—
415C4×C83—42no—
416C4×C83—81no—
417C4×C83—81no—
418C4×C83—81no—
419C4×C83—81no—
420C4×C83C2×#12411yescharacteristic
421C4×C83#53511yescharacteristic
422C4×C83#54611yescharacteristic
423C4×C83#54611yescharacteristic
424#25890C8311yesmaximal, characteristic, direct product factor, Sylow
425C2×C83—42no—
426C2×C83—44no—
427C2×C83—81no—
428C2×C83—82no—
429C2×C83#243511yescharacteristic
430C2×C83#300211yescharacteristic
431C2×C83#301211yescharacteristic
432C2×C83#329611yescharacteristic
433C2×C83#329711yescharacteristic
434C2×C83#332211yescharacteristic
435C2×C83#332311yescharacteristic
436C2×#546C2×C8311yescharacteristic
437C2×#488C2×C8311yescharacteristic, complemented
438C2×#478C2×C8311yescharacteristic, complemented
439#2562C2×C8311yescharacteristic, complemented
440#2036C2×C8311yescharacteristic, complemented
441#2035C2×C8311yescharacteristic, complemented
442#2034C2×C8311yescharacteristic, complemented
443#2033C2×C8311yescharacteristic, complemented
444#1983C2×C8311yescharacteristic, complemented
445#1954C2×C8311yescharacteristic, complemented
446#1788C2×C8311yescharacteristic, complemented
447#1788C2×C8311yescharacteristic, complemented
448#1786C2×C8311yescharacteristic, complemented
449#1786C2×C8311yescharacteristic, complemented
450C4×#102C2×C8311yescharacteristic, complemented
451C83#2589011yescharacteristic, direct product factor, Sylow
452C22×#41C22×C8311yescharacteristic
453C23×D4C22×C8311yescharacteristic
454#546—24no—
455#546—24no—
456C2×#125C22×C8311yescharacteristic, complemented
457C2×#124C22×C8311yescharacteristic
458C2×#123—21no—
459C2×C22⋊Q8C22×C8311yescharacteristic
460C2×#121—21no—
461C2×#121C22×C8311yescharacteristic
462C2×#120—21no—
463C2×C4×D4C22×C8311yescharacteristic
464C2×C4×D4C22×C8311yescharacteristic
465C22×C22⋊C4—21no—
466#488—24no—
467#478—24no—
468C2×#107C22×C8311yescharacteristic, complemented
469C2×#106C22×C8311yescharacteristic, complemented
470C2×C4⋊C8C22×C8311yescharacteristic, complemented
471C2×#103C22×C8311yescharacteristic, complemented
472C2×#103C22×C8311yescharacteristic, complemented
473C2×#103C22×C8311yescharacteristic, complemented
474C2×#103C22×C8311yescharacteristic, complemented
475C2×#102C22×C8311yescharacteristic
476C2×#102C22×C8311yescharacteristic
477C2×#102C22×C8311yescharacteristic
478C2×#102C22×C8311yescharacteristic
479C2×#102C22×C8311yescharacteristic
480C2×#102C22×C8311yescharacteristic
481C2×#102C22×C8311yescharacteristic
482C2×#102C22×C8311yescharacteristic
483C2×C22⋊C8C22×C8311yescharacteristic
484C2×C22⋊C8C22×C8311yescharacteristic
485C2×C22⋊C8C22×C8311yescharacteristic, complemented
486C2×C22⋊C8C22×C8311yescharacteristic, complemented
487C2×C4×C8C22×C8311yescharacteristic, complemented
488#400—21no—
489#394—21no—
490#388—21no—
491#388—21no—
492#380C22×C8311yescharacteristic
493#380C22×C8311yescharacteristic
494#380C22×C8311yescharacteristic, complemented
495#380C22×C8311yescharacteristic, complemented
496C4×C4⋊C4C22×C8311yescharacteristic, complemented
497#340C22×C8311yescharacteristic, complemented
498#340C22×C8311yescharacteristic, complemented
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C23×C8311yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C8311yescharacteristic
517C22×D4C23×C8311yescharacteristic
518C22×D4C23×C8311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C8311yescharacteristic
522C23×C4C23×C8311yescharacteristic
523C22×C8C23×C8311yescharacteristic
524C22×C8C23×C8311yescharacteristic
525C22×C8C23×C8311yescharacteristic
526C22×C8C23×C8311yescharacteristic
527#125—22no—
528#125—22no—
529#124—22no—
530#124D4×C8314yes—
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534#121—28no—
535#121—22no—
536#121—22no—
537#120—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4D4×C8314yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4D4×C8311yescharacteristic
546C2×C4⋊C4C23×C8311yescharacteristic
547C2×C4⋊C4C23×C8311yescharacteristic
548C2×C4⋊C4C23×C8311yescharacteristic
549C2×C4⋊C4C23×C8311yescharacteristic
550C2×C4⋊C4C23×C8311yescharacteristic
551C2×C22⋊C4—28no—
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⋊C4—21no—
561C2×C22⋊C4D4×C8311yescharacteristic
562C2×C22⋊C4D4×C8311yescharacteristic
563C2×C42—21no—
564C2×C42C23×C8311yescharacteristic
565#107—22no—
566#106—22no—
567C4⋊C8—22no—
568#103—22no—
569#103—22no—
570#103—41no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580C22⋊C8—41no—
581C22⋊C8—41no—
582C22⋊C8—41no—
583C22⋊C8—41no—
584C4×C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C8311yescharacteristic
600C24C2×D4×C8311yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C8312yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C8312yes—
636C2×D4C2×D4×C8312yes—
637C2×D4#41×C8312yes—
638C2×D4#41×C8312yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C8311yescharacteristic
664C22×C4C2×D4×C8311yescharacteristic
665C22×C4C2×D4×C8311yescharacteristic
666C22×C4C2×D4×C8311yescharacteristic
667C22×C4C24×C8311yescharacteristic
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4C2×D4×C8312yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—81no—
706C42C2×D4×C8312yes—
707C42C2×D4×C8312yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#135×C8312yes—
743C23C22×D4×C8311yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#124×C8314yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
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—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4#120×C8312yes—
799C2×C4#120×C8312yes—
800C2×C4C22×D4×C8311yescharacteristic
801C2×C4C22×D4×C8311yescharacteristic
802C2×C4C2×#41×C8311yescharacteristic
803C2×C4C2×#41×C8311yescharacteristic
804C2×C4H(5,𝔽2)×C8311yescharacteristic
805C2×C4H(5,𝔽2)×C8311yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—24no—
813C22—22no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C8311yescharacteristic
840C22#546×C8311yescharacteristic
841C22#546×C8311yescharacteristic
842C22C2×#135×C8311yescharacteristic
843C22#575×C8311yescharacteristic
844C22#576×C8311yescharacteristic
845C22#577×C8311yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C2×#124×C8311yescharacteristic
857C4#535×C8311yescharacteristic
858C4#546×C8311yescharacteristic
859C4#546×C8311yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2C83×#243511yescharacteristic
865C2C83×#300211yescharacteristic
866C2C83×#301211yescharacteristic
867C2C83×#329611yescharacteristic
868C2C83×#329711yescharacteristic
869C2C83×#332211yescharacteristic
870C2C83×#332311yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×#546×C83C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×C4×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#488×C83C2semidirect
3. C2×#478×C83C2semidirect
4. C83×#2562C2semidirect
5. C83×#2036C2semidirect
6. C83×#2035C2semidirect
7. C83×#2034C2semidirect
8. C83×#2033C2semidirect
9. C83×#1983C2semidirect
10. C83×#1954C2semidirect
11. C83×#1788C2semidirect
12. C83×#1788C2semidirect
13. C83×#1786C2semidirect
14. C83×#1786C2semidirect
15. C4×#102×C83C2semidirect
20. C2×#125×C83C22semidirect
32. C2×#107×C83C22semidirect
33. C2×#106×C83C22semidirect
34. C2×C4⋊C8×C83C22semidirect
35. C2×#103×C83C22semidirect
36. C2×#103×C83C22semidirect
37. C2×#103×C83C22semidirect
38. C2×#103×C83C22semidirect
49. C2×C22⋊C8×C83C22semidirect
50. C2×C22⋊C8×C83C22semidirect
51. C2×C4×C8×C83C22semidirect
58. #380×C83C22semidirect
59. #380×C83C22semidirect
60. C4×C4⋊C4×C83C22semidirect
61. #340×C83C22semidirect
62. #340×C83C22semidirect
424. #25890C83direct (N × H)
437. C2×#488C2×C83semidirect
438. C2×#478C2×C83semidirect
439. #2562C2×C83semidirect
440. #2036C2×C83semidirect
441. #2035C2×C83semidirect
442. #2034C2×C83semidirect
443. #2033C2×C83semidirect
444. #1983C2×C83semidirect
445. #1954C2×C83semidirect
446. #1788C2×C83semidirect
447. #1788C2×C83semidirect
448. #1786C2×C83semidirect
449. #1786C2×C83semidirect
450. C4×#102C2×C83semidirect
451. C83#25890direct (N × H)
456. C2×#125C22×C83semidirect
468. C2×#107C22×C83semidirect
469. C2×#106C22×C83semidirect
470. C2×C4⋊C8C22×C83semidirect
471. C2×#103C22×C83semidirect
472. C2×#103C22×C83semidirect
473. C2×#103C22×C83semidirect
474. C2×#103C22×C83semidirect
485. C2×C22⋊C8C22×C83semidirect
486. C2×C22⋊C8C22×C83semidirect
487. C2×C4×C8C22×C83semidirect
494. #380C22×C83semidirect
495. #380C22×C83semidirect
496. C4×C4⋊C4C22×C83semidirect
497. #340C22×C83semidirect
498. #340C22×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C832
C2×#488×C832
C2×#478×C832
C83×#25622
C83×#20362
C83×#20352
C83×#20342
C83×#20332
C83×#19832
C83×#19542
C83×#17882
C83×#17862
C4×#102×C832
#2589083