Finite Group Databasebeta

← C83×#18446 #35246270

Subgroups — C83×#18446 #35246270

Order 21248.

1032 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3534C211yesmaximal, characteristic, complemented
2C83×#3192C211yesmaximal, characteristic, complemented
3C83×#3188C211yesmaximal, characteristic, complemented
4C83×#2813C211yesmaximal, characteristic, complemented
5C83×#1618C211yesmaximal, characteristic, complemented
6C83×#1616C211yesmaximal, characteristic, complemented
7C83×#1615C211yesmaximal, characteristic, complemented
8C83×#1613C211yesmaximal, characteristic, complemented
9C83×#1600C211yesmaximal, characteristic, complemented
10C83×#1598C211yesmaximal, characteristic, complemented
11C83×#1597C211yesmaximal, characteristic, complemented
12C83×#1595C211yesmaximal, characteristic, complemented
13C83×#1519C211yesmaximal, characteristic, complemented
14C83×#1513C211yesmaximal, characteristic, complemented
15C83×#1468C211yesmaximal, characteristic, complemented
16#562×C83—21no—
17#560×C83—21no—
18#553×C83—21no—
19#551×C83—21no—
20#546×C83—21no—
21#546×C83—21no—
22#546×C83—21no—
23D42×C83—21no—
24#540×C83—21no—
25#539×C83—21no—
26#539×C83C2211yescharacteristic
27#538×C83—21no—
28#538×C83C2211yescharacteristic
29#537×C83C2211yescharacteristic
30#534×C83—21no—
31#534×C83C2211yescharacteristic
32#525×C83C2211yescharacteristic
33C2×#123×C83C2211yescharacteristic
34C2×#121×C83C2211yescharacteristic
35C2×#121×C83C2211yescharacteristic, complemented
36#484×C83C2211yescharacteristic, complemented
37#482×C83—21no—
38#481×C83—21no—
39#481×C83C2211yescharacteristic
40#481×C83C2211yescharacteristic, complemented
41#481×C83C2211yescharacteristic, complemented
42#469×C83—21no—
43#469×C83—21no—
44#466×C83—21no—
45#465×C83—21no—
46#450×C83C2211yescharacteristic, complemented
47#449×C83—21no—
48#447×C83—21no—
49#447×C83C2211yescharacteristic
50#447×C83C2211yescharacteristic, complemented
51#447×C83C2211yescharacteristic, complemented
52#407×C83C2211yescharacteristic, complemented
53C2×C22⋊C8×C83C2211yescharacteristic, complemented
54#400×C83C2211yescharacteristic, complemented
55#399×C83C2211yescharacteristic, complemented
56#396×C83—21no—
57#394×C83—21no—
58#394×C83—21no—
59#394×C83C2211yescharacteristic, complemented
60#392×C83—21no—
61#392×C83C2211yescharacteristic, complemented
62#380×C83C2211yescharacteristic, complemented
63#328×C83C2211yescharacteristic, complemented
64#328×C83C2211yescharacteristic, complemented
65#327×C83C2211yescharacteristic
66#327×C83C2211yescharacteristic
67#327×C83C2211yescharacteristic, complemented
68#327×C83C2211yescharacteristic, complemented
69#327×C83C2211yescharacteristic, complemented
70#327×C83C2211yescharacteristic, complemented
71#324×C83C2211yescharacteristic, complemented
72#324×C83C2211yescharacteristic, complemented
73#323×C83C2211yescharacteristic, complemented
74#323×C83C2211yescharacteristic, complemented
75C2×#41×C83—21no—
76C2×#41×C83D411yescharacteristic, complemented
77C22×D4×C83—21no—
78C22×D4×C83—21no—
79C22×D4×C83—21no—
80C22×D4×C83—21no—
81C22×D4×C83—21no—
82C22×D4×C83D411yescharacteristic
83C22×D4×C83D411yescharacteristic, complemented
84C22×D4×C83C2311yescharacteristic
85C23×C4×C83C2311yescharacteristic
86C2×SD16×C83—21no—
87C2×D8×C83—21no—
88C2×D8×C83—21no—
89C2×D8×C83—21no—
90C2×M16×C83—21no—
91C22×C8×C83—21no—
92#127×C83—21no—
93#126×C83—21no—
94#126×C83—21no—
95#126×C83—21no—
96#126×C83—21no—
97#125×C83—21no—
98#125×C83—21no—
99#124×C83—21no—
100#124×C83—21no—
101#124×C83—21no—
102#123×C83—21no—
103#123×C83—21no—
104#123×C83—21no—
105#123×C83—21no—
106#123×C83—21no—
107#123×C83—21no—
108#123×C83—21no—
109#123×C83—21no—
110#123×C83—21no—
111#123×C83—21no—
112#123×C83—21no—
113#123×C83—21no—
114#123×C83—21no—
115#123×C83—21no—
116C22⋊Q8×C83—21no—
117C22⋊Q8×C83—21no—
118C22⋊Q8×C83—21no—
119C22⋊Q8×C83—21no—
120C22⋊Q8×C83—21no—
121C22⋊Q8×C83D411yescharacteristic, complemented
122C22⋊Q8×C83C2311yescharacteristic
123#121×C83—21no—
124#121×C83—21no—
125#121×C83—21no—
126#121×C83—21no—
127#121×C83—21no—
128#121×C83—21no—
129#121×C83—21no—
130#121×C83—21no—
131#121×C83—21no—
132#121×C83—21no—
133#121×C83—21no—
134#121×C83—21no—
135#121×C83—21no—
136#121×C83—21no—
137#121×C83—21no—
138#121×C83—21no—
139#121×C83—21no—
140#121×C83—21no—
141#121×C83—21no—
142#121×C83D411yescharacteristic, complemented
143#121×C83D411yescharacteristic, complemented
144#121×C83D411yescharacteristic, complemented
145#121×C83C2311yescharacteristic
146#121×C83C2311yescharacteristic
147#121×C83C2311yescharacteristic
148#120×C83—21no—
149#120×C83—21no—
150#120×C83—21no—
151#120×C83—21no—
152#120×C83—21no—
153#120×C83—21no—
154#120×C83—21no—
155#120×C83—21no—
156C4×D4×C83—21no—
157C4×D4×C83—21no—
158C4×D4×C83—21no—
159C4×D4×C83—21no—
160C4×D4×C83—21no—
161C4×D4×C83—21no—
162C4×D4×C83—21no—
163C4×D4×C83—21no—
164#117×C83—21no—
165#117×C83D411yescharacteristic, complemented
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83D411yescharacteristic
169C2×C4⋊C4×C83D411yescharacteristic, complemented
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83—21no—
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83—21no—
177C2×C22⋊C4×C83—21no—
178C2×C22⋊C4×C83—21no—
179C2×C22⋊C4×C83—21no—
180C2×C22⋊C4×C83—21no—
181C2×C22⋊C4×C83D411yescharacteristic
182C2×C22⋊C4×C83D411yescharacteristic
183C2×C22⋊C4×C83C2311yescharacteristic
184#107×C83—21no—
185#106×C83—21no—
186#106×C83—21no—
187#106×C83—21no—
188#103×C83—21no—
189#102×C83—21no—
190#102×C83—21no—
191#102×C83—21no—
192#102×C83—21no—
193#102×C83—21no—
194#102×C83—21no—
195#102×C83—21no—
196C22⋊C8×C83—21no—
197C22⋊C8×C83—21no—
198C22⋊C8×C83C2311yescharacteristic
199C22⋊C8×C83C2311yescharacteristic
200C22⋊C8×C83C2311yescharacteristic
201C22⋊C8×C83C2311yescharacteristic
202#95×C83—21no—
203#95×C83—21no—
204#95×C83C2311yescharacteristic
205#95×C83C2311yescharacteristic
206C24×C83—21no—
207C24×C83—21no—
208C24×C83—21no—
209C24×C83C2×D411yescharacteristic
210C24×C83C2×D411yescharacteristic
211#41×C83—81no—
212#41×C83—81no—
213#41×C83—81no—
214C2×Q8×C83—21no—
215C2×Q8×C83C2×D411yescharacteristic
216C2×D4×C83—21no—
217C2×D4×C83—21no—
218C2×D4×C83—21no—
219C2×D4×C83—21no—
220C2×D4×C83—21no—
221C2×D4×C83—21no—
222C2×D4×C83—21no—
223C2×D4×C83—21no—
224C2×D4×C83—21no—
225C2×D4×C83—21no—
226C2×D4×C83—21no—
227C2×D4×C83—21no—
228C2×D4×C83—21no—
229C2×D4×C83—21no—
230C2×D4×C83—21no—
231C2×D4×C83—21no—
232C2×D4×C83—21no—
233C2×D4×C83—21no—
234C2×D4×C83—21no—
235C2×D4×C83—41no—
236C2×D4×C83—41no—
237C2×D4×C83—81no—
238C2×D4×C83—81no—
239C2×D4×C83—81no—
240C2×D4×C83—81no—
241C2×D4×C83—81no—
242C2×D4×C83—81no—
243C2×D4×C83—81no—
244C2×D4×C83—81no—
245C2×D4×C83—81no—
246C2×D4×C83—81no—
247C2×D4×C83—81no—
248C2×D4×C83—81no—
249C2×D4×C83—82no—
250C2×D4×C83C2×D411yescharacteristic
251C2×D4×C83C2×D411yescharacteristic
252C2×D4×C83C2×D411yescharacteristic
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83—21no—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—81no—
264C22×C4×C83C2×D411yescharacteristic
265C22×C4×C83C2×D411yescharacteristic
266C22×C4×C83C2×D411yescharacteristic
267C22×C4×C83C2×D411yescharacteristic
268C22×C4×C83C2×D411yescharacteristic
269C22×C4×C83C2×D411yescharacteristic
270C22×C4×C83C2×D411yescharacteristic
271C22×C4×C83C2×D411yescharacteristic
272C22×C4×C83C2411yescharacteristic
273SD16×C83—81no—
274D8×C83—81no—
275D8×C83—81no—
276D8×C83—81no—
277M16×C83—81no—
278C2×C8×C83—21no—
279C2×C8×C83—21no—
280C2×C8×C83—21no—
281C2×C8×C83—21no—
282C2×C8×C83—81no—
283C4⋊C4×C83—21no—
284C4⋊C4×C83—21no—
285C4⋊C4×C83—21no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83—21no—
288C4⋊C4×C83—21no—
289C4⋊C4×C83—21no—
290C4⋊C4×C83—21no—
291C4⋊C4×C83—21no—
292C4⋊C4×C83—21no—
293C4⋊C4×C83—21no—
294C4⋊C4×C83—21no—
295C4⋊C4×C83—21no—
296C4⋊C4×C83—21no—
297C4⋊C4×C83—21no—
298C4⋊C4×C83—81no—
299C4⋊C4×C83—81no—
300C4⋊C4×C83C2×D411yescharacteristic
301C4⋊C4×C83C2×D411yescharacteristic
302C4⋊C4×C83C2×D411yescharacteristic
303C4⋊C4×C83C2×D411yescharacteristic
304C22⋊C4×C83—21no—
305C22⋊C4×C83—21no—
306C22⋊C4×C83—21no—
307C22⋊C4×C83—21no—
308C22⋊C4×C83—21no—
309C22⋊C4×C83—21no—
310C22⋊C4×C83—21no—
311C22⋊C4×C83—21no—
312C22⋊C4×C83—21no—
313C22⋊C4×C83—21no—
314C22⋊C4×C83—21no—
315C22⋊C4×C83—21no—
316C22⋊C4×C83—21no—
317C22⋊C4×C83—21no—
318C22⋊C4×C83—21no—
319C22⋊C4×C83—21no—
320C22⋊C4×C83—21no—
321C22⋊C4×C83—21no—
322C22⋊C4×C83—21no—
323C22⋊C4×C83—21no—
324C22⋊C4×C83—21no—
325C22⋊C4×C83—21no—
326C22⋊C4×C83—21no—
327C22⋊C4×C83—21no—
328C22⋊C4×C83—21no—
329C22⋊C4×C83—41no—
330C22⋊C4×C83—41no—
331C22⋊C4×C83—81no—
332C22⋊C4×C83—81no—
333C22⋊C4×C83—81no—
334C22⋊C4×C83—81no—
335C22⋊C4×C83—81no—
336C42×C83—21no—
337C42×C83—21no—
338C42×C83—21no—
339C23×C83—21no—
340C23×C83—21no—
341C23×C83—21no—
342C23×C83—21no—
343C23×C83—21no—
344C23×C83—21no—
345C23×C83—21no—
346C23×C83—21no—
347C23×C83—41no—
348C23×C83—41no—
349C23×C83—42no—
350C23×C83—41no—
351C23×C83—41no—
352C23×C83—41no—
353C23×C83—41no—
354C23×C83—41no—
355C23×C83—41no—
356C23×C83—41no—
357C23×C83—41no—
358C23×C83—41no—
359C23×C83—81no—
360C23×C83—81no—
361C23×C83—81no—
362C23×C83—81no—
363C23×C83—81no—
364C23×C83#12011yescharacteristic
365C23×C83#12011yescharacteristic
366C23×C83C22×D411yescharacteristic
367Q8×C83—41no—
368Q8×C83—81no—
369D4×C83—41no—
370D4×C83—41no—
371D4×C83—41no—
372D4×C83—41no—
373D4×C83—41no—
374D4×C83—41no—
375D4×C83—41no—
376D4×C83—42no—
377D4×C83—42no—
378D4×C83—41no—
379D4×C83—41no—
380D4×C83—41no—
381D4×C83—41no—
382D4×C83—41no—
383D4×C83—41no—
384D4×C83—81no—
385D4×C83—81no—
386D4×C83—81no—
387D4×C83—81no—
388D4×C83—81no—
389D4×C83—81no—
390D4×C83—81no—
391D4×C83—81no—
392D4×C83—81no—
393D4×C83—81no—
394D4×C83—81no—
395D4×C83—81no—
396D4×C83—82no—
397D4×C83—82no—
398D4×C83—84no—
399C2×C4×C83—21no—
400C2×C4×C83—21no—
401C2×C4×C83—21no—
402C2×C4×C83—21no—
403C2×C4×C83—21no—
404C2×C4×C83—21no—
405C2×C4×C83—21no—
406C2×C4×C83—21no—
407C2×C4×C83—21no—
408C2×C4×C83—21no—
409C2×C4×C83—41no—
410C2×C4×C83—41no—
411C2×C4×C83—41no—
412C2×C4×C83—41no—
413C2×C4×C83—41no—
414C2×C4×C83—41no—
415C2×C4×C83—41no—
416C2×C4×C83—41no—
417C2×C4×C83—41no—
418C2×C4×C83—41no—
419C2×C4×C83—41no—
420C2×C4×C83—41no—
421C2×C4×C83—41no—
422C2×C4×C83—41no—
423C2×C4×C83—41no—
424C2×C4×C83—41no—
425C2×C4×C83—41no—
426C2×C4×C83—81no—
427C2×C4×C83—81no—
428C2×C4×C83—81no—
429C2×C4×C83—81no—
430C2×C4×C83—81no—
431C2×C4×C83—81no—
432C2×C4×C83—81no—
433C2×C4×C83#12011yescharacteristic
434C2×C4×C83#12011yescharacteristic
435C2×C4×C83C22×D411yescharacteristic
436C2×C4×C83C22×D411yescharacteristic
437C8×C83—41no—
438C8×C83—41no—
439C8×C83—41no—
440C8×C83—41no—
441C22×C83—21no—
442C22×C83—21no—
443C22×C83—21no—
444C22×C83—21no—
445C22×C83—21no—
446C22×C83—21no—
447C22×C83—21no—
448C22×C83—21no—
449C22×C83—41no—
450C22×C83—41no—
451C22×C83—41no—
452C22×C83—41no—
453C22×C83—41no—
454C22×C83—41no—
455C22×C83—41no—
456C22×C83—41no—
457C22×C83—41no—
458C22×C83—41no—
459C22×C83—41no—
460C22×C83—41no—
461C22×C83—81no—
462C22×C83—81no—
463C22×C83—81no—
464C22×C83—81no—
465C22×C83—81no—
466C22×C83—81no—
467C22×C83—81no—
468C22×C83—81no—
469C22×C83—81no—
470C22×C83—81no—
471C22×C83—81no—
472C22×C83—162no—
473C22×C83—162no—
474C22×C83C2×#12011yescharacteristic
475C22×C83#57611yescharacteristic
476C22×C83#57711yescharacteristic
477C4×C83—21no—
478C4×C83—21no—
479C4×C83—21no—
480C4×C83—21no—
481C4×C83—41no—
482C4×C83—41no—
483C4×C83—41no—
484C4×C83—41no—
485C4×C83—41no—
486C4×C83—41no—
487C4×C83—41no—
488C4×C83—41no—
489C4×C83—81no—
490C4×C83—81no—
491C4×C83—81no—
492#18446C8311yesmaximal, characteristic, direct product factor, Sylow
493C2×C83—21no—
494C2×C83—21no—
495C2×C83—41no—
496C2×C83—41no—
497C2×C83—81no—
498C2×C83—81no—
499C2×C83—81no—
500C2×C83—81no—
501C2×C83—161no—
502C2×C83#301211yescharacteristic
503C2×C83#302111yescharacteristic
504C2×C83#302611yescharacteristic
505#3534C2×C8311yescharacteristic, complemented
506#3192C2×C8311yescharacteristic, complemented
507#3188C2×C8311yescharacteristic, complemented
508#2813C2×C8311yescharacteristic, complemented
509#1618C2×C8311yescharacteristic, complemented
510#1616C2×C8311yescharacteristic, complemented
511#1615C2×C8311yescharacteristic, complemented
512#1613C2×C8311yescharacteristic, complemented
513#1600C2×C8311yescharacteristic, complemented
514#1598C2×C8311yescharacteristic, complemented
515#1597C2×C8311yescharacteristic, complemented
516#1595C2×C8311yescharacteristic, complemented
517#1519C2×C8311yescharacteristic, complemented
518#1513C2×C8311yescharacteristic, complemented
519#1468C2×C8311yescharacteristic, complemented
520C83#1844611yescharacteristic, direct product factor, Sylow
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C8311yescharacteristic
532#538—21no—
533#538C22×C8311yescharacteristic
534#537C22×C8311yescharacteristic
535#534—21no—
536#534C22×C8311yescharacteristic
537#525C22×C8311yescharacteristic
538C2×#123C22×C8311yescharacteristic
539C2×#121C22×C8311yescharacteristic
540C2×#121C22×C8311yescharacteristic, complemented
541#484C22×C8311yescharacteristic, complemented
542#482—21no—
543#481—21no—
544#481C22×C8311yescharacteristic
545#481C22×C8311yescharacteristic, complemented
546#481C22×C8311yescharacteristic, complemented
547#469—21no—
548#469—21no—
549#466—21no—
550#465—21no—
551#450C22×C8311yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C8311yescharacteristic
555#447C22×C8311yescharacteristic, complemented
556#447C22×C8311yescharacteristic, complemented
557#407C22×C8311yescharacteristic, complemented
558C2×C22⋊C8C22×C8311yescharacteristic, complemented
559#400C22×C8311yescharacteristic, complemented
560#399C22×C8311yescharacteristic, complemented
561#396—21no—
562#394—21no—
563#394—21no—
564#394C22×C8311yescharacteristic, complemented
565#392—21no—
566#392C22×C8311yescharacteristic, complemented
567#380C22×C8311yescharacteristic, complemented
568#328C22×C8311yescharacteristic, complemented
569#328C22×C8311yescharacteristic, complemented
570#327C22×C8311yescharacteristic
571#327C22×C8311yescharacteristic
572#327C22×C8311yescharacteristic, complemented
573#327C22×C8311yescharacteristic, complemented
574#327C22×C8311yescharacteristic, complemented
575#327C22×C8311yescharacteristic, complemented
576#324C22×C8311yescharacteristic, complemented
577#324C22×C8311yescharacteristic, complemented
578#323C22×C8311yescharacteristic, complemented
579#323C22×C8311yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C8311yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C8311yescharacteristic
588C22×D4D4×C8311yescharacteristic, complemented
589C22×D4C23×C8311yescharacteristic
590C23×C4C23×C8311yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C8311yescharacteristic, complemented
627C22⋊Q8C23×C8311yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C8311yescharacteristic, complemented
648#121D4×C8311yescharacteristic, complemented
649#121D4×C8311yescharacteristic, complemented
650#121C23×C8311yescharacteristic
651#121C23×C8311yescharacteristic
652#121C23×C8311yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C8311yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4D4×C8311yescharacteristic
674C2×C4⋊C4D4×C8311yescharacteristic, complemented
675C2×C4⋊C4C23×C8311yescharacteristic
676C2×C4⋊C4C23×C8311yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4D4×C8311yescharacteristic
687C2×C22⋊C4D4×C8311yescharacteristic
688C2×C22⋊C4C23×C8311yescharacteristic
689#107—21no—
690#106—21no—
691#106—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C8311yescharacteristic
704C22⋊C8C23×C8311yescharacteristic
705C22⋊C8C23×C8311yescharacteristic
706C22⋊C8C23×C8311yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C8311yescharacteristic
710#95C23×C8311yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C8311yescharacteristic
715C24C2×D4×C8311yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C8311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C8311yescharacteristic
756C2×D4C2×D4×C8311yescharacteristic
757C2×D4C2×D4×C8311yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C8311yescharacteristic
770C22×C4C2×D4×C8311yescharacteristic
771C22×C4C2×D4×C8311yescharacteristic
772C22×C4C2×D4×C8311yescharacteristic
773C22×C4C2×D4×C8311yescharacteristic
774C22×C4C2×D4×C8311yescharacteristic
775C22×C4C2×D4×C8311yescharacteristic
776C22×C4C2×D4×C8311yescharacteristic
777C22×C4C24×C8311yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4—81no—
805C4⋊C4C2×D4×C8311yescharacteristic
806C4⋊C4C2×D4×C8311yescharacteristic
807C4⋊C4C2×D4×C8311yescharacteristic
808C4⋊C4C2×D4×C8311yescharacteristic
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—81no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C22⋊C4—81no—
841C42—21no—
842C42—21no—
843C42—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C8311yescharacteristic
870C23#120×C8311yescharacteristic
871C23C22×D4×C8311yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—82no—
902D4—82no—
903D4—84no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C8311yescharacteristic
939C2×C4#120×C8311yescharacteristic
940C2×C4C22×D4×C8311yescharacteristic
941C2×C4C22×D4×C8311yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C8311yescharacteristic
980C22#576×C8311yescharacteristic
981C22#577×C8311yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—81no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C83×#301211yescharacteristic
1007C2C83×#302111yescharacteristic
1008C2C83×#302611yescharacteristic
subgroupG/H
center, socleC22×C83C2×#120
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3534C2semidirect
2. C83×#3192C2semidirect
3. C83×#3188C2semidirect
4. C83×#2813C2semidirect
5. C83×#1618C2semidirect
6. C83×#1616C2semidirect
7. C83×#1615C2semidirect
8. C83×#1613C2semidirect
9. C83×#1600C2semidirect
10. C83×#1598C2semidirect
11. C83×#1597C2semidirect
12. C83×#1595C2semidirect
13. C83×#1519C2semidirect
14. C83×#1513C2semidirect
15. C83×#1468C2semidirect
35. C2×#121×C83C22semidirect
36. #484×C83C22semidirect
40. #481×C83C22semidirect
41. #481×C83C22semidirect
46. #450×C83C22semidirect
50. #447×C83C22semidirect
51. #447×C83C22semidirect
52. #407×C83C22semidirect
53. C2×C22⋊C8×C83C22semidirect
54. #400×C83C22semidirect
55. #399×C83C22semidirect
59. #394×C83C22semidirect
61. #392×C83C22semidirect
62. #380×C83C22semidirect
63. #328×C83C22semidirect
64. #328×C83C22semidirect
67. #327×C83C22semidirect
68. #327×C83C22semidirect
69. #327×C83C22semidirect
70. #327×C83C22semidirect
71. #324×C83C22semidirect
72. #324×C83C22semidirect
73. #323×C83C22semidirect
74. #323×C83C22semidirect
76. C2×#41×C83D4semidirect
83. C22×D4×C83D4semidirect
121. C22⋊Q8×C83D4semidirect
142. #121×C83D4semidirect
143. #121×C83D4semidirect
144. #121×C83D4semidirect
165. #117×C83D4semidirect
169. C2×C4⋊C4×C83D4semidirect
492. #18446C83direct (N × H)
505. #3534C2×C83semidirect
506. #3192C2×C83semidirect
507. #3188C2×C83semidirect
508. #2813C2×C83semidirect
509. #1618C2×C83semidirect
510. #1616C2×C83semidirect
511. #1615C2×C83semidirect
512. #1613C2×C83semidirect
513. #1600C2×C83semidirect
514. #1598C2×C83semidirect
515. #1597C2×C83semidirect
516. #1595C2×C83semidirect
517. #1519C2×C83semidirect
518. #1513C2×C83semidirect
519. #1468C2×C83semidirect
520. C83#18446direct (N × H)
540. C2×#121C22×C83semidirect
541. #484C22×C83semidirect
545. #481C22×C83semidirect
546. #481C22×C83semidirect
551. #450C22×C83semidirect
555. #447C22×C83semidirect
556. #447C22×C83semidirect
557. #407C22×C83semidirect
558. C2×C22⋊C8C22×C83semidirect
559. #400C22×C83semidirect
560. #399C22×C83semidirect
564. #394C22×C83semidirect
566. #392C22×C83semidirect
567. #380C22×C83semidirect
568. #328C22×C83semidirect
569. #328C22×C83semidirect
572. #327C22×C83semidirect
573. #327C22×C83semidirect
574. #327C22×C83semidirect
575. #327C22×C83semidirect
576. #324C22×C83semidirect
577. #324C22×C83semidirect
578. #323C22×C83semidirect
579. #323C22×C83semidirect
581. C2×#41D4×C83semidirect
588. C22×D4D4×C83semidirect
626. C22⋊Q8D4×C83semidirect
647. #121D4×C83semidirect
648. #121D4×C83semidirect
649. #121D4×C83semidirect
670. #117D4×C83semidirect
674. C2×C4⋊C4D4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35342
C83×#31922
C83×#31882
C83×#28132
C83×#16182
C83×#16162
C83×#16152
C83×#16132
C83×#16002
C83×#15982
C83×#15972
C83×#15952
C83×#15192
C83×#15132
C83×#14682
#1844683