Finite Group Databasebeta

← C83×#24443 #35252267

Subgroups — C83×#24443 #35252267

Order 21248.

1510 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C83C211yesmaximal, characteristic
2C2×#468×C83C211yesmaximal, characteristic, complemented
3C2×#452×C83C211yesmaximal, characteristic, complemented
4C2×#452×C83C211yesmaximal, characteristic, complemented
5C2×#417×C83C211yesmaximal, characteristic, complemented
6C83×#2417C211yesmaximal, characteristic, complemented
7C83×#2041C211yesmaximal, characteristic, complemented
8C83×#2033C211yesmaximal, characteristic, complemented
9C83×#2014C211yesmaximal, characteristic, complemented
10C83×#2000C211yesmaximal, characteristic, complemented
11C83×#1878C211yesmaximal, characteristic, complemented
12C83×#1874C211yesmaximal, characteristic, complemented
13C83×#1870C211yesmaximal, characteristic, complemented
14C83×#1863C211yesmaximal, characteristic, complemented
15C83×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C22×#41×C83C2211yescharacteristic
18C22×Q16×C83C2211yescharacteristic
19C22×SD16×C83C2211yescharacteristic
20C22×SD16×C83C2211yescharacteristic
21C22×M16×C83C2211yescharacteristic
22#550×C83—24no—
23#550×C83—24no—
24C2×#127×C83—21no—
25C2×#127×C83C2211yescharacteristic
26C2×C22⋊Q8×C83C2211yescharacteristic
27C2×C22⋊Q8×C83C2211yescharacteristic
28C2×#121×C83—21no—
29C2×#121×C83—21no—
30C2×#121×C83C2211yescharacteristic
31C2×#121×C83C2211yescharacteristic
32C2×C4×Q8×C83C2211yescharacteristic
33C2×C4×D4×C83—21no—
34C2×C4×D4×C83C2211yescharacteristic
35C22×C4⋊C4×C83C2211yescharacteristic
36#468×C83—24no—
37#452×C83—24no—
38#452×C83—24no—
39C2×#107×C83C2211yescharacteristic
40#417×C83—24no—
41C2×#103×C83C2211yescharacteristic
42C2×#103×C83C2211yescharacteristic
43C2×#103×C83C2211yescharacteristic
44C2×#103×C83C2211yescharacteristic
45C2×#102×C83C2211yescharacteristic
46C2×#102×C83C2211yescharacteristic
47C2×#102×C83C2211yescharacteristic
48C2×#102×C83C2211yescharacteristic
49C2×#102×C83C2211yescharacteristic
50C2×#102×C83C2211yescharacteristic
51C2×C22⋊C8×C83C2211yescharacteristic
52C2×C22⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic
54#398×C83—21no—
55#396×C83—21no—
56#391×C83C2211yescharacteristic
57#389×C83C2211yescharacteristic
58#386×C83—21no—
59#380×C83—21no—
60#380×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic
62#340×C83C2211yescharacteristic
63#336×C83C2211yescharacteristic
64#336×C83C2211yescharacteristic
65C2×#41×C83—22no—
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—22no—
69C2×#41×C83—22no—
70C2×#41×C83—22no—
71C2×#41×C83—22no—
72C2×#41×C83—41no—
73C2×#41×C83—41no—
74C2×#41×C83—41no—
75C2×#41×C83—41no—
76C2×#41×C83D414yes—
77C22×Q8×C83C2311yescharacteristic
78C22×Q8×C83C2311yescharacteristic
79C22×D4×C83—21no—
80C22×D4×C83—21no—
81C22×D4×C83—21no—
82C22×D4×C83—21no—
83C22×D4×C83—21no—
84C22×D4×C83—21no—
85C22×D4×C83D411yescharacteristic
86C22×D4×C83C2311yescharacteristic
87C22×D4×C83C2311yescharacteristic
88C23×C4×C83—21no—
89C23×C4×C83—21no—
90C23×C4×C83—21no—
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C2×Q16×C83—22no—
94C2×Q16×C83—22no—
95C2×Q16×C83—22no—
96C2×SD16×C83—22no—
97C2×SD16×C83—22no—
98C2×SD16×C83—22no—
99C2×SD16×C83—41no—
100C2×SD16×C83—41no—
101C2×SD16×C83—41no—
102C2×M16×C83—22no—
103C2×M16×C83—22no—
104C2×M16×C83—41no—
105C22×C8×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109#127×C83—28no—
110#127×C83—22no—
111#127×C83—22no—
112C22⋊Q8×C83—22no—
113C22⋊Q8×C83—22no—
114C22⋊Q8×C83—22no—
115C22⋊Q8×C83—41no—
116#121×C83—28no—
117#121×C83—28no—
118#121×C83—22no—
119#121×C83—22no—
120#121×C83—22no—
121#121×C83D414yes—
122C4×Q8×C83—22no—
123C4×Q8×C83—22no—
124C4×D4×C83—28no—
125C4×D4×C83—22no—
126C4×D4×C83—22no—
127C2×C4⋊C4×C83—21no—
128C2×C4⋊C4×C83—22no—
129C2×C4⋊C4×C83—21no—
130C2×C4⋊C4×C83—21no—
131C2×C4⋊C4×C83—21no—
132C2×C4⋊C4×C83—21no—
133C2×C4⋊C4×C83—41no—
134C2×C4⋊C4×C83D411yescharacteristic
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83C2311yescharacteristic
137C2×C4⋊C4×C83C2311yescharacteristic
138C2×C4⋊C4×C83C2311yescharacteristic
139C2×C22⋊C4×C83—21no—
140C2×C22⋊C4×C83—21no—
141C2×C22⋊C4×C83—21no—
142C2×C22⋊C4×C83—21no—
143C2×C22⋊C4×C83—21no—
144C2×C22⋊C4×C83D411yescharacteristic
145C2×C22⋊C4×C83D411yescharacteristic
146C2×C42×C83—21no—
147C2×C42×C83C2311yescharacteristic
148#107×C83—22no—
149#103×C83—22no—
150#103×C83—22no—
151#103×C83—22no—
152#103×C83D414yescomplemented
153#102×C83—22no—
154#102×C83—22no—
155#102×C83—22no—
156#102×C83—22no—
157#102×C83—22no—
158#102×C83—41no—
159C22⋊C8×C83—22no—
160C22⋊C8×C83—22no—
161C22⋊C8×C83—41no—
162#95×C83—21no—
163#95×C83—21no—
164#95×C83—21no—
165#95×C83—21no—
166C24×C83—21no—
167C24×C83—21no—
168C24×C83C2×D411yescharacteristic
169C24×C83C2×D411yescharacteristic
170#41×C83—28no—
171#41×C83—44no—
172#41×C83—44no—
173#41×C83—44no—
174#41×C83—44no—
175#41×C83—44no—
176#41×C83—44no—
177#41×C83—44no—
178C2×Q8×C83—21no—
179C2×Q8×C83—21no—
180C2×Q8×C83—21no—
181C2×Q8×C83—21no—
182C2×Q8×C83—21no—
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83—21no—
186C2×Q8×C83—21no—
187C2×Q8×C83C2×D412yes—
188C2×Q8×C83C2×D412yes—
189C2×Q8×C83#4112yes—
190C2×D4×C83—24no—
191C2×D4×C83—24no—
192C2×D4×C83—22no—
193C2×D4×C83—24no—
194C2×D4×C83—24no—
195C2×D4×C83—24no—
196C2×D4×C83—24no—
197C2×D4×C83—22no—
198C2×D4×C83—21no—
199C2×D4×C83—21no—
200C2×D4×C83—21no—
201C2×D4×C83—21no—
202C2×D4×C83—21no—
203C2×D4×C83—21no—
204C2×D4×C83—21no—
205C2×D4×C83—21no—
206C2×D4×C83—21no—
207C2×D4×C83—21no—
208C2×D4×C83—41no—
209C2×D4×C83—42no—
210C2×D4×C83—42no—
211C2×D4×C83—42no—
212C2×D4×C83—42no—
213C2×D4×C83—42no—
214C2×D4×C83—42no—
215C2×D4×C83—81no—
216C2×D4×C83—81no—
217C2×D4×C83—81no—
218C2×D4×C83—81no—
219C2×D4×C83—81no—
220C2×D4×C83—81no—
221C2×D4×C83C2×D412yes—
222C2×D4×C83C2×D412yes—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—24no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—24no—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—42no—
242C22×C4×C83—42no—
243C22×C4×C83—42no—
244C22×C4×C83—42no—
245C22×C4×C83—42no—
246C22×C4×C83—42no—
247C22×C4×C83—81no—
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D412yes—
252C22×C4×C83C2×D412yes—
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2411yescharacteristic
255Q16×C83—44no—
256SD16×C83—44no—
257SD16×C83—44no—
258M16×C83—44no—
259C2×C8×C83—21no—
260C2×C8×C83—21no—
261C2×C8×C83—21no—
262C2×C8×C83—21no—
263C2×C8×C83—21no—
264C2×C8×C83—21no—
265C2×C8×C83—21no—
266C2×C8×C83—21no—
267C2×C8×C83—21no—
268C2×C8×C83—21no—
269C2×C8×C83—21no—
270C2×C8×C83C2×D412yes—
271C4⋊C4×C83—24no—
272C4⋊C4×C83—22no—
273C4⋊C4×C83—21no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—21no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83—21no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83—42no—
280C4⋊C4×C83—42no—
281C4⋊C4×C83—42no—
282C4⋊C4×C83—81no—
283C4⋊C4×C83C2×D412yes—
284C4⋊C4×C83C2×D412yes—
285C22⋊C4×C83—24no—
286C22⋊C4×C83—22no—
287C22⋊C4×C83—24no—
288C22⋊C4×C83—22no—
289C22⋊C4×C83—42no—
290C22⋊C4×C83—42no—
291C22⋊C4×C83—81no—
292C42×C83—24no—
293C42×C83—21no—
294C42×C83—21no—
295C23×C83—21no—
296C23×C83—21no—
297C23×C83—21no—
298C23×C83—21no—
299C23×C83—21no—
300C23×C83—21no—
301C23×C83—21no—
302C23×C83—22no—
303C23×C83—22no—
304C23×C83—21no—
305C23×C83—21no—
306C23×C83—21no—
307C23×C83—21no—
308C23×C83—21no—
309C23×C83—21no—
310C23×C83—41no—
311C23×C83—41no—
312C23×C83—41no—
313C23×C83—41no—
314C23×C83—41no—
315C23×C83—41no—
316C23×C83—41no—
317C23×C83—41no—
318C23×C83—41no—
319C23×C83—41no—
320C23×C83—41no—
321C23×C83—41no—
322C23×C83#12012yes—
323C23×C83C22×D411yescharacteristic
324Q8×C83—22no—
325Q8×C83—22no—
326Q8×C83—22no—
327Q8×C83—41no—
328Q8×C83—41no—
329Q8×C83—41no—
330Q8×C83—41no—
331Q8×C83#12114yes—
332D4×C83—22no—
333D4×C83—22no—
334D4×C83—22no—
335D4×C83—22no—
336D4×C83—44no—
337D4×C83—48no—
338D4×C83—48no—
339D4×C83—48no—
340D4×C83—41no—
341D4×C83—41no—
342D4×C83—41no—
343D4×C83—41no—
344D4×C83—84no—
345D4×C83—84no—
346D4×C83—84no—
347C2×C4×C83—21no—
348C2×C4×C83—22no—
349C2×C4×C83—21no—
350C2×C4×C83—22no—
351C2×C4×C83—21no—
352C2×C4×C83—22no—
353C2×C4×C83—21no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
358C2×C4×C83—21no—
359C2×C4×C83—22no—
360C2×C4×C83—21no—
361C2×C4×C83—22no—
362C2×C4×C83—21no—
363C2×C4×C83—21no—
364C2×C4×C83—21no—
365C2×C4×C83—21no—
366C2×C4×C83—48no—
367C2×C4×C83—48no—
368C2×C4×C83—41no—
369C2×C4×C83—41no—
370C2×C4×C83—41no—
371C2×C4×C83—41no—
372C2×C4×C83—41no—
373C2×C4×C83—41no—
374C2×C4×C83—41no—
375C2×C4×C83—41no—
376C2×C4×C83—41no—
377C2×C4×C83—41no—
378C2×C4×C83—41no—
379C2×C4×C83—41no—
380C2×C4×C83—41no—
381C2×C4×C83—41no—
382C2×C4×C83—41no—
383C2×C4×C83—41no—
384C2×C4×C83—41no—
385C2×C4×C83—84no—
386C2×C4×C83#12012yes—
387C2×C4×C83#13712yes—
388C2×C4×C83C22×D411yescharacteristic
389C2×C4×C83C22×D411yescharacteristic
390C2×C4×C83C22×D411yescharacteristic
391C2×C4×C83C2×#4111yescharacteristic
392C2×C4×C83H(5,𝔽2)11yescharacteristic
393C2×C4×C83H(5,𝔽2)11yescharacteristic
394C8×C83—22no—
395C8×C83—41no—
396C8×C83—41no—
397C8×C83—41no—
398C22×C83—22no—
399C22×C83—22no—
400C22×C83—22no—
401C22×C83—41no—
402C22×C83—41no—
403C22×C83—41no—
404C22×C83—41no—
405C22×C83—41no—
406C22×C83—42no—
407C22×C83—42no—
408C22×C83—41no—
409C22×C83—41no—
410C22×C83—42no—
411C22×C83—42no—
412C22×C83—41no—
413C22×C83—42no—
414C22×C83—42no—
415C22×C83—41no—
416C22×C83—41no—
417C22×C83—41no—
418C22×C83—81no—
419C22×C83—81no—
420C22×C83—81no—
421C22×C83—81no—
422C22×C83—81no—
423C22×C83—81no—
424C22×C83—81no—
425C22×C83—81no—
426C22×C83C2×#12011yescharacteristic
427C22×C83D4211yescharacteristic
428C22×C83#54611yescharacteristic
429C22×C83C2×#13711yescharacteristic
430C22×C83#57511yescharacteristic
431C22×C83#57611yescharacteristic
432C22×C83#57711yescharacteristic
433C4×C83—22no—
434C4×C83—24no—
435C4×C83—22no—
436C4×C83—41no—
437C4×C83—41no—
438C4×C83—42no—
439C4×C83—42no—
440C4×C83—81no—
441C4×C83—81no—
442C4×C83—81no—
443C4×C83C2×#12111yescharacteristic
444C4×C83#53411yescharacteristic
445C4×C83D4211yescharacteristic
446C4×C83#54611yescharacteristic
447#24443C8311yesmaximal, characteristic, direct product factor, Sylow
448C2×C83—42no—
449C2×C83—81no—
450C2×C83—82no—
451C2×C83—82no—
452C2×C83#241011yescharacteristic
453C2×C83#300711yescharacteristic
454C2×C83#301211yescharacteristic
455C2×C83#326811yescharacteristic
456C2×C83#327811yescharacteristic
457C2×C83#331711yescharacteristic
458C2×C83#333311yescharacteristic
459C2×#550C2×C8311yescharacteristic
460C2×#468C2×C8311yescharacteristic, complemented
461C2×#452C2×C8311yescharacteristic, complemented
462C2×#452C2×C8311yescharacteristic, complemented
463C2×#417C2×C8311yescharacteristic, complemented
464#2417C2×C8311yescharacteristic, complemented
465#2041C2×C8311yescharacteristic, complemented
466#2033C2×C8311yescharacteristic, complemented
467#2014C2×C8311yescharacteristic, complemented
468#2000C2×C8311yescharacteristic, complemented
469#1878C2×C8311yescharacteristic, complemented
470#1874C2×C8311yescharacteristic, complemented
471#1870C2×C8311yescharacteristic, complemented
472#1863C2×C8311yescharacteristic, complemented
473#1788C2×C8311yescharacteristic, complemented
474C83#2444311yescharacteristic, direct product factor, Sylow
475C22×#41C22×C8311yescharacteristic
476C22×#41C22×C8311yescharacteristic
477C22×Q16C22×C8311yescharacteristic
478C22×SD16C22×C8311yescharacteristic
479C22×SD16C22×C8311yescharacteristic
480C22×M16C22×C8311yescharacteristic
481#550—24no—
482#550—24no—
483C2×#127—21no—
484C2×#127C22×C8311yescharacteristic
485C2×C22⋊Q8C22×C8311yescharacteristic
486C2×C22⋊Q8C22×C8311yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C8311yescharacteristic
490C2×#121C22×C8311yescharacteristic
491C2×C4×Q8C22×C8311yescharacteristic
492C2×C4×D4—21no—
493C2×C4×D4C22×C8311yescharacteristic
494C22×C4⋊C4C22×C8311yescharacteristic
495#468—24no—
496#452—24no—
497#452—24no—
498C2×#107C22×C8311yescharacteristic
499#417—24no—
500C2×#103C22×C8311yescharacteristic
501C2×#103C22×C8311yescharacteristic
502C2×#103C22×C8311yescharacteristic
503C2×#103C22×C8311yescharacteristic
504C2×#102C22×C8311yescharacteristic
505C2×#102C22×C8311yescharacteristic
506C2×#102C22×C8311yescharacteristic
507C2×#102C22×C8311yescharacteristic
508C2×#102C22×C8311yescharacteristic
509C2×#102C22×C8311yescharacteristic
510C2×C22⋊C8C22×C8311yescharacteristic
511C2×C22⋊C8C22×C8311yescharacteristic
512C2×C22⋊C8C22×C8311yescharacteristic
513#398—21no—
514#396—21no—
515#391C22×C8311yescharacteristic
516#389C22×C8311yescharacteristic
517#386—21no—
518#380—21no—
519#380C22×C8311yescharacteristic
520#340C22×C8311yescharacteristic
521#340C22×C8311yescharacteristic
522#336C22×C8311yescharacteristic
523#336C22×C8311yescharacteristic
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C8314yes—
536C22×Q8C23×C8311yescharacteristic
537C22×Q8C23×C8311yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4D4×C8311yescharacteristic
545C22×D4C23×C8311yescharacteristic
546C22×D4C23×C8311yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C23×C8311yescharacteristic
551C23×C4C23×C8311yescharacteristic
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C22×C8C23×C8311yescharacteristic
565C22×C8C23×C8311yescharacteristic
566C22×C8C23×C8311yescharacteristic
567C22×C8C23×C8311yescharacteristic
568#127—28no—
569#127—22no—
570#127—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575#121—28no—
576#121—28no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121D4×C8314yes—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—28no—
584C4×D4—22no—
585C4×D4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4D4×C8311yescharacteristic
594C2×C4⋊C4C23×C8311yescharacteristic
595C2×C4⋊C4C23×C8311yescharacteristic
596C2×C4⋊C4C23×C8311yescharacteristic
597C2×C4⋊C4C23×C8311yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4D4×C8311yescharacteristic
604C2×C22⋊C4D4×C8311yescharacteristic
605C2×C42—21no—
606C2×C42C23×C8311yescharacteristic
607#107—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103D4×C8314yescomplemented
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621#95—21no—
622#95—21no—
623#95—21no—
624#95—21no—
625C24—21no—
626C24—21no—
627C24C2×D4×C8311yescharacteristic
628C24C2×D4×C8311yescharacteristic
629#41—28no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8C2×D4×C8312yes—
647C2×Q8C2×D4×C8312yes—
648C2×Q8#41×C8312yes—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4—81no—
680C2×D4C2×D4×C8312yes—
681C2×D4C2×D4×C8312yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—81no—
707C22×C4C2×D4×C8311yescharacteristic
708C22×C4C2×D4×C8311yescharacteristic
709C22×C4C2×D4×C8311yescharacteristic
710C22×C4C2×D4×C8312yes—
711C22×C4C2×D4×C8312yes—
712C22×C4C2×D4×C8311yescharacteristic
713C22×C4C24×C8311yescharacteristic
714Q16—44no—
715SD16—44no—
716SD16—44no—
717M16—44no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8C2×D4×C8312yes—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C8312yes—
743C4⋊C4C2×D4×C8312yes—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—81no—
751C42—24no—
752C42—21no—
753C42—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—22no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#120×C8312yes—
782C23C22×D4×C8311yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8#121×C8314yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—48no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—84no—
804D4—84no—
805D4—84no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—48no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4#120×C8312yes—
846C2×C4#137×C8312yes—
847C2×C4C22×D4×C8311yescharacteristic
848C2×C4C22×D4×C8311yescharacteristic
849C2×C4C22×D4×C8311yescharacteristic
850C2×C4C2×#41×C8311yescharacteristic
851C2×C4H(5,𝔽2)×C8311yescharacteristic
852C2×C4H(5,𝔽2)×C8311yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C8311yescharacteristic
886C22D42×C8311yescharacteristic
887C22#546×C8311yescharacteristic
888C22C2×#137×C8311yescharacteristic
889C22#575×C8311yescharacteristic
890C22#576×C8311yescharacteristic
891C22#577×C8311yescharacteristic
892C4—22no—
893C4—24no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—81no—
900C4—81no—
901C4—81no—
902C4C2×#121×C8311yescharacteristic
903C4#534×C8311yescharacteristic
904C4D42×C8311yescharacteristic
905C4#546×C8311yescharacteristic
906C2—42no—
907C2—81no—
908C2—82no—
909C2—82no—
910C2C83×#241011yescharacteristic
911C2C83×#300711yescharacteristic
912C2C83×#301211yescharacteristic
913C2C83×#326811yescharacteristic
914C2C83×#327811yescharacteristic
915C2C83×#331711yescharacteristic
916C2C83×#333311yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×#550×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×#468×C83C2semidirect
3. C2×#452×C83C2semidirect
4. C2×#452×C83C2semidirect
5. C2×#417×C83C2semidirect
6. C83×#2417C2semidirect
7. C83×#2041C2semidirect
8. C83×#2033C2semidirect
9. C83×#2014C2semidirect
10. C83×#2000C2semidirect
11. C83×#1878C2semidirect
12. C83×#1874C2semidirect
13. C83×#1870C2semidirect
14. C83×#1863C2semidirect
15. C83×#1788C2semidirect
152. #103×C83D4semidirect
447. #24443C83direct (N × H)
460. C2×#468C2×C83semidirect
461. C2×#452C2×C83semidirect
462. C2×#452C2×C83semidirect
463. C2×#417C2×C83semidirect
464. #2417C2×C83semidirect
465. #2041C2×C83semidirect
466. #2033C2×C83semidirect
467. #2014C2×C83semidirect
468. #2000C2×C83semidirect
469. #1878C2×C83semidirect
470. #1874C2×C83semidirect
471. #1870C2×C83semidirect
472. #1863C2×C83semidirect
473. #1788C2×C83semidirect
474. C83#24443direct (N × H)
611. #103D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C832
C2×#468×C832
C2×#452×C832
C2×#417×C832
C83×#24172
C83×#20412
C83×#20332
C83×#20142
C83×#20002
C83×#18782
C83×#18742
C83×#18702
C83×#18632
C83×#17882
#2444383