Finite Group Databasebeta

← C83×#23482 #35251306

Subgroups — C83×#23482 #35251306

Order 21248.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C83C211yesmaximal, characteristic
2C2×#428×C83C211yesmaximal, characteristic, complemented
3C2×#417×C83C211yesmaximal, characteristic, complemented
4C2×#417×C83C211yesmaximal, characteristic, complemented
5C2×#407×C83C211yesmaximal, characteristic, complemented
6C2×#380×C83C211yesmaximal, characteristic, complemented
7C83×#2036C212yesmaximal, complemented
8C83×#2035C212yesmaximal, complemented
9C83×#2034C212yesmaximal, complemented
10C83×#2033C212yesmaximal, complemented
11C83×#1736C211yesmaximal, characteristic, complemented
12C22×#41×C83C2211yescharacteristic
13C24×C4×C83C2211yescharacteristic
14C22×M16×C83C2211yescharacteristic
15C22×M16×C83C2211yescharacteristic
16#525×C83—24no—
17#525×C83—24no—
18C2×#123×C83—21no—
19C2×C22⋊Q8×C83C2211yescharacteristic
20C2×C22⋊Q8×C83C2211yescharacteristic
21C2×#121×C83C2211yescharacteristic
22C2×#121×C83C2211yescharacteristic
23C2×#120×C83—21no—
24C2×C4×D4×C83—21no—
25C2×C4×D4×C83—21no—
26C2×#117×C83C2211yescharacteristic
27C22×C4⋊C4×C83C2211yescharacteristic
28C22×C4⋊C4×C83C2211yescharacteristic
29C22×C22⋊C4×C83—21no—
30#428×C83—24no—
31C2×#107×C83C2212yescomplemented
32C2×#106×C83C2212yescomplemented
33#417×C83—24no—
34#417×C83—24no—
35C2×#103×C83C2212yescomplemented
36C2×#103×C83C2212yescomplemented
37C2×#102×C83C2212yescomplemented
38C2×#102×C83C2212yescomplemented
39#407×C83—24no—
40C2×C22⋊C8×C83C2212yes—
41C2×C22⋊C8×C83C2212yes—
42#380×C83—21no—
43#380×C83—21no—
44#380×C83C2212yes—
45#380×C83C2212yes—
46C2×#95×C83—21no—
47#340×C83C2212yescomplemented
48#340×C83C2212yescomplemented
49C25×C83D411yescharacteristic
50C2×#41×C83—22no—
51C2×#41×C83—22no—
52C2×#41×C83—22no—
53C2×#41×C83—22no—
54C2×#41×C83—22no—
55C2×#41×C83D414yes—
56C22×Q8×C83C2311yescharacteristic
57C22×D4×C83—21no—
58C22×D4×C83—21no—
59C22×D4×C83—21no—
60C22×D4×C83C2311yescharacteristic
61C23×C4×C83—21no—
62C23×C4×C83—22no—
63C23×C4×C83—22no—
64C23×C4×C83—22no—
65C23×C4×C83—22no—
66C23×C4×C83—22no—
67C23×C4×C83—22no—
68C23×C4×C83—21no—
69C23×C4×C83—21no—
70C23×C4×C83D411yescharacteristic
71C23×C4×C83D411yescharacteristic
72C23×C4×C83D411yescharacteristic
73C23×C4×C83C2311yescharacteristic
74C23×C4×C83C2311yescharacteristic
75C23×C4×C83C2311yescharacteristic
76C2×M16×C83—22no—
77C2×M16×C83—22no—
78C2×M16×C83—22no—
79C2×M16×C83—22no—
80C2×M16×C83—22no—
81C2×M16×C83D414yescomplemented
82C22×C8×C83C2312yes—
83C22×C8×C83C2312yes—
84#123×C83—28no—
85C22⋊Q8×C83—22no—
86C22⋊Q8×C83—22no—
87C22⋊Q8×C83—22no—
88C22⋊Q8×C83—22no—
89#121×C83—22no—
90#121×C83—22no—
91#121×C83—22no—
92#121×C83—22no—
93#120×C83—28no—
94C4×D4×C83—28no—
95C4×D4×C83—28no—
96#117×C83—22no—
97#117×C83D414yes—
98C2×C4⋊C4×C83—21no—
99C2×C4⋊C4×C83—21no—
100C2×C4⋊C4×C83—22no—
101C2×C4⋊C4×C83—22no—
102C2×C4⋊C4×C83—22no—
103C2×C4⋊C4×C83—22no—
104C2×C4⋊C4×C83—21no—
105C2×C4⋊C4×C83—21no—
106C2×C4⋊C4×C83C2312yes—
107C2×C4⋊C4×C83C2312yes—
108C2×C4⋊C4×C83C2311yescharacteristic
109C2×C4⋊C4×C83C2311yescharacteristic
110C2×C22⋊C4×C83—21no—
111C2×C22⋊C4×C83—21no—
112C2×C22⋊C4×C83—21no—
113C2×C22⋊C4×C83—21no—
114C2×C22⋊C4×C83—21no—
115C2×C22⋊C4×C83—22no—
116C2×C22⋊C4×C83—22no—
117C2×C22⋊C4×C83—44no—
118C2×C42×C83—21no—
119#107×C83—24no—
120#106×C83—24no—
121#103×C83—24no—
122#103×C83—24no—
123#102×C83—24no—
124#102×C83—24no—
125C22⋊C8×C83—24no—
126C22⋊C8×C83—24no—
127#95×C83—22no—
128#95×C83—22no—
129C24×C83—22no—
130C24×C83—22no—
131C24×C83—22no—
132C24×C83—22no—
133C24×C83—22no—
134C24×C83—21no—
135C24×C83—41no—
136C24×C83—41no—
137C24×C83C2×D411yescharacteristic
138C24×C83C2×D411yescharacteristic
139C24×C83C2×D411yescharacteristic
140#41×C83—28no—
141#41×C83—28no—
142#41×C83—44no—
143#41×C83—44no—
144C2×Q8×C83—21no—
145C2×Q8×C83—21no—
146C2×Q8×C83—21no—
147C2×Q8×C83—21no—
148C2×Q8×C83—21no—
149C2×Q8×C83C2×D412yes—
150C2×D4×C83—24no—
151C2×D4×C83—24no—
152C2×D4×C83—24no—
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—21no—
157C2×D4×C83—21no—
158C2×D4×C83—42no—
159C2×D4×C83—42no—
160C2×D4×C83—42no—
161C2×D4×C83—42no—
162C2×D4×C83—42no—
163C2×D4×C83—42no—
164C2×D4×C83C2×D412yes—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—22no—
172C22×C4×C83—22no—
173C22×C4×C83—24no—
174C22×C4×C83—22no—
175C22×C4×C83—22no—
176C22×C4×C83—22no—
177C22×C4×C83—22no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—22no—
191C22×C4×C83—22no—
192C22×C4×C83—44no—
193C22×C4×C83—44no—
194C22×C4×C83—42no—
195C22×C4×C83—44no—
196C22×C4×C83—42no—
197C22×C4×C83—44no—
198C22×C4×C83—42no—
199C22×C4×C83—42no—
200C22×C4×C83—42no—
201C22×C4×C83—42no—
202C22×C4×C83—42no—
203C22×C4×C83—42no—
204C22×C4×C83C2×D411yescharacteristic
205C22×C4×C83C2×D411yescharacteristic
206C22×C4×C83C2×D411yescharacteristic
207C22×C4×C83C2×D412yes—
208C22×C4×C83C2×D412yes—
209C22×C4×C83C2×D412yes—
210C22×C4×C83#4112yes—
211C22×C4×C83#4112yes—
212C22×C4×C83#4112yes—
213C22×C4×C83C2411yescharacteristic
214M16×C83—28no—
215M16×C83—44no—
216C2×C8×C83—22no—
217C2×C8×C83—22no—
218C2×C8×C83—22no—
219C2×C8×C83—22no—
220C2×C8×C83—22no—
221C2×C8×C83C2×D414yes—
222C4⋊C4×C83—24no—
223C4⋊C4×C83—24no—
224C4⋊C4×C83—21no—
225C4⋊C4×C83—21no—
226C4⋊C4×C83—22no—
227C4⋊C4×C83—22no—
228C4⋊C4×C83—22no—
229C4⋊C4×C83—22no—
230C4⋊C4×C83—42no—
231C4⋊C4×C83—42no—
232C4⋊C4×C83C2×D412yes—
233C4⋊C4×C83C2×D412yes—
234C22⋊C4×C83—24no—
235C22⋊C4×C83—24no—
236C22⋊C4×C83—24no—
237C22⋊C4×C83—24no—
238C22⋊C4×C83—24no—
239C22⋊C4×C83—44no—
240C22⋊C4×C83—44no—
241C42×C83—24no—
242C23×C83—21no—
243C23×C83—21no—
244C23×C83—21no—
245C23×C83—21no—
246C23×C83—28no—
247C23×C83—21no—
248C23×C83—21no—
249C23×C83—21no—
250C23×C83—21no—
251C23×C83—21no—
252C23×C83—21no—
253C23×C83—21no—
254C23×C83—21no—
255C23×C83—21no—
256C23×C83—21no—
257C23×C83—21no—
258C23×C83—21no—
259C23×C83—22no—
260C23×C83—44no—
261C23×C83—44no—
262C23×C83—44no—
263C23×C83—44no—
264C23×C83—44no—
265C23×C83—44no—
266C23×C83—41no—
267C23×C83—41no—
268C23×C83—41no—
269C23×C83—41no—
270C23×C83—41no—
271C23×C83—41no—
272C23×C83#12012yes—
273C23×C83#12112yes—
274C23×C83#12312yes—
275C23×C83AGL(1,ℤ/8)12yes—
276C23×C83#13712yes—
277C23×C83C22×D411yescharacteristic
278Q8×C83—22no—
279Q8×C83—22no—
280Q8×C83—41no—
281Q8×C83—41no—
282D4×C83—22no—
283D4×C83—22no—
284D4×C83—48no—
285D4×C83—48no—
286D4×C83—48no—
287D4×C83—41no—
288D4×C83—41no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—21no—
292C2×C4×C83—21no—
293C2×C4×C83—22no—
294C2×C4×C83—21no—
295C2×C4×C83—21no—
296C2×C4×C83—21no—
297C2×C4×C83—21no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83—41no—
301C2×C4×C83—41no—
302C2×C4×C83—41no—
303C2×C4×C83—41no—
304C2×C4×C83—44no—
305C2×C4×C83—41no—
306C2×C4×C83—41no—
307C2×C4×C83—41no—
308C2×C4×C83—41no—
309C2×C4×C83—41no—
310C2×C4×C83—41no—
311C2×C4×C83—41no—
312C2×C4×C83—41no—
313C2×C4×C83—44no—
314C2×C4×C83—44no—
315C2×C4×C83—48no—
316C2×C4×C83—42no—
317C2×C4×C83—42no—
318C2×C4×C83—42no—
319C2×C4×C83—42no—
320C2×C4×C83—42no—
321C2×C4×C83—42no—
322C2×C4×C83—84no—
323C2×C4×C83—84no—
324C2×C4×C83#12012yes—
325C2×C4×C83#12114yes—
326C2×C4×C83#12114yes—
327C2×C4×C83#12112yes—
328C2×C4×C83#12314yes—
329C2×C4×C83#12312yes—
330C2×C4×C83#12414yes—
331C2×C4×C83C22×D411yescharacteristic
332C2×C4×C83C22×D411yescharacteristic
333C2×C4×C83C22×D411yescharacteristic
334C2×C4×C83C2×#4111yescharacteristic
335C2×C4×C83C2×#4111yescharacteristic
336C2×C4×C83C2×#4111yescharacteristic
337C8×C83—24no—
338C8×C83—42no—
339C22×C83—22no—
340C22×C83—22no—
341C22×C83—22no—
342C22×C83—22no—
343C22×C83—22no—
344C22×C83—22no—
345C22×C83—22no—
346C22×C83—22no—
347C22×C83—22no—
348C22×C83—22no—
349C22×C83—22no—
350C22×C83—22no—
351C22×C83—416no—
352C22×C83—41no—
353C22×C83—41no—
354C22×C83—41no—
355C22×C83—41no—
356C22×C83—41no—
357C22×C83—41no—
358C22×C83—41no—
359C22×C83—41no—
360C22×C83—42no—
361C22×C83—42no—
362C22×C83—42no—
363C22×C83—81no—
364C22×C83—81no—
365C22×C83—81no—
366C22×C83—81no—
367C22×C83#39414yes—
368C22×C83C2×#12011yescharacteristic
369C22×C83C2×#12111yescharacteristic
370C22×C83C2×#12311yescharacteristic
371C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C83C2×#13711yescharacteristic
373C22×C83#57511yescharacteristic
374C22×C83#57511yescharacteristic
375C4×C83—41no—
376C4×C83—41no—
377C4×C83—42no—
378C4×C83—42no—
379C4×C83—42no—
380C4×C83—82no—
381C4×C83—82no—
382C4×C83#39414yes—
383C4×C83C2×#12111yescharacteristic
384C4×C83C2×#12111yescharacteristic
385C4×C83C2×#12311yescharacteristic
386C4×C83C2×#12411yescharacteristic
387#23482C8311yesmaximal, characteristic, direct product factor, Sylow
388C2×C83—24no—
389C2×C83—42no—
390C2×C83—42no—
391C2×C83—82no—
392C2×C83C2×#39411yescharacteristic
393C2×C83#300611yescharacteristic
394C2×C83#300711yescharacteristic
395C2×C83#305511yescharacteristic
396C2×C83#305611yescharacteristic
397C2×C83#309211yescharacteristic
398C2×C83#309311yescharacteristic
399C2×#525C2×C8311yescharacteristic
400C2×#428C2×C8311yescharacteristic, complemented
401C2×#417C2×C8311yescharacteristic, complemented
402C2×#417C2×C8311yescharacteristic, complemented
403C2×#407C2×C8311yescharacteristic, complemented
404C2×#380C2×C8311yescharacteristic, complemented
405#2036C2×C8312yescomplemented
406#2035C2×C8312yescomplemented
407#2034C2×C8312yescomplemented
408#2033C2×C8312yescomplemented
409#1736C2×C8311yescharacteristic, complemented
410C83#2348211yescharacteristic, direct product factor, Sylow
411C22×#41C22×C8311yescharacteristic
412C24×C4C22×C8311yescharacteristic
413C22×M16C22×C8311yescharacteristic
414C22×M16C22×C8311yescharacteristic
415#525—24no—
416#525—24no—
417C2×#123—21no—
418C2×C22⋊Q8C22×C8311yescharacteristic
419C2×C22⋊Q8C22×C8311yescharacteristic
420C2×#121C22×C8311yescharacteristic
421C2×#121C22×C8311yescharacteristic
422C2×#120—21no—
423C2×C4×D4—21no—
424C2×C4×D4—21no—
425C2×#117C22×C8311yescharacteristic
426C22×C4⋊C4C22×C8311yescharacteristic
427C22×C4⋊C4C22×C8311yescharacteristic
428C22×C22⋊C4—21no—
429#428—24no—
430C2×#107C22×C8312yescomplemented
431C2×#106C22×C8312yescomplemented
432#417—24no—
433#417—24no—
434C2×#103C22×C8312yescomplemented
435C2×#103C22×C8312yescomplemented
436C2×#102C22×C8312yescomplemented
437C2×#102C22×C8312yescomplemented
438#407—24no—
439C2×C22⋊C8C22×C8312yes—
440C2×C22⋊C8C22×C8312yes—
441#380—21no—
442#380—21no—
443#380C22×C8312yes—
444#380C22×C8312yes—
445C2×#95—21no—
446#340C22×C8312yescomplemented
447#340C22×C8312yescomplemented
448C25D4×C8311yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41D4×C8314yes—
455C22×Q8C23×C8311yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C8311yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4D4×C8311yescharacteristic
470C23×C4D4×C8311yescharacteristic
471C23×C4D4×C8311yescharacteristic
472C23×C4C23×C8311yescharacteristic
473C23×C4C23×C8311yescharacteristic
474C23×C4C23×C8311yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16D4×C8314yescomplemented
481C22×C8C23×C8312yes—
482C22×C8C23×C8312yes—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117D4×C8314yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C8312yes—
506C2×C4⋊C4C23×C8312yes—
507C2×C4⋊C4C23×C8311yescharacteristic
508C2×C4⋊C4C23×C8311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—44no—
517C2×C42—21no—
518#107—24no—
519#106—24no—
520#103—24no—
521#103—24no—
522#102—24no—
523#102—24no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×D4×C8311yescharacteristic
537C24C2×D4×C8311yescharacteristic
538C24C2×D4×C8311yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C8312yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C8312yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C8311yescharacteristic
604C22×C4C2×D4×C8311yescharacteristic
605C22×C4C2×D4×C8311yescharacteristic
606C22×C4C2×D4×C8312yes—
607C22×C4C2×D4×C8312yes—
608C22×C4C2×D4×C8312yes—
609C22×C4#41×C8312yes—
610C22×C4#41×C8312yes—
611C22×C4#41×C8312yes—
612C22×C4C24×C8311yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×D4×C8314yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C8312yes—
632C4⋊C4C2×D4×C8312yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#120×C8312yes—
672C23#121×C8312yes—
673C23#123×C8312yes—
674C23AGL(1,ℤ/8)×C8312yes—
675C23#137×C8312yes—
676C23C22×D4×C8311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4#120×C8312yes—
724C2×C4#121×C8314yes—
725C2×C4#121×C8314yes—
726C2×C4#121×C8312yes—
727C2×C4#123×C8314yes—
728C2×C4#123×C8312yes—
729C2×C4#124×C8314yes—
730C2×C4C22×D4×C8311yescharacteristic
731C2×C4C22×D4×C8311yescharacteristic
732C2×C4C22×D4×C8311yescharacteristic
733C2×C4C2×#41×C8311yescharacteristic
734C2×C4C2×#41×C8311yescharacteristic
735C2×C4C2×#41×C8311yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#394×C8314yes—
767C22C2×#120×C8311yescharacteristic
768C22C2×#121×C8311yescharacteristic
769C22C2×#123×C8311yescharacteristic
770C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
771C22C2×#137×C8311yescharacteristic
772C22#575×C8311yescharacteristic
773C22#575×C8311yescharacteristic
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4#394×C8314yes—
782C4C2×#121×C8311yescharacteristic
783C4C2×#121×C8311yescharacteristic
784C4C2×#123×C8311yescharacteristic
785C4C2×#124×C8311yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#394×C8311yescharacteristic
791C2C83×#300611yescharacteristic
792C2C83×#300711yescharacteristic
793C2C83×#305511yescharacteristic
794C2C83×#305611yescharacteristic
795C2C83×#309211yescharacteristic
796C2C83×#309311yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×#525×C83C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C24×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#428×C83C2semidirect
3. C2×#417×C83C2semidirect
4. C2×#417×C83C2semidirect
5. C2×#407×C83C2semidirect
6. C2×#380×C83C2semidirect
7. C83×#2036C2semidirect
8. C83×#2035C2semidirect
9. C83×#2034C2semidirect
10. C83×#2033C2semidirect
11. C83×#1736C2semidirect
31. C2×#107×C83C22semidirect
32. C2×#106×C83C22semidirect
35. C2×#103×C83C22semidirect
36. C2×#103×C83C22semidirect
37. C2×#102×C83C22semidirect
38. C2×#102×C83C22semidirect
47. #340×C83C22semidirect
48. #340×C83C22semidirect
81. C2×M16×C83D4semidirect
387. #23482C83direct (N × H)
400. C2×#428C2×C83semidirect
401. C2×#417C2×C83semidirect
402. C2×#417C2×C83semidirect
403. C2×#407C2×C83semidirect
404. C2×#380C2×C83semidirect
405. #2036C2×C83semidirect
406. #2035C2×C83semidirect
407. #2034C2×C83semidirect
408. #2033C2×C83semidirect
409. #1736C2×C83semidirect
410. C83#23482direct (N × H)
430. C2×#107C22×C83semidirect
431. C2×#106C22×C83semidirect
434. C2×#103C22×C83semidirect
435. C2×#103C22×C83semidirect
436. C2×#102C22×C83semidirect
437. C2×#102C22×C83semidirect
446. #340C22×C83semidirect
447. #340C22×C83semidirect
480. C2×M16D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C832
C2×#428×C832
C2×#417×C832
C2×#407×C832
C2×#380×C832
C83×#20362
C83×#20352
C83×#20342
C83×#20332
C83×#17362
#2348283