Finite Group Databasebeta

← #35327832

Subgroups — #35327832

Order 21248.

1506 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127608C211yesmaximal, characteristic
2C2×#19127608C211yesmaximal, characteristic
3C2×C4⋊C4×Dic83C211yesmaximal, characteristic
4C2×C4×Dic83⋊C4C211yesmaximal, characteristic
5#24905724C212yesmaximal
6#24905718C212yesmaximal
7#24905694C212yesmaximal
8#24905693C211yesmaximal, characteristic
9#24905692C211yesmaximal, characteristic
10#24905687C212yesmaximal
11C2×#391×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×Dic83⋊C4C2211yescharacteristic
15C22×Dic83⋊C4C2211yescharacteristic
16C22×C4×Dic83C2212yes—
17C22×C4×Dic83C2211yescharacteristic
18C22×C4×Dic83C2211yescharacteristic
19#19127608—24no—
20#19127608C418yescomplemented
21C4⋊C4×Dic83—24no—
22C4×Dic83⋊C4—24no—
23C2×C83⋊#95C2212yes—
24C2×C83⋊#95C2212yes—
25C2×C83⋊#95C2211yescharacteristic
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2211yescharacteristic
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C23×Q8×C83C2211yescharacteristic
35C22×C4⋊C4×C83C2211yescharacteristic
36C22×C42×C83C2211yescharacteristic
37#391×C83—24no—
38C2×#95×C83C2212yes—
39C2×#95×C83C2212yes—
40C23×Dic83C2312yes—
41C23×Dic83C2312yes—
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2311yescharacteristic
44C23×Dic83C2311yescharacteristic
45C23×Dic83C2311yescharacteristic
46C2×C4⋊Dic83—22no—
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83—22no—
49C2×C4⋊Dic83—22no—
50C2×C4⋊Dic83—22no—
51C2×C4⋊Dic83C2×C414yes—
52C2×Dic83⋊C4—22no—
53C2×Dic83⋊C4—22no—
54C2×Dic83⋊C4—22no—
55C2×Dic83⋊C4—22no—
56C2×Dic83⋊C4—22no—
57C2×Dic83⋊C4Q814yescomplemented
58C2×C4×Dic83—24no—
59C2×C4×Dic83—22no—
60C2×C4×Dic83—22no—
61C2×C4×Dic83—24no—
62C2×C4×Dic83—22no—
63C2×C4×Dic83—22no—
64C2×C4×Dic83—42no—
65C2×C4×Dic83C2×C414yes—
66C2×C4×Dic83D414yes—
67C83⋊#95—22no—
68C83⋊#95—22no—
69C83⋊#95—24no—
70C83⋊#95—24no—
71C83⋊#95—24no—
72C83⋊#95—24no—
73C83⋊#95—24no—
74C83⋊#95—42no—
75C83⋊#95—42no—
76C83⋊#95C2×C418yes—
77C83⋊#95C2×C418yes—
78C22×Q8×C83—22no—
79C22×Q8×C83—22no—
80C22×Q8×C83—22no—
81C22×Q8×C83—22no—
82C22×Q8×C83—22no—
83C22×Q8×C83—22no—
84C22×Q8×C83C2×C414yes—
85C23×C4×C83C2312yes—
86C23×C4×C83C2312yes—
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2311yescharacteristic
90C2×C4⋊C4×C83—22no—
91C2×C4⋊C4×C83—22no—
92C2×C4⋊C4×C83D414yes—
93C2×C42×C83—22no—
94C2×C42×C83—22no—
95C2×C42×C83—22no—
96#95×C83—24no—
97#95×C83—24no—
98C22×Dic83—21no—
99C22×Dic83—21no—
100C22×Dic83—21no—
101C22×Dic83—21no—
102C22×Dic83—21no—
103C22×Dic83—21no—
104C22×Dic83—21no—
105C22×Dic83—21no—
106C22×Dic83—21no—
107C22×Dic83—21no—
108C22×Dic83—22no—
109C22×Dic83—22no—
110C22×Dic83—22no—
111C22×Dic83—21no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—22no—
116C22×Dic83—21no—
117C22×Dic83—22no—
118C22×Dic83—21no—
119C22×Dic83—21no—
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—22no—
123C22×Dic83—21no—
124C22×Dic83—22no—
125C22×Dic83—22no—
126C22×Dic83—22no—
127C22×Dic83—22no—
128C22×Dic83—22no—
129C22×Dic83—22no—
130C22×Dic83—22no—
131C22×Dic83C22×C412yes—
132C22×Dic83C22×C414yes—
133C22×Dic83C22×C412yes—
134C22×Dic83C2×D412yes—
135C22×Dic83C2×D412yes—
136C22×Dic83C2×Q812yes—
137C22×Dic83C2×Q812yes—
138C22×Dic83#4112yes—
139C22×Dic83#4112yes—
140C4⋊Dic83—28no—
141C4⋊Dic83—44no—
142Dic83⋊C4—28no—
143Dic83⋊C4—28no—
144C4×Dic83—28no—
145C4×Dic83—28no—
146C4×Dic83—48no—
147C24×C83C2411yescharacteristic
148C2×Q8×C83—28no—
149C2×Q8×C83—28no—
150C2×Q8×C83—28no—
151C2×Q8×C83—44no—
152C2×Q8×C83—44no—
153C2×Q8×C83—44no—
154C2×Q8×C83—44no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—22no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—22no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—22no—
164C22×C4×C83—22no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—22no—
170C22×C4×C83—22no—
171C22×C4×C83—21no—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—22no—
175C22×C4×C83—22no—
176C22×C4×C83—21no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83C22×C414yes—
180C22×C4×C83C22×C412yes—
181C22×C4×C83C2×D412yes—
182C22×C4×C83C2×D414yes—
183C22×C4×C83C2×D412yes—
184C22×C4×C83C2×Q812yes—
185C22×C4×C83#4112yes—
186C22×C4×C83#4112yes—
187C22×C4×C83#4112yes—
188C22×C4×C83#4112yes—
189C22×C4×C83#4112yes—
190C4⋊C4×C83—28no—
191C42×C83—44no—
192C23×C83C23×C411yescharacteristic
193C23×C83C22×D411yescharacteristic
194C23×C83C22×D411yescharacteristic
195C23×C83C22×Q811yescharacteristic
196C23×C83C2×#4111yescharacteristic
197C23×C83C2×#4111yescharacteristic
198C23×C83C2×#4111yescharacteristic
199C23×C83C2×#4111yescharacteristic
200C23×C83C2×#4111yescharacteristic
201C23×C83C2×#4111yescharacteristic
202C23×C83C2×#4111yescharacteristic
203C23×C83H(5,𝔽2)11yescharacteristic
204C23×C832−1+411yescharacteristic
205C23×C832−1+411yescharacteristic
206C23×C832−1+411yescharacteristic
207Q8×C83—416no—
208C2×C4×C83—24no—
209C2×C4×C83—24no—
210C2×C4×C83—24no—
211C2×C4×C83—22no—
212C2×C4×C83—24no—
213C2×C4×C83—22no—
214C2×C4×C83—24no—
215C2×C4×C83—24no—
216C2×C4×C83—22no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—22no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83—42no—
223C2×C4×C83—42no—
224C2×C4×C83—42no—
225C2×C4×C83—42no—
226C2×C4×C83—42no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83—42no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—42no—
234C2×C4×C83—41no—
235C2×C4×C83—42no—
236C2×C4×C83#11714yes—
237C2×C4×C83C4×D414yes—
238C2×C4×C83C4×D414yes—
239C2×C4×C83#12114yes—
240C2×C4×C83#12314yes—
241C2×C4×C83#12414yes—
242C2×C4×C83#12614yes—
243C2×Dic83—22no—
244C2×Dic83—22no—
245C2×Dic83—22no—
246C2×Dic83—22no—
247C2×Dic83—22no—
248C2×Dic83—22no—
249C2×Dic83—22no—
250C2×Dic83—22no—
251C2×Dic83—22no—
252C2×Dic83—22no—
253C2×Dic83—22no—
254C2×Dic83—22no—
255C2×Dic83—22no—
256C2×Dic83—24no—
257C2×Dic83—24no—
258C2×Dic83—22no—
259C2×Dic83—22no—
260C2×Dic83—24no—
261C2×Dic83—22no—
262C2×Dic83—22no—
263C2×Dic83—22no—
264C2×Dic83—41no—
265C2×Dic83—41no—
266C2×Dic83—41no—
267C2×Dic83—41no—
268C2×Dic83—42no—
269C2×Dic83—41no—
270C2×Dic83—42no—
271C2×Dic83—41no—
272C2×Dic83—41no—
273C2×Dic83—41no—
274C2×Dic83—42no—
275C2×Dic83—42no—
276C2×Dic83—42no—
277C2×Dic83—42no—
278C2×Dic83—42no—
279C2×Dic83—42no—
280C2×Dic83—42no—
281C2×Dic83—42no—
282C2×Dic83—42no—
283C2×Dic83C4×Q814yes—
284C2×Dic83C22⋊Q814yes—
285C22×C83C2×#11711yescharacteristic
286C22×C83C2×C4×D411yescharacteristic
287C22×C83C2×C4×D411yescharacteristic
288C22×C83C2×C4×Q811yescharacteristic
289C22×C83C4×#4111yescharacteristic
290C22×C83#51911yescharacteristic
291C22×C83#52011yescharacteristic
292C22×C83C2×#12111yescharacteristic
293C22×C83C2×C22⋊Q811yescharacteristic
294C22×C83C2×#12311yescharacteristic
295C22×C83#52511yescharacteristic
296C22×C83C2×#12411yescharacteristic
297C22×C83C2×#12611yescharacteristic
298C22×C83#52911yescharacteristic
299C22×C83#53311yescharacteristic
300C22×C83#53611yescharacteristic
301C22×C83#53711yescharacteristic
302C22×C83#54111yescharacteristic
303C22×C83#54211yescharacteristic
304C22×C83#54611yescharacteristic
305C22×C83#54711yescharacteristic
306C22×C83#54811yescharacteristic
307C22×C83D4×Q811yescharacteristic
308C22×C83#55211yescharacteristic
309C22×C83#55211yescharacteristic
310C22×C83#55411yescharacteristic
311C22×C83#55611yescharacteristic
312C22×C83#55611yescharacteristic
313C22×C83#55611yescharacteristic
314C22×C83#55611yescharacteristic
315C22×C83#55611yescharacteristic
316C22×C83#55711yescharacteristic
317C22×C83#55711yescharacteristic
318C22×C83#55911yescharacteristic
319C22×C83#55911yescharacteristic
320C4×C83—42no—
321C4×C83—42no—
322C4×C83—44no—
323C4×C83—44no—
324C4×C83#38818yes—
325Dic83—24no—
326Dic83—24no—
327Dic83—42no—
328Dic83—44no—
329Dic83—42no—
330Dic83—82no—
331#14021—831nomaximal, Sylow
332C2×C83C2×#38811yescharacteristic
333C2×C83C4×C22⋊Q811yescharacteristic
334C2×C83#232311yescharacteristic
335C2×C83#235511yescharacteristic
336C2×C83#235611yescharacteristic
337C2×C83#236511yescharacteristic
338C2×C83#236711yescharacteristic
339C2×C83#241511yescharacteristic
340C2×C83#241711yescharacteristic
341C2×C83#244611yescharacteristic
342C2×C83#244711yescharacteristic
343C2×C83#251111yescharacteristic
344C2×C83#251411yescharacteristic
345C2×C83#256811yescharacteristic
346C2×C83#259211yescharacteristic
347C2×#391—831no—
348C2×#391—831no—
349C2×#391D8311yescharacteristic
350C2×C4×C4⋊C4—831no—
351C2×C4×C4⋊C4—831no—
352#1443—832no—
353#1442—832no—
354#1436—832no—
355C4⋊#95—831no—
356C4⋊#95—831no—
357#1434—832no—
358C83#1402111yescharacteristic, complemented, Sylow
359C23×Q8C2×D8311yescharacteristic
360C22×C4⋊C4—831no—
361C22×C4⋊C4—831no—
362C22×C4⋊C4—831no—
363C22×C4⋊C4—831no—
364C22×C4⋊C4C2×D8311yescharacteristic
365C22×C42—832no—
366C22×C42—831no—
367C22×C42—831no—
368C22×C42C2×D8311yescharacteristic
369#391—24no—
370#391—838no—
371#391—1664no—
372C4×C4⋊C4—1664no—
373C4×C4⋊C4—1664no—
374C2×#95—832no—
375C2×#95—832no—
376C2×#95—832no—
377C2×#95—832no—
378C2×#95—831no—
379C2×#95—832no—
380C2×#95—832no—
381C2×#95—832no—
382C2×#95—832no—
383C2×#95—832no—
384C2×#95—831no—
385C2×#95C2×D8312yes—
386C2×#95C2×D8312yes—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—22no—
393C22×Q8C4×D8314yes—
394C23×C4—831no—
395C23×C4—831no—
396C23×C4—832no—
397C23×C4—831no—
398C23×C4—831no—
399C23×C4—832no—
400C23×C4C22×D8312yes—
401C23×C4C22×D8312yes—
402C23×C4C22×D8311yescharacteristic
403C23×C4C22×D8311yescharacteristic
404C23×C4C22×D8311yescharacteristic
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—834no—
408C2×C4⋊C4—834no—
409C2×C4⋊C4—1662no—
410C2×C4⋊C4—1662no—
411C2×C4⋊C4—1662no—
412C2×C4⋊C4—1662no—
413C2×C4⋊C4—1662no—
414C2×C4⋊C4—1662no—
415C2×C4⋊C4—1662no—
416C2×C4⋊C4—1662no—
417C2×C4⋊C4—1662no—
418C2×C4⋊C4—1662no—
419C2×C4⋊C4C22⋊D8314yes—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—3322no—
424C2×C42—834no—
425C2×C42—834no—
426C2×C42—1664no—
427C2×C42—1664no—
428C2×C42—1662no—
429C2×C42—1662no—
430C2×C42—1662no—
431C2×C42—1662no—
432#95—24no—
433#95—24no—
434#95—3322no—
435#95—3322no—
436#95—838no—
437#95—838no—
438#95—1662no—
439#95—1662no—
440#95—1664no—
441#95—1664no—
442#95—1664no—
443#95—1664no—
444#95—1664no—
445C24C23×D8311yescharacteristic
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—832no—
478C22×C4—832no—
479C22×C4—832no—
480C22×C4—832no—
481C22×C4—832no—
482C22×C4—832no—
483C22×C4—832no—
484C22×C4—834no—
485C22×C4—832no—
486C22×C4—1662no—
487C22×C4—1662no—
488C22×C4—1662no—
489C22×C4—1662no—
490C22×C4—1662no—
491C22×C4—1662no—
492C22×C4—1662no—
493C22×C4—1661no—
494C22×C4—1661no—
495C22×C4—1662no—
496C22×C4—1662no—
497C22×C4—1661no—
498C22×C4—1661no—
499C22×C4—1661no—
500C22×C4—1662no—
501C22×C4—1662no—
502C22×C4—1661no—
503C22×C4—1661no—
504C22×C4—1662no—
505C22×C4—1661no—
506C22×C4—1661no—
507C22×C4—1661no—
508C22×C4—1662no—
509C22×C4—1661no—
510C22×C4—1661no—
511C22×C4—1661no—
512C22×C4—1661no—
513C22×C4—1661no—
514C22×C4—1661no—
515C22×C4—1661no—
516C22×C4—1661no—
517C22×C4—1661no—
518C22×C4—1661no—
519C22×C4C2×C4×D8314yes—
520C22×C4C2×C4×D8312yes—
521C22×C4D4×D8312yes—
522C22×C4C2×C22⋊D8314yes—
523C22×C4C2×C22⋊D8312yes—
524C22×C4Q8×D8312yes—
525C22×C4#1305058912yes—
526C22×C4#1305058912yes—
527C22×C4#1305058912yes—
528C22×C4#1305059012yes—
529C22×C4#1305059112yes—
530C4⋊C4—28no—
531C4⋊C4—3324no—
532C4⋊C4—1668no—
533C4⋊C4—1668no—
534C4⋊C4—1668no—
535C42—44no—
536C42—3328no—
537C42—1668no—
538C42—1668no—
539C23C22×C4×D8311yescharacteristic
540C23C2×D4×D8311yescharacteristic
541C23C22×C22⋊D8311yescharacteristic
542C23C2×Q8×D8311yescharacteristic
543C23#41×D8311yescharacteristic
544C23#41×D8311yescharacteristic
545C23C2×#1305058911yescharacteristic
546C23C2×#1305058911yescharacteristic
547C23C2×#1305058911yescharacteristic
548C23C2×#1305059011yescharacteristic
549C23C2×#1305059111yescharacteristic
550C23#1458183811yescharacteristic
551C23#1458183911yescharacteristic
552C23#1458184011yescharacteristic
553C23#1458184011yescharacteristic
554Q8—416no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—3321no—
584C2×C4—3322no—
585C2×C4—3321no—
586C2×C4—3321no—
587C2×C4—3322no—
588C2×C4—3321no—
589C2×C4—3321no—
590C2×C4—3322no—
591C2×C4—3322no—
592C2×C4—3321no—
593C2×C4—3321no—
594C2×C4—3321no—
595C2×C4—3322no—
596C2×C4—3322no—
597C2×C4—3322no—
598C2×C4—3322no—
599C2×C4—3322no—
600C2×C4—3322no—
601C2×C4—3322no—
602C2×C4—834no—
603C2×C4—834no—
604C2×C4—1662no—
605C2×C4—1664no—
606C2×C4—1664no—
607C2×C4—1662no—
608C2×C4—1662no—
609C2×C4—1664no—
610C2×C4—1662no—
611C2×C4—1662no—
612C2×C4—1662no—
613C2×C4—1662no—
614C2×C4—1662no—
615C2×C4—1662no—
616C2×C4—1662no—
617C2×C4—1662no—
618C2×C4—1662no—
619C2×C4—1662no—
620C2×C4—1662no—
621C2×C4—1662no—
622C2×C4—1662no—
623C2×C4—1662no—
624C2×C4—1662no—
625C2×C4#1458174814yes—
626C2×C4(C22⋊D83)⋊C414yes—
627C2×C4C4×C22⋊D8314yes—
628C2×C4#1458176314yes—
629C2×C4#1458177314yes—
630C2×C4#1458177814yes—
631C2×C4#1458178514yes—
632C22C2×#1458174811yescharacteristic
633C22C2×(C22⋊D83)⋊C411yescharacteristic
634C22C2×C4×C22⋊D8311yescharacteristic
635C22C4×Q8×D8311yescharacteristic
636C22C4×#1305059111yescharacteristic
637C22#1912817711yescharacteristic
638C22#1912818311yescharacteristic
639C22C2×#1458176311yescharacteristic
640C22C22⋊Q8×D8311yescharacteristic
641C22C2×#1458177311yescharacteristic
642C22#1912821411yescharacteristic
643C22C2×#1458177811yescharacteristic
644C22C2×#1458178511yescharacteristic
645C22#1912823011yescharacteristic
646C22#1912825611yescharacteristic
647C22#1912827411yescharacteristic
648C22#1912828111yescharacteristic
649C22#1912831211yescharacteristic
650C22#1912832011yescharacteristic
651C22#1912833911yescharacteristic
652C22#1912835011yescharacteristic
653C22#1912836211yescharacteristic
654C22Q8×C22⋊D8311yescharacteristic
655C22#1912838511yescharacteristic
656C22#1912839311yescharacteristic
657C22#1912840911yescharacteristic
658C22#1912842011yescharacteristic
659C22#1912842211yescharacteristic
660C22#1912842311yescharacteristic
661C22#1912842311yescharacteristic
662C22#1912842511yescharacteristic
663C22#1912842611yescharacteristic
664C22#1912842911yescharacteristic
665C22#1912843311yescharacteristic
666C22#1912843611yescharacteristic
667C4—42no—
668C4—42no—
669C4—44no—
670C4—44no—
671C4—3322no—
672C4—3322no—
673C4—3324no—
674C4—6642no—
675C4—1664no—
676C4—1664no—
677C4#1912758918yes—
678C2C2×#1912758911yescharacteristic
679C2#2491000111yescharacteristic
680C2#2491014811yescharacteristic
681C2#2491041911yescharacteristic
682C2#2491042711yescharacteristic
683C2#2491051711yescharacteristic
684C2#2491053011yescharacteristic
685C2#2491088811yescharacteristic
686C2#2491091011yescharacteristic
687C2#2491123511yescharacteristic
688C2#2491124611yescharacteristic
689C2#2491204011yescharacteristic
690C2#2491207311yescharacteristic
691C2#2491267711yescharacteristic
692C2#2491295011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#391×C83C2
socle, prime radical, cosocleC24×C83C24
hypercenterC2×#391D83
hypocenterC83#14021
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
20. #19127608C4semidirect
57. C2×Dic83⋊C4Q8semidirect
358. C83#14021semidirect

Maximal subgroups

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

subgroupindex
C2×#191276082
C2×C4⋊C4×Dic832
C2×C4×Dic83⋊C42
#249057242
#249057182
#249056942
#249056932
#249056922
#249056872
C2×#391×C832
#1402183