Finite Group Databasebeta

← #35416752

Subgroups — #35416752

Order 21248.

916 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D83)⋊C8C211yesmaximal, characteristic, complemented
2C2×#19127759C211yesmaximal, characteristic, complemented
3#24910705C211yesmaximal, characteristic
4#24908259C211yesmaximal, characteristic, complemented
5#24908255C211yesmaximal, characteristic, complemented
6#24908183C211yesmaximal, characteristic, complemented
7#24908072C211yesmaximal, characteristic, complemented
8#24908069C211yesmaximal, characteristic, complemented
9#24907756C211yesmaximal, characteristic, complemented
10#24907752C211yesmaximal, characteristic, complemented
11#24907640C211yesmaximal, characteristic, complemented
12#24907639C211yesmaximal, characteristic, complemented
13#24907445C211yesmaximal, characteristic, complemented
14C8×Dic83⋊C4C211yesmaximal, characteristic, complemented
15C83×#1954C211yesmaximal, characteristic, complemented
16C23×C83⋊C8C2211yescharacteristic
17C22×C8×D83C2211yescharacteristic
18C2×C4×C22⋊D83C2211yescharacteristic
19C2×C4×C22⋊D83C2211yescharacteristic
20C2×#14581751C2211yescharacteristic
21(C22⋊D83)⋊C8—24no—
22#19127759—24no—
23C2×Dic83⋊C8C2211yescharacteristic
24C2×Dic83⋊C8C2211yescharacteristic
25C2×Dic83⋊C8C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×C22⋊(C83⋊C8)C2211yescharacteristic
29C2×C22⋊(C83⋊C8)C2211yescharacteristic
30C2×C22⋊(C83⋊C8)C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34C2×#14581702C2211yescharacteristic
35C2×C8×Dic83C2211yescharacteristic
36C2×C8×Dic83C2211yescharacteristic
37#19127634C411yescharacteristic
38#19127629C411yescharacteristic
39#19127624C411yescharacteristic
40#19127623C411yescharacteristic
41#19127617C411yescharacteristic
42#19127616C411yescharacteristic
43#19127615C411yescharacteristic
44#19127609C411yescharacteristic
45C4×Dic83⋊C4C2211yescharacteristic
46C4×(C2×D83)⋊C4C2211yescharacteristic
47C4×C22⋊Dic83C2211yescharacteristic
48#19127456C2211yescharacteristic
49#19127456C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54C2×C4×D4×C83C2211yescharacteristic
55C2×C4⋊C8×C83C2211yescharacteristic
56C2×C22⋊C8×C83C2211yescharacteristic
57C2×C22⋊C8×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×C22⋊C8×C83C2211yescharacteristic
60C2×C4×C8×C83C2211yescharacteristic
61C22×C22⋊D83C2×C411yescharacteristic
62C22×C22⋊D83C2×C411yescharacteristic
63C22×C4×D83C2311yescharacteristic
64C22×C83⋊C8—22no—
65C22×C83⋊C8—41no—
66C22×C83⋊C8—41no—
67C22×C83⋊C8C2311yescharacteristic
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C2×C8×D83—22no—
72C2×C8×D83—41no—
73C2×C8×D83—41no—
74C4×C22⋊D83—22no—
75C4×C22⋊D83—22no—
76C4×C22⋊D83—41no—
77C4×C22⋊D83—41no—
78#14581751—22no—
79#14581751—22no—
80C2×C4⋊Dic83C2×C411yescharacteristic
81C2×C4⋊Dic83C2×C411yescharacteristic
82C2×Dic83⋊C4C2×C411yescharacteristic
83C2×Dic83⋊C4C2×C411yescharacteristic
84C2×Dic83⋊C4C2×C411yescharacteristic
85C2×Dic83⋊C4C2×C411yescharacteristic
86C2×C22⋊Dic83C2×C411yescharacteristic
87C2×C22⋊Dic83C2×C411yescharacteristic
88C2×C22⋊Dic83C2×C411yescharacteristic
89C2×C22⋊Dic83C2×C411yescharacteristic
90C2×C22⋊Dic83C2×C411yescharacteristic
91C2×C22⋊Dic83C2×C411yescharacteristic
92C2×(C2×D83)⋊C4C2×C411yescharacteristic
93C2×(C2×D83)⋊C4C2×C411yescharacteristic
94C2×(C2×D83)⋊C4C2×C411yescharacteristic
95C2×(C2×D83)⋊C4C2×C411yescharacteristic
96C2×C4×Dic83C2311yescharacteristic
97C2×C4×Dic83C2311yescharacteristic
98C2×C4×Dic83C2311yescharacteristic
99Dic83⋊C8—22no—
100Dic83⋊C8—22no—
101Dic83⋊C8—22no—
102Dic83⋊C8—22no—
103Dic83⋊C8—41no—
104C22⋊(C83⋊C8)—22no—
105C22⋊(C83⋊C8)—41no—
106C22⋊(C83⋊C8)—41no—
107(C2×D83)⋊C8—22no—
108(C2×D83)⋊C8—41no—
109(C2×D83)⋊C8—41no—
110#14581702—22no—
111C8×Dic83—41no—
112C8×Dic83D414yescomplemented
113C83⋊#95C2×C411yescharacteristic
114C83⋊#95C2×C411yescharacteristic
115C83⋊#95C2×C411yescharacteristic
116C83⋊#95C2×C411yescharacteristic
117C83⋊#95C2×C411yescharacteristic
118C83⋊#95C2×C411yescharacteristic
119C22×D4×C83C2×C411yescharacteristic
120C23×C4×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C22×C8×C83C2311yescharacteristic
123C22×C8×C83C2311yescharacteristic
124C22×C8×C83C2311yescharacteristic
125C22×C8×C83C2311yescharacteristic
126C4×D4×C83—41no—
127C4×D4×C83—41no—
128C2×C4⋊C4×C83C2×C411yescharacteristic
129C2×C22⋊C4×C83C2×C411yescharacteristic
130C2×C22⋊C4×C83C2×C411yescharacteristic
131C2×C42×C83C2311yescharacteristic
132C4⋊C8×C83—41no—
133C22⋊C8×C83—22no—
134C22⋊C8×C83—22no—
135C22⋊C8×C83—41no—
136C22⋊C8×C83—41no—
137C4×C8×C83—41no—
138C23×D83C22×C411yescharacteristic
139C2×C22⋊D83—22no—
140C2×C22⋊D83—22no—
141C2×C22⋊D83—22no—
142C2×C22⋊D83—22no—
143C2×C22⋊D83—22no—
144C2×C22⋊D83—41no—
145C22×Dic83C22×C411yescharacteristic
146C22×Dic83C22×C411yescharacteristic
147C22×Dic83C22×C411yescharacteristic
148C22×Dic83C22×C411yescharacteristic
149C22×Dic83C22×C411yescharacteristic
150C22×Dic83C22×C411yescharacteristic
151C22×Dic83C22×C411yescharacteristic
152C2×C4×D83—21no—
153C2×C4×D83—21no—
154C2×C4×D83—21no—
155C2×C4×D83—21no—
156C2×C4×D83—21no—
157C2×C4×D83—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—44no—
170C2×C83⋊C8C2×D412yes—
171C8×D83—44no—
172C4⋊Dic83—22no—
173C4⋊Dic83—22no—
174Dic83⋊C4—22no—
175Dic83⋊C4—22no—
176Dic83⋊C4—22no—
177Dic83⋊C4—41no—
178C22⋊Dic83—22no—
179C22⋊Dic83—22no—
180C22⋊Dic83—22no—
181C22⋊Dic83—22no—
182C22⋊Dic83—22no—
183C22⋊Dic83—41no—
184(C2×D83)⋊C4—22no—
185(C2×D83)⋊C4—22no—
186(C2×D83)⋊C4—22no—
187(C2×D83)⋊C4—41no—
188C4×Dic83—21no—
189C4×Dic83—21no—
190C4×Dic83—21no—
191C4×Dic83—21no—
192C4×Dic83C2×D412yes—
193C4×Dic83#4112yes—
194C24×C83C22×C411yescharacteristic
195C24×C83C22×C411yescharacteristic
196C2×D4×C83—22no—
197C2×D4×C83—22no—
198C2×D4×C83—41no—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
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×C83C22×C411yescharacteristic
212C22×C4×C83C22×C411yescharacteristic
213C22×C4×C83C22×C411yescharacteristic
214C22×C4×C83C22×C411yescharacteristic
215C22×C4×C83C2411yescharacteristic
216C2×C8×C83—21no—
217C2×C8×C83—21no—
218C2×C8×C83—21no—
219C2×C8×C83—21no—
220C2×C8×C83—21no—
221C2×C8×C83—21no—
222C2×C8×C83—21no—
223C2×C8×C83—21no—
224C2×C8×C83—21no—
225C2×C8×C83—21no—
226C2×C8×C83—21no—
227C2×C8×C83C2×D412yes—
228C4⋊C4×C83—41no—
229C22⋊C4×C83—41no—
230C22⋊C4×C83—41no—
231C42×C83—21no—
232C42×C83—21no—
233C23×C83—21no—
234C23×C83—21no—
235C23×C83—21no—
236C23×C83—21no—
237C23×C83—21no—
238C23×C83—21no—
239C23×C83—21no—
240C23×C83—21no—
241C23×C83—21no—
242C23×C83—21no—
243C23×C83—21no—
244C23×C83—21no—
245C23×C83—21no—
246C23×C83#13112yes—
247C23×C83C23×C411yescharacteristic
248C22×D83—21no—
249C22×D83—21no—
250C22×D83—21no—
251C22×D83—21no—
252C22×D83—21no—
253C22×D83—21no—
254C22×D83#13112yes—
255D4×C83—44no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—21no—
260C2×C4×C83—21no—
261C2×C4×C83—21no—
262C2×C4×C83—21no—
263C2×C4×C83—21no—
264C2×C4×C83—21no—
265C2×C4×C83—21no—
266C2×C4×C83—21no—
267C2×C4×C83—41no—
268C2×C4×C83—41no—
269C2×C4×C83—41no—
270C2×C4×C83—41no—
271C2×C4×C83—41no—
272C2×C4×C83—41no—
273C2×C4×C83—41no—
274C2×C4×C83—41no—
275C2×C4×C83#13112yes—
276C2×C4×C83C22×D411yescharacteristic
277C2×C4×C83C2×#4111yescharacteristic
278C2×C4×C83H(5,𝔽2)11yescharacteristic
279C2×C4×C83H(5,𝔽2)11yescharacteristic
280C2×C4×C83H(5,𝔽2)11yescharacteristic
281C2×C4×C832−1+411yescharacteristic
282C22⋊D83—28no—
283C22⋊D83—44no—
284C2×Dic83—21no—
285C2×Dic83—21no—
286C2×Dic83—21no—
287C2×Dic83—21no—
288C2×Dic83—21no—
289C2×Dic83—21no—
290C2×Dic83—21no—
291C2×Dic83—21no—
292C2×Dic83—21no—
293C2×Dic83—21no—
294C2×Dic83—21no—
295C2×Dic83—21no—
296C2×Dic83—21no—
297C2×Dic83—21no—
298C2×Dic83—21no—
299C2×Dic83—21no—
300C2×Dic83—21no—
301C2×Dic83—21no—
302C2×Dic83C4×D412yes—
303C2×Dic83C4×D412yes—
304C2×Dic83#13112yes—
305C4×D83—41no—
306C4×D83—41no—
307C4×D83—41no—
308C4×D83—41no—
309C8×C83—22no—
310C8×C83—41no—
311C8×C83—41no—
312C8×C83—41no—
313C83⋊C8—22no—
314C83⋊C8—41no—
315C83⋊C8—41no—
316C83⋊C8—41no—
317C22×C83—22no—
318C22×C83—22no—
319C22×C83—22no—
320C22×C83—41no—
321C22×C83—41no—
322C22×C83—41no—
323C22×C83—41no—
324C22×C83—41no—
325C22×C83—41no—
326C22×C83—41no—
327C22×C83—41no—
328C22×C83—41no—
329C22×C83—41no—
330C22×C83—41no—
331C22×C83C2×C4×D411yescharacteristic
332C22×C83#51811yescharacteristic
333C22×C83#52011yescharacteristic
334C22×C83C2×#13111yescharacteristic
335C22×C83C2×#13111yescharacteristic
336C22×C83C2×#13111yescharacteristic
337C22×C83C2×#13111yescharacteristic
338C2×D83—22no—
339C2×D83—22no—
340C2×D83—22no—
341C2×D83—41no—
342C2×D83—41no—
343C2×D83—41no—
344C2×D83—41no—
345C4×C83—22no—
346C4×C83—41no—
347C4×C83—41no—
348C4×C83—41no—
349C4×C83#53511yescharacteristic
350C4×C83#53711yescharacteristic
351C4×C83#54011yescharacteristic
352C4×C83#54211yescharacteristic
353Dic83—22no—
354Dic83—22no—
355Dic83—22no—
356Dic83—41no—
357Dic83—41no—
358Dic83—41no—
359Dic83—41no—
360#22134—831nomaximal, Sylow
361C2×C83—42no—
362C2×C83—81no—
363C2×C83#232411yescharacteristic
364C2×C83#292911yescharacteristic
365C2×C83#293111yescharacteristic
366C2×C83#297711yescharacteristic
367C2×C83#297711yescharacteristic
368C2×C83#299411yescharacteristic
369C2×C83#299411yescharacteristic
370D83—42no—
371C2×C8×D4—831no—
372C2×#433—831no—
373#2392—831no—
374#1955—831no—
375#1954—831no—
376#1954D8311yescharacteristic, complemented
377#1940—831no—
378#1923—831no—
379#1923—831no—
380#1869—831no—
381#1869—831no—
382#1850—831no—
383#1850—831no—
384#1798—831no—
385C8×C4⋊C4—831no—
386C83#2213411yescharacteristic, complemented, Sylow
387C23×C8—831no—
388C23×C8—831no—
389C2×C4×D4—831no—
390C2×C4×D4—831no—
391C2×C4×D4C2×D8311yescharacteristic
392C2×#117—831no—
393C8×D4—1664no—
394#433—1664no—
395C2×C4⋊C8—831no—
396C2×C4⋊C8—831no—
397C2×C4⋊C8—831no—
398C2×C4⋊C8—831no—
399C2×C4⋊C8—831no—
400C2×C4⋊C8C2×D8311yescharacteristic
401C2×C22⋊C8—831no—
402C2×C22⋊C8—831no—
403C2×C22⋊C8—831no—
404C2×C22⋊C8—831no—
405C2×C22⋊C8—831no—
406C2×C22⋊C8—831no—
407C2×C22⋊C8C2×D8311yescharacteristic
408C2×C22⋊C8C2×D8311yescharacteristic
409C2×C22⋊C8C2×D8311yescharacteristic
410C2×C22⋊C8C2×D8311yescharacteristic
411C2×#97—831no—
412C2×C4×C8—831no—
413C2×C4×C8—831no—
414C2×C4×C8C2×D8311yescharacteristic
415#398—831no—
416#397—831no—
417#396—831no—
418#396—831no—
419#394—831no—
420#394—831no—
421#394—831no—
422#392—831no—
423C4×C4⋊C4—831no—
424C4×C22⋊C4—831no—
425C4×C22⋊C4—831no—
426#336—831no—
427#336—831no—
428#336—831no—
429#336—831no—
430#336—831no—
431#336—831no—
432C22×D4—831no—
433C22×D4—831no—
434C22×D4C4×D8311yescharacteristic
435C23×C4—831no—
436C23×C4C22×D8311yescharacteristic
437C23×C4C22×D8311yescharacteristic
438C22×C8—3321no—
439C22×C8—3321no—
440C22×C8—3321no—
441C22×C8—3321no—
442C22×C8—831no—
443C22×C8—831no—
444C22×C8—831no—
445C22×C8—831no—
446C22×C8—1662no—
447C22×C8—1662no—
448C22×C8C22×D8311yescharacteristic
449C22×C8C22×D8311yescharacteristic
450C22×C8C22×D8311yescharacteristic
451C22×C8C22×D8311yescharacteristic
452C4×D4—41no—
453C4×D4—41no—
454C4×D4—3321no—
455C4×D4—3321no—
456C4×D4—1662no—
457C4×D4—1662no—
458#117—1662no—
459#117—1662no—
460C2×C4⋊C4—831no—
461C2×C4⋊C4—831no—
462C2×C4⋊C4—831no—
463C2×C4⋊C4—831no—
464C2×C4⋊C4—831no—
465C2×C4⋊C4—831no—
466C2×C4⋊C4C4×D8311yescharacteristic
467C2×C22⋊C4—831no—
468C2×C22⋊C4—831no—
469C2×C22⋊C4—831no—
470C2×C22⋊C4—831no—
471C2×C22⋊C4—831no—
472C2×C22⋊C4—831no—
473C2×C22⋊C4—831no—
474C2×C22⋊C4—831no—
475C2×C22⋊C4—831no—
476C2×C22⋊C4—831no—
477C2×C22⋊C4C4×D8311yescharacteristic
478C2×C22⋊C4C4×D8311yescharacteristic
479C2×C42—831no—
480C2×C42—831no—
481C2×C42—831no—
482C2×C42C22×D8311yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—3321no—
485C4⋊C8—1662no—
486C4⋊C8—1662no—
487C4⋊C8—1662no—
488C4⋊C8—1662no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—41no—
492C22⋊C8—41no—
493C22⋊C8—3321no—
494C22⋊C8—3321no—
495C22⋊C8—3321no—
496C22⋊C8—3321no—
497C22⋊C8—1662no—
498C22⋊C8—1662no—
499#97—1662no—
500C4×C8—41no—
501C4×C8—3321no—
502C4×C8—834no—
503#95—831no—
504#95—831no—
505#95—831no—
506#95—831no—
507#95—831no—
508#95—831no—
509C24—831no—
510C24C2×C4×D8311yescharacteristic
511C24C2×C4×D8311yescharacteristic
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—41no—
515C2×D4—3321no—
516C2×D4—1662no—
517C2×D4—1662no—
518C2×D4—1662no—
519C2×D4—1662no—
520C2×D4—1662no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—831no—
534C22×C4—831no—
535C22×C4—831no—
536C22×C4—831no—
537C22×C4—831no—
538C22×C4—831no—
539C22×C4—831no—
540C22×C4—1661no—
541C22×C4—1661no—
542C22×C4—1661no—
543C22×C4—1661no—
544C22×C4—1661no—
545C22×C4—1661no—
546C22×C4C2×C4×D8311yescharacteristic
547C22×C4C2×C4×D8311yescharacteristic
548C22×C4C2×C4×D8311yescharacteristic
549C22×C4C2×C4×D8311yescharacteristic
550C22×C4C23×D8311yescharacteristic
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—3324no—
563C2×C8—3324no—
564C2×C8—832no—
565C2×C8—1661no—
566C2×C8—1661no—
567C2×C8—1661no—
568C2×C8—1661no—
569C2×C8—1661no—
570C2×C8—1661no—
571C2×C8—1661no—
572C2×C8—1661no—
573C2×C8—1661no—
574C2×C8—1661no—
575C2×C8—1661no—
576C2×C8D4×D8312yes—
577C4⋊C4—41no—
578C4⋊C4—3321no—
579C4⋊C4—1662no—
580C4⋊C4—1662no—
581C4⋊C4—1662no—
582C4⋊C4—1662no—
583C4⋊C4—1662no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—3321no—
587C22⋊C4—3321no—
588C22⋊C4—1662no—
589C22⋊C4—1662no—
590C22⋊C4—1662no—
591C22⋊C4—1662no—
592C22⋊C4—1662no—
593C22⋊C4—1662no—
594C22⋊C4—1662no—
595C22⋊C4—1662no—
596C42—21no—
597C42—21no—
598C42—832no—
599C42—832no—
600C42—1661no—
601C42—1661no—
602C42—1661no—
603C42—1661no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—832no—
618C23—1661no—
619C23—1661no—
620C23—1661no—
621C23—1661no—
622C23—1661no—
623C23—1661no—
624C23#1458179812yes—
625C23C22×C4×D8311yescharacteristic
626D4—44no—
627D4—3324no—
628D4—1668no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—3321no—
649C2×C4—3321no—
650C2×C4—3321no—
651C2×C4—3321no—
652C2×C4—832no—
653C2×C4—832no—
654C2×C4—832no—
655C2×C4—1661no—
656C2×C4—1661no—
657C2×C4—1661no—
658C2×C4—1661no—
659C2×C4—1661no—
660C2×C4—1661no—
661C2×C4—1661no—
662C2×C4—1661no—
663C2×C4—1661no—
664C2×C4—1661no—
665C2×C4—1661no—
666C2×C4—1661no—
667C2×C4—1661no—
668C2×C4—1661no—
669C2×C4—1661no—
670C2×C4—1661no—
671C2×C4—1661no—
672C2×C4—1661no—
673C2×C4#1458180012yes—
674C2×C4C2×D4×D8311yescharacteristic
675C2×C4#41×D8311yescharacteristic
676C2×C4#1458183711yescharacteristic
677C2×C4#1458183711yescharacteristic
678C2×C4#1458183711yescharacteristic
679C2×C4#1458183911yescharacteristic
680C8—22no—
681C8—41no—
682C8—41no—
683C8—41no—
684C8—3321no—
685C8—3321no—
686C8—3321no—
687C8—1662no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—3321no—
703C22—3321no—
704C22—3321no—
705C22—3321no—
706C22—1662no—
707C22—1662no—
708C22—1662no—
709C22C4×D4×D8311yescharacteristic
710C22#1912817411yescharacteristic
711C22#1912818011yescharacteristic
712C22#131×D8311yescharacteristic
713C22#131×D8311yescharacteristic
714C22C2×#1458179811yescharacteristic
715C22C2×#1458180011yescharacteristic
716C4—22no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—3321no—
721C4—3321no—
722C4—3321no—
723C4—3321no—
724C4—1662no—
725C4—1662no—
726C4—1662no—
727C4#1912826411yescharacteristic
728C4#1912827811yescharacteristic
729C4#1912830111yescharacteristic
730C4#1912831511yescharacteristic
731C2—42no—
732C2—81no—
733C2—3322no—
734C2#2491014911yescharacteristic
735C2#2491615211yescharacteristic
736C2#2491617211yescharacteristic
737C2#2491651511yescharacteristic
738C2#2491651711yescharacteristic
739C2#2491662011yescharacteristic
740C2#2491662411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1954C2
prime radical#19127609C4
cosocleC22×C4×C83C24
hypercenter#1954D83
hypocenterC83#22134
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×(C22⋊D83)⋊C8C2semidirect
2. C2×#19127759C2semidirect
4. #24908259C2semidirect
5. #24908255C2semidirect
6. #24908183C2semidirect
7. #24908072C2semidirect
8. #24908069C2semidirect
9. #24907756C2semidirect
10. #24907752C2semidirect
11. #24907640C2semidirect
12. #24907639C2semidirect
13. #24907445C2semidirect
14. C8×Dic83⋊C4C2semidirect
15. C83×#1954C2semidirect
112. C8×Dic83D4semidirect
376. #1954D83semidirect
386. C83#22134semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D83)⋊C82
C2×#191277592
#249107052
#249082592
#249082552
#249081832
#249080722
#249080692
#249077562
#249077522
#249076402
#249076392
#249074452
C8×Dic83⋊C42
C83×#19542
#2213483