Finite Group Databasebeta

← #35420701

Subgroups — #35420701

Order 21248.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128416C211yesmaximal, characteristic
2C2×#19127773C211yesmaximal, characteristic, complemented
3#24908435C211yesmaximal, characteristic, complemented
4#24908415C211yesmaximal, characteristic, complemented
5#24907899C211yesmaximal, characteristic, complemented
6#24907889C211yesmaximal, characteristic, complemented
7#24907785C211yesmaximal, characteristic, complemented
8#24907780C211yesmaximal, characteristic, complemented
9#24907555C211yesmaximal, characteristic, complemented
10#24907555C211yesmaximal, characteristic, complemented
11#24907470C211yesmaximal, characteristic, complemented
12#24907291C211yesmaximal, characteristic, complemented
13#24907182C211yesmaximal, characteristic, complemented
14#24907179C211yesmaximal, characteristic, complemented
15C83×#2352C211yesmaximal, characteristic, complemented
16C22×#13050574C2211yescharacteristic
17C23×C83⋊C8C2211yescharacteristic
18#19128416—24no—
19#19128416C418yescomplemented
20C2×#14581792C2211yescharacteristic
21C2×#14581778—21no—
22C2×#14581778—21no—
23C2×#14581766C2211yescharacteristic
24C2×#14581766C2211yescharacteristic
25C2×#14581763—21no—
26C2×C4×D332C2211yescharacteristic
27C2×#14581751C2211yescharacteristic
28C2×#14581751C2211yescharacteristic
29C2×#14581750—21no—
30#19127773—24no—
31C2×C4⋊(C83⋊C8)C2211yescharacteristic
32C2×#14581712C2211yescharacteristic
33C2×#14581712C2211yescharacteristic
34C2×#14581712C2211yescharacteristic
35C2×#14581712C2211yescharacteristic
36C2×C22⋊(C83⋊C8)C2211yescharacteristic
37C2×C22⋊(C83⋊C8)C2211yescharacteristic
38C2×#14581703C2211yescharacteristic
39#19127463C2211yescharacteristic
40#19127463C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51C2×C4×D4×C83C2211yescharacteristic
52C2×#117×C83C2211yescharacteristic
53C22×C4⋊C4×C83C2211yescharacteristic
54#388×C83—21no—
55#387×C83—21no—
56#386×C83—21no—
57#382×C83C2211yescharacteristic
58#380×C83C2211yescharacteristic
59#380×C83C2211yescharacteristic
60C4×C4⋊C4×C83C2211yescharacteristic
61C4×C22⋊C4×C83—21no—
62C22×Dic166—21no—
63C22×D332C2311yescharacteristic
64C22×C22⋊D83—21no—
65C22×C22⋊D83—21no—
66C22×C4×D83—21no—
67C2×#13050574—22no—
68C2×#13050574—22no—
69C2×#13050574—41no—
70C22×C83⋊C8—22no—
71C22×C83⋊C8—22no—
72C22×C83⋊C8—41no—
73C22×C83⋊C8C2311yescharacteristic
74C22×C83⋊C8C2311yescharacteristic
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77#14581792—22no—
78#14581792C2×C414yescomplemented
79#14581778—28no—
80#14581778—28no—
81#14581766—22no—
82#14581766—22no—
83#14581766C2×C414yes—
84#14581766C2×C414yescomplemented
85#14581763—28no—
86C4×D332—22no—
87C4×D332C2×C414yescomplemented
88#14581751—22no—
89#14581751—22no—
90#14581751C2×C414yes—
91#14581751C2×C414yescomplemented
92#14581750—28no—
93C2×C4⋊Dic83—21no—
94C2×C4⋊Dic83C2311yescharacteristic
95C2×C4⋊Dic83C2311yescharacteristic
96C2×C4⋊Dic83C2311yescharacteristic
97C2×C22⋊Dic83—21no—
98C2×C22⋊Dic83—21no—
99C2×(C2×D83)⋊C4—21no—
100C2×(C2×D83)⋊C4—21no—
101C2×(C2×D83)⋊C4—21no—
102C2×C4×Dic83—21no—
103C2×C4×Dic83—21no—
104C4⋊(C83⋊C8)—22no—
105#14581712—22no—
106#14581712—22no—
107#14581712—41no—
108#14581712—41no—
109C22⋊(C83⋊C8)—22no—
110C22⋊(C83⋊C8)—22no—
111#14581703—22no—
112C22×D4×C83D411yescharacteristic
113C23×C4×C83—21no—
114C23×C4×C83C2311yescharacteristic
115C23×C4×C83C2311yescharacteristic
116C4×D4×C83C2×C414yes—
117C4×D4×C83D414yes—
118#117×C83—22no—
119#117×C83—41no—
120C2×C4⋊C4×C83—22no—
121C2×C4⋊C4×C83—21no—
122C2×C4⋊C4×C83—41no—
123C2×C4⋊C4×C83D411yescharacteristic
124C2×C4⋊C4×C83C2311yescharacteristic
125C2×C4⋊C4×C83C2311yescharacteristic
126C2×C4⋊C4×C83C2311yescharacteristic
127C2×C4⋊C4×C83C2311yescharacteristic
128C2×C22⋊C4×C83—21no—
129C2×C22⋊C4×C83—21no—
130C2×C22⋊C4×C83—21no—
131C2×C22⋊C4×C83D411yescharacteristic
132C2×C22⋊C4×C83D411yescharacteristic
133C2×C42×C83—21no—
134C2×C42×C83—21no—
135C2×C42×C83C2311yescharacteristic
136#95×C83—21no—
137#95×C83—21no—
138#95×C83—21no—
139#95×C83—21no—
140#95×C83—21no—
141C23×D83—21no—
142C2×Dic166—24no—
143C2×Dic166—81no—
144C2×Dic166—81no—
145C2×D332—21no—
146C2×D332—21no—
147C2×D332—21no—
148C2×D332—21no—
149C2×D332—21no—
150C2×D332C22×C412yes—
151C2×C22⋊D83—24no—
152C2×C22⋊D83—24no—
153C2×C22⋊D83—81no—
154C2×C22⋊D83—81no—
155C2×C22⋊D83—81no—
156C2×C22⋊D83—81no—
157C22×Dic83—21no—
158C22×Dic83—21no—
159C22×Dic83—21no—
160C2×C4×D83—24no—
161C2×C4×D83—42no—
162C2×C4×D83—42no—
163#13050574—44no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—21no—
174C2×C83⋊C8—21no—
175C2×C83⋊C8—44no—
176C2×C83⋊C8#4112yes—
177C4⋊Dic83—24no—
178C4⋊Dic83—21no—
179C4⋊Dic83—21no—
180C4⋊Dic83—21no—
181C4⋊Dic83C22×C412yes—
182C4⋊Dic83C22×C412yes—
183C4⋊Dic83C22×C412yes—
184C22⋊Dic83—24no—
185C22⋊Dic83—24no—
186(C2×D83)⋊C4—24no—
187(C2×D83)⋊C4—24no—
188(C2×D83)⋊C4—24no—
189C4×Dic83—24no—
190C4×Dic83—24no—
191C24×C83C2×D411yescharacteristic
192C24×C83C2×D411yescharacteristic
193C2×D4×C83—41no—
194C2×D4×C83—41no—
195C2×D4×C83C22⋊C414yes—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
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—42no—
209C22×C4×C83—42no—
210C22×C4×C83—81no—
211C22×C4×C83C22×C412yes—
212C22×C4×C83C22×C412yes—
213C22×C4×C83C2×D411yescharacteristic
214C22×C4×C83C2×D411yescharacteristic
215C22×C4×C83C2×D411yescharacteristic
216C22×C4×C83C2×D411yescharacteristic
217C22×C4×C83C2×D412yes—
218C22×C4×C83C2×D412yes—
219C22×C4×C83C2411yescharacteristic
220C4⋊C4×C83—21no—
221C4⋊C4×C83—21no—
222C4⋊C4×C83—21no—
223C4⋊C4×C83—21no—
224C4⋊C4×C83—21no—
225C4⋊C4×C83—21no—
226C4⋊C4×C83—21no—
227C4⋊C4×C83—42no—
228C4⋊C4×C83C22⋊C414yes—
229C4⋊C4×C83#4112yes—
230C22⋊C4×C83—42no—
231C22⋊C4×C83—42no—
232C22⋊C4×C83—81no—
233C22⋊C4×C83C22⋊C414yes—
234C22⋊C4×C83C22⋊C414yes—
235C42×C83—42no—
236C42×C83—81no—
237C42×C83C22×C412yes—
238C42×C83C2×D412yes—
239C23×C83—21no—
240C23×C83—21no—
241C23×C83—21no—
242C23×C83—21no—
243C23×C83—21no—
244C23×C83—21no—
245C23×C83—21no—
246C23×C83—21no—
247C23×C83—21no—
248C23×C83—21no—
249C23×C83—21no—
250C23×C83—21no—
251C23×C83C2×C22⋊C412yes—
252C23×C83C2×C22⋊C412yes—
253C23×C83C22×D411yescharacteristic
254C22×D83—22no—
255C22×D83—41no—
256C22×D83—41no—
257C22×D83—41no—
258C22×D83—41no—
259C22×D83—41no—
260C22×D83—41no—
261D4×C83—44no—
262C2×C4×C83—21no—
263C2×C4×C83—21no—
264C2×C4×C83—21no—
265C2×C4×C83—21no—
266C2×C4×C83—21no—
267C2×C4×C83—21no—
268C2×C4×C83—21no—
269C2×C4×C83—21no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—41no—
280C2×C4×C83—41no—
281C2×C4×C83—41no—
282C2×C4×C83—41no—
283C2×C4×C83—41no—
284C2×C4×C83—41no—
285C2×C4×C83—41no—
286C2×C4×C83—41no—
287C2×C4×C83—41no—
288C2×C4×C83—41no—
289C2×C4×C83—41no—
290C2×C4×C83—84no—
291C2×C4×C83C2×C22⋊C412yes—
292C2×C4×C83C2×C22⋊C412yes—
293C2×C4×C83C2×C22⋊C412yes—
294C2×C4×C83C2×C22⋊C412yes—
295C2×C4×C83C23×C411yescharacteristic
296C2×C4×C83C22×D411yescharacteristic
297C2×C4×C83C2×#4111yescharacteristic
298C2×C4×C83C2×#4111yescharacteristic
299C2×C4×C83H(5,𝔽2)11yescharacteristic
300C2×C4×C832−1+411yescharacteristic
301C22⋊D83—84no—
302C22⋊D83—84no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—41no—
307C2×Dic83—41no—
308C2×Dic83—41no—
309C2×Dic83—41no—
310C2×Dic83—41no—
311C2×Dic83—41no—
312D332—22no—
313D332—22no—
314D332—41no—
315D332—41no—
316C4×D83—48no—
317Dic166—84no—
318C83⋊C8—22no—
319C83⋊C8—41no—
320C83⋊C8—41no—
321C83⋊C8—41no—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—41no—
329C22×C83—41no—
330C22×C83—41no—
331C22×C83—41no—
332C22×C83—41no—
333C22×C83—41no—
334C22×C83—41no—
335C22×C83—41no—
336C22×C83C22×C22⋊C411yescharacteristic
337C22×C83#54611yescharacteristic
338C22×C83#54711yescharacteristic
339C22×C83#57511yescharacteristic
340C22×C83#57511yescharacteristic
341C22×C83#57611yescharacteristic
342C22×C83#57711yescharacteristic
343C2×D83—42no—
344C2×D83—42no—
345C2×D83—42no—
346C2×D83—81no—
347C2×D83—81no—
348C2×D83—81no—
349C2×D83—81no—
350C4×C83—22no—
351C4×C83—22no—
352C4×C83—22no—
353C4×C83—22no—
354C4×C83—42no—
355C4×C83—81no—
356C4×C83—81no—
357C4×C83—81no—
358C4×C83C4×#4111yescharacteristic
359C4×C83#52011yescharacteristic
360C4×C83#54611yescharacteristic
361C4×C83#54711yescharacteristic
362Dic83—42no—
363Dic83—42no—
364Dic83—42no—
365#22492—831nomaximal, Sylow
366C2×C83—42no—
367C2×C83—42no—
368C2×C83#233911yescharacteristic
369C2×C83#289611yescharacteristic
370C2×C83#289711yescharacteristic
371C2×C83#331911yescharacteristic
372C2×C83#332111yescharacteristic
373C2×C83#334711yescharacteristic
374C2×C83#334811yescharacteristic
375D83—82no—
376C2×#555—831no—
377C2×#435—831no—
378#2352D8311yescharacteristic, complemented
379#1993—831no—
380#1988—831no—
381#1895—831no—
382#1893—831no—
383#1875—831no—
384#1874—831no—
385#1825—831no—
386#1825—831no—
387#1804—831no—
388#1762—831no—
389#1736—831no—
390#1735—831no—
391C83#2249211yescharacteristic, complemented, Sylow
392C22×M16—831no—
393C23×C8—831no—
394#555—838no—
395#555—1664no—
396C2×C4⋊Q8—831no—
397C2×#124—1661no—
398C2×#124—1661no—
399C2×#121—831no—
400C2×#121—831no—
401C2×#121—1661no—
402C2×C4×D4—831no—
403C2×C4×D4C2×D8311yescharacteristic
404C2×#117—831no—
405C2×#117—831no—
406C2×#117—1661no—
407C2×#117C2×D8311yescharacteristic
408C22×C4⋊C4C2×D8311yescharacteristic
409#435—1664no—
410C2×C4⋊C8—831no—
411C2×#102—831no—
412C2×#102—831no—
413C2×#102—831no—
414C2×#102—831no—
415C2×C22⋊C8—831no—
416C2×C22⋊C8—831no—
417C2×#97—831no—
418#388—21no—
419#387—21no—
420#386—21no—
421#382C2×D8311yescharacteristic
422#380C2×D8311yescharacteristic
423#380C2×D8311yescharacteristic
424C4×C4⋊C4C2×D8311yescharacteristic
425C4×C22⋊C4—21no—
426#340—831no—
427#340—831no—
428#340—831no—
429#340—831no—
430#340—831no—
431#340—831no—
432#340—831no—
433#340—831no—
434#340—831no—
435#340—831no—
436#340—831no—
437#340—831no—
438C22×Q8—1661no—
439C22×D4—831no—
440C22×D4—1661no—
441C22×D4—1661no—
442C22×D4C22⋊D8311yescharacteristic
443C23×C4—21no—
444C23×C4—1661no—
445C23×C4C22×D8311yescharacteristic
446C23×C4C22×D8311yescharacteristic
447C2×M16—3321no—
448C2×M16—1662no—
449C2×M16—1662no—
450C22×C8—3321no—
451C22×C8—831no—
452C22×C8—831no—
453C22×C8—831no—
454C22×C8—831no—
455C22×C8—1662no—
456C22×C8—1662no—
457C4⋊Q8—834no—
458C4⋊Q8—1662no—
459#124—1668no—
460#124—1668no—
461#121—834no—
462#121—834no—
463#121—1668no—
464#121—1662no—
465#121—1662no—
466C4×D4—834no—
467C4×D4—1662no—
468C4×D4C4×D8314yes—
469C4×D4D33214yes—
470#117—22no—
471#117—41no—
472#117—834no—
473#117—834no—
474#117—1662no—
475#117—1662no—
476#117—1668no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—831no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4—831no—
483C2×C4⋊C4—1661no—
484C2×C4⋊C4C22⋊D8311yescharacteristic
485C2×C4⋊C4C22×D8311yescharacteristic
486C2×C4⋊C4C22×D8311yescharacteristic
487C2×C4⋊C4C22×D8311yescharacteristic
488C2×C4⋊C4C22×D8311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1661no—
493C2×C22⋊C4—1661no—
494C2×C22⋊C4—1661no—
495C2×C22⋊C4—1661no—
496C2×C22⋊C4—1661no—
497C2×C22⋊C4C22⋊D8311yescharacteristic
498C2×C22⋊C4C22⋊D8311yescharacteristic
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—1661no—
502C2×C42—1661no—
503C2×C42C22×D8311yescharacteristic
504C4⋊C8—1662no—
505#102—3321no—
506#102—3321no—
507#102—1662no—
508#102—1662no—
509C22⋊C8—1662no—
510C22⋊C8—1662no—
511#97—1662no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517C24—1661no—
518C24C2×C22⋊D8311yescharacteristic
519C24C2×C22⋊D8311yescharacteristic
520C2×Q8—6641no—
521C2×Q8—6641no—
522C2×Q8—1664no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—832no—
526C2×D4—6641no—
527C2×D4—6641no—
528C2×D4—6641no—
529C2×D4—6641no—
530C2×D4—1664no—
531C2×D4—1664no—
532C2×D4—1661no—
533C2×D4—1661no—
534C2×D4—1661no—
535C2×D4—1661no—
536C2×D4—1661no—
537C2×D4(C2×D83)⋊C414yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—3322no—
554C22×C4—3322no—
555C22×C4—1661no—
556C22×C4—1661no—
557C22×C4—1661no—
558C22×C4—1664no—
559C22×C4C2×C4×D8312yes—
560C22×C4C2×C4×D8312yes—
561C22×C4C2×C22⋊D8311yescharacteristic
562C22×C4C2×C22⋊D8311yescharacteristic
563C22×C4C2×C22⋊D8311yescharacteristic
564C22×C4C2×C22⋊D8311yescharacteristic
565C22×C4C2×D33212yes—
566C22×C4C2×D33212yes—
567C22×C4C23×D8311yescharacteristic
568M16—3324no—
569C2×C8—3324no—
570C2×C8—832no—
571C2×C8—1661no—
572C2×C8—1661no—
573C2×C8—1661no—
574C2×C8—1661no—
575C2×C8—1661no—
576C2×C8—1661no—
577C2×C8—1661no—
578C2×C8—1661no—
579C2×C8—1661no—
580C2×C8—1661no—
581C2×C8—1661no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—832no—
591C4⋊C4—832no—
592C4⋊C4—832no—
593C4⋊C4—1661no—
594C4⋊C4—1661no—
595C4⋊C4—1661no—
596C4⋊C4—1664no—
597C4⋊C4(C2×D83)⋊C414yes—
598C4⋊C4#1305058912yes—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—1664no—
603C22⋊C4—1664no—
604C22⋊C4—1664no—
605C22⋊C4—1664no—
606C22⋊C4—1664no—
607C22⋊C4(C2×D83)⋊C414yes—
608C22⋊C4(C2×D83)⋊C414yes—
609C42—42no—
610C42—81no—
611C42—1664no—
612C42—1664no—
613C42C2×C4×D8312yes—
614C42C2×D33212yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—3321no—
628C23—3321no—
629C23—3321no—
630C23—3321no—
631C23—3321no—
632C23—3321no—
633C23—1662no—
634C23C2×(C2×D83)⋊C412yes—
635C23C2×(C2×D83)⋊C412yes—
636C23C22×C22⋊D8311yescharacteristic
637Q8—6644no—
638D4—44no—
639D4—3321no—
640D4—3321no—
641D4—6644no—
642D4—6644no—
643D4—1662no—
644D4—1662no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4—3328no—
675C2×C4—3321no—
676C2×C4—3321no—
677C2×C4—3321no—
678C2×C4—3321no—
679C2×C4—3321no—
680C2×C4—3321no—
681C2×C4—1662no—
682C2×C4—1662no—
683C2×C4—1662no—
684C2×C4C2×(C2×D83)⋊C412yes—
685C2×C4C2×(C2×D83)⋊C412yes—
686C2×C4C2×(C2×D83)⋊C412yes—
687C2×C4C2×(C2×D83)⋊C412yes—
688C2×C4C22×C4×D8311yescharacteristic
689C2×C4C22×D33211yescharacteristic
690C2×C4#41×D8311yescharacteristic
691C2×C4C2×#1305058911yescharacteristic
692C2×C4#1458183711yescharacteristic
693C2×C4#1458183911yescharacteristic
694C8—3321no—
695C8—3321no—
696C8—3321no—
697C8—1662no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—3322no—
713C22—3322no—
714C22—3322no—
715C22—6641no—
716C22—6641no—
717C22—6641no—
718C22—6641no—
719C22C22×(C2×D83)⋊C411yescharacteristic
720C22#1912834511yescharacteristic
721C22#1912835011yescharacteristic
722C22#1912849911yescharacteristic
723C22#1912849911yescharacteristic
724C22#1912850411yescharacteristic
725C22#1912850911yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—3322no—
735C4—3322no—
736C4—3322no—
737C4C4×#1305058911yescharacteristic
738C4#1912818011yescharacteristic
739C4#1912834611yescharacteristic
740C4#1912835511yescharacteristic
741C2—42no—
742C2—42no—
743C2—6642no—
744C2#2491028811yescharacteristic
745C2#2491598011yescharacteristic
746C2#2491598611yescharacteristic
747C2#2491961911yescharacteristic
748C2#2491964911yescharacteristic
749C2#2491995711yescharacteristic
750C2#2491997211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#2352C2
socleC23×C83C22×D4
prime radicalC2×#19128416C2
cosocleC22×C4×C83C24
hypercenter#2352D83
hypocenterC83#22492
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#19127773C2semidirect
3. #24908435C2semidirect
4. #24908415C2semidirect
5. #24907899C2semidirect
6. #24907889C2semidirect
7. #24907785C2semidirect
8. #24907780C2semidirect
9. #24907555C2semidirect
10. #24907555C2semidirect
11. #24907470C2semidirect
12. #24907291C2semidirect
13. #24907182C2semidirect
14. #24907179C2semidirect
15. C83×#2352C2semidirect
19. #19128416C4semidirect
78. #14581792C2×C4semidirect
84. #14581766C2×C4semidirect
87. C4×D332C2×C4semidirect
91. #14581751C2×C4semidirect
378. #2352D83semidirect
391. C83#22492semidirect

Maximal subgroups

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

subgroupindex
C2×#191284162
C2×#191277732
#249084352
#249084152
#249078992
#249078892
#249077852
#249077802
#249075552
#249074702
#249072912
#249071822
#249071792
C83×#23522
#2249283