Finite Group Databasebeta

← #35420797

Subgroups — #35420797

Order 21248.

1186 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127773C211yesmaximal, characteristic, complemented
2#24910412C211yesmaximal, characteristic, complemented
3#24908433C211yesmaximal, characteristic, complemented
4#24908421C211yesmaximal, characteristic, complemented
5#24907902C211yesmaximal, characteristic, complemented
6#24907892C211yesmaximal, characteristic, complemented
7#24907786C211yesmaximal, characteristic, complemented
8#24907786C211yesmaximal, characteristic, complemented
9#24907558C211yesmaximal, characteristic, complemented
10#24907549C211yesmaximal, characteristic, complemented
11#24907463C211yesmaximal, characteristic, complemented
12#24907288C211yesmaximal, characteristic, complemented
13#24907182C211yesmaximal, characteristic, complemented
14#24907179C211yesmaximal, characteristic, complemented
15C2×#553×C83C211yesmaximal, characteristic
16C22×#13050574C2211yescharacteristic
17C23×C83⋊C8C2211yescharacteristic
18C2×#14581751C2211yescharacteristic
19C2×#14581751C2211yescharacteristic
20#19127773—24no—
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×#14581713C2211yescharacteristic
23C2×#14581713C2211yescharacteristic
24C2×#14581713C2211yescharacteristic
25C2×#14581713C2211yescharacteristic
26C2×C22⋊(C83⋊C8)C2211yescharacteristic
27C2×C22⋊(C83⋊C8)C2211yescharacteristic
28C2×#14581703C2211yescharacteristic
29#19127604—21no—
30#19127594—21no—
31#19127594—21no—
32#19127571C2211yescharacteristic
33#19127561C2211yescharacteristic
34#19127561C2211yescharacteristic
35C4⋊C4×Dic83—21no—
36C4×C4⋊Dic83C2211yescharacteristic
37#19127463C2211yescharacteristic
38#19127463C2211yescharacteristic
39#19127463C2211yescharacteristic
40#19127463C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#553×C83—24no—
50#553×C83C418yescomplemented
51C2×#126×C83—21no—
52C2×#125×C83C2211yescharacteristic
53C2×#123×C83—21no—
54C2×#121×C83—21no—
55C2×#121×C83C2211yescharacteristic
56C2×#121×C83C2211yescharacteristic
57C2×C4×D4×C83—21no—
58C2×C4×D4×C83C2211yescharacteristic
59C2×C4×D4×C83C2211yescharacteristic
60C2×#117×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C2×#13050574—22no—
63C2×#13050574—22no—
64C2×#13050574—41no—
65C22×C83⋊C8—22no—
66C22×C83⋊C8—22no—
67C22×C83⋊C8—41no—
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72#14581751—22no—
73#14581751—22no—
74#14581751—41no—
75#14581751—41no—
76C2×C4⋊Dic83—21no—
77C2×C4⋊Dic83—21no—
78C2×C4⋊Dic83C2311yescharacteristic
79C2×C4⋊Dic83C2311yescharacteristic
80C2×C4⋊Dic83C2311yescharacteristic
81C2×C4⋊Dic83C2311yescharacteristic
82C2×C22⋊Dic83—21no—
83C2×C22⋊Dic83—21no—
84C2×C22⋊Dic83—21no—
85C2×C22⋊Dic83—21no—
86C2×C4×Dic83—21no—
87C2×C4×Dic83—21no—
88C2×C4×Dic83—21no—
89C4⋊(C83⋊C8)—22no—
90#14581713—22no—
91#14581713—22no—
92#14581713—41no—
93#14581713—41no—
94C22⋊(C83⋊C8)—22no—
95C22⋊(C83⋊C8)—22no—
96#14581703—22no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C22×D4×C83—21no—
101C22×D4×C83—21no—
102C22×D4×C83D411yescharacteristic
103C22×D4×C83C2311yescharacteristic
104C23×C4×C83—21no—
105C23×C4×C83—21no—
106C23×C4×C83C2311yescharacteristic
107C23×C4×C83C2311yescharacteristic
108#126×C83—28no—
109#125×C83—22no—
110#125×C83C2×C414yes—
111#123×C83—28no—
112#121×C83—28no—
113#121×C83—22no—
114#121×C83—22no—
115#121×C83C2×C414yes—
116#121×C83C2×C414yes—
117C4×D4×C83—28no—
118C4×D4×C83—22no—
119C4×D4×C83C2×C414yes—
120C4×D4×C83C2×C414yes—
121C4×D4×C83D414yes—
122#117×C83—22no—
123#117×C83C2×C414yes—
124C2×C4⋊C4×C83—21no—
125C2×C4⋊C4×C83—22no—
126C2×C4⋊C4×C83—21no—
127C2×C4⋊C4×C83—21no—
128C2×C4⋊C4×C83C2×C414yes—
129C2×C4⋊C4×C83D411yescharacteristic
130C2×C4⋊C4×C83C2311yescharacteristic
131C2×C4⋊C4×C83C2311yescharacteristic
132C2×C4⋊C4×C83C2311yescharacteristic
133C2×C22⋊C4×C83—21no—
134C2×C22⋊C4×C83—21no—
135C2×C22⋊C4×C83—21no—
136C2×C22⋊C4×C83—21no—
137C2×C22⋊C4×C83D411yescharacteristic
138C2×C22⋊C4×C83D411yescharacteristic
139C2×C42×C83—21no—
140C2×C42×C83C2311yescharacteristic
141C22×Dic83—21no—
142C22×Dic83—21no—
143C22×Dic83—21no—
144C22×Dic83—21no—
145#13050574—44no—
146C2×C83⋊C8—21no—
147C2×C83⋊C8—21no—
148C2×C83⋊C8—21no—
149C2×C83⋊C8—21no—
150C2×C83⋊C8—21no—
151C2×C83⋊C8—21no—
152C2×C83⋊C8—21no—
153C2×C83⋊C8—21no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—44no—
158C2×C83⋊C8#4112yes—
159C4⋊Dic83—21no—
160C4⋊Dic83—21no—
161C4⋊Dic83—21no—
162C4⋊Dic83—21no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83—21no—
166C4⋊Dic83—42no—
167C4⋊Dic83—81no—
168C4⋊Dic83#4112yes—
169C22⋊Dic83—42no—
170C22⋊Dic83—42no—
171C22⋊Dic83—81no—
172C22⋊Dic83—81no—
173C4×Dic83—42no—
174C4×Dic83—42no—
175C4×Dic83—42no—
176C24×C83—21no—
177C24×C83C2×D411yescharacteristic
178C24×C83C2×D411yescharacteristic
179C2×D4×C83—24no—
180C2×D4×C83—24no—
181C2×D4×C83—21no—
182C2×D4×C83—21no—
183C2×D4×C83—21no—
184C2×D4×C83—21no—
185C2×D4×C83—21no—
186C2×D4×C83—41no—
187C2×D4×C83—41no—
188C2×D4×C83—42no—
189C2×D4×C83—42no—
190C2×D4×C83—81no—
191C2×D4×C83—81no—
192C2×D4×C83C22⋊C414yes—
193C2×D4×C83C22×C412yes—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
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—24no—
206C22×C4×C83—24no—
207C22×C4×C83—81no—
208C22×C4×C83—81no—
209C22×C4×C83—81no—
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—24no—
221C4⋊C4×C83—24no—
222C4⋊C4×C83—24no—
223C4⋊C4×C83—21no—
224C4⋊C4×C83—21no—
225C4⋊C4×C83—21no—
226C4⋊C4×C83C22⋊C414yes—
227C4⋊C4×C83C22×C412yes—
228C4⋊C4×C83C22×C412yes—
229C4⋊C4×C83C22×C412yes—
230C22⋊C4×C83—24no—
231C22⋊C4×C83—24no—
232C22⋊C4×C83—24no—
233C22⋊C4×C83—24no—
234C22⋊C4×C83C22⋊C414yes—
235C22⋊C4×C83C22⋊C414yes—
236C42×C83—24no—
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×C83—22no—
252C23×C83—41no—
253C23×C83—41no—
254C23×C83—41no—
255C23×C83—41no—
256C23×C83—41no—
257C23×C83—41no—
258C23×C83C2×C22⋊C412yes—
259C23×C83C2×C22⋊C412yes—
260C23×C83C22×D411yescharacteristic
261D4×C83—22no—
262D4×C83—22no—
263D4×C83—44no—
264D4×C83—48no—
265D4×C83—41no—
266D4×C83—41no—
267D4×C83—84no—
268C2×C4×C83—21no—
269C2×C4×C83—21no—
270C2×C4×C83—21no—
271C2×C4×C83—21no—
272C2×C4×C83—21no—
273C2×C4×C83—21no—
274C2×C4×C83—21no—
275C2×C4×C83—21no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—41no—
288C2×C4×C83—41no—
289C2×C4×C83—41no—
290C2×C4×C83—41no—
291C2×C4×C83—41no—
292C2×C4×C83—41no—
293C2×C4×C83—84no—
294C2×C4×C83—84no—
295C2×C4×C83C2×C22⋊C412yes—
296C2×C4×C83C2×C22⋊C412yes—
297C2×C4×C83C2×C22⋊C412yes—
298C2×C4×C83C2×C22⋊C412yes—
299C2×C4×C83C23×C411yescharacteristic
300C2×C4×C83C22×D411yescharacteristic
301C2×C4×C83C2×#4111yescharacteristic
302C2×C4×C83C2×#4111yescharacteristic
303C2×C4×C83H(5,𝔽2)11yescharacteristic
304C2×C4×C832−1+411yescharacteristic
305C2×Dic83—22no—
306C2×Dic83—41no—
307C2×Dic83—41no—
308C2×Dic83—41no—
309C2×Dic83—41no—
310C2×Dic83—41no—
311C2×Dic83—41no—
312C2×Dic83—41no—
313C2×Dic83—41no—
314C2×Dic83—41no—
315C2×Dic83—41no—
316C2×Dic83—41no—
317C83⋊C8—22no—
318C83⋊C8—41no—
319C83⋊C8—41no—
320C83⋊C8—41no—
321C22×C83—22no—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—41no—
328C22×C83—41no—
329C22×C83—41no—
330C22×C83—41no—
331C22×C83—41no—
332C22×C83—41no—
333C22×C83—41no—
334C22×C83—41no—
335C22×C83—42no—
336C22×C83—42no—
337C22×C83—42no—
338C22×C83—81no—
339C22×C83—81no—
340C22×C83—81no—
341C22×C83—81no—
342C22×C83C22×C22⋊C411yescharacteristic
343C22×C83#54611yescharacteristic
344C22×C83#54711yescharacteristic
345C22×C83#57511yescharacteristic
346C22×C83#57511yescharacteristic
347C22×C83#57611yescharacteristic
348C22×C83#57711yescharacteristic
349C4×C83—22no—
350C4×C83—22no—
351C4×C83—22no—
352C4×C83—22no—
353C4×C83—42no—
354C4×C83—42no—
355C4×C83—42no—
356C4×C83C4×#4111yescharacteristic
357C4×C83#52011yescharacteristic
358C4×C83#54611yescharacteristic
359C4×C83#54711yescharacteristic
360Dic83—42no—
361Dic83—81no—
362Dic83—81no—
363Dic83—81no—
364#22498—831nomaximal, Sylow
365C2×C83—42no—
366C2×C83—42no—
367C2×C83—82no—
368C2×C83#233911yescharacteristic
369C2×C83#289611yescharacteristic
370C2×C83#289711yescharacteristic
371C2×C83#330711yescharacteristic
372C2×C83#330911yescharacteristic
373C2×C83#334711yescharacteristic
374C2×C83#335011yescharacteristic
375C2×#553D8311yescharacteristic
376C2×#435—831no—
377#2354—831no—
378#1992—831no—
379#1989—831no—
380#1895—831no—
381#1893—831no—
382#1875—831no—
383#1875—831no—
384#1825—831no—
385#1823—831no—
386#1802—831no—
387#1762—831no—
388#1736—831no—
389#1735—831no—
390C83#2249811yescharacteristic, complemented, Sylow
391C22×M16—831no—
392C23×C8—831no—
393#553—24no—
394#553Dic8318yescomplemented
395C2×#126—21no—
396C2×#125C2×D8311yescharacteristic
397C2×#123—21no—
398C2×#121—21no—
399C2×#121C2×D8311yescharacteristic
400C2×#121C2×D8311yescharacteristic
401C2×C4×D4—21no—
402C2×C4×D4C2×D8311yescharacteristic
403C2×C4×D4C2×D8311yescharacteristic
404C2×#117—831no—
405C2×#117—831no—
406C2×#117C2×D8311yescharacteristic
407C22×C4⋊C4C2×D8311yescharacteristic
408#435—1664no—
409C2×C4⋊C8—831no—
410C2×#102—831no—
411C2×#102—831no—
412C2×#102—831no—
413C2×#102—831no—
414C2×C22⋊C8—831no—
415C2×C22⋊C8—831no—
416C2×#97—831no—
417#390—1661no—
418#388—1661no—
419#388—1661no—
420#384—831no—
421#380—831no—
422#380—831no—
423C4×C4⋊C4—831no—
424C4×C4⋊C4—1661no—
425#340—831no—
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—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4C22⋊D8311yescharacteristic
440C22×D4C22×D8311yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C22×D8311yescharacteristic
444C23×C4C22×D8311yescharacteristic
445C2×M16—3321no—
446C2×M16—1662no—
447C2×M16—1662no—
448C22×C8—3321no—
449C22×C8—831no—
450C22×C8—831no—
451C22×C8—831no—
452C22×C8—831no—
453C22×C8—1662no—
454C22×C8—1662no—
455#126—28no—
456#125—22no—
457#125C2×Dic8314yes—
458#123—28no—
459#121—28no—
460#121—22no—
461#121—22no—
462#121C2×Dic8314yes—
463#121C2×Dic8314yes—
464C4×D4—28no—
465C4×D4—22no—
466C4×D4C2×Dic8314yes—
467C4×D4C2×Dic8314yes—
468C4×D4C22⋊D8314yes—
469#117—22no—
470#117—3321no—
471#117—3321no—
472#117—1662no—
473#117—1662no—
474#117C2×Dic8314yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—831no—
480C2×C4⋊C4—831no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4—831no—
483C2×C4⋊C4—1661no—
484C2×C4⋊C4—1661no—
485C2×C4⋊C4C2×Dic8314yes—
486C2×C4⋊C4C22⋊D8311yescharacteristic
487C2×C4⋊C4C22×D8311yescharacteristic
488C2×C4⋊C4C22×D8311yescharacteristic
489C2×C4⋊C4C22×D8311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1661no—
495C2×C22⋊C4—1661no—
496C2×C22⋊C4—1661no—
497C2×C22⋊C4—1661no—
498C2×C22⋊C4C22⋊D8311yescharacteristic
499C2×C22⋊C4C22⋊D8311yescharacteristic
500C2×C42—21no—
501C2×C42—1661no—
502C2×C42—1661no—
503C2×C42—1661no—
504C2×C42C22×D8311yescharacteristic
505C4⋊C8—1662no—
506#102—3321no—
507#102—3321no—
508#102—1662no—
509#102—1662no—
510C22⋊C8—1662no—
511C22⋊C8—1662no—
512#97—1662no—
513#95—1661no—
514#95—1661no—
515#95—1661no—
516C24—21no—
517C24C2×C22⋊D8311yescharacteristic
518C24C2×C22⋊D8311yescharacteristic
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—81no—
531C2×D4—81no—
532C2×D4C22⋊Dic8314yes—
533C2×D4C22×Dic8312yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—1661no—
552C22×C4—1661no—
553C22×C4—1661no—
554C22×C4—1661no—
555C22×C4C22×Dic8312yes—
556C22×C4C22×Dic8312yes—
557C22×C4C2×C22⋊D8312yes—
558C22×C4C2×C22⋊D8312yes—
559C22×C4C2×C22⋊D8311yescharacteristic
560C22×C4C2×C22⋊D8311yescharacteristic
561C22×C4C2×C22⋊D8311yescharacteristic
562C22×C4C2×C22⋊D8311yescharacteristic
563C22×C4C23×D8311yescharacteristic
564M16—3324no—
565C2×C8—3324no—
566C2×C8—832no—
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×C8—1661no—
577C2×C8—1661no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—3322no—
585C4⋊C4—832no—
586C4⋊C4—6641no—
587C4⋊C4—1661no—
588C4⋊C4—1661no—
589C4⋊C4—1661no—
590C4⋊C4—1661no—
591C4⋊C4—1661no—
592C4⋊C4—1661no—
593C4⋊C4—1661no—
594C4⋊C4C22⋊Dic8314yes—
595C4⋊C4C22×Dic8312yes—
596C4⋊C4C22×Dic8312yes—
597C4⋊C4C22×Dic8312yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—3322no—
603C22⋊C4—3322no—
604C22⋊C4—6641no—
605C22⋊C4—6641no—
606C22⋊C4C22⋊Dic8314yes—
607C22⋊C4C22⋊Dic8314yes—
608C42—24no—
609C42—3322no—
610C42—3322no—
611C42—3322no—
612C42C22×Dic8312yes—
613C42C2×C22⋊D8312yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C2×C22⋊Dic8312yes—
634C23C2×C22⋊Dic8312yes—
635C23C22×C22⋊D8311yescharacteristic
636D4—22no—
637D4—22no—
638D4—44no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—84no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
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—84no—
669C2×C4—84no—
670C2×C4—3321no—
671C2×C4—3321no—
672C2×C4—3321no—
673C2×C4—3321no—
674C2×C4—3321no—
675C2×C4—3321no—
676C2×C4—3321no—
677C2×C4—3321no—
678C2×C4—3321no—
679C2×C4—3321no—
680C2×C4—3321no—
681C2×C4—1662no—
682C2×C4C2×C22⋊Dic8312yes—
683C2×C4C2×C22⋊Dic8312yes—
684C2×C4C2×C22⋊Dic8312yes—
685C2×C4C2×C22⋊Dic8312yes—
686C2×C4C23×Dic8311yescharacteristic
687C2×C4C22×C22⋊D8311yescharacteristic
688C2×C4#41×D8311yescharacteristic
689C2×C4#41×D8311yescharacteristic
690C2×C4#1458183811yescharacteristic
691C2×C4#1458183911yescharacteristic
692C8—3321no—
693C8—3321no—
694C8—3321no—
695C8—1662no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C22×C22⋊Dic8311yescharacteristic
718C22#1912833911yescharacteristic
719C22#1912835011yescharacteristic
720C22#1912849911yescharacteristic
721C22#1912849911yescharacteristic
722C22#1912850411yescharacteristic
723C22#1912851211yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—3322no—
732C4—6641no—
733C4—6641no—
734C4—6641no—
735C4#41×Dic8311yescharacteristic
736C4#1912818411yescharacteristic
737C4#1912833911yescharacteristic
738C4#1912835011yescharacteristic
739C2—42no—
740C2—42no—
741C2—82no—
742C2#2491029311yescharacteristic
743C2#2491598211yescharacteristic
744C2#2491598911yescharacteristic
745C2#2491943311yescharacteristic
746C2#2491946311yescharacteristic
747C2#2491995711yescharacteristic
748C2#2492000211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
Fitting, prime radicalC2×#553×C83C2
socleC23×C83C22×D4
cosocleC22×C4×C83C24
hypercenterC2×#553D83
hypocenterC83#22498
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#19127773C2semidirect
2. #24910412C2semidirect
3. #24908433C2semidirect
4. #24908421C2semidirect
5. #24907902C2semidirect
6. #24907892C2semidirect
7. #24907786C2semidirect
8. #24907786C2semidirect
9. #24907558C2semidirect
10. #24907549C2semidirect
11. #24907463C2semidirect
12. #24907288C2semidirect
13. #24907182C2semidirect
14. #24907179C2semidirect
50. #553×C83C4semidirect
390. C83#22498semidirect
394. #553Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191277732
#249104122
#249084332
#249084212
#249079022
#249078922
#249077862
#249075582
#249075492
#249074632
#249072882
#249071822
#249071792
C2×#553×C832
#2249883