Finite Group Databasebeta

← #35409669

Subgroups — #35409669

Order 21248.

1134 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128322C211yesmaximal, characteristic
2C2×#19127657C211yesmaximal, characteristic, complemented
3#24908435C211yesmaximal, characteristic, complemented
4#24908423C211yesmaximal, characteristic, complemented
5#24908277C211yesmaximal, characteristic, complemented
6#24908272C211yesmaximal, characteristic, complemented
7#24907899C211yesmaximal, characteristic
8#24907894C211yesmaximal, characteristic, complemented
9#24907889C211yesmaximal, characteristic
10#24907884C211yesmaximal, characteristic, complemented
11#24907296C211yesmaximal, characteristic, complemented
12#24907291C211yesmaximal, characteristic, complemented
13C4×#14581715C211yesmaximal, characteristic, complemented
14C4×#14581712C211yesmaximal, characteristic, complemented
15C83×#2314C211yesmaximal, characteristic, complemented
16C22×#13050574C2211yescharacteristic
17C23×C83⋊C8C2211yescharacteristic
18#19128322—24no—
19#19128322C418yescomplemented
20C2×#14581792C2211yescharacteristic
21C2×#14581787—21no—
22C2×#14581780C2211yescharacteristic
23C2×#14581778—21no—
24C2×#14581774—21no—
25C2×#14581771C2211yescharacteristic
26C2×#14581770—21no—
27C2×#14581766C2211yescharacteristic
28C2×C4×Dic166C2211yescharacteristic
29C2×C4×D332C2211yescharacteristic
30C2×#14581715C2211yescharacteristic
31C2×#14581715C2211yescharacteristic
32C2×#14581715C2211yescharacteristic
33C2×#14581715C2211yescharacteristic
34C2×#14581712C2211yescharacteristic
35C2×#14581712C2211yescharacteristic
36C2×#14581712C2211yescharacteristic
37C2×#14581712C2211yescharacteristic
38#19127657—24no—
39C2×#14581703C2211yescharacteristic
40C2×#14581703C2211yescharacteristic
41C2×C4×C83⋊C8C2211yescharacteristic
42C2×C4×C83⋊C8C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51C2×#117×C83C2211yescharacteristic
52#388×C83—21no—
53#388×C83—21no—
54#387×C83—21no—
55#387×C83—21no—
56#384×C83C2211yescharacteristic
57#382×C83C2211yescharacteristic
58#380×C83C2211yescharacteristic
59#380×C83C2211yescharacteristic
60C4×C4⋊C4×C83C2211yescharacteristic
61C4×C4⋊C4×C83C2211yescharacteristic
62C22×Dic166—21no—
63C22×Dic166C2311yescharacteristic
64C22×D332C2311yescharacteristic
65C22×C22⋊D83—21no—
66C22×C4×D83—21no—
67C2×#13050574—22no—
68C2×#13050574—22no—
69C2×#13050574—22no—
70C22×C83⋊C8—22no—
71C22×C83⋊C8—22no—
72C22×C83⋊C8—22no—
73C22×C83⋊C8C2311yescharacteristic
74C22×C83⋊C8C2311yescharacteristic
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77#14581792—22no—
78#14581792C2×C414yes—
79#14581787—28no—
80#14581780—22no—
81#14581780C2×C414yes—
82#14581778—28no—
83#14581774—28no—
84#14581771—22no—
85#14581771C2×C414yes—
86#14581770—28no—
87#14581766—22no—
88#14581766C2×C414yes—
89C4×Dic166—22no—
90C4×Dic166C2×C414yes—
91C4×D332—22no—
92C4×D332C2×C414yes—
93C2×C4⋊Dic83—21no—
94C2×C4⋊Dic83C2311yescharacteristic
95C2×C4⋊Dic83C2311yescharacteristic
96C2×Dic83⋊C4—21no—
97C2×Dic83⋊C4—21no—
98C2×C22⋊Dic83—21no—
99C2×(C2×D83)⋊C4—21no—
100C2×(C2×D83)⋊C4—21no—
101C2×(C2×D83)⋊C4—21no—
102C2×(C2×D83)⋊C4—21no—
103C2×C4×Dic83—21no—
104#14581715—22no—
105#14581715—22no—
106#14581715—22no—
107#14581715—22no—
108#14581712—22no—
109#14581712—22no—
110#14581712—22no—
111#14581712—22no—
112#14581703—22no—
113#14581703—22no—
114C4×C83⋊C8—22no—
115C4×C83⋊C8—22no—
116C23×C4×C83C2311yescharacteristic
117#117×C83C2×C414yes—
118#117×C83D414yes—
119C2×C4⋊C4×C83—21no—
120C2×C4⋊C4×C83—21no—
121C2×C4⋊C4×C83D411yescharacteristic
122C2×C4⋊C4×C83D411yescharacteristic
123C2×C4⋊C4×C83C2311yescharacteristic
124C2×C4⋊C4×C83C2311yescharacteristic
125C2×C4⋊C4×C83C2311yescharacteristic
126C2×C4⋊C4×C83C2311yescharacteristic
127C2×C22⋊C4×C83—21no—
128C2×C22⋊C4×C83—21no—
129C2×C22⋊C4×C83D411yescharacteristic
130C2×C22⋊C4×C83D411yescharacteristic
131C2×C42×C83—21no—
132C2×C42×C83—21no—
133C2×C42×C83C2311yescharacteristic
134C2×C42×C83C2311yescharacteristic
135#95×C83—21no—
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—21no—
143C2×Dic166—21no—
144C2×Dic166—21no—
145C2×Dic166—21no—
146C2×Dic166—21no—
147C2×Dic166—24no—
148C2×Dic166—81no—
149C2×Dic166—81no—
150C2×Dic166C22×C412yes—
151C2×D332—21no—
152C2×D332—21no—
153C2×D332—21no—
154C2×D332—21no—
155C2×D332—21no—
156C2×D332C22×C412yes—
157C2×C22⋊D83—24no—
158C2×C22⋊D83—81no—
159C2×C22⋊D83—81no—
160C22×Dic83—21no—
161C22×Dic83—21no—
162C22×Dic83—21no—
163C2×C4×D83—24no—
164C2×C4×D83—81no—
165C2×C4×D83—81no—
166#13050574—28no—
167C2×C83⋊C8—28no—
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—21no—
176C2×C83⋊C8#4112yes—
177C2×C83⋊C8#4112yes—
178C2×C83⋊C8#4112yes—
179C2×C83⋊C8#4112yes—
180C4⋊Dic83—24no—
181C4⋊Dic83—21no—
182C4⋊Dic83—21no—
183C4⋊Dic83C22×C412yes—
184C4⋊Dic83C22×C412yes—
185Dic83⋊C4—24no—
186Dic83⋊C4—24no—
187C22⋊Dic83—24no—
188(C2×D83)⋊C4—24no—
189(C2×D83)⋊C4—24no—
190(C2×D83)⋊C4—24no—
191(C2×D83)⋊C4—24no—
192C4×Dic83—24no—
193C24×C83C2×D411yescharacteristic
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×C83C22×C412yes—
203C22×C4×C83C2×D411yescharacteristic
204C22×C4×C83C2×D411yescharacteristic
205C22×C4×C83C2×D411yescharacteristic
206C22×C4×C83C2×D411yescharacteristic
207C22×C4×C83C2×D411yescharacteristic
208C22×C4×C83C2×D412yes—
209C22×C4×C83C2411yescharacteristic
210C4⋊C4×C83—21no—
211C4⋊C4×C83—21no—
212C4⋊C4×C83—21no—
213C4⋊C4×C83—21no—
214C4⋊C4×C83—21no—
215C4⋊C4×C83—21no—
216C4⋊C4×C83—21no—
217C4⋊C4×C83—21no—
218C4⋊C4×C83—81no—
219C4⋊C4×C83—81no—
220C4⋊C4×C83C22⋊C414yes—
221C4⋊C4×C83C22⋊C414yes—
222C22⋊C4×C83—81no—
223C22⋊C4×C83—81no—
224C22⋊C4×C83C22⋊C414yes—
225C22⋊C4×C83C22⋊C414yes—
226C42×C83—81no—
227C42×C83—81no—
228C42×C83C22×C412yes—
229C42×C83C22×C412yes—
230C42×C83C2×D412yes—
231C42×C83C2×D412yes—
232C23×C83—21no—
233C23×C83—21no—
234C23×C83—21no—
235C23×C83—21no—
236C23×C83—21no—
237C23×C83—21no—
238C23×C83C2×C22⋊C412yes—
239C23×C83C22×D411yescharacteristic
240C22×D83—22no—
241C22×D83—41no—
242C22×D83—41no—
243C22×D83—41no—
244C22×D83—41no—
245C22×D83—41no—
246C22×D83—41no—
247C2×C4×C83—21no—
248C2×C4×C83—21no—
249C2×C4×C83—21no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—21no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—22no—
258C2×C4×C83—22no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—41no—
262C2×C4×C83—41no—
263C2×C4×C83—41no—
264C2×C4×C83—41no—
265C2×C4×C83—41no—
266C2×C4×C83—41no—
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×C83C2×C22⋊C412yes—
274C2×C4×C83C2×C22⋊C412yes—
275C2×C4×C83C2×C22⋊C412yes—
276C2×C4×C83C2×C22⋊C412yes—
277C2×C4×C83C2×C22⋊C412yes—
278C2×C4×C83C23×C411yescharacteristic
279C2×C4×C83C22×D411yescharacteristic
280C2×C4×C83C2×#4111yescharacteristic
281C2×C4×C83C2×#4111yescharacteristic
282C2×C4×C83C2×#4111yescharacteristic
283C2×C4×C83C2×#4111yescharacteristic
284C22⋊D83—84no—
285C2×Dic83—22no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—41no—
289C2×Dic83—41no—
290C2×Dic83—41no—
291C2×Dic83—41no—
292C2×Dic83—41no—
293C2×Dic83—41no—
294D332—22no—
295D332—22no—
296D332—41no—
297D332—41no—
298C4×D83—84no—
299Dic166—22no—
300Dic166—22no—
301Dic166—41no—
302Dic166—41no—
303Dic166—84no—
304C83⋊C8—22no—
305C83⋊C8—22no—
306C83⋊C8—22no—
307C83⋊C8—22no—
308C22×C83—22no—
309C22×C83—22no—
310C22×C83—22no—
311C22×C83—41no—
312C22×C83—41no—
313C22×C83—41no—
314C22×C83—41no—
315C22×C83C22×C22⋊C411yescharacteristic
316C22×C83#53211yescharacteristic
317C22×C83#53211yescharacteristic
318C22×C83#57611yescharacteristic
319C22×C83#57711yescharacteristic
320C22×C83#57711yescharacteristic
321C22×C83#57811yescharacteristic
322C2×D83—42no—
323C2×D83—42no—
324C2×D83—42no—
325C2×D83—81no—
326C2×D83—81no—
327C2×D83—81no—
328C2×D83—81no—
329C4×C83—22no—
330C4×C83—22no—
331C4×C83—22no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—81no—
335C4×C83—81no—
336C4×C83—81no—
337C4×C83—81no—
338C4×C83C4×#4111yescharacteristic
339C4×C83C4×#4111yescharacteristic
340C4×C83#52511yescharacteristic
341C4×C83#52511yescharacteristic
342Dic83—42no—
343Dic83—42no—
344Dic83—42no—
345#21412—831nomaximal, Sylow
346C2×C83—42no—
347C2×C83#229711yescharacteristic
348C2×C83#289711yescharacteristic
349C2×C83#289811yescharacteristic
350C2×C83#317311yescharacteristic
351C2×C83#317511yescharacteristic
352C2×C83#317811yescharacteristic
353C2×C83#317911yescharacteristic
354D83—82no—
355C2×#542—831no—
356C2×#405—831no—
357#2314D8311yescharacteristic, complemented
358#1993—831no—
359#1990—831no—
360#1959—831no—
361#1958—831no—
362#1895—831no—
363#1894—831no—
364#1893—831no—
365#1892—831no—
366#1763—831no—
367#1762—831no—
368C4×#103—831no—
369C4×#102—831no—
370C83#2141211yescharacteristic, complemented, Sylow
371C22×M16—831no—
372C23×C8—831no—
373#542—838no—
374#542—1664no—
375C2×C4⋊Q8—831no—
376C2×#126—1661no—
377C2×#124—831no—
378C2×#124—1661no—
379C2×#123—1661no—
380C2×C22⋊Q8—831no—
381C2×C22⋊Q8—1661no—
382C2×#121—831no—
383C2×C4×Q8—831no—
384C2×C4×D4—831no—
385C2×#117C2×D8311yescharacteristic
386C2×#103—831no—
387C2×#103—831no—
388C2×#103—831no—
389C2×#103—831no—
390C2×#102—831no—
391C2×#102—831no—
392C2×#102—831no—
393C2×#102—831no—
394#405—1664no—
395C2×#97—831no—
396C2×#97—831no—
397C2×C4×C8—831no—
398C2×C4×C8—831no—
399#388—21no—
400#388—21no—
401#387—21no—
402#387—21no—
403#384C2×D8311yescharacteristic
404#382C2×D8311yescharacteristic
405#380C2×D8311yescharacteristic
406#380C2×D8311yescharacteristic
407C4×C4⋊C4C2×D8311yescharacteristic
408C4×C4⋊C4C2×D8311yescharacteristic
409#340—831no—
410#340—831no—
411#340—831no—
412#340—831no—
413#340—831no—
414#340—831no—
415#340—831no—
416#340—831no—
417C22×Q8—831no—
418C22×Q8—1661no—
419C22×D4—831no—
420C22×D4—1661no—
421C23×C4—1661no—
422C23×C4C22×D8311yescharacteristic
423C2×M16—1662no—
424C2×M16—1662no—
425C2×M16—1662no—
426C22×C8—831no—
427C22×C8—831no—
428C22×C8—831no—
429C22×C8—831no—
430C22×C8—1662no—
431C22×C8—1662no—
432C22×C8—1662no—
433C4⋊Q8—834no—
434C4⋊Q8—1662no—
435#126—1668no—
436#124—834no—
437#124—1668no—
438#124—1662no—
439#123—1668no—
440C22⋊Q8—834no—
441C22⋊Q8—1662no—
442C22⋊Q8—1668no—
443#121—834no—
444#121—1662no—
445C4×Q8—834no—
446C4×Q8—1662no—
447C4×D4—834no—
448C4×D4—1662no—
449#117C4×D8314yes—
450#117D33214yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—831no—
454C2×C4⋊C4—831no—
455C2×C4⋊C4—1661no—
456C2×C4⋊C4—1661no—
457C2×C4⋊C4—1661no—
458C2×C4⋊C4C22⋊D8311yescharacteristic
459C2×C4⋊C4C22⋊D8311yescharacteristic
460C2×C4⋊C4C22×D8311yescharacteristic
461C2×C4⋊C4C22×D8311yescharacteristic
462C2×C4⋊C4C22×D8311yescharacteristic
463C2×C4⋊C4C22×D8311yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1661no—
467C2×C22⋊C4—1661no—
468C2×C22⋊C4—1661no—
469C2×C22⋊C4—1661no—
470C2×C22⋊C4—1661no—
471C2×C22⋊C4C22⋊D8311yescharacteristic
472C2×C22⋊C4C22⋊D8311yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—1661no—
476C2×C42C22×D8311yescharacteristic
477C2×C42C22×D8311yescharacteristic
478#103—1662no—
479#103—1662no—
480#103—1662no—
481#103—1662no—
482#102—1662no—
483#102—1662no—
484#102—1662no—
485#102—1662no—
486#97—1662no—
487#97—1662no—
488C4×C8—1662no—
489C4×C8—1662no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C24—1661no—
497C24C2×C22⋊D8311yescharacteristic
498C2×Q8—832no—
499C2×Q8—6641no—
500C2×Q8—6641no—
501C2×Q8—1661no—
502C2×Q8—1661no—
503C2×Q8—1661no—
504C2×Q8—1661no—
505C2×Q8—1661no—
506C2×Q8—1664no—
507C2×D4—832no—
508C2×D4—6641no—
509C2×D4—6641no—
510C2×D4—1664no—
511C2×D4—1661no—
512C2×D4—1661no—
513C2×D4—1661no—
514C2×D4—1661no—
515C2×D4—1661no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—6641no—
525C22×C4—6641no—
526C22×C4—1661no—
527C22×C4—1661no—
528C22×C4—1661no—
529C22×C4—1664no—
530C22×C4C2×C4×D8312yes—
531C22×C4C2×C22⋊D8311yescharacteristic
532C22×C4C2×C22⋊D8311yescharacteristic
533C22×C4C2×C22⋊D8311yescharacteristic
534C22×C4C2×C22⋊D8311yescharacteristic
535C22×C4C2×C22⋊D8311yescharacteristic
536C22×C4C2×D33212yes—
537C22×C4C23×D8311yescharacteristic
538M16—1668no—
539C2×C8—832no—
540C2×C8—832no—
541C2×C8—832no—
542C2×C8—832no—
543C2×C8—1668no—
544C2×C8—1661no—
545C2×C8—1661no—
546C2×C8—1661no—
547C2×C8—1661no—
548C2×C8—1661no—
549C2×C8—1661no—
550C2×C8—1661no—
551C2×C8—1661no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—832no—
563C4⋊C4—832no—
564C4⋊C4—1661no—
565C4⋊C4—1661no—
566C4⋊C4—1664no—
567C4⋊C4—1664no—
568C4⋊C4—1664no—
569C4⋊C4(C2×D83)⋊C414yes—
570C4⋊C4(C2×D83)⋊C414yes—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—1664no—
574C22⋊C4—1664no—
575C22⋊C4—1664no—
576C22⋊C4—1664no—
577C22⋊C4—1664no—
578C22⋊C4(C2×D83)⋊C414yes—
579C22⋊C4(C2×D83)⋊C414yes—
580C42—81no—
581C42—81no—
582C42—1664no—
583C42C2×C4×D8312yes—
584C42C2×C4×D8312yes—
585C42C2×D33212yes—
586C42C2×D33212yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—3321no—
594C23—3321no—
595C23—3321no—
596C23—3321no—
597C23—3321no—
598C23—3321no—
599C23—1662no—
600C23C2×(C2×D83)⋊C412yes—
601C23C22×C22⋊D8311yescharacteristic
602Q8—3321no—
603Q8—3321no—
604Q8—6644no—
605Q8—1662no—
606Q8—1662no—
607D4—3321no—
608D4—3321no—
609D4—6644no—
610D4—1662no—
611D4—1662no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—3321no—
639C2×C4—3321no—
640C2×C4—3321no—
641C2×C4—3321no—
642C2×C4—3321no—
643C2×C4—3321no—
644C2×C4—6644no—
645C2×C4—1662no—
646C2×C4—1662no—
647C2×C4—1662no—
648C2×C4C2×(C2×D83)⋊C412yes—
649C2×C4C2×(C2×D83)⋊C412yes—
650C2×C4C2×(C2×D83)⋊C412yes—
651C2×C4C2×(C2×D83)⋊C412yes—
652C2×C4C2×(C2×D83)⋊C412yes—
653C2×C4C22×C4×D8311yescharacteristic
654C2×C4C22×D33211yescharacteristic
655C2×C4#41×D8311yescharacteristic
656C2×C4#41×D8311yescharacteristic
657C2×C4#41×D8311yescharacteristic
658C2×C4#41×D8311yescharacteristic
659C8—1662no—
660C8—1662no—
661C8—1662no—
662C8—1662no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—3322no—
671C22—3322no—
672C22—3322no—
673C22—6641no—
674C22—6641no—
675C22—6641no—
676C22—6641no—
677C22C22×(C2×D83)⋊C411yescharacteristic
678C22#1912824711yescharacteristic
679C22#1912824711yescharacteristic
680C22#1912850411yescharacteristic
681C22#1912850911yescharacteristic
682C22#1912851211yescharacteristic
683C22#1912851611yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—3322no—
694C4—3322no—
695C4—3322no—
696C4#1912816911yescharacteristic
697C4#1912816911yescharacteristic
698C4#1912821311yescharacteristic
699C4#1912821311yescharacteristic
700C2—42no—
701C2—6642no—
702C2#2490995111yescharacteristic
703C2#2491598611yescharacteristic
704C2#2491599311yescharacteristic
705C2#2491807411yescharacteristic
706C2#2491809611yescharacteristic
707C2#2491813311yescharacteristic
708C2#2491814811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#2314C2
socleC23×C83C22×D4
prime radicalC2×#14581766C22
cosocleC22×C4×C83C24
hypercenter#2314D83
hypocenterC83#21412
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. C2×#19127657C2semidirect
3. #24908435C2semidirect
4. #24908423C2semidirect
5. #24908277C2semidirect
6. #24908272C2semidirect
8. #24907894C2semidirect
10. #24907884C2semidirect
11. #24907296C2semidirect
12. #24907291C2semidirect
13. C4×#14581715C2semidirect
14. C4×#14581712C2semidirect
15. C83×#2314C2semidirect
19. #19128322C4semidirect
357. #2314D83semidirect
370. C83#21412semidirect

Maximal subgroups

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

subgroupindex
C2×#191283222
C2×#191276572
#249084352
#249084232
#249082772
#249082722
#249078992
#249078942
#249078892
#249078842
#249072962
#249072912
C4×#145817152
C4×#145817122
C83×#23142
#2141283