Finite Group Databasebeta

← #35420739

Subgroups — #35420739

Order 21248.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128421C211yesmaximal, characteristic
2#24910392C211yesmaximal, characteristic
3#24908436C211yesmaximal, characteristic, complemented
4#24908410C211yesmaximal, characteristic, complemented
5#24907896C211yesmaximal, characteristic, complemented
6#24907886C211yesmaximal, characteristic, complemented
7#24907773C211yesmaximal, characteristic, complemented
8#24907768C211yesmaximal, characteristic, complemented
9#24907559C211yesmaximal, characteristic, complemented
10#24907559C211yesmaximal, characteristic, complemented
11#24907479C211yesmaximal, characteristic, complemented
12#24907294C211yesmaximal, characteristic, complemented
13#24907183C211yesmaximal, characteristic, complemented
14#24907180C211yesmaximal, characteristic, complemented
15C2×#435×C83C211yesmaximal, characteristic
16#19128421—24no—
17#19128421C418yescomplemented
18C2×#14581792C2211yescharacteristic
19C2×#14581785—21no—
20C2×#14581785—21no—
21C2×#14581779—21no—
22C2×#14581771C2211yescharacteristic
23C2×#14581771C2211yescharacteristic
24C2×C4×Dic166C2211yescharacteristic
25C2×#14581757—21no—
26C2×#14581751C2211yescharacteristic
27C2×#14581751C2211yescharacteristic
28C2×#14581751C2211yescharacteristic
29C22×C4⋊Dic83C2211yescharacteristic
30C2×#14581717C2211yescharacteristic
31C2×#14581717C2211yescharacteristic
32C2×#14581717C2211yescharacteristic
33C2×#14581717C2211yescharacteristic
34#19127594—21no—
35#19127587—21no—
36#19127581—21no—
37#19127567C2211yescharacteristic
38#19127561C2211yescharacteristic
39#19127561C2211yescharacteristic
40C4×C4⋊Dic83C2211yescharacteristic
41C22⋊C4×Dic83—21no—
42#19127464C2211yescharacteristic
43#19127464C2211yescharacteristic
44#19127464C2211yescharacteristic
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127464C2211yescharacteristic
50#19127464C2211yescharacteristic
51#19127464C2211yescharacteristic
52#19127464C2211yescharacteristic
53#19127464C2211yescharacteristic
54C22×M16×C83C2211yescharacteristic
55C23×C8×C83C2211yescharacteristic
56C2×C4×D4×C83C2211yescharacteristic
57#435×C83—24no—
58C2×C4⋊C8×C83C2211yescharacteristic
59C2×C22⋊C8×C83C2211yescharacteristic
60C2×C22⋊C8×C83C2211yescharacteristic
61C2×#97×C83C2211yescharacteristic
62C22×Dic166—21no—
63C22×Dic166C2311yescharacteristic
64C23×Dic83—21no—
65#14581792—22no—
66#14581792C2×C414yescomplemented
67#14581785—28no—
68#14581785—28no—
69#14581779—28no—
70#14581771—22no—
71#14581771—22no—
72#14581771C2×C414yes—
73#14581771C2×C414yescomplemented
74C4×Dic166—22no—
75C4×Dic166C2×C414yescomplemented
76#14581757—28no—
77#14581751—22no—
78#14581751—22no—
79#14581751—22no—
80#14581751—41no—
81#14581751C2×C414yes—
82#14581751C2×C414yescomplemented
83C2×C4⋊Dic83—22no—
84C2×C4⋊Dic83—21no—
85C2×C4⋊Dic83—21no—
86C2×C4⋊Dic83—41no—
87C2×C4⋊Dic83C2311yescharacteristic
88C2×C4⋊Dic83C2311yescharacteristic
89C2×C4⋊Dic83C2311yescharacteristic
90C2×C4⋊Dic83C2311yescharacteristic
91C2×C4⋊Dic83C2311yescharacteristic
92C2×C4⋊Dic83C2311yescharacteristic
93C2×C4⋊Dic83C2311yescharacteristic
94C2×Dic83⋊C4—21no—
95C2×Dic83⋊C4—21no—
96C2×Dic83⋊C4—21no—
97C2×C22⋊Dic83—21no—
98C2×C22⋊Dic83—21no—
99C2×C22⋊Dic83—21no—
100C2×C22⋊Dic83—21no—
101C2×C22⋊Dic83—21no—
102C2×C22⋊Dic83—21no—
103C2×C22⋊Dic83—21no—
104C2×C4×Dic83—21no—
105C2×C4×Dic83—21no—
106C2×C4×Dic83—21no—
107C2×C4×Dic83—21no—
108C2×C4×Dic83—21no—
109#14581717—22no—
110#14581717—22no—
111#14581717—41no—
112#14581717—41no—
113C83⋊#95—21no—
114C83⋊#95—21no—
115C83⋊#95—21no—
116C83⋊#95—21no—
117C83⋊#95—21no—
118C22×D4×C83D411yescharacteristic
119C23×C4×C83C2311yescharacteristic
120C23×C4×C83C2311yescharacteristic
121C2×M16×C83—22no—
122C2×M16×C83—22no—
123C2×M16×C83—41no—
124C22×C8×C83—22no—
125C22×C8×C83—22no—
126C22×C8×C83—41no—
127C22×C8×C83C2311yescharacteristic
128C22×C8×C83C2311yescharacteristic
129C22×C8×C83C2311yescharacteristic
130C22×C8×C83C2311yescharacteristic
131C4×D4×C83C2×C414yes—
132C4×D4×C83D414yes—
133C2×C4⋊C4×C83D411yescharacteristic
134C2×C22⋊C4×C83D411yescharacteristic
135C2×C22⋊C4×C83D411yescharacteristic
136C2×C42×C83C2311yescharacteristic
137C4⋊C8×C83—22no—
138C22⋊C8×C83—22no—
139C22⋊C8×C83—22no—
140#97×C83—22no—
141C2×Dic166—21no—
142C2×Dic166—21no—
143C2×Dic166—21no—
144C2×Dic166—21no—
145C2×Dic166—24no—
146C2×Dic166—21no—
147C2×Dic166—42no—
148C2×Dic166—42no—
149C2×Dic166C22×C412yes—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
154C22×Dic83—21no—
155C22×Dic83—21no—
156C22×Dic83—21no—
157C22×Dic83—21no—
158C22×Dic83—42no—
159C22×Dic83—42no—
160C22×Dic83—81no—
161C4⋊Dic83—24no—
162C4⋊Dic83—21no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83—21no—
166C4⋊Dic83—21no—
167C4⋊Dic83—21no—
168C4⋊Dic83—21no—
169C4⋊Dic83—21no—
170C4⋊Dic83—21no—
171C4⋊Dic83—21no—
172C4⋊Dic83—42no—
173C4⋊Dic83C22×C412yes—
174C4⋊Dic83C22×C412yes—
175C4⋊Dic83C22×C412yes—
176C4⋊Dic83#4112yes—
177Dic83⋊C4—24no—
178Dic83⋊C4—24no—
179Dic83⋊C4—24no—
180C22⋊Dic83—24no—
181C22⋊Dic83—24no—
182C22⋊Dic83—24no—
183C22⋊Dic83—24no—
184C22⋊Dic83—42no—
185C22⋊Dic83—42no—
186C22⋊Dic83—81no—
187C4×Dic83—24no—
188C4×Dic83—24no—
189C4×Dic83—24no—
190C4×Dic83—42no—
191C4×Dic83—81no—
192C24×C83C2×D411yescharacteristic
193C24×C83C2×D411yescharacteristic
194C2×D4×C83—41no—
195C2×D4×C83—41no—
196C2×D4×C83C22⋊C414yes—
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×C83C22×C412yes—
206C22×C4×C83C22×C412yes—
207C22×C4×C83C2×D412yes—
208C22×C4×C83C2×D412yes—
209C22×C4×C83C2×D411yescharacteristic
210C22×C4×C83C2×D411yescharacteristic
211C22×C4×C83C2×D411yescharacteristic
212C22×C4×C83C2×D411yescharacteristic
213C22×C4×C83C2411yescharacteristic
214M16×C83—44no—
215C2×C8×C83—21no—
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—44no—
227C2×C8×C83#4112yes—
228C4⋊C4×C83C22⋊C414yes—
229C22⋊C4×C83C22⋊C414yes—
230C22⋊C4×C83C22⋊C414yes—
231C42×C83C22×C412yes—
232C42×C83C2×D412yes—
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×C83C2×C22⋊C412yes—
246C23×C83C2×C22⋊C412yes—
247C23×C83C22×D411yescharacteristic
248D4×C83—44no—
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—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83C2×C22⋊C412yes—
266C2×C4×C83C2×C22⋊C412yes—
267C2×C4×C83C2×C22⋊C412yes—
268C2×C4×C83C2×C22⋊C412yes—
269C2×C4×C83C23×C411yescharacteristic
270C2×C4×C83C22×D411yescharacteristic
271C2×C4×C83C2×#4111yescharacteristic
272C2×C4×C83C2×#4111yescharacteristic
273C2×C4×C83H(5,𝔽2)11yescharacteristic
274C2×C4×C832−1+411yescharacteristic
275C2×Dic83—22no—
276C2×Dic83—22no—
277C2×Dic83—22no—
278C2×Dic83—22no—
279C2×Dic83—22no—
280C2×Dic83—41no—
281C2×Dic83—41no—
282C2×Dic83—41no—
283C2×Dic83—41no—
284C2×Dic83—41no—
285C2×Dic83—41no—
286C2×Dic83—41no—
287C2×Dic83—41no—
288C2×Dic83—41no—
289C2×Dic83—41no—
290C2×Dic83—41no—
291C2×Dic83—41no—
292C2×Dic83—41no—
293C2×Dic83—41no—
294C2×Dic83—41no—
295C2×Dic83—41no—
296C2×Dic83—41no—
297C2×Dic83—41no—
298C2×Dic83—41no—
299C2×Dic83—84no—
300Dic166—22no—
301Dic166—22no—
302Dic166—48no—
303Dic166—41no—
304Dic166—41no—
305C8×C83—22no—
306C8×C83—41no—
307C8×C83—41no—
308C8×C83—41no—
309C22×C83—22no—
310C22×C83—22no—
311C22×C83—22no—
312C22×C83—22no—
313C22×C83—22no—
314C22×C83—22no—
315C22×C83—41no—
316C22×C83—41no—
317C22×C83—41no—
318C22×C83—41no—
319C22×C83—41no—
320C22×C83—41no—
321C22×C83—41no—
322C22×C83—41no—
323C22×C83C22×C22⋊C411yescharacteristic
324C22×C83#54611yescharacteristic
325C22×C83#54711yescharacteristic
326C22×C83#57511yescharacteristic
327C22×C83#57511yescharacteristic
328C22×C83#57711yescharacteristic
329C22×C83#57811yescharacteristic
330C4×C83—22no—
331C4×C83—22no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83C4×#4111yescharacteristic
335C4×C83#52011yescharacteristic
336C4×C83#54611yescharacteristic
337C4×C83#54711yescharacteristic
338Dic83—42no—
339Dic83—42no—
340Dic83—42no—
341Dic83—42no—
342Dic83—42no—
343Dic83—81no—
344Dic83—81no—
345Dic83—81no—
346#22494—831nomaximal, Sylow
347C2×C83—42no—
348C2×C83—42no—
349C2×C83#233911yescharacteristic
350C2×C83#289611yescharacteristic
351C2×C83#289811yescharacteristic
352C2×C83#331111yescharacteristic
353C2×C83#331311yescharacteristic
354C2×C83#334911yescharacteristic
355C2×C83#335011yescharacteristic
356C2×#556—831no—
357C2×#435D8311yescharacteristic
358#2352—831no—
359#1993—831no—
360#1987—831no—
361#1894—831no—
362#1892—831no—
363#1873—831no—
364#1872—831no—
365#1825—831no—
366#1825—831no—
367#1805—831no—
368#1763—831no—
369#1736—831no—
370#1735—831no—
371C83#2249411yescharacteristic, complemented, Sylow
372C22×M16C2×D8311yescharacteristic
373C23×C8C2×D8311yescharacteristic
374#556—838no—
375#556—1664no—
376C2×C4⋊Q8—831no—
377C2×#126—1661no—
378C2×#126—1661no—
379C2×#124—1661no—
380C2×C22⋊Q8—831no—
381C2×C22⋊Q8—831no—
382C2×C4×Q8—831no—
383C2×C4×Q8—1661no—
384C2×C4×D4C2×D8311yescharacteristic
385C2×#117—831no—
386C2×#117—831no—
387C2×#117—831no—
388C22×C4⋊C4—831no—
389#435—24no—
390C2×C4⋊C8C2×D8311yescharacteristic
391C2×#103—831no—
392C2×#103—831no—
393C2×#103—831no—
394C2×#103—831no—
395C2×C22⋊C8C2×D8311yescharacteristic
396C2×C22⋊C8C2×D8311yescharacteristic
397C2×#97C2×D8311yescharacteristic
398#388—1661no—
399#387—1661no—
400#386—1661no—
401#382—831no—
402#380—831no—
403#380—831no—
404C4×C4⋊C4—831no—
405C4×C22⋊C4—1661no—
406#340—831no—
407#340—831no—
408#340—831no—
409#340—831no—
410#340—831no—
411#340—831no—
412#340—831no—
413#340—831no—
414#340—831no—
415#340—831no—
416#340—831no—
417#340—831no—
418C22×Q8—831no—
419C22×Q8—1661no—
420C22×D4D33211yescharacteristic
421C23×C4—1661no—
422C23×C4C22×D8311yescharacteristic
423C23×C4C22×D8311yescharacteristic
424C2×M16—22no—
425C2×M16—22no—
426C2×M16—41no—
427C22×C8—22no—
428C22×C8—22no—
429C22×C8—41no—
430C22×C8C22×D8311yescharacteristic
431C22×C8C22×D8311yescharacteristic
432C22×C8C22×D8311yescharacteristic
433C22×C8C22×D8311yescharacteristic
434C4⋊Q8—834no—
435C4⋊Q8—1662no—
436#126—1668no—
437#126—1668no—
438#124—1668no—
439C22⋊Q8—834no—
440C22⋊Q8—834no—
441C22⋊Q8—1662no—
442C22⋊Q8—1662no—
443C4×Q8—834no—
444C4×Q8—1668no—
445C4×Q8—1662no—
446C4×D4C4×D8314yes—
447C4×D4C22⋊D8314yes—
448#117—3321no—
449#117—834no—
450#117—834no—
451#117—1662no—
452#117—1662no—
453#117—1662no—
454C2×C4⋊C4—3321no—
455C2×C4⋊C4—831no—
456C2×C4⋊C4—831no—
457C2×C4⋊C4—831no—
458C2×C4⋊C4—831no—
459C2×C4⋊C4—831no—
460C2×C4⋊C4—831no—
461C2×C4⋊C4—831no—
462C2×C4⋊C4—1661no—
463C2×C4⋊C4—1662no—
464C2×C4⋊C4—1661no—
465C2×C4⋊C4—1661no—
466C2×C4⋊C4—1661no—
467C2×C4⋊C4—1661no—
468C2×C4⋊C4D33211yescharacteristic
469C2×C22⋊C4—1661no—
470C2×C22⋊C4—1661no—
471C2×C22⋊C4—1661no—
472C2×C22⋊C4—1661no—
473C2×C22⋊C4—1661no—
474C2×C22⋊C4—1661no—
475C2×C22⋊C4—1661no—
476C2×C22⋊C4D33211yescharacteristic
477C2×C22⋊C4D33211yescharacteristic
478C2×C42—1661no—
479C2×C42—1661no—
480C2×C42—1661no—
481C2×C42—1661no—
482C2×C42—1661no—
483C2×C42C22×D8311yescharacteristic
484C4⋊C8—22no—
485#103—3321no—
486#103—3321no—
487#103—1662no—
488#103—1662no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491#97—22no—
492#95—1661no—
493#95—1661no—
494#95—1661no—
495#95—1661no—
496#95—1661no—
497C24C2×D33211yescharacteristic
498C24C2×D33211yescharacteristic
499C2×Q8—3322no—
500C2×Q8—3322no—
501C2×Q8—832no—
502C2×Q8—1661no—
503C2×Q8—1661no—
504C2×Q8—1661no—
505C2×Q8—1661no—
506C2×Q8—1661no—
507C2×Q8—1664no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4(C2×D83)⋊C414yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—3322no—
520C22×C4—3322no—
521C22×C4—6641no—
522C22×C4—1661no—
523C22×C4—1661no—
524C22×C4—1661no—
525C22×C4—1661no—
526C22×C4—1661no—
527C22×C4—1661no—
528C22×C4—1661no—
529C22×C4—1661no—
530C22×C4C2×C4×D8312yes—
531C22×C4C2×C4×D8312yes—
532C22×C4C2×C22⋊D8312yes—
533C22×C4C2×C22⋊D8312yes—
534C22×C4C2×D33211yescharacteristic
535C22×C4C2×D33211yescharacteristic
536C22×C4C2×D33211yescharacteristic
537C22×C4C2×D33211yescharacteristic
538C22×C4C23×D8311yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—44no—
552C2×C8#1305058912yes—
553C4⋊C4—3322no—
554C4⋊C4—832no—
555C4⋊C4—832no—
556C4⋊C4—832no—
557C4⋊C4—832no—
558C4⋊C4—1661no—
559C4⋊C4—1661no—
560C4⋊C4—1661no—
561C4⋊C4—1661no—
562C4⋊C4—1661no—
563C4⋊C4—1661no—
564C4⋊C4—1661no—
565C4⋊C4—1661no—
566C4⋊C4—1661no—
567C4⋊C4—1661no—
568C4⋊C4—1664no—
569C4⋊C4—1664no—
570C4⋊C4—1664no—
571C4⋊C4—1664no—
572C4⋊C4(C2×D83)⋊C414yes—
573C22⋊C4—3322no—
574C22⋊C4—3322no—
575C22⋊C4—6641no—
576C22⋊C4—1664no—
577C22⋊C4—1664no—
578C22⋊C4—1664no—
579C22⋊C4—1664no—
580C22⋊C4(C2×D83)⋊C414yes—
581C22⋊C4(C2×D83)⋊C414yes—
582C42—3322no—
583C42—6641no—
584C42—1664no—
585C42—1664no—
586C42—1664no—
587C42C2×C4×D8312yes—
588C42C2×C22⋊D8312yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×(C2×D83)⋊C412yes—
602C23C2×(C2×D83)⋊C412yes—
603C23C22×D33211yescharacteristic
604Q8—3328no—
605Q8—3321no—
606Q8—3321no—
607Q8—1662no—
608Q8—1662no—
609D4—44no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—3321no—
627C2×C4—3321no—
628C2×C4—3321no—
629C2×C4—3321no—
630C2×C4—3321no—
631C2×C4—3321no—
632C2×C4—3321no—
633C2×C4—3321no—
634C2×C4—3321no—
635C2×C4—3321no—
636C2×C4—3321no—
637C2×C4—3321no—
638C2×C4—3321no—
639C2×C4—3321no—
640C2×C4—3321no—
641C2×C4—3321no—
642C2×C4—3321no—
643C2×C4—3321no—
644C2×C4—3321no—
645C2×C4—6644no—
646C2×C4—1662no—
647C2×C4—1662no—
648C2×C4—1662no—
649C2×C4—1662no—
650C2×C4—1662no—
651C2×C4C2×(C2×D83)⋊C412yes—
652C2×C4C2×(C2×D83)⋊C412yes—
653C2×C4C2×(C2×D83)⋊C412yes—
654C2×C4C2×(C2×D83)⋊C412yes—
655C2×C4C22×C4×D8311yescharacteristic
656C2×C4C22×C22⋊D8311yescharacteristic
657C2×C4#41×D8311yescharacteristic
658C2×C4C2×#1305058911yescharacteristic
659C2×C4#1458183711yescharacteristic
660C2×C4#1458183911yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×(C2×D83)⋊C411yescharacteristic
680C22#1912834611yescharacteristic
681C22#1912835511yescharacteristic
682C22#1912850111yescharacteristic
683C22#1912850111yescharacteristic
684C22#1912851311yescharacteristic
685C22#1912851811yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—3322no—
691C4—3322no—
692C4—3322no—
693C4—3322no—
694C4—3322no—
695C4—6641no—
696C4—6641no—
697C4—6641no—
698C4C4×#1305058911yescharacteristic
699C4#1912818011yescharacteristic
700C4#1912834511yescharacteristic
701C4#1912835011yescharacteristic
702C2—42no—
703C2—42no—
704C2#2491028811yescharacteristic
705C2#2491598311yescharacteristic
706C2#2491599711yescharacteristic
707C2#2491950111yescharacteristic
708C2#2491953111yescharacteristic
709C2#2491999511yescharacteristic
710C2#2492001011yescharacteristic
subgroupG/H
centerC23C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×#435×C83C2
socleC23×C83C22×D4
prime radicalC22×D4×C83D4
cosocleC22×C4×C83C24
hypercenterC2×#435D83
hypocenterC83#22494
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #24908436C2semidirect
4. #24908410C2semidirect
5. #24907896C2semidirect
6. #24907886C2semidirect
7. #24907773C2semidirect
8. #24907768C2semidirect
9. #24907559C2semidirect
10. #24907559C2semidirect
11. #24907479C2semidirect
12. #24907294C2semidirect
13. #24907183C2semidirect
14. #24907180C2semidirect
17. #19128421C4semidirect
66. #14581792C2×C4semidirect
73. #14581771C2×C4semidirect
75. C4×Dic166C2×C4semidirect
82. #14581751C2×C4semidirect
371. C83#22494semidirect

Maximal subgroups

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

subgroupindex
C2×#191284212
#249103922
#249084362
#249084102
#249078962
#249078862
#249077732
#249077682
#249075592
#249074792
#249072942
#249071832
#249071802
C2×#435×C832
#2249483