Finite Group Databasebeta

← #35577053

Subgroups — #35577053

Order 21248.

2834 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128298C211yesmaximal, characteristic, complemented
2#24915755C212yesmaximal, complemented
3#24915750C211yesmaximal, characteristic, complemented
4#24915745C211yesmaximal, characteristic
5#24913276C211yesmaximal, characteristic, complemented
6#24913243C212yesmaximal, complemented
7#24913205C211yesmaximal, characteristic, complemented
8#24911718C214yesmaximal, complemented
9#24911598C214yesmaximal, complemented
10#24911272C214yesmaximal, complemented
11#24911198C214yesmaximal, complemented
12#24910132C212yesmaximal, complemented
13#24910066C211yesmaximal, characteristic, complemented
14C4×#14581761C212yesmaximal, complemented
15C23×C4⋊C4×C83C211yesmaximal, characteristic, complemented
16#19128298—28no—
17C2×#14581787C2212yescomplemented
18C2×#14581782C2212yescomplemented
19C2×#14581777C2212yescomplemented
20C2×#14581775C2212yes—
21C2×#14581775C2212yes—
22C2×#14581771C2211yescharacteristic
23C2×#14581771C2212yes—
24C2×#14581770C2212yescomplemented
25C2×#14581766C2211yescharacteristic
26C2×#14581766C2212yes—
27C2×#14581761C2212yes—
28C2×C4×C22⋊D83C2212yes—
29C2×C4×C22⋊D83C2214yes—
30#19127640C2212yescomplemented
31#19127639C2214yescomplemented
32#19127636C2214yescomplemented
33#19127634C2214yescomplemented
34#19127632C2214yescomplemented
35#19127631C2212yescomplemented
36#19127627C2214yescomplemented
37#19127623C2214yescomplemented
38#19127621C2212yescomplemented
39#19127618C2212yescomplemented
40#19127596C2214yescomplemented
41#19127591C2214yescomplemented
42#19127587C2214yescomplemented
43#19127587C2214yescomplemented
44#19127582C2214yescomplemented
45#19127580C2212yes—
46#19127580C2214yes—
47#19127580C2214yes—
48#19127580C2214yes—
49#19127580C2212yes—
50#19127580C2214yes—
51#19127574C2212yes—
52#19127574C2214yes—
53#19127574C2214yes—
54#19127574C2214yes—
55#19127574C2212yes—
56#19127574C2214yes—
57#19127572C2214yescomplemented
58#19127564C2212yes—
59#19127564C2212yes—
60#19127561C2211yescharacteristic
61#19127561C2212yes—
62#19127561C2211yescharacteristic
63#19127561C2212yes—
64#19127557C2212yes—
65C4×C22⋊Dic83C2212yes—
66C4×C22⋊Dic83C2214yes—
67C24×C4×C83C2211yescharacteristic
68C24×C4×C83C2211yescharacteristic
69C24×C4×C83C2211yescharacteristic
70C22×C4⋊C4×C83—28no—
71C22×C4⋊C4×C83C2211yescharacteristic
72C22×C4⋊C4×C83C2211yescharacteristic
73C22×C4⋊C4×C83C2211yescharacteristic
74C22×C4⋊C4×C83C2214yes—
75C22×C4⋊C4×C83C2214yes—
76C22×C4⋊C4×C83C2211yescharacteristic
77C22×Dic166C2311yescharacteristic
78C22×D332C2311yescharacteristic
79C22×C22⋊D83C2314yes—
80C22×C22⋊D83C2312yes—
81C22×C4×D83C2312yes—
82#14581787—28no—
83#14581782—28no—
84#14581777—28no—
85#14581775—28no—
86#14581775—28no—
87#14581771—24no—
88#14581771—44no—
89#14581770—28no—
90#14581766—24no—
91#14581766—44no—
92#14581761—28no—
93C4×C22⋊D83—28no—
94C4×C22⋊D83—48no—
95C2×C4⋊Dic83C2311yescharacteristic
96C2×C4⋊Dic83C2311yescharacteristic
97C2×C4⋊Dic83C2312yes—
98C2×C4⋊Dic83C2312yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2312yes—
101C2×Dic83⋊C4C2312yes—
102C2×Dic83⋊C4C2312yes—
103C2×Dic83⋊C4C2312yes—
104C2×Dic83⋊C4C2314yes—
105C2×Dic83⋊C4C2314yes—
106C2×C22⋊Dic83C2312yes—
107C2×C22⋊Dic83C2314yes—
108C2×C22⋊Dic83C2312yes—
109C2×C22⋊Dic83C2314yes—
110C2×C22⋊Dic83C2312yes—
111C2×C22⋊Dic83C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×(C2×D83)⋊C4C2312yes—
114C2×(C2×D83)⋊C4C2312yes—
115C2×(C2×D83)⋊C4C2312yes—
116C2×(C2×D83)⋊C4C2312yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×C4×Dic83C2312yes—
120C2×C4×Dic83C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2312yes—
123C83⋊#95C2314yes—
124C83⋊#95C2312yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C25×C83C2311yescharacteristic
133C23×C4×C83—24no—
134C23×C4×C83—24no—
135C23×C4×C83—24no—
136C23×C4×C83—24no—
137C23×C4×C83—24no—
138C23×C4×C83—44no—
139C23×C4×C83—44no—
140C23×C4×C83C2314yes—
141C23×C4×C83C2312yes—
142C23×C4×C83C2312yes—
143C23×C4×C83C2314yes—
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2311yescharacteristic
146C23×C4×C83C2311yescharacteristic
147C23×C4×C83C2311yescharacteristic
148C23×C4×C83C2311yescharacteristic
149C23×C4×C83C2311yescharacteristic
150C2×C4⋊C4×C83—24no—
151C2×C4⋊C4×C83—24no—
152C2×C4⋊C4×C83—24no—
153C2×C4⋊C4×C83—216no—
154C2×C4⋊C4×C83—216no—
155C2×C4⋊C4×C83D418yescomplemented
156C2×C4⋊C4×C83C2314yes—
157C2×C4⋊C4×C83C2312yes—
158C2×C4⋊C4×C83C2312yes—
159C2×C4⋊C4×C83C2314yes—
160C2×C4⋊C4×C83C2312yes—
161C2×C4⋊C4×C83C2312yes—
162C23×D83C2412yes—
163C2×Dic166—22no—
164C2×Dic166—42no—
165C2×D332—22no—
166C2×D332—42no—
167C2×C22⋊D83—24no—
168C2×C22⋊D83—24no—
169C2×C22⋊D83—28no—
170C2×C22⋊D83—24no—
171C2×C22⋊D83—28no—
172C2×C22⋊D83—28no—
173C22×Dic83C2412yes—
174C22×Dic83C2414yes—
175C22×Dic83C2412yes—
176C22×Dic83C2412yes—
177C22×Dic83C2414yes—
178C2×C4×D83—24no—
179C2×C4×D83—44no—
180C4⋊Dic83—22no—
181C4⋊Dic83—22no—
182C4⋊Dic83—42no—
183C4⋊Dic83—42no—
184Dic83⋊C4—24no—
185Dic83⋊C4—24no—
186Dic83⋊C4—24no—
187Dic83⋊C4—24no—
188Dic83⋊C4—28no—
189Dic83⋊C4—44no—
190Dic83⋊C4—44no—
191C22⋊Dic83—24no—
192C22⋊Dic83—24no—
193C22⋊Dic83—28no—
194C22⋊Dic83—24no—
195C22⋊Dic83—28no—
196C22⋊Dic83—28no—
197(C2×D83)⋊C4—24no—
198(C2×D83)⋊C4—24no—
199(C2×D83)⋊C4—24no—
200(C2×D83)⋊C4—24no—
201(C2×D83)⋊C4—28no—
202(C2×D83)⋊C4—44no—
203(C2×D83)⋊C4—44no—
204C4×Dic83—24no—
205C4×Dic83—44no—
206C24×C83—22no—
207C24×C83—22no—
208C24×C83—24no—
209C24×C83—24no—
210C24×C83#4114yes—
211C24×C83C2411yescharacteristic
212C24×C83C2412yes—
213C22×C4×C83—232no—
214C22×C4×C83—22no—
215C22×C4×C83—28no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—28no—
220C22×C4×C83—28no—
221C22×C4×C83—22no—
222C22×C4×C83—22no—
223C22×C4×C83—24no—
224C22×C4×C83—24no—
225C22×C4×C83—28no—
226C22×C4×C83—28no—
227C22×C4×C83—24no—
228C22×C4×C83—24no—
229C22×C4×C83—42no—
230C22×C4×C83—44no—
231C22×C4×C83—42no—
232C22×C4×C83—42no—
233C22×C4×C83—42no—
234C22×C4×C83—42no—
235C22×C4×C83—42no—
236C22×C4×C83—416no—
237C22×C4×C83—416no—
238C22×C4×C83C2×D414yes—
239C22×C4×C83C2×D414yes—
240C22×C4×C83C2×D414yes—
241C22×C4×C83#4114yes—
242C22×C4×C83C2412yes—
243C22×C4×C83C2412yes—
244C22×C4×C83C2412yes—
245C22×C4×C83C2411yescharacteristic
246C22×C4×C83C2411yescharacteristic
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C4⋊C4×C83—28no—
250C4⋊C4×C83—24no—
251C4⋊C4×C83—24no—
252C4⋊C4×C83—28no—
253C4⋊C4×C83C2×D418yes—
254C4⋊C4×C83C2×D418yes—
255C23×C83—28no—
256C23×C83—28no—
257C23×C83—216no—
258C23×C83—28no—
259C23×C83—216no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83—22no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83C22×D412yes—
267C23×C83C2×#4112yes—
268C23×C83C2×#4112yes—
269C23×C83C2×#4114yes—
270C23×C83H(5,𝔽2)14yes—
271C23×C832−1+414yes—
272C23×C83C2511yescharacteristic
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D83—24no—
277C22×D83—24no—
278C2×C4×C83—232no—
279C2×C4×C83—28no—
280C2×C4×C83—28no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—24no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—24no—
292C2×C4×C83—22no—
293C2×C4×C83—44no—
294C2×C4×C83—44no—
295C2×C4×C83—48no—
296C2×C4×C83—416no—
297C2×C4×C83—48no—
298C2×C4×C83—44no—
299C2×C4×C83—44no—
300C2×C4×C83C22×D414yes—
301C2×C4×C83C22×D414yes—
302C2×C4×C83C22×D412yes—
303C2×C4×C83C22×D412yes—
304C2×C4×C83C2×#4114yes—
305C22⋊D83—48no—
306C22⋊D83—416no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—24no—
311C2×Dic83—22no—
312C2×Dic83—24no—
313C2×Dic83—22no—
314C2×Dic83—24no—
315C2×Dic83—24no—
316C2×Dic83—24no—
317C2×Dic83—24no—
318C2×Dic83—24no—
319C2×Dic83—24no—
320D332—82no—
321C4×D83—84no—
322Dic166—82no—
323C22×C83—232no—
324C22×C83—24no—
325C22×C83—24no—
326C22×C83—24no—
327C22×C83—22no—
328C22×C83—24no—
329C22×C83—22no—
330C22×C83—24no—
331C22×C83—24no—
332C22×C83—24no—
333C22×C83—24no—
334C22×C83#52514yes—
335C22×C83#53918yescomplemented
336C22×C83C23×D411yescharacteristic
337C22×C83C22×#4111yescharacteristic
338C22×C83C22×#4111yescharacteristic
339C22×C83C2×H(5,𝔽2)12yes—
340C22×C83C2×2−1+412yes—
341C2×D83—42no—
342C2×D83—44no—
343C2×D83—42no—
344C2×D83—42no—
345C2×D83—44no—
346C4×C83—24no—
347C4×C83—24no—
348C4×C83—22no—
349C4×C83—24no—
350C4×C83—22no—
351C4×C83—42no—
352C4×C83—42no—
353Dic83—42no—
354Dic83—44no—
355Dic83—42no—
356Dic83—42no—
357Dic83—44no—
358#34989—831nomaximal, Sylow
359C2×C83—24no—
360C2×C83—28no—
361C2×C83C2×#52511yescharacteristic
362C2×C83C2×#53912yes—
363C2×C83#348411yescharacteristic
364C2×C83#348611yescharacteristic
365C2×C83#349212yes—
366D83—82no—
367C2×#539—831no—
368C23×C4⋊C4D8311yescharacteristic, complemented
369#2849—832no—
370#2848—831no—
371#2847—831no—
372#2627—831no—
373#2623—832no—
374#2618—831no—
375#2481—834no—
376#2473—834no—
377#2449—834no—
378#2443—834no—
379#2322—832no—
380#2313—831no—
381C4×#120—832no—
382C83#3498911yescharacteristic, complemented, Sylow
383C24×C4C2×D8311yescharacteristic
384C24×C4C2×D8311yescharacteristic
385C24×C4C2×D8311yescharacteristic
386#539—1668no—
387C2×#126—832no—
388C2×#125—832no—
389C2×#123—832no—
390C2×#123—832no—
391C2×#123—832no—
392C2×C22⋊Q8—832no—
393C2×C22⋊Q8—831no—
394C2×C22⋊Q8—832no—
395C2×#121—832no—
396C2×#121—831no—
397C2×#120—832no—
398C2×C4×D4—834no—
399C2×C4×D4—832no—
400C22×C4⋊C4—28no—
401C22×C4⋊C4C2×D8311yescharacteristic
402C22×C4⋊C4C2×D8311yescharacteristic
403C22×C4⋊C4C2×D8311yescharacteristic
404C22×C4⋊C4C2×D8314yes—
405C22×C4⋊C4C2×D8314yes—
406C22×C4⋊C4C2×D8311yescharacteristic
407#400—834no—
408#400—832no—
409#399—834no—
410#398—832no—
411#398—834no—
412#398—834no—
413#397—834no—
414#396—834no—
415#395—832no—
416#394—832no—
417#389—834no—
418#388—834no—
419#387—834no—
420#387—834no—
421#387—834no—
422#386—832no—
423#386—834no—
424#386—834no—
425#386—834no—
426#386—832no—
427#386—834no—
428#385—832no—
429#385—834no—
430#385—834no—
431#385—834no—
432#385—832no—
433#385—834no—
434#385—834no—
435#381—832no—
436#381—832no—
437#380—831no—
438#380—831no—
439#380—832no—
440#380—832no—
441#379—832no—
442C4×C22⋊C4—832no—
443C4×C22⋊C4—834no—
444C25C22×D8311yescharacteristic
445C22×Q8—831no—
446C22×D4—832no—
447C22×D4—834no—
448C22×D4—831no—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—24no—
454C23×C4—44no—
455C23×C4—44no—
456C23×C4—832no—
457C23×C4C22×D8314yes—
458C23×C4C22×D8314yes—
459C23×C4C22×D8312yes—
460C23×C4C22×D8312yes—
461C23×C4C22×D8311yescharacteristic
462C23×C4C22×D8311yescharacteristic
463C23×C4C22×D8311yescharacteristic
464C23×C4C22×D8311yescharacteristic
465C23×C4C22×D8311yescharacteristic
466C23×C4C22×D8311yescharacteristic
467#126—1668no—
468#125—1668no—
469#123—1668no—
470#123—1668no—
471#123—1668no—
472C22⋊Q8—3324no—
473C22⋊Q8—1664no—
474C22⋊Q8—1668no—
475#121—3324no—
476#121—1664no—
477#120—1668no—
478C4×D4—3328no—
479C4×D4—1668no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—216no—
484C2×C4⋊C4—216no—
485C2×C4⋊C4—834no—
486C2×C4⋊C4—832no—
487C2×C4⋊C4—832no—
488C2×C4⋊C4—834no—
489C2×C4⋊C4—832no—
490C2×C4⋊C4—831no—
491C2×C4⋊C4—832no—
492C2×C4⋊C4—832no—
493C2×C4⋊C4—831no—
494C2×C4⋊C4—832no—
495C2×C4⋊C4—834no—
496C2×C4⋊C4C22⋊D8318yescomplemented
497C2×C4⋊C4C22×D8314yes—
498C2×C4⋊C4C22×D8312yes—
499C2×C4⋊C4C22×D8312yes—
500C2×C4⋊C4C22×D8314yes—
501C2×C4⋊C4C22×D8312yes—
502C2×C4⋊C4C22×D8312yes—
503C2×C22⋊C4—834no—
504C2×C22⋊C4—834no—
505C2×C22⋊C4—832no—
506C2×C22⋊C4—834no—
507C2×C22⋊C4—832no—
508C2×C22⋊C4—834no—
509C2×C22⋊C4—832no—
510C2×C22⋊C4—834no—
511C2×C22⋊C4—832no—
512C2×C22⋊C4—832no—
513C2×C22⋊C4—832no—
514C2×C22⋊C4—832no—
515C2×C22⋊C4—834no—
516C2×C42—834no—
517C2×C42—832no—
518#95—834no—
519#95—834no—
520#95—834no—
521#95—832no—
522#95—834no—
523#95—832no—
524#95—834no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95—834no—
529C24—22no—
530C24—22no—
531C24—24no—
532C24—24no—
533C24—832no—
534C24#1305059014yes—
535C24C23×D8311yescharacteristic
536C24C23×D8312yes—
537C2×Q8—3322no—
538C2×Q8—1662no—
539C2×D4—3322no—
540C2×D4—1664no—
541C2×D4—1664no—
542C2×D4—1668no—
543C2×D4—1664no—
544C2×D4—1668no—
545C2×D4—1668no—
546C2×D4—1662no—
547C22×C4—232no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—28no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—28no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—42no—
564C22×C4—44no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—416no—
571C22×C4—416no—
572C22×C4—3324no—
573C22×C4—834no—
574C22×C4—832no—
575C22×C4—834no—
576C22×C4—832no—
577C22×C4—832no—
578C22×C4—1664no—
579C22×C4C2×C22⋊D8314yes—
580C22×C4C2×C22⋊D8314yes—
581C22×C4C2×C22⋊D8314yes—
582C22×C4#1305059014yes—
583C22×C4C23×D8312yes—
584C22×C4C23×D8312yes—
585C22×C4C23×D8312yes—
586C22×C4C23×D8312yes—
587C22×C4C23×D8311yescharacteristic
588C22×C4C23×D8311yescharacteristic
589C22×C4C23×D8312yes—
590C4⋊C4—28no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—28no—
594C4⋊C4—3324no—
595C4⋊C4—3322no—
596C4⋊C4—3324no—
597C4⋊C4—3322no—
598C4⋊C4—1664no—
599C4⋊C4—1662no—
600C4⋊C4—1664no—
601C4⋊C4—1664no—
602C4⋊C4—1662no—
603C4⋊C4—1664no—
604C4⋊C4—1668no—
605C4⋊C4C2×C22⋊D8318yes—
606C4⋊C4C2×C22⋊D8318yes—
607C22⋊C4—3324no—
608C22⋊C4—3324no—
609C22⋊C4—1664no—
610C22⋊C4—1664no—
611C22⋊C4—1668no—
612C22⋊C4—1664no—
613C22⋊C4—1668no—
614C22⋊C4—1668no—
615C22⋊C4—1664no—
616C22⋊C4—1664no—
617C22⋊C4—1664no—
618C22⋊C4—1664no—
619C22⋊C4—1668no—
620C42—3324no—
621C42—1664no—
622C23—28no—
623C23—28no—
624C23—216no—
625C23—28no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—216no—
633C23—1662no—
634C23—1662no—
635C23—1662no—
636C23—1664no—
637C23—1664no—
638C23C22×C22⋊D8312yes—
639C23C2×#1305059012yes—
640C23C2×#1305059012yes—
641C23C2×#1305059014yes—
642C23#1458183714yes—
643C23#1458184014yes—
644C23C24×D8311yescharacteristic
645Q8—6642no—
646D4—3328no—
647D4—33216no—
648D4—6642no—
649C2×C4—232no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—416no—
667C2×C4—48no—
668C2×C4—48no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—6644no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1664no—
676C2×C4—1662no—
677C2×C4—1664no—
678C2×C4—1662no—
679C2×C4—1664no—
680C2×C4—1664no—
681C2×C4—1664no—
682C2×C4—1664no—
683C2×C4—1664no—
684C2×C4—1664no—
685C2×C4C22×C22⋊D8314yes—
686C2×C4C22×C22⋊D8314yes—
687C2×C4C22×C22⋊D8312yes—
688C2×C4C22×C22⋊D8312yes—
689C2×C4C2×#1305059014yes—
690C22—232no—
691C22—22no—
692C22—24no—
693C22—22no—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—24no—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—3322no—
702C22—3322no—
703C22—3324no—
704C22—3322no—
705C22—3324no—
706C22#1912821214yes—
707C22#1912829818yescomplemented
708C22C23×C22⋊D8311yescharacteristic
709C22C22×#1305059011yescharacteristic
710C22C22×#1305059011yescharacteristic
711C22C2×#1458183712yes—
712C22C2×#1458184012yes—
713C4—24no—
714C4—22no—
715C4—22no—
716C4—24no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—3322no—
721C4—3322no—
722C4—3324no—
723C4—3322no—
724C4—3324no—
725C2—24no—
726C2—28no—
727C2—6642no—
728C2C2×#1912821211yescharacteristic
729C2C2×#1912829812yes—
730C2#2492109811yescharacteristic
731C2#2492111411yescharacteristic
732C2#2492117212yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC23×C4⋊C4×C83C2
prime radical#24915745C2
hypercenterC23×C4⋊C4D83
hypocenterC83#34989
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#19128298C2semidirect
2. #24915755C2semidirect
3. #24915750C2semidirect
5. #24913276C2semidirect
6. #24913243C2semidirect
7. #24913205C2semidirect
8. #24911718C2semidirect
9. #24911598C2semidirect
10. #24911272C2semidirect
11. #24911198C2semidirect
12. #24910132C2semidirect
13. #24910066C2semidirect
14. C4×#14581761C2semidirect
15. C23×C4⋊C4×C83C2semidirect
17. C2×#14581787C22semidirect
18. C2×#14581782C22semidirect
19. C2×#14581777C22semidirect
24. C2×#14581770C22semidirect
30. #19127640C22semidirect
31. #19127639C22semidirect
32. #19127636C22semidirect
33. #19127634C22semidirect
34. #19127632C22semidirect
35. #19127631C22semidirect
36. #19127627C22semidirect
37. #19127623C22semidirect
38. #19127621C22semidirect
39. #19127618C22semidirect
40. #19127596C22semidirect
41. #19127591C22semidirect
42. #19127587C22semidirect
43. #19127587C22semidirect
44. #19127582C22semidirect
57. #19127572C22semidirect
155. C2×C4⋊C4×C83D4semidirect
335. C22×C83#539semidirect
368. C23×C4⋊C4D83semidirect
382. C83#34989semidirect
496. C2×C4⋊C4C22⋊D83semidirect
707. C22#19128298semidirect

Maximal subgroups

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

subgroupindex
C2×#191282982
#249157552
#249157502
#249157452
#249132762
#249132432
#249132052
#249117182
#249115982
#249112722
#249111982
#249101322
#249100662
C4×#145817612
C23×C4⋊C4×C832
#3498983