Finite Group Databasebeta

← #35577045

Subgroups — #35577045

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
1C22×C4⋊C4×D83C211yesmaximal, characteristic, complemented
2#24915752C212yesmaximal, complemented
3#24915747C211yesmaximal, characteristic, complemented
4#24915742C211yesmaximal, characteristic
5#24913278C211yesmaximal, characteristic, complemented
6#24913245C212yesmaximal, complemented
7#24913207C211yesmaximal, characteristic, complemented
8#24911720C214yesmaximal, complemented
9#24911600C214yesmaximal, complemented
10#24911269C214yesmaximal, complemented
11#24911195C214yesmaximal, complemented
12#24910128C212yesmaximal, complemented
13#24910066C211yesmaximal, characteristic, complemented
14C4×#14581760C212yesmaximal, complemented
15C2×#539×C83C211yesmaximal, characteristic, complemented
16C23×C4×D83C2211yescharacteristic
17C23×C4×D83C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C2×#14581773C2212yes—
20C2×#14581768C2212yes—
21C2×#14581763C2212yes—
22C2×#14581760C2212yes—
23C2×C4×C22⋊D83C2214yes—
24C22×C4⋊Dic83C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C2×C4⋊C4×D83—28no—
28C2×C4⋊C4×D83C2214yes—
29C2×C4⋊C4×D83C2214yes—
30#19127640C2214yescomplemented
31#19127639C2212yescomplemented
32#19127637C2214yescomplemented
33#19127634C2214yescomplemented
34#19127632C2212yescomplemented
35#19127631C2214yescomplemented
36#19127626C2214yescomplemented
37#19127624C2214yescomplemented
38#19127620C2212yescomplemented
39#19127615C2212yescomplemented
40#19127596C2214yescomplemented
41#19127595C2214yescomplemented
42#19127587C2214yescomplemented
43#19127587C2214yescomplemented
44#19127585C2214yescomplemented
45#19127581C2212yes—
46#19127581C2212yes—
47#19127577C2214yes—
48#19127577C2214yes—
49#19127577C2214yes—
50#19127577C2214yes—
51#19127574C2214yescomplemented
52#19127573C2212yes—
53#19127573C2212yes—
54#19127572C2214yes—
55#19127572C2214yes—
56#19127572C2214yes—
57#19127572C2214yes—
58#19127564C2212yes—
59#19127562C2212yes—
60#19127561C2211yescharacteristic
61#19127561C2211yescharacteristic
62#19127558C2212yes—
63#19127558C2212yes—
64#19127556C2212yes—
65C4×(C2×D83)⋊C4C2214yes—
66C4×C22⋊Dic83C2212yes—
67#539×C83—28no—
68C2×#126×C83C2212yescomplemented
69C2×#125×C83C2212yescomplemented
70C2×#123×C83C2212yes—
71C2×#123×C83C2212yescomplemented
72C2×C22⋊Q8×C83C2211yescharacteristic
73C2×C22⋊Q8×C83C2212yescomplemented
74C2×#121×C83C2211yescharacteristic
75C2×C4×D4×C83C2212yes—
76C22×C4⋊C4×C83C2211yescharacteristic
77C24×D83C2311yescharacteristic
78C22×C22⋊D83C2314yes—
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C22×C4×D83—24no—
83C22×C4×D83—24no—
84C22×C4×D83—24no—
85C22×C4×D83—24no—
86C22×C4×D83—24no—
87C22×C4×D83—44no—
88C22×C4×D83—44no—
89C22×C4×D83C2314yes—
90C22×C4×D83C2312yes—
91C22×C4×D83C2312yes—
92C22×C4×D83C2314yes—
93#14581773—28no—
94#14581768—44no—
95#14581763—44no—
96#14581760—28no—
97C4×C22⋊D83—48no—
98C2×C4⋊Dic83—24no—
99C2×C4⋊Dic83C2314yes—
100C2×C4⋊Dic83C2312yes—
101C2×C4⋊Dic83C2312yes—
102C2×Dic83⋊C4—24no—
103C2×Dic83⋊C4—24no—
104C2×Dic83⋊C4C2314yes—
105C2×Dic83⋊C4C2314yes—
106C2×Dic83⋊C4C2312yes—
107C2×Dic83⋊C4C2312yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C4⋊C4×D83—216no—
111C4⋊C4×D83—216no—
112C2×C22⋊Dic83C2312yes—
113C2×C22⋊Dic83C2312yes—
114C2×C22⋊Dic83C2314yes—
115C2×C22⋊Dic83C2314yes—
116C2×C22⋊Dic83C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×C4×Dic83C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2312yes—
124C83⋊#95C2312yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C22×Q8×C83C2311yescharacteristic
133C22×D4×C83C2312yes—
134C22×D4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2312yes—
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139#126×C83—28no—
140#125×C83—28no—
141#123×C83—28no—
142#123×C83—28no—
143C22⋊Q8×C83—24no—
144C22⋊Q8×C83—28no—
145#121×C83—24no—
146C4×D4×C83—28no—
147C2×C4⋊C4×C83D418yescomplemented
148C2×C4⋊C4×C83C2311yescharacteristic
149C2×C4⋊C4×C83C2311yescharacteristic
150C2×C4⋊C4×C83C2312yes—
151C2×C4⋊C4×C83C2312yes—
152C2×C4⋊C4×C83C2312yes—
153C2×C4⋊C4×C83C2312yes—
154C2×C4⋊C4×C83C2312yes—
155C2×C4⋊C4×C83C2312yes—
156C2×C22⋊C4×C83C2312yes—
157C2×C22⋊C4×C83C2312yes—
158C2×C22⋊C4×C83C2312yes—
159C2×C22⋊C4×C83C2312yes—
160C2×C22⋊C4×C83C2312yes—
161C2×C42×C83C2312yes—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83—24no—
165C23×D83—24no—
166C23×D83#4114yes—
167C23×D83C2412yes—
168C2×C22⋊D83—28no—
169C2×C22⋊D83—28no—
170C2×C22⋊D83—28no—
171C22×Dic83—22no—
172C22×Dic83—22no—
173C22×Dic83—22no—
174C22×Dic83—22no—
175C22×Dic83—42no—
176C22×Dic83—42no—
177C22×Dic83#4114yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2414yes—
181C22×Dic83C2414yes—
182C22×Dic83C2412yes—
183C2×C4×D83—232no—
184C2×C4×D83—28no—
185C2×C4×D83—28no—
186C2×C4×D83—28no—
187C2×C4×D83—24no—
188C2×C4×D83—24no—
189C2×C4×D83—28no—
190C2×C4×D83—28no—
191C2×C4×D83—24no—
192C2×C4×D83—24no—
193C2×C4×D83—42no—
194C2×C4×D83—44no—
195C2×C4×D83—42no—
196C2×C4×D83—416no—
197C2×C4×D83—416no—
198C4⋊Dic83—28no—
199C4⋊Dic83—42no—
200C4⋊Dic83—42no—
201Dic83⋊C4—28no—
202Dic83⋊C4—24no—
203Dic83⋊C4—24no—
204Dic83⋊C4—28no—
205Dic83⋊C4—44no—
206Dic83⋊C4—44no—
207C22⋊Dic83—24no—
208C22⋊Dic83—24no—
209C22⋊Dic83—28no—
210C22⋊Dic83—44no—
211C22⋊Dic83—44no—
212(C2×D83)⋊C4—28no—
213(C2×D83)⋊C4—28no—
214(C2×D83)⋊C4—28no—
215C4×Dic83—44no—
216C24×C83C2412yes—
217C24×C83C2411yescharacteristic
218C2×Q8×C83—22no—
219C2×Q8×C83—42no—
220C2×D4×C83—24no—
221C2×D4×C83—24no—
222C2×D4×C83—24no—
223C2×D4×C83—22no—
224C2×D4×C83—42no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—24no—
228C22×C4×C83—42no—
229C22×C4×C83—42no—
230C22×C4×C83—44no—
231C22×C4×C83C2×D414yes—
232C22×C4×C83C2×D414yes—
233C22×C4×C83C2×D414yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2411yescharacteristic
240C22×C4×C83C2411yescharacteristic
241C4⋊C4×C83—24no—
242C4⋊C4×C83—22no—
243C4⋊C4×C83—24no—
244C4⋊C4×C83—24no—
245C4⋊C4×C83—22no—
246C4⋊C4×C83—24no—
247C4⋊C4×C83C2×D418yes—
248C4⋊C4×C83C2×D418yes—
249C22⋊C4×C83—24no—
250C22⋊C4×C83—24no—
251C22⋊C4×C83—24no—
252C22⋊C4×C83—24no—
253C22⋊C4×C83—24no—
254C42×C83—24no—
255C23×C83—22no—
256C23×C83—22no—
257C23×C83—22no—
258C23×C83—22no—
259C23×C83—22no—
260C23×C83—24no—
261C23×C83—24no—
262C23×C83C22×D412yes—
263C23×C83C2×#4112yes—
264C23×C83C2×#4112yes—
265C23×C83C2511yescharacteristic
266C22×D83—28no—
267C22×D83—28no—
268C22×D83—216no—
269C22×D83—28no—
270C22×D83—22no—
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—216no—
275C22×D83C2×#4114yes—
276C22×D83H(5,𝔽2)14yes—
277C22×D832−1+414yes—
278Q8×C83—82no—
279D4×C83—48no—
280D4×C83—82no—
281C2×C4×C83—28no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—24no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—24no—
293C2×C4×C83—24no—
294C2×C4×C83—44no—
295C2×C4×C83—44no—
296C2×C4×C83—84no—
297C2×C4×C83C22×D414yes—
298C2×C4×C83C22×D414yes—
299C2×C4×C83C22×D412yes—
300C2×C4×C83C22×D412yes—
301C22⋊D83—416no—
302C2×Dic83—28no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—24no—
308C2×Dic83—24no—
309C2×Dic83—24no—
310C2×Dic83—24no—
311C2×Dic83—22no—
312C2×Dic83—24no—
313C2×Dic83—22no—
314C2×Dic83—24no—
315C2×Dic83—24no—
316C2×Dic83—44no—
317C2×Dic83—44no—
318C2×Dic83C2×#4114yes—
319C4×D83—232no—
320C4×D83—416no—
321C4×D83—48no—
322C4×D83—48no—
323C22×C83—24no—
324C22×C83—22no—
325C22×C83—22no—
326C22×C83—24no—
327C22×C83—42no—
328C22×C83—44no—
329C22×C83—42no—
330C22×C83—42no—
331C22×C83—44no—
332C22×C83#52514yes—
333C22×C83C23×D411yescharacteristic
334C22×C83C22×#4111yescharacteristic
335C22×C83C22×#4111yescharacteristic
336C22×C83C2×H(5,𝔽2)12yes—
337C22×C83C2×2−1+412yes—
338C2×D83—232no—
339C2×D83—24no—
340C2×D83—24no—
341C2×D83—24no—
342C2×D83—24no—
343C2×D83—24no—
344C2×D83—24no—
345C2×D83#53918yescomplemented
346C4×C83—24no—
347C4×C83—24no—
348C4×C83—22no—
349C4×C83—22no—
350C4×C83—42no—
351C4×C83—42no—
352C4×C83—42no—
353Dic83—24no—
354Dic83—44no—
355Dic83—42no—
356Dic83—42no—
357Dic83—44no—
358#34989—831nomaximal, Sylow
359C2×C83—24no—
360C2×C83—82no—
361C2×C83C2×#52511yescharacteristic
362C2×C83C2×#53912yes—
363C2×C83#348411yescharacteristic
364C2×C83#348611yescharacteristic
365C2×C83#349212yes—
366D83—28no—
367C2×#539D8311yescharacteristic, complemented
368C23×C4⋊C4—831no—
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×C4—831no—
384C24×C4—831no—
385C24×C4—831no—
386#539—28no—
387C2×#126C2×D8312yescomplemented
388C2×#125C2×D8312yescomplemented
389C2×#123—832no—
390C2×#123C2×D8312yes—
391C2×#123C2×D8312yescomplemented
392C2×C22⋊Q8—832no—
393C2×C22⋊Q8C2×D8311yescharacteristic
394C2×C22⋊Q8C2×D8312yescomplemented
395C2×#121—832no—
396C2×#121C2×D8311yescharacteristic
397C2×#120—832no—
398C2×C4×D4—834no—
399C2×C4×D4C2×D8312yes—
400C22×C4⋊C4—831no—
401C22×C4⋊C4—831no—
402C22×C4⋊C4—831no—
403C22×C4⋊C4—834no—
404C22×C4⋊C4—834no—
405C22×C4⋊C4—1668no—
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—832no—
424#386—834no—
425#386—834no—
426#386—834no—
427#386—834no—
428#385—834no—
429#385—834no—
430#385—834no—
431#385—834no—
432#385—834no—
433#385—832no—
434#385—832no—
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—
444C25—831no—
445C22×Q8C22×D8311yescharacteristic
446C22×D4—834no—
447C22×D4C22×D8312yes—
448C22×D4C22×D8311yescharacteristic
449C23×C4—3324no—
450C23×C4—3324no—
451C23×C4—831no—
452C23×C4—831no—
453C23×C4—834no—
454C23×C4—832no—
455C23×C4—832no—
456C23×C4—831no—
457C23×C4—834no—
458C23×C4—1664no—
459C23×C4—1664no—
460C23×C4—1664no—
461C23×C4—1664no—
462C23×C4—1664no—
463C23×C4C22×D8311yescharacteristic
464C23×C4C22×D8312yes—
465C23×C4C22×D8311yescharacteristic
466C23×C4C22×D8311yescharacteristic
467#126—28no—
468#125—28no—
469#123—28no—
470#123—28no—
471#123—1668no—
472C22⋊Q8—24no—
473C22⋊Q8—28no—
474C22⋊Q8—3324no—
475#121—24no—
476#121—3324no—
477#120—1668no—
478C4×D4—28no—
479C4×D4—3328no—
480C2×C4⋊C4—834no—
481C2×C4⋊C4—832no—
482C2×C4⋊C4—832no—
483C2×C4⋊C4—834no—
484C2×C4⋊C4—834no—
485C2×C4⋊C4—832no—
486C2×C4⋊C4—832no—
487C2×C4⋊C4—834no—
488C2×C4⋊C4—834no—
489C2×C4⋊C4—1664no—
490C2×C4⋊C4—1664no—
491C2×C4⋊C4—1664no—
492C2×C4⋊C4—16616no—
493C2×C4⋊C4—16616no—
494C2×C4⋊C4C22⋊D8318yescomplemented
495C2×C4⋊C4C22×D8312yes—
496C2×C4⋊C4C22×D8311yescharacteristic
497C2×C4⋊C4C22×D8312yes—
498C2×C4⋊C4C22×D8311yescharacteristic
499C2×C4⋊C4C22×D8312yes—
500C2×C4⋊C4C22×D8312yes—
501C2×C4⋊C4C22×D8312yes—
502C2×C4⋊C4C22×D8312yes—
503C2×C22⋊C4—834no—
504C2×C22⋊C4—834no—
505C2×C22⋊C4—832no—
506C2×C22⋊C4—832no—
507C2×C22⋊C4—834no—
508C2×C22⋊C4—834no—
509C2×C22⋊C4—834no—
510C2×C22⋊C4—834no—
511C2×C22⋊C4C22×D8312yes—
512C2×C22⋊C4C22×D8312yes—
513C2×C22⋊C4C22×D8312yes—
514C2×C22⋊C4C22×D8312yes—
515C2×C22⋊C4C22×D8312yes—
516C2×C42—834no—
517C2×C42C22×D8312yes—
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—832no—
530C24—834no—
531C24—1664no—
532C24—1664no—
533C24—1662no—
534C24—1662no—
535C24C23×D8312yes—
536C24C23×D8311yescharacteristic
537C2×Q8—22no—
538C2×Q8—42no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—22no—
543C2×D4—42no—
544C2×D4—1668no—
545C2×D4—1668no—
546C2×D4—1668no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—44no—
553C22×C4—3324no—
554C22×C4—3322no—
555C22×C4—3322no—
556C22×C4—33216no—
557C22×C4—33216no—
558C22×C4—3322no—
559C22×C4—3322no—
560C22×C4—834no—
561C22×C4—832no—
562C22×C4—834no—
563C22×C4—834no—
564C22×C4—832no—
565C22×C4—832no—
566C22×C4—1668no—
567C22×C4—1664no—
568C22×C4—1664no—
569C22×C4—1668no—
570C22×C4—1668no—
571C22×C4—16632no—
572C22×C4—1662no—
573C22×C4—1662no—
574C22×C4—1668no—
575C22×C4—1664no—
576C22×C4—1664no—
577C22×C4—1662no—
578C22×C4—1662no—
579C22×C4—1668no—
580C22×C4C2×C22⋊D8314yes—
581C22×C4C2×C22⋊D8314yes—
582C22×C4C2×C22⋊D8314yes—
583C22×C4C23×D8312yes—
584C22×C4C23×D8312yes—
585C22×C4C23×D8312yes—
586C22×C4C23×D8312yes—
587C22×C4C23×D8312yes—
588C22×C4C23×D8311yescharacteristic
589C22×C4C23×D8311yescharacteristic
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—24no—
596C4⋊C4—3324no—
597C4⋊C4—3322no—
598C4⋊C4—3324no—
599C4⋊C4—3322no—
600C4⋊C4—1668no—
601C4⋊C4—1668no—
602C4⋊C4—1664no—
603C4⋊C4—1664no—
604C4⋊C4—1668no—
605C4⋊C4C2×C22⋊D8318yes—
606C4⋊C4C2×C22⋊D8318yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—3324no—
613C22⋊C4—3324no—
614C22⋊C4—1668no—
615C22⋊C4—1668no—
616C22⋊C4—1668no—
617C22⋊C4—1668no—
618C22⋊C4—1664no—
619C22⋊C4—1664no—
620C42—24no—
621C42—3324no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—834no—
630C23—834no—
631C23—834no—
632C23—16616no—
633C23—1668no—
634C23—1668no—
635C23—16616no—
636C23—1668no—
637C23—1662no—
638C23—1662no—
639C23—1662no—
640C23—1662no—
641C23C22×C22⋊D8312yes—
642C23#41×D8312yes—
643C23#41×D8312yes—
644C23C24×D8311yescharacteristic
645Q8—82no—
646D4—48no—
647D4—82no—
648D4—33216no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—84no—
665C2×C4—33216no—
666C2×C4—3328no—
667C2×C4—3328no—
668C2×C4—3324no—
669C2×C4—3324no—
670C2×C4—834no—
671C2×C4—16632no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1664no—
675C2×C4—1664no—
676C2×C4—1664no—
677C2×C4—1664no—
678C2×C4—1662no—
679C2×C4—1664no—
680C2×C4—1662no—
681C2×C4—1664no—
682C2×C4—1664no—
683C2×C4—1668no—
684C2×C4—1662no—
685C2×C4—1662no—
686C2×C4C22×C22⋊D8314yes—
687C2×C4C22×C22⋊D8314yes—
688C2×C4C22×C22⋊D8312yes—
689C2×C4C22×C22⋊D8312yes—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—24no—
694C22—42no—
695C22—42no—
696C22—44no—
697C22—42no—
698C22—44no—
699C22—838no—
700C22—16632no—
701C22—1664no—
702C22—1664no—
703C22—1664no—
704C22—1664no—
705C22—1664no—
706C22—1664no—
707C22#1912820814yes—
708C22C23×C22⋊D8311yescharacteristic
709C22C2×#41×D8311yescharacteristic
710C22C2×#41×D8311yescharacteristic
711C22H(5,𝔽2)×D8312yes—
712C222−1+4×D8312yes—
713C4—24no—
714C4—22no—
715C4—22no—
716C4—24no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—3322no—
721C4—3322no—
722C4—3324no—
723C4—3324no—
724C4—1664no—
725C2—24no—
726C2—82no—
727C2—1668no—
728C2C2×#1912820811yescharacteristic
729C2#539×D8312yes—
730C2#2492109411yescharacteristic
731C2#2492111111yescharacteristic
732C2#2492116812yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC2×#539×C83C2
prime radical#24915742C2
hypercenterC2×#539D83
hypocenterC83#34989
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D83C2semidirect
2. #24915752C2semidirect
3. #24915747C2semidirect
5. #24913278C2semidirect
6. #24913245C2semidirect
7. #24913207C2semidirect
8. #24911720C2semidirect
9. #24911600C2semidirect
10. #24911269C2semidirect
11. #24911195C2semidirect
12. #24910128C2semidirect
13. #24910066C2semidirect
14. C4×#14581760C2semidirect
15. C2×#539×C83C2semidirect
30. #19127640C22semidirect
31. #19127639C22semidirect
32. #19127637C22semidirect
33. #19127634C22semidirect
34. #19127632C22semidirect
35. #19127631C22semidirect
36. #19127626C22semidirect
37. #19127624C22semidirect
38. #19127620C22semidirect
39. #19127615C22semidirect
40. #19127596C22semidirect
41. #19127595C22semidirect
42. #19127587C22semidirect
43. #19127587C22semidirect
44. #19127585C22semidirect
51. #19127574C22semidirect
68. C2×#126×C83C22semidirect
69. C2×#125×C83C22semidirect
71. C2×#123×C83C22semidirect
73. C2×C22⋊Q8×C83C22semidirect
147. C2×C4⋊C4×C83D4semidirect
345. C2×D83#539semidirect
367. C2×#539D83semidirect
382. C83#34989semidirect
387. C2×#126C2×D83semidirect
388. C2×#125C2×D83semidirect
391. C2×#123C2×D83semidirect
394. C2×C22⋊Q8C2×D83semidirect
494. C2×C4⋊C4C22⋊D83semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D832
#249157522
#249157472
#249157422
#249132782
#249132452
#249132072
#249117202
#249116002
#249112692
#249111952
#249101282
#249100662
C4×#145817602
C2×#539×C832
#3498983