Finite Group Databasebeta

← #27555018

Subgroups — #27555018

Order 13568.

1992 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20280423C211yesmaximal, characteristic, complemented
2#20280402C212yesmaximal, complemented
3#20280205C211yesmaximal, characteristic, complemented
4#20279982C212yesmaximal, complemented
5#20279783C211yesmaximal, characteristic
6#20279559C212yesmaximal, complemented
7#20279529C212yesmaximal, complemented
8#20278898C212yesmaximal, complemented
9#20278868C212yesmaximal, complemented
10#20278007C211yesmaximal, characteristic, complemented
11#20278003C211yesmaximal, characteristic, complemented
12#20277960C212yesmaximal, complemented
13#20277256C212yesmaximal, complemented
14#20277254C211yesmaximal, characteristic, complemented
15#20277225C212yesmaximal, complemented
16#20277207C212yesmaximal, complemented
17#20277151C212yesmaximal, complemented
18#117×Dic53C212yesmaximal, complemented
19C53×#2609C211yesmaximal, characteristic, complemented
20C2×#13133205C2211yescharacteristic
21C2×#13133203C2212yes—
22C2×#13133189C2212yes—
23C2×#13133182C2211yescharacteristic
24C2×#13133182C2211yescharacteristic
25C2×D4×Dic53C2211yescharacteristic
26C2×#13133179C2211yescharacteristic
27C2×#13133177C2212yes—
28C2×#13133177C2212yes—
29C2×#13133176C2212yes—
30C2×#13133175C2212yes—
31C22×C4×Dic53C2212yes—
32#16810563C2211yescharacteristic
33#16810562C2211yescharacteristic
34#16810557C2212yes—
35#16810556C2212yes—
36#16810554C2211yescharacteristic
37#16810552C2212yes—
38#16810551C2212yes—
39#16810545C2212yes—
40#16810544C2211yescharacteristic
41#16810543C2212yes—
42#16810543C2211yescharacteristic
43#16810540C2212yes—
44#16810539C2212yes—
45#16810539C2212yes—
46#16810537C2211yescharacteristic
47#16810535C2212yes—
48#16810532C2212yes—
49#16810528C2211yescharacteristic
50#16810527C2212yes—
51#16810524C2211yescharacteristic
52#16810523C2212yes—
53#16810523C2212yes—
54#16810520C2212yes—
55#16810517C2212yes—
56#16810515C2212yes—
57#16810515C2212yes—
58#16810515C2212yes—
59#16810514C2212yes—
60#16810514C2212yes—
61#16810513C2212yes—
62#16810513C2212yes—
63#16810513C2212yes—
64#16810512C2212yes—
65#16810512C2212yes—
66#16810512C2212yes—
67#16810511C2212yes—
68#16810510C2212yes—
69#16810509C2212yes—
70#16810508C2212yes—
71#16810506C2212yes—
72#16810504C2212yes—
73#16810502C2212yes—
74#16810502C2212yes—
75#16810500C2212yes—
76#16810498C2212yes—
77#16810487C2212yes—
78#16810481C2212yes—
79C4⋊C4×Dic53C2212yes—
80C4⋊C4×Dic53C2212yes—
81C4⋊C4×Dic53C2212yes—
82C4⋊C4×Dic53C2212yes—
83#16810474C2212yes—
84C22⋊C4×Dic53C2212yes—
85C22⋊C4×Dic53C2212yes—
86C22⋊C4×Dic53C2212yes—
87C22⋊C4×Dic53C2212yes—
88C22⋊C4×Dic53C2212yes—
89#16810470C2212yes—
90#16810470C2212yes—
91#16810470C2212yes—
92#16810469C2212yes—
93#16810469C2212yes—
94#16810468C2211yescharacteristic
95#16810468C2211yescharacteristic
96C42×Dic53C2211yescharacteristic
97C42×Dic53C2212yes—
98C2×#117×C53C2212yes—
99C53×#398C2211yescharacteristic
100C53×#396C2212yes—
101C53×#394C2211yescharacteristic
102C53×#388C2212yes—
103C53×#387C2212yes—
104C53×#386C2212yes—
105C53×#385C2212yes—
106C53×#382C2211yescharacteristic
107C22×Dic106C2311yescharacteristic
108C22×Dic106C2311yescharacteristic
109C22×D212C2311yescharacteristic
110C22×C22⋊D53C2312yes—
111C22×C22⋊D53C2312yes—
112C23×Dic53C2312yes—
113C23×Dic53C2312yes—
114C22×C4×D53C2312yes—
115#13133205—24no—
116#13133203—28no—
117#13133189—28no—
118#13133182—42no—
119#13133182—42no—
120D4×Dic53—42no—
121#13133179—42no—
122#13133177—28no—
123#13133177—44no—
124#13133176—28no—
125#13133175—28no—
126C2×C4⋊Dic53C2312yes—
127C2×C4⋊Dic53C2312yes—
128C2×C4⋊Dic53C2312yes—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×#11719919C2312yes—
131C2×#11719919C2312yes—
132C2×#11719919C2312yes—
133C2×#11719919C2312yes—
134C2×#11719919C2311yescharacteristic
135C2×#11719919C2311yescharacteristic
136C2×#11719919C2312yes—
137C2×C22⋊Dic53C2312yes—
138C2×C22⋊Dic53C2312yes—
139C2×C22⋊Dic53C2312yes—
140C2×C22⋊Dic53C2312yes—
141C2×#11719921C2312yes—
142C2×#11719921C2312yes—
143C2×#11719921C2312yes—
144C2×#11719921C2312yes—
145C2×#11719921C2312yes—
146C2×#11719921C2312yes—
147C2×#11719921C2312yes—
148C2×#11719921C2312yes—
149C2×#11719921C2312yes—
150C2×#11719921C2312yes—
151C2×#11719921C2312yes—
152C2×C4×Dic53—28no—
153C2×C4×Dic53C2312yes—
154C2×C4×Dic53C2312yes—
155C2×C4×Dic53C2312yes—
156C2×C4×Dic53C2312yes—
157C2×C4×Dic53C2312yes—
158C2×C4×Dic53C2312yes—
159C2×C4×Dic53C2312yes—
160C2×C4×Dic53C2312yes—
161C2×C4×Dic53C2311yescharacteristic
162C2×C4×Dic53C2311yescharacteristic
163C2×C4×Dic53C2311yescharacteristic
164C2×C4×Dic53C2312yes—
165C2×C4×Dic53C2311yescharacteristic
166C2×C4×Dic53C2312yes—
167#13133124C2312yes—
168#13133124C2312yes—
169#13133124C2311yescharacteristic
170#13133124C2312yes—
171#13133124C2312yes—
172#13133124C2312yes—
173#13133124C2312yes—
174#13133124C2312yes—
175#13133124C2311yescharacteristic
176#13133124C2312yes—
177#13133124C2312yes—
178#13133124C2312yes—
179#13133124C2312yes—
180#13133124C2312yes—
181#13133124C2312yes—
182#13133124C2312yes—
183#13133124C2312yes—
184#13133124C2312yes—
185C22×D4×C53C2311yescharacteristic
186C23×C4×C53C2312yes—
187#117×C53—28no—
188C2×C4⋊C4×C53C2312yes—
189C2×C4⋊C4×C53C2312yes—
190C2×C4⋊C4×C53C2312yes—
191C2×C4⋊C4×C53C2311yescharacteristic
192C2×C4⋊C4×C53C2311yescharacteristic
193C2×C4⋊C4×C53C2311yescharacteristic
194C2×C22⋊C4×C53C2312yes—
195C2×C22⋊C4×C53C2312yes—
196C2×C22⋊C4×C53C2312yes—
197C2×C22⋊C4×C53C2312yes—
198C2×C22⋊C4×C53C2312yes—
199C2×C42×C53C2312yes—
200C2×C42×C53C2311yescharacteristic
201#95×C53C2312yes—
202#95×C53C2312yes—
203#95×C53C2312yes—
204#95×C53C2311yescharacteristic
205#95×C53C2311yescharacteristic
206#95×C53C2312yes—
207C24×C53C2412yes—
208C23×D53C2412yes—
209C2×D4×C53—24no—
210C2×D4×C53—41no—
211C22×C4×C53—24no—
212C22×C4×C53—24no—
213C22×C4×C53—24no—
214C22×C4×C53C2411yescharacteristic
215C22×C4×C53C2411yescharacteristic
216C22×C4×C53C2412yes—
217C22×C4×C53C2412yes—
218C22×C4×C53C2412yes—
219C22×C4×C53C2412yes—
220C22×C4×C53C2412yes—
221C22×C4×C53C2411yescharacteristic
222C2×C22⋊D53—24no—
223C2×C22⋊D53—24no—
224C2×C22⋊D53—24no—
225C2×C22⋊D53—24no—
226C2×C22⋊D53—42no—
227C2×C22⋊D53—42no—
228C22×Dic53—24no—
229C22×Dic53—24no—
230C22×Dic53—24no—
231C22×Dic53—24no—
232C22×Dic53—24no—
233C22×Dic53—42no—
234C22×Dic53C2412yes—
235C22×Dic53C2412yes—
236C22×Dic53C2411yescharacteristic
237C22×Dic53C2411yescharacteristic
238C22×Dic53C2411yescharacteristic
239C22×Dic53C2412yes—
240C22×Dic53C2412yes—
241C22×Dic53C2412yes—
242C22×Dic53C2411yescharacteristic
243C2×D212—22no—
244C2×D212—41no—
245C2×D212—41no—
246C2×C4×D53—24no—
247C2×C4×D53—24no—
248C2×C4×D53—24no—
249C2×Dic106—22no—
250C2×Dic106—24no—
251C2×Dic106—41no—
252C2×Dic106—41no—
253C2×Dic106—41no—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—24no—
256C4⋊C4×C53—24no—
257C4⋊C4×C53—41no—
258C4⋊C4×C53—41no—
259C4⋊C4×C53—41no—
260C22⋊C4×C53—24no—
261C22⋊C4×C53—24no—
262C22⋊C4×C53—24no—
263C22⋊C4×C53—24no—
264C22⋊C4×C53—42no—
265C42×C53—24no—
266C42×C53#4114yes—
267C22⋊Dic53—24no—
268C22⋊Dic53—42no—
269C22⋊Dic53—42no—
270C22⋊Dic53#4118yes—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277#11719921—24no—
278#11719921—24no—
279#11719921—42no—
280#11719921—42no—
281#11719921—42no—
282C4⋊Dic53—24no—
283C4⋊Dic53—24no—
284C4⋊Dic53—24no—
285C4⋊Dic53—41no—
286#11719919—24no—
287#11719919—24no—
288#11719919—42no—
289#11719919—42no—
290#11719919—42no—
291#11719919—41no—
292#11719919—41no—
293C4×Dic53—24no—
294C4×Dic53—24no—
295C4×Dic53—24no—
296C4×Dic53—24no—
297C4×Dic53—24no—
298C4×Dic53—24no—
299C4×Dic53—24no—
300C4×Dic53—24no—
301C4×Dic53—22no—
302C4×Dic53—22no—
303C4×Dic53—22no—
304C4×Dic53—41no—
305C4×Dic53—42no—
306C4×Dic53#4118yes—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53C2×#4114yes—
314C23×C53C2511yescharacteristic
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322D4×C53—44no—
323C2×C4×C53—216no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—21no—
339C2×C4×C53—22no—
340C2×C4×C53—21no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53C2×#4114yes—
344C2×C4×C53C2×#4112yes—
345C2×C4×C53C2×#4114yes—
346C22⋊D53—48no—
347C22⋊D53—48no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—21no—
355C2×Dic53—21no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—21no—
362C2×Dic53—21no—
363C2×Dic53—22no—
364C2×Dic53—21no—
365C2×Dic53—21no—
366C2×Dic53—21no—
367C2×Dic53—22no—
368C2×Dic53—48no—
369C2×Dic53—48no—
370C2×Dic53C2×#4114yes—
371C2×Dic53C2×#4114yes—
372C2×Dic53C2×#4114yes—
373C2×Dic53C2×#4114yes—
374C2×Dic53H(5,𝔽2)12yes—
375D212—44no—
376C4×D53—48no—
377Dic106—44no—
378Dic106—44no—
379#34874—531nomaximal, Sylow
380C22×C53—24no—
381C22×C53—24no—
382C22×C53—24no—
383C22×C53—42no—
384C22×C53—42no—
385C22×C53—42no—
386C22×C53—42no—
387C22×C53C22×#4112yes—
388C22×C53C22×#4112yes—
389C22×C53C22×#4111yescharacteristic
390C22×C53C2×H(5,𝔽2)11yescharacteristic
391C22×C53#58511yescharacteristic
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—42no—
399C4×C53—24no—
400C4×C53—24no—
401C4×C53—22no—
402C4×C53—42no—
403C4×C53—42no—
404C4×C53—42no—
405C4×C53—41no—
406C4×C53—41no—
407Dic53—24no—
408Dic53—24no—
409Dic53—24no—
410Dic53—41no—
411Dic53—41no—
412Dic53—42no—
413Dic53—42no—
414Dic53—41no—
415Dic53#55514yes—
416#2612—531no—
417#2610—532no—
418#2609D5311yescharacteristic, complemented
419#2593—531no—
420#2574—532no—
421#2555—531no—
422#2531—532no—
423#2529—532no—
424#2476—532no—
425#2474—532no—
426#2399—531no—
427#2398—531no—
428#2392—532no—
429C4×#124—532no—
430C4×#124—531no—
431C4×#121—532no—
432#2298—532no—
433#2290—532no—
434C4×#117—532no—
435C2×C53—44no—
436C2×C53#344412yes—
437C2×C53#346011yescharacteristic
438C2×C53C2×#55511yescharacteristic
439C2×C53#347512yes—
440C2×C53#348111yescharacteristic
441D53—82no—
442C2×#124—532no—
443C2×#124—531no—
444C2×#121—532no—
445C2×C4×Q8—531no—
446C2×C4×Q8—531no—
447C2×C4×D4—531no—
448C2×C4×D4—531no—
449C2×C4×D4—532no—
450C2×C4×D4—532no—
451C2×#117—532no—
452C2×#117—532no—
453C2×#117C2×D5312yes—
454C22×C42—532no—
455#400—531no—
456#400—531no—
457#398—532no—
458#398—531no—
459#398—532no—
460#398C2×D5311yescharacteristic
461#397—532no—
462#397—532no—
463#396—532no—
464#396C2×D5312yes—
465#395—532no—
466#395—531no—
467#395—531no—
468#394—531no—
469#394—532no—
470#394—532no—
471#394—532no—
472#394C2×D5311yescharacteristic
473#393—532no—
474#392—532no—
475#391—531no—
476#391—532no—
477#390—531no—
478#390—532no—
479#390—532no—
480#389—532no—
481#388—532no—
482#388—532no—
483#388—532no—
484#388—532no—
485#388—532no—
486#388—532no—
487#388—532no—
488#388—532no—
489#388—532no—
490#388—532no—
491#388—532no—
492#388—532no—
493#388—532no—
494#388C2×D5312yes—
495#387—532no—
496#387—532no—
497#387—532no—
498#387—532no—
499#387—532no—
500#387C2×D5312yes—
501#386—532no—
502#386—532no—
503#386—532no—
504#386C2×D5312yes—
505#385—532no—
506#385C2×D5312yes—
507#382—532no—
508#382C2×D5311yescharacteristic
509#380—532no—
510C4×C4⋊C4—532no—
511C4×C4⋊C4—532no—
512C4×C4⋊C4—532no—
513C4×C4⋊C4—532no—
514C4×C4⋊C4—532no—
515C4×C22⋊C4—532no—
516C4×C22⋊C4—532no—
517C4×C22⋊C4—532no—
518C4×C22⋊C4—532no—
519C4×C22⋊C4—532no—
520C4×C22⋊C4—532no—
521C4×C22⋊C4—532no—
522C4×C22⋊C4—532no—
523#376—532no—
524#376—532no—
525#376—531no—
526#376—531no—
527C43—531no—
528C43—532no—
529C53#3487411yescharacteristic, complemented, Sylow
530C22×Q8—531no—
531C22×Q8—531no—
532C22×D4—532no—
533C22×D4—532no—
534C22×D4—531no—
535C22×D4C22×D5311yescharacteristic
536C23×C4—532no—
537C23×C4—532no—
538C23×C4—532no—
539C23×C4C22×D5312yes—
540#124—1068no—
541#124—1064no—
542#121—1068no—
543C4×Q8—2122no—
544C4×Q8—2122no—
545C4×D4—1068no—
546C4×D4—2124no—
547C4×D4—2122no—
548C4×D4—2122no—
549#117—28no—
550#117—1068no—
551#117—1068no—
552C2×C4⋊C4—532no—
553C2×C4⋊C4—532no—
554C2×C4⋊C4—532no—
555C2×C4⋊C4—532no—
556C2×C4⋊C4—532no—
557C2×C4⋊C4—532no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—532no—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—532no—
563C2×C4⋊C4C22×D5312yes—
564C2×C4⋊C4C22×D5312yes—
565C2×C4⋊C4C22×D5312yes—
566C2×C4⋊C4C22×D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C4⋊C4C22×D5311yescharacteristic
569C2×C22⋊C4—532no—
570C2×C22⋊C4—532no—
571C2×C22⋊C4—532no—
572C2×C22⋊C4—532no—
573C2×C22⋊C4—532no—
574C2×C22⋊C4—532no—
575C2×C22⋊C4—532no—
576C2×C22⋊C4—532no—
577C2×C22⋊C4—532no—
578C2×C22⋊C4—532no—
579C2×C22⋊C4—532no—
580C2×C22⋊C4—532no—
581C2×C22⋊C4—532no—
582C2×C22⋊C4—532no—
583C2×C22⋊C4—532no—
584C2×C22⋊C4C22×D5312yes—
585C2×C22⋊C4C22×D5312yes—
586C2×C22⋊C4C22×D5312yes—
587C2×C22⋊C4C22×D5312yes—
588C2×C22⋊C4C22×D5312yes—
589C2×C42—532no—
590C2×C42—532no—
591C2×C42—532no—
592C2×C42—532no—
593C2×C42—532no—
594C2×C42—531no—
595C2×C42—531no—
596C2×C42—531no—
597C2×C42—532no—
598C2×C42—532no—
599C2×C42—532no—
600C2×C42—532no—
601C2×C42—531no—
602C2×C42—532no—
603C2×C42—1068no—
604C2×C42C22×D5312yes—
605C2×C42C22×D5311yescharacteristic
606#95—532no—
607#95—532no—
608#95—532no—
609#95—532no—
610#95—532no—
611#95—532no—
612#95—532no—
613#95—532no—
614#95—532no—
615#95—531no—
616#95—532no—
617#95—531no—
618#95—532no—
619#95—532no—
620#95—532no—
621#95—532no—
622#95—532no—
623#95—532no—
624#95C22×D5311yescharacteristic
625#95C22×D5311yescharacteristic
626#95C22×D5312yes—
627#95C22×D5312yes—
628#95C22×D5312yes—
629#95C22×D5312yes—
630C24—532no—
631C24C23×D5312yes—
632C2×Q8—1064no—
633C2×Q8—1062no—
634C2×Q8—2121no—
635C2×Q8—2121no—
636C2×Q8—2121no—
637C2×D4—24no—
638C2×D4—41no—
639C2×D4—1064no—
640C2×D4—1064no—
641C2×D4—1064no—
642C2×D4—1064no—
643C2×D4—1062no—
644C2×D4—2121no—
645C2×D4—2121no—
646C2×D4—2122no—
647C2×D4—2122no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—531no—
652C22×C4—532no—
653C22×C4—532no—
654C22×C4—532no—
655C22×C4—532no—
656C22×C4—532no—
657C22×C4—531no—
658C22×C4—531no—
659C22×C4—531no—
660C22×C4—1064no—
661C22×C4—1064no—
662C22×C4—1064no—
663C22×C4—1064no—
664C22×C4—1064no—
665C22×C4—1064no—
666C22×C4—1064no—
667C22×C4—1064no—
668C22×C4—2122no—
669C22×C4C23×D5312yes—
670C22×C4C23×D5311yescharacteristic
671C22×C4C23×D5312yes—
672C22×C4C23×D5312yes—
673C22×C4C23×D5311yescharacteristic
674C22×C4C23×D5312yes—
675C22×C4C23×D5311yescharacteristic
676C22×C4C23×D5312yes—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—41no—
683C4⋊C4—1064no—
684C4⋊C4—1064no—
685C4⋊C4—1064no—
686C4⋊C4—1064no—
687C4⋊C4—1064no—
688C4⋊C4—2122no—
689C4⋊C4—2121no—
690C4⋊C4—2122no—
691C4⋊C4—2121no—
692C4⋊C4—2121no—
693C4⋊C4—2122no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—42no—
699C22⋊C4—538no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C22⋊C4—1064no—
706C22⋊C4—1064no—
707C22⋊C4—1064no—
708C22⋊C4—1064no—
709C22⋊C4—2122no—
710C22⋊C4—2122no—
711C22⋊C4—2122no—
712C22⋊C4—2122no—
713C22⋊C4—2122no—
714C42—24no—
715C42—538no—
716C42—1064no—
717C42—1064no—
718C42—1064no—
719C42—1064no—
720C42—1064no—
721C42—1062no—
722C42—1064no—
723C42—1062no—
724C42—1062no—
725C42—1064no—
726C42—1064no—
727C42—2121no—
728C42—2122no—
729C42#1171994714yes—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—1062no—
737C23—1062no—
738C23—1062no—
739C23—1062no—
740C23—1062no—
741C23—1062no—
742C23—1062no—
743C23#41×D5314yes—
744C23C24×D5311yescharacteristic
745Q8—2124no—
746Q8—2124no—
747D4—44no—
748D4—2124no—
749D4—2128no—
750D4—2128no—
751C2×C4—216no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—534no—
772C2×C4—532no—
773C2×C4—534no—
774C2×C4—534no—
775C2×C4—534no—
776C2×C4—1062no—
777C2×C4—1062no—
778C2×C4—1062no—
779C2×C4—1062no—
780C2×C4—1062no—
781C2×C4—1062no—
782C2×C4—1062no—
783C2×C4—1062no—
784C2×C4—1062no—
785C2×C4—1062no—
786C2×C4—1062no—
787C2×C4—1061no—
788C2×C4—1061no—
789C2×C4—1061no—
790C2×C4—1061no—
791C2×C4—1061no—
792C2×C4—1062no—
793C2×C4—1062no—
794C2×C4—1061no—
795C2×C4—1061no—
796C2×C4—2128no—
797C2×C4—2128no—
798C2×C4—2128no—
799C2×C4#41×D5314yes—
800C2×C4C2×#1171994714yes—
801C2×C4C2×#1171994712yes—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—2122no—
810C22—2122no—
811C22—2122no—
812C22—2122no—
813C22—2122no—
814C22—2122no—
815C22—2122no—
816C22C2×#41×D5312yes—
817C22C2×#41×D5312yes—
818C22C22×#1171994711yescharacteristic
819C22H(5,𝔽2)×D5311yescharacteristic
820C22#1681146011yescharacteristic
821C4—24no—
822C4—24no—
823C4—22no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—534no—
830C4—1064no—
831C4—1064no—
832C4—1064no—
833C4—2122no—
834C4—2121no—
835C4—2121no—
836C4—2121no—
837C4—2122no—
838C2—44no—
839C2—4242no—
840C2#2028800712yes—
841C2#2028813211yescharacteristic
842C2#555×D5311yescharacteristic
843C2#2028826812yes—
844C2#2028831811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
FittingC53×#2609C2
prime radical#20279783C2
hypercenter#2609D53
hypocenterC53#34874
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2609

Complements

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

NH ≅ G/Ntype
1. #20280423C2semidirect
2. #20280402C2semidirect
3. #20280205C2semidirect
4. #20279982C2semidirect
6. #20279559C2semidirect
7. #20279529C2semidirect
8. #20278898C2semidirect
9. #20278868C2semidirect
10. #20278007C2semidirect
11. #20278003C2semidirect
12. #20277960C2semidirect
13. #20277256C2semidirect
14. #20277254C2semidirect
15. #20277225C2semidirect
16. #20277207C2semidirect
17. #20277151C2semidirect
18. #117×Dic53C2semidirect
19. C53×#2609C2semidirect
418. #2609D53semidirect
529. C53#34874semidirect

Maximal subgroups

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

subgroupindex
#202804232
#202804022
#202802052
#202799822
#202797832
#202795592
#202795292
#202788982
#202788682
#202780072
#202780032
#202779602
#202772562
#202772542
#202772252
#202772072
#202771512
#117×Dic532
C53×#26092
#3487453