Finite Group Databasebeta

← #28248596

Subgroups — #28248596

Order 13568.

2050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288007C211yesmaximal, characteristic
2#20283685C214yesmaximal, complemented
3#20283683C214yesmaximal, complemented
4#20283675C214yesmaximal, complemented
5C8×#11719947C214yesmaximal, complemented
6#20283648C211yesmaximal, characteristic, complemented
7#20283647C211yesmaximal, characteristic, complemented
8#20283425C211yesmaximal, characteristic, complemented
9#20283423C211yesmaximal, characteristic, complemented
10#20283410C211yesmaximal, characteristic, complemented
11#20283409C211yesmaximal, characteristic, complemented
12#20283405C211yesmaximal, characteristic, complemented
13#20283358C211yesmaximal, characteristic, complemented
14#20283355C211yesmaximal, characteristic, complemented
15#20283344C211yesmaximal, characteristic, complemented
16#20283137C211yesmaximal, characteristic, complemented
17#131×Dic53C211yesmaximal, characteristic, complemented
18C22×C8×Dic53C211yesmaximal, characteristic, complemented
19C53×#2929C211yesmaximal, characteristic, complemented
20C2×#13133225C2211yescharacteristic
21C2×#13133224C2211yescharacteristic
22C2×#13133223C2211yescharacteristic
23C23×#88322C2211yescharacteristic
24#16811176C2211yescharacteristic
25#16811175C412yes—
26#16811169C2211yescharacteristic
27#16811168C412yes—
28#16811159C412yes—
29#16811154C412yes—
30#16811153C2214yes—
31#16811150C414yes—
32#16811134C2211yescharacteristic
33#16811129C414yes—
34#41×Dic53C2211yescharacteristic
35#16811091C2211yescharacteristic
36C4×#11719947C2214yes—
37C22×C4×Dic53C2211yescharacteristic
38#16810752C2214yescomplemented
39#16810751C2214yescomplemented
40C8×Dic106C2214yescomplemented
41#16810747C2214yescomplemented
42#16810699C2214yescomplemented
43#16810698C2214yescomplemented
44#16810695C2214yes—
45#16810694C2214yes—
46#16810691C2214yes—
47D4×#88322C2214yes—
48C8×C22⋊D53C2214yes—
49C8×C22⋊D53C2214yescomplemented
50#16810686C2214yes—
51#16810686C2214yescomplemented
52#16810683C2214yescomplemented
53#16810681C2214yescomplemented
54#16810677C2214yes—
55#16810675C2214yescomplemented
56#16810673C2214yes—
57#16810673C2214yescomplemented
58#16810651C2211yescharacteristic
59#16810650C2211yescharacteristic
60#16810649C2211yescharacteristic
61#16810646C2211yescharacteristic
62#16810646C2211yescharacteristic
63#16810591C2211yescharacteristic
64#16810590C2211yescharacteristic
65#16810589C2211yescharacteristic
66#16810587C2211yescharacteristic
67#16810581C2211yescharacteristic
68#16810581C2212yescomplemented
69#16810580C2212yescomplemented
70#16810579C2211yescharacteristic
71#16810578C2211yescharacteristic
72#16810578C2212yescomplemented
73#16810577C2212yescomplemented
74#16810575C2212yescomplemented
75M16×Dic53C2211yescharacteristic
76M16×Dic53C2211yescharacteristic
77M16×Dic53C2212yescomplemented
78C2×C8×Dic53C2211yescharacteristic
79C2×C8×Dic53C2211yescharacteristic
80C2×C8×Dic53C2212yes—
81C2×C8×Dic53C2212yes—
82C2×C8×Dic53C2211yescharacteristic
83C2×C8×Dic53C2212yes—
84C2×C8×Dic53C2212yes—
85C2×C8×Dic53C2211yescharacteristic
86C2×C8×Dic53C2212yescomplemented
87C4×C8×D53C2212yescomplemented
88C2×#131×C53C2211yescharacteristic
89C23×C8×C53C2211yescharacteristic
90C53×#525C2211yescharacteristic
91C53×#435C2214yes—
92C8×D4×C53C2214yes—
93C53×#424C2211yescharacteristic
94C53×#408C2211yescharacteristic
95C53×#407C2211yescharacteristic
96C53×#405C2211yescharacteristic
97C2×#11719945C2311yescharacteristic
98C2×#11719947C2×C414yes—
99C23×Dic53C2×C412yes—
100#13133225—24no—
101#13133224—24no—
102#13133223—24no—
103C2×#11719917C2311yescharacteristic
104C2×#11719917C2311yescharacteristic
105C2×#11719917C2312yes—
106C2×#11719912C2312yes—
107C2×#11719912C2312yes—
108C22×#88322—24no—
109C22×#88322C2311yescharacteristic
110C22×#88322C2312yes—
111C22×#88322C2312yes—
112C22×#88322C2312yes—
113C22×#88322C2311yescharacteristic
114C2×C8×D53C2312yes—
115C2×C8×D53C2312yes—
116#13133216C2×C412yes—
117#13133215C2×C411yescharacteristic
118#13133213C2×C411yescharacteristic
119#13133212C2×C414yes—
120#13133210C2×C414yes—
121#13133208C2×C412yes—
122#13133207C2×C414yes—
123#13133206C2×C411yescharacteristic
124#13133204C2×C411yescharacteristic
125#13133203C2×C414yes—
126#13133201C2×C414yes—
127#13133200C2×C412yes—
128#13133198C2×C414yes—
129#13133196C2×C412yes—
130#13133194C2×C414yes—
131#13133194C2×C414yes—
132#13133191C2×C412yes—
133#13133189C2×C414yes—
134#13133189C2×C414yes—
135#13133186C2×C412yes—
136Q8×Dic53C2×C412yes—
137C4×Dic106C2314yes—
138#13133182C2×C414yes—
139#13133182C2×C412yes—
140D4×Dic53C2×C414yes—
141D4×Dic53C2×C414yes—
142D4×Dic53C2×C412yes—
143#13133179C2×C412yes—
144C4×C22⋊D53C2314yes—
145C4×C22⋊D53C2314yes—
146#13133177C2×C414yes—
147#13133177C2×C414yes—
148#13133177C2×C414yes—
149#13133176C2311yescharacteristic
150#13133176C2312yes—
151#13133175C2×C414yes—
152#13133174C2312yes—
153#13133173C2×C414yes—
154#13133173C2×C414yes—
155C2×C4×Dic53C2×C412yes—
156C2×C4×Dic53C2×C412yes—
157C2×C4×Dic53C2×C412yes—
158C2×C4×Dic53C2311yescharacteristic
159C2×C4×Dic53C2312yes—
160C2×C4×Dic53C2312yes—
161C2×C4×Dic53C2311yescharacteristic
162C2×C4×Dic53C2312yes—
163C42×D53C2312yes—
164C4⋊#88322C2314yes—
165#13133146C2314yes—
166#13133146C2314yes—
167#13133146C2314yes—
168#13133146C2314yes—
169C22⋊#88322C2314yes—
170C22⋊#88322C2314yes—
171#13133129C2314yes—
172#13133129C2314yes—
173#13133128C2312yes—
174#13133127C2312yes—
175#13133127C2312yes—
176#13133127C2312yes—
177#13133127C2312yes—
178C4×#88322C2312yes—
179C8×Dic53C2312yes—
180C8×Dic53C2311yescharacteristic
181C8×Dic53C2312yes—
182C8×Dic53C2311yescharacteristic
183C8×Dic53C2311yescharacteristic
184C8×Dic53C2311yescharacteristic
185C8×Dic53C2312yes—
186C8×Dic53C2312yes—
187C8×Dic53C2312yes—
188C8×Dic53C2312yes—
189C8×Dic53C2312yes—
190C8×Dic53C2312yes—
191C8×Dic53C2312yes—
192C8×Dic53C2312yes—
193C2×#41×C53C2311yescharacteristic
194C23×C4×C53C2311yescharacteristic
195#131×C53—24no—
196C2×M16×C53C2311yescharacteristic
197C2×M16×C53C2311yescharacteristic
198C2×M16×C53C2312yes—
199C22×C8×C53—24no—
200C22×C8×C53C2311yescharacteristic
201C22×C8×C53C2312yes—
202C22×C8×C53C2312yes—
203C22×C8×C53C2312yes—
204C22×C8×C53C2311yescharacteristic
205#123×C53C2×C412yes—
206C22⋊Q8×C53C2×C412yes—
207#121×C53C2×C412yes—
208#120×C53C2×C412yes—
209C4×D4×C53C2314yes—
210#117×C53C2311yescharacteristic
211C4⋊C8×C53C2314yes—
212C22⋊C8×C53C2314yes—
213C22⋊C8×C53C2314yes—
214#97×C53C2312yes—
215C4×C8×C53C2312yes—
216C24×C53C22×C411yescharacteristic
217#41×C53—22no—
218#41×C53—22no—
219C2×Q8×C53C22×C411yescharacteristic
220C2×D4×C53C22×C414yes—
221C2×D4×C53C22×C412yes—
222C2×D4×C53C22×C411yescharacteristic
223C22×C4×C53—22no—
224C22×C4×C53—22no—
225C22×C4×C53C22×C412yes—
226C22×C4×C53C22×C411yescharacteristic
227C22×C4×C53C2412yes—
228C22×C4×C53C2412yes—
229C22×C4×C53C2411yescharacteristic
230C2×C22⋊D53C22×C412yes—
231C2×C22⋊D53C22×C414yes—
232C2×C22⋊D53C22×C414yes—
233C22×Dic53—28no—
234C22×Dic53C22×C412yes—
235C22×Dic53C22×C412yes—
236C22×Dic53C22×C412yes—
237C22×Dic53C22×C412yes—
238C22×Dic53C22×C412yes—
239C22×Dic53C22×C414yes—
240C22×Dic53C22×C412yes—
241#11719947—216no—
242#11719945—22no—
243#11719945—22no—
244C2×D212C22×C411yescharacteristic
245C2×C4×D53C22×C414yes—
246C2×C4×D53C2412yes—
247C2×Dic106C22×C411yescharacteristic
248C2×Dic106C22×C414yes—
249M16×C53—22no—
250M16×C53—22no—
251M16×C53—24no—
252C2×C8×C53—22no—
253C2×C8×C53—24no—
254C2×C8×C53—24no—
255C2×C8×C53—24no—
256C2×C8×C53#4114yescomplemented
257C2×C8×C53C2412yes—
258C2×C8×C53C2412yes—
259C2×C8×C53C2412yes—
260C2×C8×C53C2411yescharacteristic
261C2×C8×C53C2411yescharacteristic
262C4⋊C4×C53C22×C412yes—
263C4⋊C4×C53C22×C414yes—
264C22⋊C4×C53C22×C412yes—
265C22⋊C4×C53C22×C414yes—
266C22⋊C4×C53C22×C414yes—
267C42×C53C2412yes—
268C22⋊Dic53C22×C414yes—
269C22⋊Dic53C22×C414yes—
270C22⋊Dic53C22×C412yes—
271C22⋊Dic53C22×C414yes—
272#11719921C22×C414yes—
273#11719921C22×C414yes—
274#11719921C22×C414yes—
275C4⋊Dic53C22×C414yes—
276C4⋊Dic53C22×C412yes—
277C4⋊Dic53C22×C414yes—
278#11719919C22×C414yes—
279#11719919C22×C414yes—
280#11719919C22×C414yes—
281#11719919C22×C414yes—
282#11719919C22×C414yes—
283C4×Dic53C22×C414yes—
284C4×Dic53C22×C412yes—
285C4×Dic53C22×C412yes—
286C4×Dic53C22×C412yes—
287C4×Dic53C22×C412yes—
288C4×Dic53C22×C411yescharacteristic
289C4×Dic53C22×C412yes—
290C4×Dic53C22×C411yescharacteristic
291C4×Dic53C22×C414yes—
292C4×Dic53C2411yescharacteristic
293C4×Dic53C2411yescharacteristic
294C4×Dic53C2412yes—
295C4×Dic53C2412yes—
296#11719917—22no—
297#11719917—22no—
298#11719917—24no—
299C2×#88322—22no—
300C2×#88322—24no—
301C2×#88322—24no—
302C2×#88322—24no—
303C2×#88322#4114yescomplemented
304C2×#88322C2412yes—
305C2×#88322C2412yes—
306C2×#88322C2412yes—
307C2×#88322C2411yescharacteristic
308C2×#88322C2411yescharacteristic
309#11719912—24no—
310#11719912—24no—
311C8×D53—24no—
312C8×D53—24no—
313C23×C53—22no—
314C23×C53—24no—
315C23×C53C23×C412yes—
316C23×C53C23×C411yescharacteristic
317C23×C53C23×C412yes—
318C22×D53C23×C412yes—
319Q8×C53—22no—
320D4×C53—24no—
321D4×C53—28no—
322D4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—24no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53C23×C414yes—
330C2×C4×C53C23×C412yes—
331C2×C4×C53C23×C412yes—
332C2×C4×C53C23×C411yescharacteristic
333C2×C4×C53C2×#4112yes—
334C2×C4×C53C2×#4112yes—
335C2×C4×C53C2511yescharacteristic
336C22⋊D53—24no—
337C22⋊D53—28no—
338C22⋊D53—28no—
339C2×Dic53—24no—
340C2×Dic53—28no—
341C2×Dic53—24no—
342C2×Dic53—24no—
343C2×Dic53—24no—
344C2×Dic53—24no—
345C2×Dic53#13118yescomplemented
346C2×Dic53C23×C412yes—
347C2×Dic53C23×C414yes—
348C2×Dic53C23×C412yes—
349C2×Dic53C23×C412yes—
350C2×Dic53C23×C412yes—
351C2×Dic53C23×C412yes—
352D212—22no—
353C4×D53—22no—
354C4×D53—22no—
355C4×D53—28no—
356Dic106—22no—
357Dic106—28no—
358C8×C53—22no—
359C8×C53—22no—
360C8×C53—22no—
361C8×C53C2×#4112yes—
362C8×C53C2×#4112yes—
363#88322—22no—
364#88322—22no—
365#88322—22no—
366#88322C2×#4112yes—
367#88322C2×#4112yes—
368#60204—531nomaximal, Sylow
369C22×C53—28no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—24no—
375C22×C53C4×#4112yes—
376C22×C53C2×#13114yes—
377C22×C53C24×C411yescharacteristic
378C2×D53—22no—
379C2×D53—24no—
380C4×C53—22no—
381C4×C53—22no—
382C4×C53—24no—
383C4×C53C4×#4112yes—
384C4×C53C22×#4111yescharacteristic
385C4×C53C22×#4111yescharacteristic
386Dic53—22no—
387Dic53—24no—
388Dic53—22no—
389Dic53—22no—
390Dic53C2×#13114yes—
391Dic53C2×#13114yes—
392#3444—531no—
393#2966—534no—
394#2966—534no—
395#2965—534no—
396C8×#41—534no—
397#2960—531no—
398#2960—531no—
399#2931—531no—
400#2931—531no—
401#2929—531no—
402#2929—531no—
403#2929—531no—
404#2929D5311yescharacteristic, complemented
405#2922—531no—
406#2922—531no—
407#2920—531no—
408C4×#131—531no—
409C4×#131—531no—
410C22×C4×C8—531no—
411C2×C53—22no—
412C2×C53—24no—
413C2×C53—42no—
414C2×C53C2×C4×#4111yescharacteristic
415C2×C53C22×#13112yes—
416D53—42no—
417C2×#131—531no—
418C2×#131—531no—
419C2×#131—531no—
420C2×#131C2×D5311yescharacteristic
421C23×C8—531no—
422C23×C8C2×D5311yescharacteristic
423#533—532no—
424#533—531no—
425#532—531no—
426#532—532no—
427#529—534no—
428#529—532no—
429#529—532no—
430#529—534no—
431#525—531no—
432#525—534no—
433#525C2×D5311yescharacteristic
434C4×#41—531no—
435C4×#41—534no—
436C4×#41—531no—
437C22×C42—531no—
438#446—534no—
439#446—534no—
440C8×Q8—534no—
441C8×Q8—534no—
442#436—534no—
443#436—534no—
444#435—534no—
445#435—534no—
446#435—534no—
447#435C2×D5314yes—
448C8×D4—534no—
449C8×D4—534no—
450C8×D4—534no—
451C8×D4—534no—
452C8×D4—534no—
453C8×D4C2×D5314yes—
454#433—534no—
455#433—534no—
456#432—534no—
457#431—534no—
458#431—534no—
459#431—534no—
460#424—531no—
461#424—531no—
462#424—531no—
463#424C2×D5311yescharacteristic
464#423—531no—
465#423—531no—
466#408—531no—
467#408—531no—
468#408—531no—
469#408C2×D5311yescharacteristic
470#407—531no—
471#407C2×D5311yescharacteristic
472#405—531no—
473#405—532no—
474#405—531no—
475#405—532no—
476#405—531no—
477#405—532no—
478#405—532no—
479#405C2×D5311yescharacteristic
480C4×M16—531no—
481C4×M16—531no—
482C4×M16—532no—
483C4×M16—532no—
484C2×C4×C8—531no—
485C2×C4×C8—531no—
486C2×C4×C8—531no—
487C2×C4×C8—531no—
488C2×C4×C8—532no—
489C2×C4×C8—532no—
490C2×C4×C8—532no—
491C2×C4×C8—532no—
492C2×C4×C8—532no—
493C2×C4×C8—532no—
494C53#6020411yescharacteristic, complemented, Sylow
495C2×#41—534no—
496C2×#41—531no—
497C2×#41C22×D5311yescharacteristic
498C23×C4—532no—
499C23×C4C22×D5311yescharacteristic
500#131—24no—
501#131—1064no—
502#131—1064no—
503#131—1064no—
504C2×M16—531no—
505C2×M16—531no—
506C2×M16—532no—
507C2×M16—532no—
508C2×M16—532no—
509C2×M16C22×D5311yescharacteristic
510C2×M16C22×D5311yescharacteristic
511C2×M16C22×D5312yes—
512C22×C8—24no—
513C22×C8—531no—
514C22×C8—531no—
515C22×C8—532no—
516C22×C8—532no—
517C22×C8—532no—
518C22×C8—532no—
519C22×C8—532no—
520C22×C8—1064no—
521C22×C8C22×D5311yescharacteristic
522C22×C8C22×D5312yes—
523C22×C8C22×D5312yes—
524C22×C8C22×D5312yes—
525C22×C8C22×D5311yescharacteristic
526C4⋊Q8—531no—
527C4⋊Q8—532no—
528#127—531no—
529#126—534no—
530#126—534no—
531#125—534no—
532#125—532no—
533#124—531no—
534#124—531no—
535#124—534no—
536#123—534no—
537#123—532no—
538#123—534no—
539#123C4×D5312yes—
540C22⋊Q8—532no—
541C22⋊Q8—534no—
542C22⋊Q8—534no—
543C22⋊Q8C4×D5312yes—
544#121—534no—
545#121—534no—
546#121—532no—
547#121C4×D5312yes—
548#120—532no—
549#120C4×D5312yes—
550C4×Q8—532no—
551C4×Q8—534no—
552C4×Q8—532no—
553C4×Q8—534no—
554C4×D4—534no—
555C4×D4—534no—
556C4×D4—532no—
557C4×D4—534no—
558C4×D4—534no—
559C4×D4—532no—
560C4×D4—534no—
561C4×D4—534no—
562C4×D4—534no—
563C4×D4C22×D5314yes—
564#117—531no—
565#117—532no—
566#117—534no—
567#117—534no—
568#117—534no—
569#117—532no—
570#117C22×D5311yescharacteristic
571C2×C42—532no—
572C2×C42—532no—
573C2×C42—532no—
574C2×C42—532no—
575C2×C42—531no—
576C2×C42—532no—
577C2×C42—532no—
578C2×C42—531no—
579C2×C42—532no—
580C4⋊C8—534no—
581C4⋊C8—534no—
582C4⋊C8—534no—
583C4⋊C8—534no—
584C4⋊C8—534no—
585C4⋊C8C22×D5314yes—
586C22⋊C8—534no—
587C22⋊C8—534no—
588C22⋊C8—534no—
589C22⋊C8—534no—
590C22⋊C8C22×D5314yes—
591C22⋊C8C22×D5314yes—
592#97—532no—
593#97—532no—
594#97—532no—
595#97—532no—
596#97—532no—
597#97C22×D5312yes—
598C4×C8—531no—
599C4×C8—531no—
600C4×C8—532no—
601C4×C8—532no—
602C4×C8—532no—
603C4×C8—532no—
604C4×C8—532no—
605C4×C8—532no—
606C4×C8—532no—
607C4×C8—532no—
608C4×C8—531no—
609C4×C8—531no—
610C4×C8—532no—
611C4×C8—532no—
612C4×C8—532no—
613C4×C8C22×D5312yes—
614C24C2×C4×D5311yescharacteristic
615#41—22no—
616#41—22no—
617#41—10616no—
618#41—1062no—
619#41—1062no—
620C2×Q8—534no—
621C2×Q8—531no—
622C2×Q8C2×C4×D5311yescharacteristic
623C2×D4—532no—
624C2×D4—534no—
625C2×D4—534no—
626C2×D4—531no—
627C2×D4C2×C4×D5312yes—
628C2×D4C2×C4×D5311yescharacteristic
629C2×D4C2×C4×D5314yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—532no—
633C22×C4—532no—
634C22×C4—532no—
635C22×C4—532no—
636C22×C4—532no—
637C22×C4—532no—
638C22×C4—534no—
639C22×C4—534no—
640C22×C4—532no—
641C22×C4—1068no—
642C22×C4C2×C4×D5312yes—
643C22×C4C2×C4×D5311yescharacteristic
644C22×C4C23×D5312yes—
645C22×C4C23×D5312yes—
646C22×C4C23×D5311yescharacteristic
647M16—22no—
648M16—22no—
649M16—24no—
650M16—1064no—
651M16—1064no—
652M16—1062no—
653M16—1062no—
654M16—1064no—
655C2×C8—22no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—534no—
660C2×C8—531no—
661C2×C8—531no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—532no—
665C2×C8—1064no—
666C2×C8—1064no—
667C2×C8—1064no—
668C2×C8—1064no—
669C2×C8—1062no—
670C2×C8—1064no—
671C2×C8#1171994714yescomplemented
672C2×C8C23×D5312yes—
673C2×C8C23×D5312yes—
674C2×C8C23×D5312yes—
675C2×C8C23×D5311yescharacteristic
676C2×C8C23×D5311yescharacteristic
677C4⋊C4—534no—
678C4⋊C4—534no—
679C4⋊C4—532no—
680C4⋊C4—534no—
681C4⋊C4—534no—
682C4⋊C4—534no—
683C4⋊C4—534no—
684C4⋊C4—534no—
685C4⋊C4C2×C4×D5314yes—
686C4⋊C4C2×C4×D5312yes—
687C22⋊C4—532no—
688C22⋊C4—534no—
689C22⋊C4—534no—
690C22⋊C4—534no—
691C22⋊C4—534no—
692C22⋊C4—534no—
693C22⋊C4—534no—
694C22⋊C4C2×C4×D5314yes—
695C22⋊C4C2×C4×D5314yes—
696C22⋊C4C2×C4×D5312yes—
697C42—532no—
698C42—532no—
699C42—532no—
700C42—532no—
701C42—531no—
702C42—532no—
703C42—531no—
704C42—534no—
705C42—534no—
706C42—531no—
707C42—531no—
708C42—532no—
709C42—532no—
710C42C23×D5312yes—
711C23—22no—
712C23—24no—
713C23—532no—
714C23C22×C4×D5312yes—
715C23C22×C4×D5311yescharacteristic
716C23C22×C4×D5312yes—
717Q8—22no—
718Q8—1068no—
719Q8—1062no—
720D4—24no—
721D4—28no—
722D4—22no—
723D4—1068no—
724D4—1064no—
725D4—1068no—
726D4—1062no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—538no—
734C2×C4—532no—
735C2×C4—532no—
736C2×C4—532no—
737C2×C4—532no—
738C2×C4—534no—
739C2×C4—532no—
740C2×C4—1068no—
741C2×C4—1064no—
742C2×C4—1064no—
743C2×C4—1064no—
744C2×C4—1064no—
745C2×C4—1068no—
746C2×C4—1064no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4C22×C4×D5312yes—
750C2×C4C22×C4×D5312yes—
751C2×C4C22×C4×D5314yes—
752C2×C4C22×C4×D5311yescharacteristic
753C2×C4#41×D5312yes—
754C2×C4C2×#1171994712yes—
755C2×C4C24×D5311yescharacteristic
756C8—22no—
757C8—22no—
758C8—22no—
759C8—532no—
760C8—532no—
761C8—1062no—
762C8—1062no—
763C8—1062no—
764C8C2×#1171994712yes—
765C8C2×#1171994712yes—
766C22—28no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—1064no—
773C22—1062no—
774C22C4×#1171994712yes—
775C22#131×D5314yes—
776C22C23×C4×D5311yescharacteristic
777C4—24no—
778C4—22no—
779C4—22no—
780C4—534no—
781C4—534no—
782C4—1062no—
783C4—1062no—
784C4—1064no—
785C4—1062no—
786C4C4×#1171994712yes—
787C4C2×#41×D5311yescharacteristic
788C4C22×#1171994711yescharacteristic
789C2—22no—
790C2—24no—
791C2—42no—
792C2—2122no—
793C2C2×C4×#1171994711yescharacteristic
794C2C2×#131×D5312yes—
subgroupG/H
centerC2×C8C23×D53
commutator, socleC22×C53C24×C4
FrattiniC2×C4C24×D53
FittingC53×#2929C2
prime radical#20288007C2
cosocleC2×C4×C53C25
hypercenter#2929D53
hypocenterC53#60204
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C8 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #20283685C2semidirect
3. #20283683C2semidirect
4. #20283675C2semidirect
5. C8×#11719947C2semidirect
6. #20283648C2semidirect
7. #20283647C2semidirect
8. #20283425C2semidirect
9. #20283423C2semidirect
10. #20283410C2semidirect
11. #20283409C2semidirect
12. #20283405C2semidirect
13. #20283358C2semidirect
14. #20283355C2semidirect
15. #20283344C2semidirect
16. #20283137C2semidirect
17. #131×Dic53C2semidirect
18. C22×C8×Dic53C2semidirect
19. C53×#2929C2semidirect
38. #16810752C22semidirect
39. #16810751C22semidirect
40. C8×Dic106C22semidirect
41. #16810747C22semidirect
42. #16810699C22semidirect
43. #16810698C22semidirect
49. C8×C22⋊D53C22semidirect
51. #16810686C22semidirect
52. #16810683C22semidirect
53. #16810681C22semidirect
55. #16810675C22semidirect
57. #16810673C22semidirect
68. #16810581C22semidirect
69. #16810580C22semidirect
72. #16810578C22semidirect
73. #16810577C22semidirect
74. #16810575C22semidirect
77. M16×Dic53C22semidirect
86. C2×C8×Dic53C22semidirect
87. C4×C8×D53C22semidirect
256. C2×C8×C53#41semidirect
303. C2×#88322#41semidirect
345. C2×Dic53#131semidirect
404. #2929D53semidirect
494. C53#60204semidirect
671. C2×C8#11719947semidirect

Maximal subgroups

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

subgroupindex
#202880072
#202836852
#202836832
#202836752
C8×#117199472
#202836482
#202836472
#202834252
#202834232
#202834102
#202834092
#202834052
#202833582
#202833552
#202833442
#202831372
#131×Dic532
C22×C8×Dic532
C53×#29292
#6020453