Finite Group Databasebeta

← #28247674

Subgroups — #28247674

Order 13568.

4902 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811460C211yesmaximal, characteristic
2C2×#16811388C211yesmaximal, characteristic, complemented
3#520×D53C211yesmaximal, characteristic, complemented
4#20283248C211yesmaximal, characteristic, complemented
5#20283247C213yesmaximal, complemented
6#20283243C213yesmaximal, complemented
7#20283242C211yesmaximal, characteristic, complemented
8#20283239C213yesmaximal, complemented
9#20283238C211yesmaximal, characteristic, complemented
10#20283237C213yesmaximal, complemented
11#20283233C213yesmaximal, complemented
12#20283230C213yesmaximal, complemented
13C2×#16810623C213yesmaximal, complemented
14#417×D53C213yesmaximal, complemented
15C53×#2898C211yesmaximal, characteristic, complemented
16#16811460—28no—
17#16811460C4116yescomplemented
18C2×#13133265—21no—
19C2×#13133265C2213yes—
20C2×#13133263—23no—
21C2×#13133263C2211yescharacteristic
22C2×#13133263C2213yes—
23C22×#11719949—21no—
24C22×#11719949C2213yes—
25C2×#41×D53—23no—
26C2×#41×D53C2213yes—
27C2×#41×D53C2211yescharacteristic
28#16811388—28no—
29C2×#13133225C2213yescomplemented
30C2×#13133224C2211yescharacteristic, complemented
31C2×#13133223C2213yescomplemented
32C22×#11719912C2213yescomplemented
33C2×M16×D53C2213yescomplemented
34#16811106C2211yescharacteristic, complemented
35#16811105—21no—
36#16811104C2213yescomplemented
37#16811103C2213yescomplemented
38#16811102—23no—
39C4×Q8×D53—21no—
40C4×D4×D53—23no—
41#117×D53C2213yescomplemented
42C2×C4⋊C4×D53C2213yescomplemented
43#16810632C2213yescomplemented
44#16810630C2213yescomplemented
45#16810630C2213yescomplemented
46#16810629C2213yescomplemented
47#16810627C2213yescomplemented
48#16810626C2213yescomplemented
49#16810626C2213yescomplemented
50#16810625C2213yescomplemented
51#16810624C2213yescomplemented
52#16810623C2216yescomplemented
53#16810623C2213yescomplemented
54#16810623C2216yescomplemented
55#16810623C2216yescomplemented
56#16810623C2213yescomplemented
57#16810622C2213yescomplemented
58#16810621C2213yescomplemented
59#16810621C2211yescharacteristic, complemented
60#16810620C2213yescomplemented
61#16810619C2213yescomplemented
62#16810618C2216yescomplemented
63#16810618C2216yescomplemented
64#16810617C2213yescomplemented
65C2×#13133141C2213yescomplemented
66#103×D53C2216yescomplemented
67C2×#13133139C2213yescomplemented
68C2×#13133137C2213yescomplemented
69#102×D53C2216yescomplemented
70C2×2−1+4×C53C2211yescharacteristic
71C2×#131×C53C2211yescharacteristic, complemented
72C53×#520C2211yescharacteristic, complemented
73C53×#419C2213yescomplemented
74C53×#417C2213yescomplemented
75C53×#416C2213yescomplemented
76C2×#103×C53C2213yescomplemented
77#13133265—216no—
78#13133265—212no—
79#13133265C2×C4124yescomplemented
80#13133263—24no—
81#13133263—248no—
82#13133263—212no—
83#13133263C2×C4124yescomplemented
84#13133263C2×C418yescomplemented
85C2×#11719949—21no—
86C2×#11719949—216no—
87C2×#11719949—23no—
88C2×#11719949—23no—
89C2×#11719949—23no—
90C2×#11719949—212no—
91C2×#11719949C2×C4124yescomplemented
92C2×#11719949D411yescharacteristic
93C2×#11719949C2313yes—
94C2×#11719949C2316yes—
95C2×#11719945—26no—
96C2×#11719945—23no—
97C2×#11719945—23no—
98C2×#11719945C2313yes—
99C2×#11719945C2313yes—
100C2×#11719947—23no—
101C2×#11719947D413yes—
102C2×#11719947C2311yescharacteristic
103#41×D53—248no—
104#41×D53—212no—
105#41×D53C2×C418yes—
106#41×D53C2×C4124yescomplemented
107#41×D53D418yes—
108C2×Q8×D53—23no—
109C2×Q8×D53D411yescharacteristic
110C2×Q8×D53C2313yes—
111C22×D212—23no—
112C22×D212—23no—
113C22×D212C2313yes—
114C2×D4×D53—23no—
115C2×D4×D53—23no—
116C2×D4×D53—26no—
117C2×D4×D53D413yes—
118C2×D4×D53C2313yes—
119C22×C4×D53—23no—
120C22×C4×D53—23no—
121C22×C4×D53—23no—
122C22×C4×D53C2313yes—
123#13133225—212no—
124#13133224—24no—
125#13133223—212no—
126C2×#11719917C2313yes—
127C2×#11719912—212no—
128C2×#11719912C2313yes—
129C2×#11719912C2311yescharacteristic
130C2×#11719912C2313yes—
131C2×#11719912C2313yes—
132M16×D53—212no—
133C22×#88322C2313yes—
134C2×C8×D53C2316yes—
135Q8×Dic53—21no—
136C4×Dic106—23no—
137#13133182—23no—
138C4×D212—23no—
139D4×Dic53—23no—
140#13133179—23no—
141C4×C22⋊D53—26no—
142#13133177—26no—
143#13133176C2313yes—
144#13133175C2313yes—
145#13133175C2313yes—
146#13133174—23no—
147#13133173—23no—
148C2×C4⋊Dic53C2313yes—
149C2×#11719919—23no—
150C4⋊C4×D53—23no—
151C4⋊C4×D53—23no—
152C4⋊C4×D53C2313yes—
153C4⋊C4×D53C2316yes—
154C4⋊C4×D53C2311yescharacteristic
155C22⋊C4×D53—23no—
156C42×D53—23no—
157#13133142C2313yes—
158#13133142C2311yescharacteristic
159#13133141C2316yes—
160#13133141C2313yes—
161#13133141C2313yes—
162#13133140C2313yes—
163#13133140C2311yescharacteristic
164#13133139C2316yes—
165#13133139C2313yes—
166#13133139C2313yes—
167#13133138C2313yes—
168#13133138C2311yescharacteristic
169#13133137C2316yes—
170#13133137C2313yes—
171#13133137C2313yes—
1722−1+4×C53—24no—
1732−1+4×C53C2×C418yescomplemented
174C2×#41×C53—23no—
175C2×#41×C53C2313yes—
176C2×#41×C53C2311yescharacteristic
177C22×Q8×C53—21no—
178C22×Q8×C53C2313yes—
179#131×C53—24no—
180C2×M16×C53C2313yes—
181C22×C8×C53C2313yes—
182C4×Q8×C53—21no—
183C4×D4×C53—23no—
184#117×C53C2313yes—
185C2×C4⋊C4×C53C2313yes—
186#103×C53C2316yes—
187#103×C53C2313yes—
188#103×C53C2313yes—
189#102×C53C2313yes—
190#102×C53C2311yescharacteristic
191C23×D53—23no—
192C23×D53—23no—
193C23×D53C2×D413yes—
194#41×C53—224no—
195#41×C53—26no—
196#41×C53C22×C414yes—
197#41×C53C22×C4112yescomplemented
198#41×C53C2×D414yes—
199C2×Q8×C53—28no—
200C2×Q8×C53—23no—
201C2×Q8×C53—26no—
202C2×Q8×C53C22×C4112yescomplemented
203C2×Q8×C53C2×D411yescharacteristic
204C2×Q8×C53C2413yes—
205C2×D4×C53—23no—
206C2×D4×C53C2×D413yes—
207C2×D4×C53C2411yescharacteristic
208C22×C4×C53—23no—
209C22×C4×C53—23no—
210C22×C4×C53—23no—
211C22×C4×C53C2413yes—
212C2×C22⋊D53—23no—
213C2×C22⋊D53—21no—
214C2×C22⋊D53—23no—
215C2×C22⋊D53C2×D416yes—
216C22×Dic53—21no—
217C22×Dic53—23no—
218C22×Dic53C2×D413yes—
219#11719949—28no—
220#11719949—224no—
221#11719949—224no—
222#11719949—224no—
223#11719949—26no—
224#11719949—212no—
225#11719949C22⋊C418yes—
226#11719949C22×C4112yes—
227#11719949C22×C4124yescomplemented
228Q8×D53—26no—
229Q8×D53—224no—
230Q8×D53C22⋊C418yes—
231Q8×D53C22×C4112yescomplemented
232#11719947—224no—
233#11719947—22no—
234#11719947C22⋊C4124yes—
235#11719947C22×C414yes—
236D4×D53—224no—
237D4×D53—224no—
238D4×D53—248no—
239D4×D53—26no—
240D4×D53C22⋊C4124yes—
241D4×D53C22×C4112yescomplemented
242#11719945—26no—
243#11719945—248no—
244#11719945—224no—
245#11719945—224no—
246#11719945C22×C4112yes—
247#11719945C22×C4112yescomplemented
248#11719945C2×D4112yes—
249C2×D212—224no—
250C2×D212—23no—
251C2×D212—26no—
252C2×D212—23no—
253C2×D212—26no—
254C2×D212—224no—
255C2×D212C22×C4112yescomplemented
256C2×D212C2×D413yes—
257C2×D212C2413yes—
258C2×C4×D53—23no—
259C2×C4×D53—23no—
260C2×C4×D53—224no—
261C2×C4×D53—23no—
262C2×C4×D53—26no—
263C2×C4×D53—224no—
264C2×C4×D53—21no—
265C2×C4×D53—23no—
266C2×C4×D53—26no—
267C2×C4×D53—86no—
268C2×C4×D53C22×C4112yes—
269C2×C4×D53C2×D413yes—
270C2×C4×D53C2×D413yes—
271C2×C4×D53C2×D4112yes—
272C2×C4×D53C2411yescharacteristic
273C2×C4×D53C2413yes—
274C2×Dic106—23no—
275C2×Dic106C2×D413yes—
276C2×Dic106C2411yescharacteristic
277M16×C53—26no—
278C2×C8×C53—26no—
279C2×C8×C53C2411yescharacteristic
280C2×C8×C53C2413yes—
281C4⋊C4×C53—23no—
282C4⋊C4×C53C2413yes—
283C4⋊C4×C53C2411yescharacteristic
284C22⋊C4×C53—23no—
285C42×C53—23no—
286C22⋊Dic53—23no—
287#11719921—23no—
288#11719921—23no—
289C4⋊Dic53—23no—
290C4⋊Dic53C2413yes—
291C4⋊Dic53C2411yescharacteristic
292#11719919—23no—
293#11719919—26no—
294#11719919—21no—
295C4×Dic53—23no—
296C4×Dic53—23no—
297C4×Dic53—23no—
298#11719917—26no—
299C2×#88322—26no—
300C2×#88322C2413yes—
301C2×#88322C2411yescharacteristic
302#11719912—26no—
303#11719912—22no—
304#11719912—26no—
305#11719912—26no—
306C8×D53—212no—
307C23×C53—21no—
308C23×C53C22×D413yes—
309C22×D53—23no—
310C22×D53—212no—
311C22×D53—212no—
312C22×D53—43no—
313C22×D53—43no—
314C22×D53—83no—
315C22×D53—83no—
316C22×D53—83no—
317C22×D53—83no—
318C22×D53C2×C22⋊C4112yes—
319C22×D53C22×D411yescharacteristic
320C22×D53C22×D413yes—
321Q8×C53—212no—
322Q8×C53—23no—
323Q8×C53C2×C22⋊C414yes—
324Q8×C53C23×C416yes—
325D4×C53—212no—
326D4×C53—21no—
327D4×C53C2×C22⋊C4112yes—
328D4×C53C23×C412yes—
329C2×C4×C53—212no—
330C2×C4×C53—23no—
331C2×C4×C53—212no—
332C2×C4×C53—23no—
333C2×C4×C53—21no—
334C2×C4×C53—83no—
335C2×C4×C53C23×C416yes—
336C2×C4×C53C22×D413yes—
337C2×C4×C53C22×D416yes—
338C2×C4×C53C2511yescharacteristic
339C22⋊D53—212no—
340C22⋊D53—24no—
341C22⋊D53—212no—
342C22⋊D53C2×C22⋊C4124yes—
343C2×Dic53—21no—
344C2×Dic53—24no—
345C2×Dic53—23no—
346C2×Dic53—21no—
347C2×Dic53—83no—
348C2×Dic53C2×C22⋊C4112yes—
349C2×Dic53C22×D413yes—
350C2×Dic53C22×D411yescharacteristic
351D212—212no—
352D212—224no—
353D212—212no—
354D212—23no—
355D212C2×C22⋊C4112yes—
356D212C23×C416yes—
357C4×D53—212no—
358C4×D53—212no—
359C4×D53—212no—
360C4×D53—224no—
361C4×D53—42no—
362C4×D53—46no—
363C4×D53—86no—
364C4×D53C2×C22⋊C4112yes—
365C4×D53C2×C22⋊C4112yes—
366C4×D53C23×C412yes—
367C4×D53C23×C416yes—
368C4×D53C22×D412yes—
369C4×D53C22×D416yes—
370Dic106—21no—
371Dic106—212no—
372Dic106C2×C22⋊C4112yes—
373Dic106C23×C412yes—
374C8×C53—23no—
375C8×C53—21no—
376#88322—23no—
377#88322—21no—
378#60089—531nomaximal, Sylow
379C22×C53—23no—
380C22×C53—23no—
381C22×C53—22no—
382C22×C53—41no—
383C22×C53—41no—
384C22×C53C22×C22⋊C416yes—
385C22×C53C23×D411yescharacteristic
386C2×D53—21no—
387C2×D53—23no—
388C2×D53—21no—
389C2×D53—23no—
390C2×D53—26no—
391C2×D53—412no—
392C2×D53—43no—
393C2×D53—43no—
394C2×D53—812no—
395C2×D53—812no—
396C2×D53C22×C22⋊C416yes—
397C2×D53C22×C22⋊C412yes—
398C4×C53—26no—
399C4×C53—43no—
400C4×C53—41no—
401C4×C53C22×C22⋊C416yes—
402C4×C53C24×C411yescharacteristic
403C4×C53C23×D411yescharacteristic
404Dic53—22no—
405Dic53—43no—
406Dic53—41no—
407Dic53C22×C22⋊C416yes—
408Dic53C22×C22⋊C412yes—
409C2×#585—531no—
410C2×#568—531no—
411C2×#520—531no—
412#2898—533no—
413#2898—533no—
414#2898—531no—
415#2898D5311yescharacteristic, complemented
416#2897—533no—
417#2897—533no—
418#2897—531no—
419#2897—531no—
420#2896—533no—
421#2896—533no—
422C2×#417—533no—
423C2×#417—533no—
424C2×C53—26no—
425C2×C53—42no—
426C2×C53C23×C22⋊C411yescharacteristic
427C2×C53#358511yescharacteristic
428C2×C53#358611yescharacteristic
429D53—22no—
430D53—26no—
431D53—46no—
432#585—5316no—
433#585—1068no—
434C2×2−1+4—533no—
435C2×2−1+4—1061no—
436C2×2−1+4C2×D5311yescharacteristic
437C2×H(5,𝔽2)—533no—
438C2×H(5,𝔽2)—531no—
439C2×H(5,𝔽2)—1063no—
440C22×#41—531no—
441C22×#41—533no—
442C22×#41—533no—
443C22×#41—1061no—
444C22×#41—1063no—
445#568—1068no—
446C2×#131—531no—
447C2×#131—533no—
448C2×#131—533no—
449C2×#131C2×D5311yescharacteristic, complemented
450C22×M16—533no—
451C22×M16—533no—
452#520—531no—
453#520—533no—
454#520—533no—
455#520—1063no—
456#520—1061no—
457#520C2×D5311yescharacteristic, complemented
458C2×C4×Q8—1061no—
459C2×C4×D4—1063no—
460C2×#117—533no—
461C22×C4⋊C4—533no—
462#419—533no—
463#419—533no—
464#419—533no—
465#419C2×D5313yescomplemented
466#418—533no—
467#418—533no—
468#418—533no—
469#418—533no—
470#417—533no—
471#417—533no—
472#417—533no—
473#417—536no—
474#417—533no—
475#417—536no—
476#417—536no—
477#417—533no—
478#417—533no—
479#417—531no—
480#417C2×D5313yescomplemented
481#416—533no—
482#416—533no—
483#416—533no—
484#416—536no—
485#416—536no—
486#416C2×D5313yescomplemented
487C2×#103—533no—
488C2×#103—536no—
489C2×#103C2×D5313yescomplemented
490C2×#102—533no—
491C2×#102—533no—
492C2×#102—536no—
493C53#6008911yescharacteristic, complemented, Sylow
4942−1+4—24no—
4952−1+4—5324no—
4962−1+4—10616no—
4972−1+4—10612no—
4982−1+4C4×D5318yescomplemented
499H(5,𝔽2)—538no—
500H(5,𝔽2)—5324no—
501H(5,𝔽2)—10648no—
502H(5,𝔽2)—10612no—
503H(5,𝔽2)—1064no—
504C2×#41—23no—
505C2×#41—538no—
506C2×#41—538no—
507C2×#41—531no—
508C2×#41—533no—
509C2×#41—533no—
510C2×#41—5324no—
511C2×#41—5324no—
512C2×#41—533no—
513C2×#41—536no—
514C2×#41—531no—
515C2×#41—533no—
516C2×#41—1063no—
517C2×#41—1066no—
518C2×#41—1063no—
519C2×#41—1063no—
520C2×#41—1063no—
521C2×#41—1063no—
522C2×#41—10612no—
523C2×#41—10612no—
524C2×#41—1063no—
525C2×#41—10616no—
526C2×#41—10648no—
527C2×#41—1061no—
528C2×#41C22×D5313yes—
529C2×#41C22×D5311yescharacteristic
530C22×Q8—21no—
531C22×Q8—531no—
532C22×Q8—533no—
533C22×Q8—1063no—
534C22×Q8C22×D5313yes—
535C22×D4—533no—
536C22×D4—533no—
537C22×D4—533no—
538C22×D4—1063no—
539C22×D4—1063no—
540C22×D4—1066no—
541C22×D4—1063no—
542C22×D4—1063no—
543C23×C4—533no—
544C23×C4—1063no—
545C23×C4—1063no—
546C23×C4—1063no—
547#131—24no—
548#131—10612no—
549#131—10612no—
550#131—1064no—
551C2×M16—533no—
552C2×M16—533no—
553C2×M16—531no—
554C2×M16—533no—
555C2×M16—533no—
556C2×M16—10612no—
557C2×M16—10612no—
558C2×M16C22×D5313yes—
559C22×C8—533no—
560C22×C8—536no—
561C22×C8C22×D5313yes—
562C4×Q8—21no—
563C4×Q8—1063no—
564C4×Q8—1063no—
565C4×Q8—1061no—
566C4×D4—23no—
567C4×D4—1063no—
568C4×D4—1066no—
569C4×D4—1063no—
570C4×D4—1066no—
571C4×D4—1063no—
572#117—533no—
573#117—533no—
574#117—533no—
575#117—1063no—
576#117—1063no—
577#117C22×D5313yes—
578C2×C4⋊C4—533no—
579C2×C4⋊C4—533no—
580C2×C4⋊C4—536no—
581C2×C4⋊C4—531no—
582C2×C4⋊C4—1063no—
583C2×C4⋊C4—1063no—
584C2×C4⋊C4—1063no—
585C2×C4⋊C4C22×D5313yes—
586C2×C22⋊C4—1063no—
587C2×C42—1063no—
588#103—536no—
589#103—533no—
590#103—533no—
591#103—533no—
592#103—531no—
593#103—533no—
594#103—531no—
595#103C22×D5316yes—
596#103C22×D5313yes—
597#103C22×D5313yes—
598#102—533no—
599#102—531no—
600#102—536no—
601#102—533no—
602#102—533no—
603#102—536no—
604#102—533no—
605#102—533no—
606#102C22×D5313yes—
607#102C22×D5311yescharacteristic
608C24—533no—
609C24—1063no—
610C24—1063no—
611#41—224no—
612#41—26no—
613#41—538no—
614#41—5324no—
615#41—5312no—
616#41—5312no—
617#41—5312no—
618#41—5324no—
619#41—534no—
620#41—5312no—
621#41—10624no—
622#41—10648no—
623#41—10624no—
624#41—10624no—
625#41—1062no—
626#41—10624no—
627#41—1066no—
628#41—10624no—
629#41—10612no—
630#41—10624no—
631#41—1068no—
632#41—1066no—
633#41C2×C4×D5314yes—
634#41C2×C4×D53112yescomplemented
635#41D4×D5314yes—
636C2×Q8—28no—
637C2×Q8—23no—
638C2×Q8—26no—
639C2×Q8—538no—
640C2×Q8—533no—
641C2×Q8—5312no—
642C2×Q8—531no—
643C2×Q8—1063no—
644C2×Q8—1066no—
645C2×Q8—10624no—
646C2×Q8C2×C4×D53112yescomplemented
647C2×Q8D4×D5311yescharacteristic
648C2×Q8C23×D5313yes—
649C2×D4—23no—
650C2×D4—536no—
651C2×D4—5324no—
652C2×D4—5312no—
653C2×D4—5312no—
654C2×D4—533no—
655C2×D4—533no—
656C2×D4—10624no—
657C2×D4—1066no—
658C2×D4—1063no—
659C2×D4—10624no—
660C2×D4—1066no—
661C2×D4—1063no—
662C2×D4—10648no—
663C2×D4—10624no—
664C2×D4—1061no—
665C2×D4—1063no—
666C2×D4—10624no—
667C2×D4—1063no—
668C2×D4—1066no—
669C2×D4D4×D5313yes—
670C2×D4C23×D5311yescharacteristic
671C22×C4—23no—
672C22×C4—23no—
673C22×C4—23no—
674C22×C4—533no—
675C22×C4—5312no—
676C22×C4—533no—
677C22×C4—533no—
678C22×C4—5312no—
679C22×C4—531no—
680C22×C4—533no—
681C22×C4—1063no—
682C22×C4—1066no—
683C22×C4—10624no—
684C22×C4—10624no—
685C22×C4—1063no—
686C22×C4—1066no—
687C22×C4—1061no—
688C22×C4—1063no—
689C22×C4—1061no—
690C22×C4—1063no—
691C22×C4—1063no—
692C22×C4—4246no—
693C22×C4C23×D5313yes—
694M16—26no—
695M16—1062no—
696M16—1066no—
697M16—1066no—
698M16—1066no—
699M16—1066no—
700C2×C8—26no—
701C2×C8—533no—
702C2×C8—531no—
703C2×C8—10612no—
704C2×C8—1066no—
705C2×C8C23×D5313yes—
706C2×C8C23×D5311yescharacteristic
707C4⋊C4—23no—
708C4⋊C4—533no—
709C4⋊C4—531no—
710C4⋊C4—1063no—
711C4⋊C4—1066no—
712C4⋊C4—1061no—
713C4⋊C4—1063no—
714C4⋊C4C23×D5313yes—
715C4⋊C4C23×D5311yescharacteristic
716C22⋊C4—23no—
717C22⋊C4—1063no—
718C22⋊C4—1063no—
719C22⋊C4—1063no—
720C42—23no—
721C42—1063no—
722C42—1063no—
723C42—1063no—
724C23—21no—
725C23—533no—
726C23—531no—
727C23—5312no—
728C23—10612no—
729C23—10612no—
730C23—1063no—
731C23—4243no—
732C23—4243no—
733C23—4243no—
734C23—4243no—
735C23—2123no—
736C23—2123no—
737C23C2×D4×D5313yes—
738Q8—212no—
739Q8—23no—
740Q8—5312no—
741Q8—532no—
742Q8—10612no—
743Q8—1061no—
744Q8C22⋊C4×D5314yes—
745Q8C22×C4×D5316yes—
746D4—212no—
747D4—21no—
748D4—5324no—
749D4—5312no—
750D4—536no—
751D4—10612no—
752D4—10624no—
753D4—10612no—
754D4—1064no—
755D4—10612no—
756D4—10612no—
757D4—1063no—
758D4C22⋊C4×D53112yes—
759D4C22×C4×D5312yes—
760C2×C4—212no—
761C2×C4—23no—
762C2×C4—212no—
763C2×C4—21no—
764C2×C4—23no—
765C2×C4—83no—
766C2×C4—5312no—
767C2×C4—533no—
768C2×C4—531no—
769C2×C4—5312no—
770C2×C4—5312no—
771C2×C4—532no—
772C2×C4—536no—
773C2×C4—536no—
774C2×C4—532no—
775C2×C4—10612no—
776C2×C4—10624no—
777C2×C4—10612no—
778C2×C4—1064no—
779C2×C4—1061no—
780C2×C4—10612no—
781C2×C4—1061no—
782C2×C4—1063no—
783C2×C4—4246no—
784C2×C4—4243no—
785C2×C4—2122no—
786C2×C4—2126no—
787C2×C4C22×C4×D5316yes—
788C2×C4C2×D4×D5313yes—
789C2×C4C2×D4×D5316yes—
790C2×C4C24×D5311yescharacteristic
791C8—21no—
792C8—23no—
793C8—1063no—
794C8—1061no—
795C22—23no—
796C22—23no—
797C22—22no—
798C22—41no—
799C22—41no—
800C22—532no—
801C22—536no—
802C22—1063no—
803C22—1061no—
804C22—1061no—
805C22—1063no—
806C22—1066no—
807C22—42412no—
808C22—42412no—
809C22—21212no—
810C22—2123no—
811C22—2123no—
812C22C2×C22⋊C4×D5316yes—
813C22C22×D4×D5311yescharacteristic
814C4—26no—
815C4—43no—
816C4—41no—
817C4—532no—
818C4—536no—
819C4—1062no—
820C4—2123no—
821C4—2121no—
822C4C2×C22⋊C4×D5316yes—
823C4C23×C4×D5311yescharacteristic
824C4C22×D4×D5311yescharacteristic
825C2—26no—
826C2—42no—
827C2—1066no—
828C2—1062no—
829C2—2126no—
830C2C22×C22⋊C4×D5311yescharacteristic
831C2#2028949311yescharacteristic
832C2#2028950011yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC53×#2898C2
socleC22×C53C23×D4
prime radicalC2×#16811460C2
cosocleC2×C4×C53C25
hypercenter#2898D53
hypocenterC53#60089
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2898

Complements

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

NH ≅ G/Ntype
2. C2×#16811388C2semidirect
3. #520×D53C2semidirect
4. #20283248C2semidirect
5. #20283247C2semidirect
6. #20283243C2semidirect
7. #20283242C2semidirect
8. #20283239C2semidirect
9. #20283238C2semidirect
10. #20283237C2semidirect
11. #20283233C2semidirect
12. #20283230C2semidirect
13. C2×#16810623C2semidirect
14. #417×D53C2semidirect
15. C53×#2898C2semidirect
17. #16811460C4semidirect
29. C2×#13133225C22semidirect
30. C2×#13133224C22semidirect
31. C2×#13133223C22semidirect
32. C22×#11719912C22semidirect
33. C2×M16×D53C22semidirect
34. #16811106C22semidirect
36. #16811104C22semidirect
37. #16811103C22semidirect
41. #117×D53C22semidirect
42. C2×C4⋊C4×D53C22semidirect
43. #16810632C22semidirect
44. #16810630C22semidirect
45. #16810630C22semidirect
46. #16810629C22semidirect
47. #16810627C22semidirect
48. #16810626C22semidirect
49. #16810626C22semidirect
50. #16810625C22semidirect
51. #16810624C22semidirect
52. #16810623C22semidirect
53. #16810623C22semidirect
54. #16810623C22semidirect
55. #16810623C22semidirect
56. #16810623C22semidirect
57. #16810622C22semidirect
58. #16810621C22semidirect
59. #16810621C22semidirect
60. #16810620C22semidirect
61. #16810619C22semidirect
62. #16810618C22semidirect
63. #16810618C22semidirect
64. #16810617C22semidirect
65. C2×#13133141C22semidirect
66. #103×D53C22semidirect
67. C2×#13133139C22semidirect
68. C2×#13133137C22semidirect
69. #102×D53C22semidirect
71. C2×#131×C53C22semidirect
72. C53×#520C22semidirect
73. C53×#419C22semidirect
74. C53×#417C22semidirect
75. C53×#416C22semidirect
76. C2×#103×C53C22semidirect
79. #13133265C2×C4semidirect
83. #13133263C2×C4semidirect
84. #13133263C2×C4semidirect
91. C2×#11719949C2×C4semidirect
106. #41×D53C2×C4semidirect
173. 2−1+4×C53C2×C4semidirect
197. #41×C53C22×C4semidirect
202. C2×Q8×C53C22×C4semidirect
227. #11719949C22×C4semidirect
231. Q8×D53C22×C4semidirect
241. D4×D53C22×C4semidirect
247. #11719945C22×C4semidirect
255. C2×D212C22×C4semidirect
415. #2898D53semidirect
449. C2×#131C2×D53semidirect
457. #520C2×D53semidirect
465. #419C2×D53semidirect
480. #417C2×D53semidirect
486. #416C2×D53semidirect
489. C2×#103C2×D53semidirect
493. C53#60089semidirect
498. 2−1+4C4×D53semidirect
634. #41C2×C4×D53semidirect
646. C2×Q8C2×C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168114602
C2×#168113882
#520×D532
#202832482
#202832472
#202832432
#202832422
#202832392
#202832382
#202832372
#202832332
#202832302
C2×#168106232
#417×D532
C53×#28982
#6008953