Finite Group Databasebeta

← #28247671

Subgroups — #28247671

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×#16811458C211yesmaximal, characteristic
2C2×#16811388C211yesmaximal, characteristic, complemented
3#520×D53C211yesmaximal, characteristic, complemented
4#20283249C211yesmaximal, characteristic, complemented
5#20283246C213yesmaximal, complemented
6#20283245C211yesmaximal, characteristic, complemented
7#20283244C213yesmaximal, complemented
8#20283241C211yesmaximal, characteristic, complemented
9#20283240C213yesmaximal, complemented
10#20283236C213yesmaximal, complemented
11#20283230C213yesmaximal, complemented
12#20283229C213yesmaximal, complemented
13C2×#16810621C213yesmaximal, complemented
14#417×D53C213yesmaximal, complemented
15C53×#2897C211yesmaximal, characteristic, complemented
16#16811458—28no—
17#16811458C4116yescomplemented
18C2×#13133264—21no—
19C2×#13133264C2211yescharacteristic
20C2×#13133264C2213yes—
21C2×#13133262—23no—
22C2×#13133262C2213yes—
23C22×#11719947—23no—
24C22×#11719947C2213yes—
25C2×#41×D53—21no—
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#16810633C2213yescomplemented
44#16810631C2213yescomplemented
45#16810630C2213yescomplemented
46#16810630C2213yescomplemented
47#16810628C2213yescomplemented
48#16810626C2213yescomplemented
49#16810626C2213yescomplemented
50#16810625C2213yescomplemented
51#16810624C2213yescomplemented
52#16810623C2213yescomplemented
53#16810623C2211yescharacteristic, complemented
54#16810622C2213yescomplemented
55#16810621C2216yescomplemented
56#16810621C2213yescomplemented
57#16810621C2216yescomplemented
58#16810621C2216yescomplemented
59#16810621C2213yescomplemented
60#16810620C2213yescomplemented
61#16810619C2213yescomplemented
62#16810617C2213yescomplemented
63#16810616C2216yescomplemented
64#16810616C2216yescomplemented
65C2×#13133142C2213yescomplemented
66C2×#13133140C2213yescomplemented
67#103×D53C2216yescomplemented
68C2×#13133138C2213yescomplemented
69#102×D53C2216yescomplemented
70C2×H(5,𝔽2)×C53C2211yescharacteristic
71C2×#131×C53C2211yescharacteristic, complemented
72C53×#520C2211yescharacteristic, complemented
73C53×#418C2213yescomplemented
74C53×#417C2213yescomplemented
75C53×#416C2213yescomplemented
76C2×#102×C53C2213yescomplemented
77#13133264—24no—
78#13133264—216no—
79#13133264—212no—
80#13133264C2×C4124yescomplemented
81#13133264C2×C418yescomplemented
82#13133262—248no—
83#13133262—212no—
84#13133262C2×C4124yescomplemented
85C2×#11719949D411yescharacteristic
86C2×#11719949C2311yescharacteristic
87C2×#11719945—23no—
88C2×#11719945—23no—
89C2×#11719945C2313yes—
90C2×#11719945C2313yes—
91C2×#11719947—23no—
92C2×#11719947—26no—
93C2×#11719947—23no—
94C2×#11719947—248no—
95C2×#11719947—23no—
96C2×#11719947—23no—
97C2×#11719947—212no—
98C2×#11719947—23no—
99C2×#11719947C2×C4124yescomplemented
100C2×#11719947D413yes—
101C2×#11719947C2313yes—
102C2×#11719947C2316yes—
103#41×D53—216no—
104#41×D53—212no—
105#41×D53C2×C418yes—
106#41×D53C2×C4124yescomplemented
107#41×D53D418yes—
108C22×Dic106—23no—
109C22×Dic106C2313yes—
110C2×Q8×D53—21no—
111C2×Q8×D53D411yescharacteristic
112C2×Q8×D53C2313yes—
113C22×C22⋊D53—23no—
114C22×C22⋊D53—26no—
115C2×D4×D53—23no—
116C2×D4×D53—23no—
117C2×D4×D53D413yes—
118C2×D4×D53C2313yes—
119C23×Dic53—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#13133142C2316yes—
158#13133142C2313yes—
159#13133142C2313yes—
160#13133141C2313yes—
161#13133141C2311yescharacteristic
162#13133140C2316yes—
163#13133140C2313yes—
164#13133140C2313yes—
165#13133139C2313yes—
166#13133139C2311yescharacteristic
167#13133138C2316yes—
168#13133138C2313yes—
169#13133138C2313yes—
170#13133137C2313yes—
171#13133137C2311yescharacteristic
172H(5,𝔽2)×C53—24no—
173H(5,𝔽2)×C53C2×C418yescomplemented
174C2×#41×C53—21no—
175C2×#41×C53C2313yes—
176C2×#41×C53C2311yescharacteristic
177C22×D4×C53—23no—
178C22×D4×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×C53C2313yes—
187#103×C53C2311yescharacteristic
188#102×C53C2316yes—
189#102×C53C2313yes—
190#102×C53C2313yes—
191C24×C53—23no—
192C23×D53—23no—
193C23×D53C2×D413yes—
194#41×C53—28no—
195#41×C53—26no—
196#41×C53C22×C414yes—
197#41×C53C22×C4112yescomplemented
198#41×C53C2×D414yes—
199C2×Q8×C53C2×D411yescharacteristic
200C2×Q8×C53C2411yescharacteristic
201C2×D4×C53—23no—
202C2×D4×C53—224no—
203C2×D4×C53—23no—
204C2×D4×C53—26no—
205C2×D4×C53C22×C4112yescomplemented
206C2×D4×C53C2×D413yes—
207C2×D4×C53C2413yes—
208C22×C4×C53—23no—
209C22×C4×C53—23no—
210C22×C4×C53C2413yes—
211C2×C22⋊D53—23no—
212C2×C22⋊D53—224no—
213C2×C22⋊D53—23no—
214C2×C22⋊D53—26no—
215C2×C22⋊D53—248no—
216C2×C22⋊D53—23no—
217C2×C22⋊D53C2×D416yes—
218C22×Dic53—23no—
219C22×Dic53—224no—
220C22×Dic53—23no—
221C22×Dic53—26no—
222C22×Dic53—23no—
223C22×Dic53C2×D413yes—
224#11719949—22no—
225#11719949C22⋊C418yes—
226#11719949C22×C414yes—
227Q8×D53—28no—
228Q8×D53—26no—
229Q8×D53C22⋊C418yes—
230Q8×D53C22×C4112yescomplemented
231#11719947—224no—
232#11719947—248no—
233#11719947—224no—
234#11719947—224no—
235#11719947—224no—
236#11719947—26no—
237#11719947—212no—
238#11719947—224no—
239#11719947C22⋊C4124yes—
240#11719947C22×C4112yes—
241#11719947C22×C4124yescomplemented
242D4×D53—224no—
243D4×D53—224no—
244D4×D53—26no—
245D4×D53C22⋊C4124yes—
246D4×D53C22×C4112yescomplemented
247#11719945—26no—
248#11719945—224no—
249#11719945—224no—
250#11719945C22×C4112yes—
251#11719945C22×C4112yescomplemented
252#11719945C2×D4112yes—
253C2×D212—21no—
254C2×D212C2×D413yes—
255C2×D212C2411yescharacteristic
256C2×C4×D53—23no—
257C2×C4×D53—23no—
258C2×C4×D53—21no—
259C2×C4×D53—224no—
260C2×C4×D53—21no—
261C2×C4×D53—23no—
262C2×C4×D53—26no—
263C2×C4×D53—86no—
264C2×C4×D53C22×C4112yes—
265C2×C4×D53C2×D413yes—
266C2×C4×D53C2×D413yes—
267C2×C4×D53C2×D4112yes—
268C2×C4×D53C2411yescharacteristic
269C2×C4×D53C2413yes—
270C2×Dic106—23no—
271C2×Dic106—26no—
272C2×Dic106—23no—
273C2×Dic106—224no—
274C2×Dic106C22×C4112yescomplemented
275C2×Dic106C2×D413yes—
276C2×Dic106C2413yes—
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—23no—
308C23×C53—212no—
309C23×C53—83no—
310C23×C53—83no—
311C23×C53C22×D413yes—
312C22×D53—21no—
313C22×D53—212no—
314C22×D53—43no—
315C22×D53—43no—
316C22×D53—83no—
317C22×D53—83no—
318C22×D53C2×C22⋊C4112yes—
319C22×D53C22×D411yescharacteristic
320C22×D53C22×D413yes—
321Q8×C53—21no—
322Q8×C53C2×C22⋊C414yes—
323Q8×C53C23×C412yes—
324D4×C53—212no—
325D4×C53—212no—
326D4×C53—23no—
327D4×C53C2×C22⋊C4112yes—
328D4×C53C23×C416yes—
329C2×C4×C53—21no—
330C2×C4×C53—212no—
331C2×C4×C53—23no—
332C2×C4×C53—21no—
333C2×C4×C53—83no—
334C2×C4×C53C23×C416yes—
335C2×C4×C53C22×D413yes—
336C2×C4×C53C22×D416yes—
337C2×C4×C53C2511yescharacteristic
338C22⋊D53—212no—
339C22⋊D53—212no—
340C22⋊D53—224no—
341C22⋊D53—212no—
342C22⋊D53C2×C22⋊C4124yes—
343C2×Dic53—212no—
344C2×Dic53—23no—
345C2×Dic53—224no—
346C2×Dic53—212no—
347C2×Dic53—23no—
348C2×Dic53—21no—
349C2×Dic53—83no—
350C2×Dic53C2×C22⋊C4112yes—
351C2×Dic53C22×D413yes—
352C2×Dic53C22×D411yescharacteristic
353D212—24no—
354D212—21no—
355D212C2×C22⋊C4112yes—
356D212C23×C412yes—
357C4×D53—212no—
358C4×D53—212no—
359C4×D53—24no—
360C4×D53—42no—
361C4×D53—46no—
362C4×D53—86no—
363C4×D53C2×C22⋊C4112yes—
364C4×D53C2×C22⋊C4112yes—
365C4×D53C23×C412yes—
366C4×D53C23×C416yes—
367C4×D53C22×D412yes—
368C4×D53C22×D416yes—
369Dic106—212no—
370Dic106—23no—
371Dic106—212no—
372Dic106C2×C22⋊C4112yes—
373Dic106C23×C416yes—
374C8×C53—23no—
375C8×C53—21no—
376#88322—23no—
377#88322—21no—
378#60089—531nomaximal, Sylow
379C22×C53—23no—
380C22×C53—23no—
381C22×C53—26no—
382C22×C53—43no—
383C22×C53—43no—
384C22×C53—812no—
385C22×C53C22×C22⋊C416yes—
386C22×C53C23×D411yescharacteristic
387C2×D53—21no—
388C2×D53—23no—
389C2×D53—21no—
390C2×D53—23no—
391C2×D53—22no—
392C2×D53—412no—
393C2×D53—41no—
394C2×D53—41no—
395C2×D53—812no—
396C2×D53C22×C22⋊C416yes—
397C2×D53C22×C22⋊C412yes—
398C4×C53—22no—
399C4×C53—43no—
400C4×C53—41no—
401C4×C53C22×C22⋊C416yes—
402C4×C53C24×C411yescharacteristic
403C4×C53C23×D411yescharacteristic
404Dic53—26no—
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#2898—531no—
416#2897—533no—
417#2897—533no—
418#2897—531no—
419#2897D5311yescharacteristic, complemented
420#2896—533no—
421#2896—533no—
422C2×#417—533no—
423C2×#417—533no—
424C2×C53—26no—
425C2×C53—46no—
426C2×C53C23×C22⋊C411yescharacteristic
427C2×C53#358511yescharacteristic
428C2×C53#358611yescharacteristic
429D53—22no—
430D53—26no—
431D53—42no—
432#585—5316no—
433#585—1068no—
434C2×2−1+4—533no—
435C2×2−1+4—531no—
436C2×2−1+4—1061no—
437C2×H(5,𝔽2)—533no—
438C2×H(5,𝔽2)—1063no—
439C2×H(5,𝔽2)C2×D5311yescharacteristic
440C22×#41—531no—
441C22×#41—533no—
442C22×#41—533no—
443C22×#41—1063no—
444C22×#41—1061no—
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#419—533no—
466#418—533no—
467#418—533no—
468#418—533no—
469#418C2×D5313yescomplemented
470#417—533no—
471#417—533no—
472#417—533no—
473#417—533no—
474#417—531no—
475#417—536no—
476#417—533no—
477#417—536no—
478#417—536no—
479#417—533no—
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—533no—
489C2×#103—536no—
490C2×#102—533no—
491C2×#102—536no—
492C2×#102C2×D5313yescomplemented
493C53#6008911yescharacteristic, complemented, Sylow
4942−1+4—538no—
4952−1+4—5324no—
4962−1+4—10616no—
4972−1+4—10612no—
4982−1+4—1064no—
499H(5,𝔽2)—24no—
500H(5,𝔽2)—5324no—
501H(5,𝔽2)—10648no—
502H(5,𝔽2)—10612no—
503H(5,𝔽2)C4×D5318yescomplemented
504C2×#41—21no—
505C2×#41—538no—
506C2×#41—538no—
507C2×#41—531no—
508C2×#41—533no—
509C2×#41—533no—
510C2×#41—5324no—
511C2×#41—531no—
512C2×#41—5324no—
513C2×#41—533no—
514C2×#41—536no—
515C2×#41—533no—
516C2×#41—1063no—
517C2×#41—1063no—
518C2×#41—1063no—
519C2×#41—1063no—
520C2×#41—1063no—
521C2×#41—10612no—
522C2×#41—10612no—
523C2×#41—1066no—
524C2×#41—1063no—
525C2×#41—10648no—
526C2×#41—10616no—
527C2×#41—1063no—
528C2×#41C22×D5313yes—
529C2×#41C22×D5311yescharacteristic
530C22×Q8—531no—
531C22×Q8—533no—
532C22×Q8—533no—
533C22×Q8—1063no—
534C22×Q8—1061no—
535C22×D4—23no—
536C22×D4—533no—
537C22×D4—533no—
538C22×D4—1063no—
539C22×D4—1063no—
540C22×D4—1066no—
541C22×D4—1063no—
542C22×D4C22×D5313yes—
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—533no—
589#103—531no—
590#103—536no—
591#103—533no—
592#103—533no—
593#103—536no—
594#103—533no—
595#103—533no—
596#103C22×D5313yes—
597#103C22×D5311yescharacteristic
598#102—536no—
599#102—533no—
600#102—533no—
601#102—533no—
602#102—531no—
603#102—533no—
604#102—531no—
605#102C22×D5316yes—
606#102C22×D5313yes—
607#102C22×D5313yes—
608C24—23no—
609C24—533no—
610C24—1063no—
611#41—28no—
612#41—26no—
613#41—538no—
614#41—5324no—
615#41—5312no—
616#41—5312no—
617#41—534no—
618#41—5312no—
619#41—5324no—
620#41—5312no—
621#41—10624no—
622#41—10624no—
623#41—10624no—
624#41—10624no—
625#41—1066no—
626#41—10624no—
627#41—10612no—
628#41—1062no—
629#41—10648no—
630#41—10624no—
631#41—10624no—
632#41—1066no—
633#41C2×C4×D5314yes—
634#41C2×C4×D53112yescomplemented
635#41D4×D5314yes—
636C2×Q8—538no—
637C2×Q8—533no—
638C2×Q8—5312no—
639C2×Q8—5312no—
640C2×Q8—533no—
641C2×Q8—1063no—
642C2×Q8—10624no—
643C2×Q8—1066no—
644C2×Q8—1068no—
645C2×Q8—1063no—
646C2×Q8—1066no—
647C2×Q8D4×D5311yescharacteristic
648C2×Q8C23×D5311yescharacteristic
649C2×D4—23no—
650C2×D4—224no—
651C2×D4—23no—
652C2×D4—26no—
653C2×D4—536no—
654C2×D4—5324no—
655C2×D4—5312no—
656C2×D4—533no—
657C2×D4—531no—
658C2×D4—1061no—
659C2×D4—1066no—
660C2×D4—1063no—
661C2×D4—10624no—
662C2×D4—10624no—
663C2×D4—10648no—
664C2×D4—1066no—
665C2×D4—1063no—
666C2×D4—10624no—
667C2×D4—1063no—
668C2×D4C2×C4×D53112yescomplemented
669C2×D4D4×D5313yes—
670C2×D4C23×D5313yes—
671C22×C4—23no—
672C22×C4—23no—
673C22×C4—533no—
674C22×C4—5312no—
675C22×C4—533no—
676C22×C4—533no—
677C22×C4—5312no—
678C22×C4—531no—
679C22×C4—533no—
680C22×C4—1061no—
681C22×C4—10624no—
682C22×C4—1063no—
683C22×C4—1066no—
684C22×C4—1061no—
685C22×C4—1063no—
686C22×C4—1063no—
687C22×C4—1066no—
688C22×C4—10624no—
689C22×C4—1063no—
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—531no—
702C2×C8—533no—
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—23no—
725C23—212no—
726C23—83no—
727C23—83no—
728C23—533no—
729C23—531no—
730C23—5312no—
731C23—10612no—
732C23—1061no—
733C23—4243no—
734C23—4243no—
735C23—2123no—
736C23—2123no—
737C23C2×D4×D5313yes—
738Q8—21no—
739Q8—5312no—
740Q8—536no—
741Q8—10612no—
742Q8—10612no—
743Q8—1063no—
744Q8C22⋊C4×D5314yes—
745Q8C22×C4×D5312yes—
746D4—212no—
747D4—212no—
748D4—23no—
749D4—5324no—
750D4—5312no—
751D4—532no—
752D4—1064no—
753D4—10612no—
754D4—10612no—
755D4—10624no—
756D4—10612no—
757D4—1061no—
758D4C22⋊C4×D53112yes—
759D4C22×C4×D5316yes—
760C2×C4—21no—
761C2×C4—212no—
762C2×C4—21no—
763C2×C4—23no—
764C2×C4—83no—
765C2×C4—5312no—
766C2×C4—533no—
767C2×C4—531no—
768C2×C4—5312no—
769C2×C4—5312no—
770C2×C4—532no—
771C2×C4—536no—
772C2×C4—536no—
773C2×C4—532no—
774C2×C4—1064no—
775C2×C4—10612no—
776C2×C4—10612no—
777C2×C4—10624no—
778C2×C4—10612no—
779C2×C4—1063no—
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—26no—
798C22—43no—
799C22—43no—
800C22—812no—
801C22—532no—
802C22—536no—
803C22—1063no—
804C22—1061no—
805C22—1061no—
806C22—1063no—
807C22—1062no—
808C22—42412no—
809C22—21212no—
810C22—2121no—
811C22—2121no—
812C22C2×C22⋊C4×D5316yes—
813C22C22×D4×D5311yescharacteristic
814C4—22no—
815C4—43no—
816C4—41no—
817C4—532no—
818C4—536no—
819C4—1066no—
820C4—2123no—
821C4—2121no—
822C4C2×C22⋊C4×D5316yes—
823C4C23×C4×D5311yescharacteristic
824C4C22×D4×D5311yescharacteristic
825C2—26no—
826C2—46no—
827C2—1066no—
828C2—1062no—
829C2—2122no—
830C2C22×C22⋊C4×D5311yescharacteristic
831C2#2028949011yescharacteristic
832C2#2028949711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC53×#2897C2
socleC22×C53C23×D4
prime radicalC2×#16811458C2
cosocleC2×C4×C53C25
hypercenter#2897D53
hypocenterC53#60089
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. C2×#16811388C2semidirect
3. #520×D53C2semidirect
4. #20283249C2semidirect
5. #20283246C2semidirect
6. #20283245C2semidirect
7. #20283244C2semidirect
8. #20283241C2semidirect
9. #20283240C2semidirect
10. #20283236C2semidirect
11. #20283230C2semidirect
12. #20283229C2semidirect
13. C2×#16810621C2semidirect
14. #417×D53C2semidirect
15. C53×#2897C2semidirect
17. #16811458C4semidirect
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. #16810633C22semidirect
44. #16810631C22semidirect
45. #16810630C22semidirect
46. #16810630C22semidirect
47. #16810628C22semidirect
48. #16810626C22semidirect
49. #16810626C22semidirect
50. #16810625C22semidirect
51. #16810624C22semidirect
52. #16810623C22semidirect
53. #16810623C22semidirect
54. #16810622C22semidirect
55. #16810621C22semidirect
56. #16810621C22semidirect
57. #16810621C22semidirect
58. #16810621C22semidirect
59. #16810621C22semidirect
60. #16810620C22semidirect
61. #16810619C22semidirect
62. #16810617C22semidirect
63. #16810616C22semidirect
64. #16810616C22semidirect
65. C2×#13133142C22semidirect
66. C2×#13133140C22semidirect
67. #103×D53C22semidirect
68. C2×#13133138C22semidirect
69. #102×D53C22semidirect
71. C2×#131×C53C22semidirect
72. C53×#520C22semidirect
73. C53×#418C22semidirect
74. C53×#417C22semidirect
75. C53×#416C22semidirect
76. C2×#102×C53C22semidirect
80. #13133264C2×C4semidirect
81. #13133264C2×C4semidirect
84. #13133262C2×C4semidirect
99. C2×#11719947C2×C4semidirect
106. #41×D53C2×C4semidirect
173. H(5,𝔽2)×C53C2×C4semidirect
197. #41×C53C22×C4semidirect
205. C2×D4×C53C22×C4semidirect
230. Q8×D53C22×C4semidirect
241. #11719947C22×C4semidirect
246. D4×D53C22×C4semidirect
251. #11719945C22×C4semidirect
274. C2×Dic106C22×C4semidirect
419. #2897D53semidirect
449. C2×#131C2×D53semidirect
457. #520C2×D53semidirect
469. #418C2×D53semidirect
480. #417C2×D53semidirect
486. #416C2×D53semidirect
492. C2×#102C2×D53semidirect
493. C53#60089semidirect
503. H(5,𝔽2)C4×D53semidirect
634. #41C2×C4×D53semidirect
668. C2×D4C2×C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168114582
C2×#168113882
#520×D532
#202832492
#202832462
#202832452
#202832442
#202832412
#202832402
#202832362
#202832302
#202832292
C2×#168106212
#417×D532
C53×#28972
#6008953