Finite Group Databasebeta

← #27290956

Subgroups — #27290956

Order 13568.

1264 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810640C211yesmaximal, characteristic, complemented
2#20283234C211yesmaximal, characteristic, complemented
3C2×#16810597C211yesmaximal, characteristic, complemented
4C2×#16810597C211yesmaximal, characteristic, complemented
5#20274453C211yesmaximal, characteristic, complemented
6#20274426C211yesmaximal, characteristic, complemented
7C2×C53×#575C211yesmaximal, characteristic
8C22×#11719917C2211yescharacteristic
9C2×#13133176C2211yescharacteristic
10C2×#13133176C2211yescharacteristic
11C2×#13133176C2211yescharacteristic
12#16810640—22no—
13#16810640—22no—
14C2×#13133144—22no—
15#16810632—21no—
16#16810628—21no—
17#16810624—22no—
18#16810619—22no—
19#16810597—22no—
20#16810597—22no—
21#16810597—22no—
22#16810597—22no—
23C2×#13133132—22no—
24C2×#13133132—22no—
25#16810391—22no—
26#16810384—22no—
27C22×#41×C53C2211yescharacteristic
28C22×#41×C53C2211yescharacteristic
29C53×#575—22no—
30C53×#575—22no—
31C53×#575—22no—
32C53×#575—22no—
33C2×#137×C53—21no—
34C2×#137×C53C412yescomplemented
35C2×AGL(1,ℤ/8)×C53—21no—
36C2×AGL(1,ℤ/8)×C53C412yescomplemented
37C2×#135×C53—22no—
38C22×M16×C53C2211yescharacteristic
39C2×#11719917—21no—
40C2×#11719917—21no—
41C2×#11719917—21no—
42C2×#11719917—21no—
43C2×#11719917—21no—
44C2×#11719917D412yes—
45C22×#88322—21no—
46#13133176—21no—
47#13133176—21no—
48#13133176—21no—
49#13133176—21no—
50#13133176—21no—
51#13133176—21no—
52#13133176—21no—
53#13133176—21no—
54#13133176—21no—
55#13133176—21no—
56#13133176D412yes—
57#13133176D412yes—
58C2×C4⋊Dic53—21no—
59C2×C4⋊Dic53—21no—
60C2×C4⋊Dic53—21no—
61C2×C22⋊Dic53—21no—
62C2×C22⋊Dic53—21no—
63C2×C22⋊Dic53D412yes—
64C2×C4×Dic53—21no—
65C2×C4×Dic53—21no—
66C2×C4×Dic53—21no—
67#13133144—28no—
68#13133141—24no—
69#13133138—24no—
70#13133132—28no—
71#13133132—28no—
72C2×#41×C53—21no—
73C2×#41×C53—21no—
74C2×#41×C53—21no—
75C2×#41×C53—21no—
76C2×#41×C53—21no—
77C2×#41×C53—21no—
78C2×#41×C53—21no—
79C2×#41×C53—21no—
80C2×#41×C53—21no—
81C2×#41×C53—21no—
82C2×#41×C53—21no—
83C2×#41×C53—21no—
84C2×#41×C53—21no—
85C2×#41×C53—21no—
86C2×#41×C53—21no—
87C2×#41×C53—21no—
88C2×#41×C53—21no—
89C2×#41×C53—21no—
90C2×#41×C53—21no—
91C2×#41×C53—21no—
92C2×#41×C53C2×C412yes—
93C2×#41×C53D412yes—
94C2×#41×C53D412yes—
95C2×#41×C53D412yes—
96C22×Q8×C53C2×C411yescharacteristic
97C22×Q8×C53D411yescharacteristic
98C22×D4×C53—21no—
99C22×D4×C53—21no—
100C22×D4×C53C2×C411yescharacteristic
101C22×D4×C53D411yescharacteristic
102C23×C4×C53—21no—
103C23×C4×C53—21no—
104C23×C4×C53C2311yescharacteristic
105#137×C53—24no—
106#137×C53—24no—
107#137×C53—24no—
108#137×C53—24no—
109AGL(1,ℤ/8)×C53—24no—
110AGL(1,ℤ/8)×C53—24no—
111AGL(1,ℤ/8)×C53—24no—
112AGL(1,ℤ/8)×C53—24no—
113#135×C53—28no—
114#135×C53—28no—
115C2×Q16×C53—22no—
116C2×SD16×C53—22no—
117C2×SD16×C53—22no—
118C2×D8×C53—22no—
119C2×M16×C53—21no—
120C2×M16×C53—21no—
121C2×M16×C53—21no—
122C2×M16×C53C2×C412yes—
123C2×M16×C53D412yes—
124C2×M16×C53D412yes—
125C22×C8×C53—21no—
126C24×C53—21no—
127C24×C53—21no—
128C24×C53C2×D411yescharacteristic
129#41×C53—22no—
130#41×C53—22no—
131#41×C53—22no—
132#41×C53—22no—
133#41×C53—22no—
134#41×C53—22no—
135#41×C53—22no—
136#41×C53—22no—
137#41×C53—22no—
138#41×C53—22no—
139#41×C53—22no—
140#41×C53—22no—
141#41×C53—22no—
142#41×C53—22no—
143#41×C53—22no—
144#41×C53—22no—
145#41×C53—41no—
146#41×C53—41no—
147#41×C53—41no—
148#41×C53—41no—
149#41×C53—41no—
150#41×C53—41no—
151#41×C53—41no—
152#41×C53—41no—
153#41×C53—41no—
154#41×C53—41no—
155#41×C53—41no—
156#41×C53—41no—
157#41×C53—41no—
158#41×C53—41no—
159#41×C53—41no—
160#41×C53—41no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53C22⋊C412yes—
172C2×Q8×C53C22⋊C412yes—
173C2×D4×C53—22no—
174C2×D4×C53—22no—
175C2×D4×C53—22no—
176C2×D4×C53—22no—
177C2×D4×C53—21no—
178C2×D4×C53—21no—
179C2×D4×C53—21no—
180C2×D4×C53—21no—
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—41no—
188C2×D4×C53—41no—
189C2×D4×C53—41no—
190C2×D4×C53—41no—
191C2×D4×C53—41no—
192C2×D4×C53—41no—
193C2×D4×C53—41no—
194C2×D4×C53—41no—
195C2×D4×C53C22⋊C412yes—
196C2×D4×C53C22⋊C412yes—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—22no—
202C22×C4×C53—22no—
203C22×C4×C53—41no—
204C22×C4×C53—41no—
205C22×C4×C53—41no—
206C22×C4×C53—41no—
207C22×C4×C53—41no—
208C22×C4×C53—41no—
209C22×C4×C53—41no—
210C22×C4×C53—41no—
211C22×C4×C53C22×C411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53#4111yescharacteristic
222C22×C4×C53#4111yescharacteristic
223C22×C4×C53#4111yescharacteristic
224C22×C4×C53#4111yescharacteristic
225C22×Dic53—22no—
226C22×Dic53—41no—
227C22×Dic53—41no—
228Q16×C53—28no—
229SD16×C53—28no—
230SD16×C53—28no—
231D8×C53—28no—
232M16×C53—22no—
233M16×C53—22no—
234M16×C53—22no—
235M16×C53C22⋊C414yes—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53—22no—
239C22⋊Dic53—22no—
240C22⋊Dic53—22no—
241C22⋊Dic53—22no—
242C22⋊Dic53—22no—
243C22⋊Dic53—41no—
244C22⋊Dic53—41no—
245C4⋊Dic53—22no—
246C4⋊Dic53—22no—
247C4⋊Dic53—41no—
248C4⋊Dic53—41no—
249C4⋊Dic53—41no—
250C4⋊Dic53—41no—
251C4×Dic53—22no—
252C4×Dic53—22no—
253C4×Dic53—41no—
254C4×Dic53—41no—
255C4×Dic53—41no—
256C4×Dic53—41no—
257#11719917—22no—
258#11719917—22no—
259#11719917—41no—
260#11719917—41no—
261C2×#88322—22no—
262C2×#88322—41no—
263C2×#88322—41no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53—81no—
271C23×C53—82no—
272C23×C53—82no—
273C23×C53C4×D411yescharacteristic
274C23×C53#12011yescharacteristic
275C23×C53#12011yescharacteristic
276C23×C53#12111yescharacteristic
277C23×C53#12111yescharacteristic
278C23×C53#12111yescharacteristic
279C23×C53#12711yescharacteristic
280Q8×C53—22no—
281Q8×C53—22no—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—41no—
285Q8×C53—41no—
286Q8×C53—41no—
287Q8×C53—41no—
288D4×C53—22no—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—42no—
293D4×C53—42no—
294D4×C53—42no—
295D4×C53—42no—
296D4×C53—42no—
297D4×C53—42no—
298D4×C53—42no—
299D4×C53—42no—
300D4×C53—41no—
301D4×C53—41no—
302D4×C53—41no—
303D4×C53—41no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53C2×C22⋊C411yescharacteristic
319C2×C4×C53C2×C22⋊C411yescharacteristic
320C2×C4×C53C2×C22⋊C411yescharacteristic
321C2×C4×C53C4×D411yescharacteristic
322C2×C4×C53C4×D411yescharacteristic
323C2×C4×C53C4×D411yescharacteristic
324C2×C4×C53#12011yescharacteristic
325C2×C4×C53#12011yescharacteristic
326C2×C4×C53#12011yescharacteristic
327C2×C4×C53#12011yescharacteristic
328C2×C4×C53#12011yescharacteristic
329C2×C4×C53#12011yescharacteristic
330C2×C4×C53#12111yescharacteristic
331C2×C4×C53#12111yescharacteristic
332C2×C4×C53#12111yescharacteristic
333C2×C4×C53#12111yescharacteristic
334C2×C4×C53#12111yescharacteristic
335C2×C4×C53#12111yescharacteristic
336C2×C4×C53#12111yescharacteristic
337C2×C4×C53#12111yescharacteristic
338C2×C4×C53#12111yescharacteristic
339C2×C4×C53#12311yescharacteristic
340C2×C4×C53#12311yescharacteristic
341C2×C4×C53#12311yescharacteristic
342C2×C4×C53#12311yescharacteristic
343C2×C4×C53#12411yescharacteristic
344C2×C4×C53#12411yescharacteristic
345C2×C4×C53#12711yescharacteristic
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349C2×Dic53—82no—
350C2×Dic53—82no—
351C2×Dic53—82no—
352C8×C53—24no—
353#88322—42no—
354#11033—531nomaximal, Sylow
355C22×C53—41no—
356C22×C53—41no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53—41no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—82no—
365C22×C53—82no—
366C22×C53—82no—
367C22×C53—82no—
368C22×C53—82no—
369C22×C53—82no—
370C22×C53#38611yescharacteristic
371C22×C53#38611yescharacteristic
372C22×C53#39011yescharacteristic
373C22×C53#39211yescharacteristic
374C22×C53#39211yescharacteristic
375C22×C53#39211yescharacteristic
376C22×C53#39411yescharacteristic
377C4×C53—42no—
378C4×C53—42no—
379C4×C53#37911yescharacteristic
380C4×C53#38611yescharacteristic
381C4×C53#38611yescharacteristic
382C4×C53#39011yescharacteristic
383C4×C53#39211yescharacteristic
384C4×C53#39411yescharacteristic
385C4×C53#39411yescharacteristic
386C4×C53#39411yescharacteristic
387Dic53—82no—
388Dic53—82no—
389Dic53—82no—
390C2×#575D5311yescharacteristic
391C2×#421—531no—
392#2896—531no—
393C2×#410—531no—
394C2×#410—531no—
395#1742—531no—
396#1733—531no—
397C2×C53—21no—
398C2×C53—21no—
399C2×C53—21no—
400C2×C53—21no—
401C2×C53—21no—
402C2×C53—21no—
403C2×C53—21no—
404C2×C53—82no—
405C2×C53—82no—
406C2×C53#143811yescharacteristic
407C22×#41C2×D5311yescharacteristic
408C22×#41C2×D5311yescharacteristic
409#575—22no—
410#575—22no—
411#575—22no—
412#575—22no—
413C2×#137—21no—
414C2×#137Dic5312yescomplemented
415C2×AGL(1,ℤ/8)—21no—
416C2×AGL(1,ℤ/8)Dic5312yescomplemented
417C2×#135—22no—
418C22×M16—531no—
419C22×M16C2×D5311yescharacteristic
420C2×#117—531no—
421C2×#117—531no—
422C2×#117—531no—
423#421—1062no—
424#421—1062no—
425C2×#104—1062no—
426#419—1061no—
427#418—1061no—
428#417—1062no—
429#416—1062no—
430#410—1062no—
431#410—1062no—
432#410—1062no—
433#410—1062no—
434C2×#99—1062no—
435C2×#99—1062no—
436#343—1062no—
437#339—1062no—
438C53#1103311yescharacteristic, complemented, Sylow
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41C2×Dic5312yes—
460C2×#41C22⋊D5312yes—
461C2×#41C22⋊D5312yes—
462C2×#41C22⋊D5312yes—
463C22×Q8C2×Dic5311yescharacteristic
464C22×Q8C22⋊D5311yescharacteristic
465C22×D4—21no—
466C22×D4—21no—
467C22×D4C2×Dic5311yescharacteristic
468C22×D4C22⋊D5311yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4C22×D5311yescharacteristic
472#137—24no—
473#137—24no—
474#137—24no—
475#137—24no—
476AGL(1,ℤ/8)—24no—
477AGL(1,ℤ/8)—24no—
478AGL(1,ℤ/8)—24no—
479AGL(1,ℤ/8)—24no—
480#135—28no—
481#135—28no—
482C2×Q16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×D8—22no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—532no—
490C2×M16—1061no—
491C2×M16—1061no—
492C2×M16—1061no—
493C2×M16—1061no—
494C2×M16—1061no—
495C2×M16C2×Dic5312yes—
496C2×M16C22⋊D5312yes—
497C2×M16C22⋊D5312yes—
498C22×C8—21no—
499C22×C8—1061no—
500#117—532no—
501#117—532no—
502#117—1061no—
503#117—1061no—
504#117—1061no—
505#117—1061no—
506#117—1061no—
507#117—1061no—
508#117—1061no—
509#117—1061no—
510#117—1061no—
511#117—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C22⋊C4—532no—
516C2×C22⋊C4—1061no—
517C2×C22⋊C4—1061no—
518C2×C42—1061no—
519C2×C42—1061no—
520C2×C42—1061no—
521#104—1068no—
522#103—1064no—
523#102—1064no—
524#99—1068no—
525#99—1068no—
526C24—21no—
527C24—21no—
528C24D4×D5311yescharacteristic
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8C22⋊Dic5312yes—
572C2×Q8C22⋊Dic5312yes—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4C22⋊Dic5312yes—
596C2×D4C22⋊Dic5312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—1062no—
612C22×C4—2121no—
613C22×C4—2121no—
614C22×C4D4×D5311yescharacteristic
615C22×C4D4×D5311yescharacteristic
616C22×C4D4×D5311yescharacteristic
617C22×C4#1171994711yescharacteristic
618C22×C4#1171994711yescharacteristic
619C22×C4#1171994711yescharacteristic
620C22×C4#1171994711yescharacteristic
621C22×C4C22×Dic5311yescharacteristic
622C22×C4C2×C22⋊D5311yescharacteristic
623C22×C4C2×C22⋊D5311yescharacteristic
624C22×C4C2×C22⋊D5311yescharacteristic
625C22×C4C2×C22⋊D5311yescharacteristic
626C22×C4C2×C22⋊D5311yescharacteristic
627C22×C4C2×C22⋊D5311yescharacteristic
628Q16—28no—
629SD16—28no—
630SD16—28no—
631D8—28no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—1062no—
636M16—1062no—
637M16—2121no—
638M16—2121no—
639M16C22⋊Dic5314yes—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—1062no—
644C2×C8—2121no—
645C2×C8—2121no—
646C4⋊C4—1062no—
647C4⋊C4—1062no—
648C4⋊C4—2121no—
649C4⋊C4—2121no—
650C4⋊C4—2121no—
651C4⋊C4—2121no—
652C22⋊C4—1062no—
653C22⋊C4—1062no—
654C22⋊C4—1062no—
655C22⋊C4—1062no—
656C22⋊C4—2121no—
657C22⋊C4—2121no—
658C42—1062no—
659C42—1062no—
660C42—2121no—
661C42—2121no—
662C42—2121no—
663C42—2121no—
664C23—22no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—81no—
671C23—82no—
672C23—82no—
673C23D4×Dic5311yescharacteristic
674C23#1313318511yescharacteristic
675C23#1313318511yescharacteristic
676C23#1313318811yescharacteristic
677C23#1313318911yescharacteristic
678C23#1313318911yescharacteristic
679C23#1313321311yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—4242no—
719C2×C4—4242no—
720C2×C4—4242no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4C2×C22⋊Dic5311yescharacteristic
725C2×C4C2×C22⋊Dic5311yescharacteristic
726C2×C4C2×C22⋊Dic5311yescharacteristic
727C2×C4D4×Dic5311yescharacteristic
728C2×C4D4×Dic5311yescharacteristic
729C2×C4D4×Dic5311yescharacteristic
730C2×C4#1313318511yescharacteristic
731C2×C4#1313318511yescharacteristic
732C2×C4#1313318611yescharacteristic
733C2×C4#1313318611yescharacteristic
734C2×C4#1313318611yescharacteristic
735C2×C4#1313318611yescharacteristic
736C2×C4#1313318811yescharacteristic
737C2×C4#1313318811yescharacteristic
738C2×C4#1313318811yescharacteristic
739C2×C4#1313318911yescharacteristic
740C2×C4#1313318911yescharacteristic
741C2×C4#1313318911yescharacteristic
742C2×C4#1313318911yescharacteristic
743C2×C4#1313318911yescharacteristic
744C2×C4#1313318911yescharacteristic
745C2×C4#1313319811yescharacteristic
746C2×C4#1313319811yescharacteristic
747C2×C4#1313319811yescharacteristic
748C2×C4#1313319811yescharacteristic
749C2×C4#1313320411yescharacteristic
750C2×C4#1313320411yescharacteristic
751C2×C4#1313321311yescharacteristic
752C8—24no—
753C8—2122no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22#1681050311yescharacteristic
770C22#1681050311yescharacteristic
771C22#1681052611yescharacteristic
772C22#1681053111yescharacteristic
773C22#1681053111yescharacteristic
774C22#1681053111yescharacteristic
775C22#1681053711yescharacteristic
776C4—42no—
777C4—42no—
778C4—4242no—
779C4—4242no—
780C4—4242no—
781C4#1681047911yescharacteristic
782C4#1681050311yescharacteristic
783C4#1681050311yescharacteristic
784C4#1681052611yescharacteristic
785C4#1681053111yescharacteristic
786C4#1681053711yescharacteristic
787C4#1681053711yescharacteristic
788C4#1681053711yescharacteristic
789C2—21no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—82no—
797C2—82no—
798C2#2027295611yescharacteristic
subgroupG/H
centerC4#16810537
commutatorC22×C4×C53C22×C4
FrattiniC23×C4C22×D53
Fitting, prime radicalC2×C53×#575C2
socleC2×C53#1438
cosocleC23×C4×C53C23
hypercenterC2×#575D53
hypocenterC53#11033
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#16810640C2semidirect
2. #20283234C2semidirect
3. C2×#16810597C2semidirect
4. C2×#16810597C2semidirect
5. #20274453C2semidirect
6. #20274426C2semidirect
34. C2×#137×C53C4semidirect
36. C2×AGL(1,ℤ/8)×C53C4semidirect
414. C2×#137Dic53semidirect
416. C2×AGL(1,ℤ/8)Dic53semidirect
438. C53#11033semidirect

Maximal subgroups

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

subgroupindex
C2×#168106402
#202832342
C2×#168105972
#202744532
#202744262
C2×C53×#5752
#1103353