Finite Group Databasebeta

← C2×#20286726 #28260799

Subgroups — C2×#20286726 #28260799

Order 13568.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811323C211yesmaximal, characteristic, complemented
2C2×#16811295C211yesmaximal, characteristic, complemented
3#20286726C2116yesmaximal, direct product factor
4C2×#16810988C211yesmaximal, characteristic, complemented
5C2×#16810950C211yesmaximal, characteristic, complemented
6C2×#16810938C211yesmaximal, characteristic, complemented
7C2×#16810930C211yesmaximal, characteristic, complemented
8C2×#16810875C211yesmaximal, characteristic, complemented
9C2×#16810858C211yesmaximal, characteristic, complemented
10C2×#16810818C211yesmaximal, characteristic, complemented
11C2×#16810767C211yesmaximal, characteristic, complemented
12C2×#16810767C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810623C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719949C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811323—24no—
24#16811323C2218yescomplemented
25#16811295—24no—
26#16811295C2218yescomplemented
27C2×#13133214—21no—
28C2×#13133214C2211yescharacteristic
29C2×#13133210—21no—
30C2×#13133209C2211yescharacteristic
31C2×#13133200—21no—
32C2×#13133192—21no—
33C2×#13133192—21no—
34C2×#13133192C2211yescharacteristic
35C2×#13133192C2211yescharacteristic
36C2×#13133190—21no—
37C2×#13133188C2211yescharacteristic
38C2×#13133188C2211yescharacteristic
39C2×C4×D212—21no—
40C2×C4×D212C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×#13133175C2211yescharacteristic
43C2×C4⋊C4×D53C2211yescharacteristic
44#16810988C2218yescomplemented
45#16810950C2218yescomplemented
46#16810938C2218yescomplemented
47#16810930C2218yescomplemented
48#16810875C2218yescomplemented
49#16810858C2218yescomplemented
50#16810818C2218yescomplemented
51#16810767C2218yescomplemented
52#16810767C2218yescomplemented
53#16810696C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×C4⋊#88322C2211yescharacteristic
57#16810623C2218yescomplemented
58#16810618C2218yescomplemented
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—22no—
79C2×#11719949—24no—
80C2×#11719949—24no—
81C2×#11719949—42no—
82C2×#11719949—42no—
83C2×#11719949C2314yes—
84C2×#11719949C2314yes—
85C22×D212—21no—
86C22×D212—21no—
87C22×D212—21no—
88C22×D212—21no—
89C22×D212—21no—
90C22×D212—21no—
91C22×D212D411yescharacteristic
92C22×D212C2311yescharacteristic
93C22×D212C2311yescharacteristic
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53—21no—
98C22×C4×D53—21no—
99C22×C4×D53C2311yescharacteristic
100C22×C4×D53C2311yescharacteristic
101C2×#11719922—42no—
102C2×#11719922—42no—
103C2×#11719922C2314yes—
104C2×#11719922C2314yes—
105C2×#11719912—42no—
106C2×#11719912C2314yes—
107C22×#88322C2311yescharacteristic
108C22×#88322C2311yescharacteristic
109C2×C8×D53—42no—
110C2×C8×D53C2314yes—
111#13133214—22no—
112#13133214—28no—
113#13133214C2314yes—
114#13133210—28no—
115#13133209—22no—
116#13133209C2314yes—
117#13133200—28no—
118#13133192—28no—
119#13133192—28no—
120#13133192—22no—
121#13133192—22no—
122#13133192C2314yes—
123#13133192C2314yes—
124#13133190—28no—
125#13133188—22no—
126#13133188—22no—
127#13133188C2314yes—
128#13133188C2314yes—
129C4×D212—28no—
130C4×D212D414yes—
131C4×D212C2314yes—
132C4×C22⋊D53—28no—
133#13133175—22no—
134#13133175C2314yes—
135C2×C4⋊Dic53D411yescharacteristic
136C2×C4⋊Dic53C2311yescharacteristic
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C4⋊C4×D53—22no—
142C4⋊C4×D53C2314yes—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151#13133150C2314yes—
152#13133148C2314yes—
153C4⋊#88322C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158#13133139C2314yes—
159#13133139C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133129C2314yes—
163#13133129C2314yes—
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C2×SD16×C53—24no—
168C2×SD16×C53C2314yes—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C4×D4×C53—22no—
174C4×D4×C53C2314yes—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#107×C53C2314yes—
182#103×C53C2314yes—
183#102×C53C2314yes—
184#97×C53C2314yes—
185C24×C53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C23×D53C2×D411yescharacteristic
189C23×D53C2×D411yescharacteristic
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53#4114yes—
193C2×Q8×C53C2412yes—
194C2×D4×C53—21no—
195C2×D4×C53—22no—
196C2×D4×C53—22no—
197C2×D4×C53C2412yes—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—82no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—44no—
209C2×C22⋊D53—82no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214#11719949—28no—
215#11719949—28no—
216#11719949—44no—
217#11719949—44no—
218#11719949—48no—
219#11719949—48no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—22no—
223C2×D212—22no—
224C2×D212—24no—
225C2×D212—24no—
226C2×D212—24no—
227C2×D212—21no—
228C2×D212—21no—
229C2×D212—24no—
230C2×D212—24no—
231C2×D212—24no—
232C2×D212—42no—
233C2×D212—44no—
234C2×D212—44no—
235C2×D212—44no—
236C2×D212—82no—
237C2×D212—82no—
238C2×D212—82no—
239C2×D212C2×D414yes—
240C2×D212C2412yes—
241C2×D212C2412yes—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—22no—
245C2×C4×D53—22no—
246C2×C4×D53—24no—
247C2×C4×D53—24no—
248C2×C4×D53—24no—
249C2×C4×D53—44no—
250C2×C4×D53—44no—
251C2×C4×D53—82no—
252C2×C4×D53C2×D412yes—
253C2×C4×D53C2×D412yes—
254C2×C4×D53C2412yes—
255C2×C4×D53C2412yes—
256SD16×C53—28no—
257C2×C8×C53—22no—
258C2×C8×C53—22no—
259C2×C8×C53C2412yes—
260C2×C8×C53C2412yes—
261C4⋊C4×C53—24no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C22⋊C4×C53—24no—
267C42×C53—24no—
268C42×C53C2×D412yes—
269C42×C53C2412yes—
270C22⋊Dic53—24no—
271C22⋊Dic53—24no—
272#11719922—44no—
273#11719922—44no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277#11719921C2×D414yes—
278#11719921C2×D414yes—
279C4⋊Dic53—21no—
280C4⋊Dic53—21no—
281C4⋊Dic53C2×D414yes—
282C4⋊Dic53C2412yes—
283C4⋊Dic53C2412yes—
284#11719919—24no—
285#11719919—24no—
286#11719919—24no—
287C4×Dic53—24no—
288C2×#88322—22no—
289C2×#88322—22no—
290C2×#88322C2412yes—
291C2×#88322C2412yes—
292#11719912—44no—
293C8×D53—44no—
294C23×C53—22no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53C22×D411yescharacteristic
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—42no—
312C22×D53—42no—
313C22×D53C22×D412yes—
314C22×D53C22×D412yes—
315Q8×C53—24no—
316Q8×C53—22no—
317Q8×C53C2×#4114yes—
318D4×C53—22no—
319D4×C53—22no—
320D4×C53—42no—
321C2×C4×C53—24no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53—84no—
330C2×C4×C53C22×D412yes—
331C2×C4×C53C22×D412yes—
332C2×C4×C53C22×D411yescharacteristic
333C2×C4×C53C2×#4112yes—
334C2×C4×C53H(5,𝔽2)12yes—
335C2×C4×C53C2511yescharacteristic
336C22⋊D53—48no—
337C22⋊D53—84no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346D212—22no—
347D212—22no—
348D212—22no—
349D212—22no—
350D212—44no—
351D212—48no—
352D212—48no—
353D212—48no—
354D212—42no—
355D212—42no—
356D212—84no—
357D212—84no—
358D212—84no—
359C4×D53—24no—
360C4×D53—24no—
361C4×D53—22no—
362C4×D53—22no—
363C4×D53—22no—
364C4×D53—22no—
365C4×D53—48no—
366C4×D53—48no—
367C4×D53—84no—
368C8×C53—22no—
369C8×C53—22no—
370#88322—22no—
371#88322—22no—
372C2×#3309—531nomaximal, Sylow
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—42no—
376C22×C53—84no—
377C22×C53#54612yes—
378C22×C53#57512yes—
379C22×C53#57612yes—
380C22×C53C23×D411yescharacteristic
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—22no—
385C2×D53—22no—
386C2×D53—22no—
387C2×D53—44no—
388C2×D53—44no—
389C2×D53—42no—
390C2×D53—42no—
391C2×D53—42no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—84no—
396C2×D53—84no—
397C4×C53—24no—
398C4×C53—22no—
399C4×C53—22no—
400C4×C53—42no—
401C4×C53—42no—
402C4×C53#54612yes—
403C4×C53C22×#4111yescharacteristic
404C4×C53C2×H(5,𝔽2)11yescharacteristic
405Dic53—22no—
406Dic53—22no—
407Dic53—42no—
408Dic53—42no—
409C2×#553—531no—
410C2×#550—531no—
411#3309—5316no—
412C2×#490—531no—
413C2×#482—531no—
414C2×#480—531no—
415C2×#479—531no—
416C2×#469—531no—
417C2×#466—531no—
418C2×#459—531no—
419C2×#449—531no—
420C2×#449—531no—
421C2×#440D5311yescharacteristic, complemented
422C2×#435—531no—
423C2×#417—531no—
424C2×#416—531no—
425C2×C53—82no—
426C2×C53#330914yescomplemented
427C2×C53C2×#54611yescharacteristic
428C2×C53C2×#57511yescharacteristic
429C2×C53C2×#57611yescharacteristic
430D53—42no—
431D53—42no—
432D53—82no—
433D53—82no—
434C22×#41—531no—
435C22×#41—531no—
436C22×SD16C2×D5311yescharacteristic
437C22×D8—531no—
438C22×D8—531no—
439C22×M16—531no—
440C23×C8—531no—
441#553—538no—
442#553—1064no—
443#550—538no—
444#550—1064no—
445C2×#127—531no—
446C2×#127—1061no—
447C2×#126—1061no—
448C2×#125—531no—
449C2×#123—1061no—
450C2×#121—531no—
451C2×#121—531no—
452C2×#121—531no—
453C2×#121—531no—
454C2×#121—1061no—
455C2×#121—1061no—
456C2×#121—1061no—
457C2×C4×Q8C2×D5311yescharacteristic
458C2×C4×D4—531no—
459C2×C4×D4—1061no—
460C2×C4×D4—1061no—
461C2×C4×D4C2×D5311yescharacteristic
462C2×#117—531no—
463C22×C4⋊C4—531no—
464#490—538no—
465#482—538no—
466#480—538no—
467#479—538no—
468#469—538no—
469#466—538no—
470#459—538no—
471#449—538no—
472#449—538no—
473#440C2×D5318yescomplemented
474#435—538no—
475C2×#107—531no—
476C2×#107C2×D5311yescharacteristic
477C2×#106—531no—
478C2×C4⋊C8—531no—
479#417—538no—
480#416—538no—
481C2×#103—531no—
482C2×#103—531no—
483C2×#103C2×D5311yescharacteristic
484C2×#102—531no—
485C2×#102—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102C2×D5311yescharacteristic
491C2×C22⋊C8—531no—
492C2×C22⋊C8—531no—
493C2×#97C2×D5311yescharacteristic
494C53C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—534no—
496C2×#41—534no—
497C2×#41—1062no—
498C2×#41—1062no—
499C2×#41—1064no—
500C2×#41—1064no—
501C2×#41—2122no—
502C2×#41—2122no—
503C22×Q8C22×D5311yescharacteristic
504C22×D4—531no—
505C22×D4—531no—
506C22×D4—531no—
507C22×D4—1061no—
508C22×D4—1061no—
509C22×D4—1061no—
510C22×D4—1061no—
511C22×D4—1061no—
512C22×D4—1061no—
513C22×D4—1061no—
514C22×D4—1061no—
515C22×D4C22×D5311yescharacteristic
516C23×C4—21no—
517C23×C4—531no—
518C23×C4—531no—
519C23×C4—1061no—
520C23×C4—1061no—
521C23×C4—1061no—
522C2×SD16—24no—
523C2×SD16C22×D5314yes—
524C2×D8—534no—
525C2×D8—534no—
526C2×D8—2122no—
527C2×D8—2122no—
528C2×M16—534no—
529C2×M16—2122no—
530C22×C8—531no—
531C22×C8—531no—
532C22×C8—534no—
533C22×C8—2122no—
534C22×C8C22×D5311yescharacteristic
535C22×C8C22×D5311yescharacteristic
536#127—534no—
537#127—1068no—
538#127—1062no—
539#126—1068no—
540#125—534no—
541#125—1062no—
542#123—1068no—
543#121—534no—
544#121—534no—
545#121—534no—
546#121—534no—
547#121—1068no—
548#121—1068no—
549#121—1068no—
550#121—1062no—
551#121—1062no—
552#121—1062no—
553#121—1062no—
554C4×Q8—22no—
555C4×Q8C22×D5314yes—
556C4×D4—22no—
557C4×D4—534no—
558C4×D4—534no—
559C4×D4—1068no—
560C4×D4—1068no—
561C4×D4C22×D5314yes—
562#117—534no—
563#117—1062no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—531no—
566C2×C4⋊C4—531no—
567C2×C4⋊C4—531no—
568C2×C4⋊C4—534no—
569C2×C4⋊C4—1062no—
570C2×C4⋊C4—1061no—
571C2×C4⋊C4—1061no—
572C2×C4⋊C4—1061no—
573C2×C4⋊C4C22×D5311yescharacteristic
574C2×C4⋊C4C22×D5311yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—531no—
577C2×C22⋊C4—531no—
578C2×C22⋊C4—1061no—
579C2×C22⋊C4—1061no—
580C2×C22⋊C4—1061no—
581C2×C22⋊C4—1061no—
582C2×C22⋊C4—1061no—
583C2×C42—21no—
584C2×C42—1061no—
585C2×C42C22×D5311yescharacteristic
586#107—534no—
587#107C22×D5314yes—
588#106—534no—
589C4⋊C8—534no—
590#103—534no—
591#103—534no—
592#103C22×D5314yes—
593#102—534no—
594#102—534no—
595#102—534no—
596#102—534no—
597#102—534no—
598#102—534no—
599#102C22×D5314yes—
600C22⋊C8—534no—
601C22⋊C8—534no—
602#97C22×D5314yes—
603C24—21no—
604C24—531no—
605C24—531no—
606C24—1061no—
607C24—1061no—
608#41—1068no—
609#41—1068no—
610#41—2124no—
611#41—2124no—
612#41—2128no—
613#41—2128no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8#1171994514yes—
617C2×Q8C23×D5312yes—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—534no—
622C2×D4—532no—
623C2×D4—532no—
624C2×D4—1064no—
625C2×D4—1064no—
626C2×D4—1064no—
627C2×D4—1064no—
628C2×D4—1064no—
629C2×D4—1064no—
630C2×D4—1064no—
631C2×D4—1064no—
632C2×D4—1061no—
633C2×D4—1061no—
634C2×D4—1062no—
635C2×D4—1062no—
636C2×D4—1062no—
637C2×D4—1062no—
638C2×D4—4242no—
639C2×D4—4242no—
640C2×D4—4242no—
641C2×D4—4242no—
642C2×D4—2122no—
643C2×D4—2124no—
644C2×D4—2124no—
645C2×D4—2124no—
646C2×D4—2124no—
647C2×D4C23×D5312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—24no—
652C22×C4—82no—
653C22×C4—531no—
654C22×C4—531no—
655C22×C4—532no—
656C22×C4—532no—
657C22×C4—532no—
658C22×C4—532no—
659C22×C4—1064no—
660C22×C4—1064no—
661C22×C4—1064no—
662C22×C4—1062no—
663C22×C4—1062no—
664C22×C4—1062no—
665C22×C4—1062no—
666C22×C4—1061no—
667C22×C4—1061no—
668C22×C4—4242no—
669C22×C4—2124no—
670C22×C4—2124no—
671C22×C4D4×D5311yescharacteristic
672C22×C4D4×D5311yescharacteristic
673C22×C4C23×D5311yescharacteristic
674SD16—28no—
675D8—2124no—
676D8—2124no—
677M16—2124no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—532no—
681C2×C8—532no—
682C2×C8—1062no—
683C2×C8—1062no—
684C2×C8—2124no—
685C2×C8C23×D5312yes—
686C2×C8C23×D5312yes—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—534no—
691C4⋊C4—532no—
692C4⋊C4—532no—
693C4⋊C4—1064no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4—1064no—
697C4⋊C4—1064no—
698C4⋊C4C23×D5312yes—
699C4⋊C4C23×D5312yes—
700C22⋊C4—24no—
701C22⋊C4—534no—
702C22⋊C4—534no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C22⋊C4—1064no—
706C22⋊C4—1064no—
707C22⋊C4—1064no—
708C42—24no—
709C42—1064no—
710C42D4×D5312yes—
711C42C23×D5312yes—
712C23—22no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—532no—
717C23—532no—
718C23—1062no—
719C23—1062no—
720C23—1062no—
721C23—1062no—
722C23—1062no—
723C23—1062no—
724C23—1062no—
725C23—1062no—
726C23—2122no—
727C23—2122no—
728C23—2122no—
729C23—2122no—
730C23—2122no—
731C23—2122no—
732C23C2×D4×D5311yescharacteristic
733Q8—24no—
734Q8—22no—
735Q8C2×#1171994514yes—
736D4—22no—
737D4—22no—
738D4—42no—
739D4—1062no—
740D4—1062no—
741D4—1062no—
742D4—1062no—
743D4—4244no—
744D4—4244no—
745D4—4244no—
746D4—4244no—
747D4—2124no—
748D4—2128no—
749D4—2128no—
750D4—2128no—
751D4—2128no—
752D4—2122no—
753D4—2122no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—84no—
763C2×C4—532no—
764C2×C4—532no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—1064no—
768C2×C4—1064no—
769C2×C4—1062no—
770C2×C4—1062no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—1062no—
774C2×C4—1062no—
775C2×C4—4244no—
776C2×C4—2128no—
777C2×C4—2128no—
778C2×C4—2122no—
779C2×C4—2122no—
780C2×C4C2×D4×D5312yes—
781C2×C4C2×D4×D5312yes—
782C2×C4C2×D4×D5311yescharacteristic
783C2×C4C2×#1171994512yes—
784C2×C4#1313326312yes—
785C2×C4C24×D5311yescharacteristic
786C8—22no—
787C8—22no—
788C8—1062no—
789C8—1062no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—84no—
794C22—1062no—
795C22—1062no—
796C22—1062no—
797C22—1062no—
798C22—1062no—
799C22—1062no—
800C22—4244no—
801C22—4244no—
802C22—2122no—
803C22—2122no—
804C22—2122no—
805C22—2122no—
806C22—2122no—
807C22—2122no—
808C22—2124no—
809C22—2124no—
810C22#1681126912yes—
811C22#1681142212yes—
812C22#1681142712yes—
813C22C22×D4×D5311yescharacteristic
814C4—24no—
815C4—22no—
816C4—22no—
817C4—42no—
818C4—42no—
819C4—1062no—
820C4—1062no—
821C4—2122no—
822C4—2122no—
823C4#1681126912yes—
824C4C22×#1171994511yescharacteristic
825C4C2×#1313326311yescharacteristic
826C2—82no—
827C2—4242no—
828C2—4242no—
829C2—2122no—
830C2—2122no—
831C2#2028672614yesdirect product factor
832C2C2×#1681126911yescharacteristic
833C2C2×#1681142211yescharacteristic
834C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
hypercenterC2×#440D53
hypocenterC53C2×#3309
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16811323C2semidirect
2. C2×#16811295C2semidirect
3. #20286726C2direct (N × H)
4. C2×#16810988C2semidirect
5. C2×#16810950C2semidirect
6. C2×#16810938C2semidirect
7. C2×#16810930C2semidirect
8. C2×#16810875C2semidirect
9. C2×#16810858C2semidirect
10. C2×#16810818C2semidirect
11. C2×#16810767C2semidirect
12. C2×#16810767C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810623C2semidirect
15. C2×#16810618C2semidirect
16. C2×C53×#440C2semidirect
24. #16811323C22semidirect
26. #16811295C22semidirect
44. #16810988C22semidirect
45. #16810950C22semidirect
46. #16810938C22semidirect
47. #16810930C22semidirect
48. #16810875C22semidirect
49. #16810858C22semidirect
50. #16810818C22semidirect
51. #16810767C22semidirect
52. #16810767C22semidirect
53. #16810696C22semidirect
57. #16810623C22semidirect
58. #16810618C22semidirect
72. C53×#440C22semidirect
421. C2×#440D53semidirect
426. C2×C53#3309semidirect
473. #440C2×D53semidirect
494. C53C2×#3309semidirect
831. C2#20286726direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113232
C2×#168112952
#202867262
C2×#168109882
C2×#168109502
C2×#168109382
C2×#168109302
C2×#168108752
C2×#168108582
C2×#168108182
C2×#168107672
C2×#168106962
C2×#168106232
C2×#168106182
C2×C53×#4402
C2×#330953