Finite Group Databasebeta

← C2×#20286660 #28260562

Subgroups — C2×#20286660 #28260562

Order 13568.

2262 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×#16811337C211yesmaximal, characteristic, complemented
2C2×#16811291C211yesmaximal, characteristic, complemented
3#20286660C2116yesmaximal, direct product factor
4C2×#16810968C211yesmaximal, characteristic, complemented
5C2×#16810950C211yesmaximal, characteristic, complemented
6C2×#16810944C211yesmaximal, characteristic, complemented
7C2×#16810917C211yesmaximal, characteristic, complemented
8C2×#16810858C211yesmaximal, characteristic, complemented
9C2×#16810816C211yesmaximal, characteristic, complemented
10C2×#16810766C211yesmaximal, characteristic, complemented
11C2×#16810765C211yesmaximal, characteristic, complemented
12C2×#16810714C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D53C211yesmaximal, characteristic, complemented
14C2×#16810620C211yesmaximal, characteristic, complemented
15C2×#16810616C211yesmaximal, characteristic, complemented
16C2×C53×#466C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811337—24no—
23#16811337C2218yescomplemented
24#16811291—24no—
25#16811291C2218yescomplemented
26C2×#13133216C2211yescharacteristic
27C2×#13133213—21no—
28C2×#13133213C2211yescharacteristic
29C2×#13133204—21no—
30C2×#13133203—21no—
31C2×#13133192C2211yescharacteristic
32C2×#13133190—21no—
33C2×#13133189—21no—
34C2×#13133189—21no—
35C2×#13133188C2211yescharacteristic
36C2×#13133182C2211yescharacteristic
37C2×D4×Dic53C2211yescharacteristic
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133177—21no—
40C2×#13133176C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42C2×#13133173—21no—
43#16810968C2218yescomplemented
44#16810950C2218yescomplemented
45#16810944C2218yescomplemented
46#16810917C2218yescomplemented
47#16810858C2218yescomplemented
48#16810816C2218yescomplemented
49#16810766C2218yescomplemented
50#16810765C2218yescomplemented
51#16810714C2218yescomplemented
52C8×C22⋊D53C2218yescomplemented
53C2×#13133150C2211yescharacteristic
54C2×#13133148C2211yescharacteristic
55C2×#13133146C2211yescharacteristic
56#16810620C2218yescomplemented
57#16810616C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×D8×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#466C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C2×#11719947—22no—
82C2×#11719947—24no—
83C2×#11719947—42no—
84C2×#11719947C2314yes—
85C22×Dic106—21no—
86C22×Dic106C2311yescharacteristic
87C22×D212—21no—
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53D411yescharacteristic
95C23×Dic53—21no—
96C23×Dic53—21no—
97C22×C4×D53—21no—
98C22×C4×D53C2311yescharacteristic
99C2×#11719923—24no—
100C2×#11719923C2314yes—
101C2×#11719922—42no—
102C2×#11719922C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C2×C8×D53—42no—
106C2×C8×D53C2314yes—
107#13133216—22no—
108#13133216C2314yes—
109#13133213—22no—
110#13133213—28no—
111#13133213C2314yes—
112#13133204—28no—
113#13133203—28no—
114#13133192—22no—
115#13133192C2314yes—
116#13133190—28no—
117#13133189—28no—
118#13133189—28no—
119#13133188—22no—
120#13133188C2314yes—
121#13133182—22no—
122#13133182C2314yes—
123D4×Dic53—22no—
124D4×Dic53C2314yes—
125C4×C22⋊D53D414yes—
126C4×C22⋊D53C2314yes—
127#13133177—28no—
128#13133176—22no—
129#13133176C2314yes—
130#13133175—22no—
131#13133175C2314yes—
132#13133173—28no—
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919D411yescharacteristic
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53D411yescharacteristic
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921D411yescharacteristic
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133140C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133137C2314yes—
160C22⋊#88322C2314yes—
161#13133129C2314yes—
162C8×Dic53C2314yes—
163C22×D4×C53—21no—
164C22×D4×C53—21no—
165C22×D4×C53C2311yescharacteristic
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53C2311yescharacteristic
168C2×D8×C53—42no—
169C2×D8×C53C2314yes—
170C22×C8×C53—42no—
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2314yes—
174#121×C53—22no—
175#121×C53—22no—
176#121×C53C2314yes—
177#121×C53C2314yes—
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182#107×C53C2314yes—
183#102×C53C2314yes—
184#102×C53C2314yes—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C23×D53—21no—
189C23×D53C2×D411yescharacteristic
190C2×D4×C53—24no—
191C2×D4×C53—24no—
192C2×D4×C53—21no—
193C2×D4×C53—21no—
194C2×D4×C53—22no—
195C2×D4×C53—22no—
196C2×D4×C53—22no—
197C2×D4×C53—22no—
198C2×D4×C53—82no—
199C2×D4×C53—82no—
200C2×D4×C53C2412yes—
201C2×D4×C53C2412yes—
202C22×C4×C53—22no—
203C22×C4×C53—22no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D412yes—
208C22×C4×C53C2412yes—
209C22×C4×C53C2411yescharacteristic
210C2×C22⋊D53—24no—
211C2×C22⋊D53—24no—
212C2×C22⋊D53—24no—
213C2×C22⋊D53—24no—
214C2×C22⋊D53—24no—
215C2×C22⋊D53—24no—
216C2×C22⋊D53—44no—
217C2×C22⋊D53—44no—
218C2×C22⋊D53—44no—
219C2×C22⋊D53—82no—
220C2×C22⋊D53—82no—
221C2×C22⋊D53C2×D414yes—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—24no—
226C22×Dic53—24no—
227C22×Dic53—44no—
228C22×Dic53—44no—
229C22×Dic53C2×D411yescharacteristic
230C22×Dic53C2×D411yescharacteristic
231C22×Dic53C2×D411yescharacteristic
232#11719947—28no—
233#11719947—44no—
234#11719947—48no—
235#11719945—28no—
236#11719945—44no—
237#11719945—48no—
238C2×D212—22no—
239C2×D212—22no—
240C2×D212—21no—
241C2×D212—24no—
242C2×D212—82no—
243C2×D212C2412yes—
244C2×C4×D53—22no—
245C2×C4×D53—22no—
246C2×C4×D53—24no—
247C2×C4×D53—44no—
248C2×C4×D53C2×D412yes—
249C2×C4×D53C2412yes—
250C2×Dic106—21no—
251C2×Dic106—22no—
252C2×Dic106—24no—
253C2×Dic106—82no—
254C2×Dic106#4114yes—
255C2×Dic106C2412yes—
256D8×C53—44no—
257C2×C8×C53—22no—
258C2×C8×C53—22no—
259C2×C8×C53—44no—
260C2×C8×C53C2412yes—
261C2×C8×C53C2412yes—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C22⋊C4×C53—24no—
267C22⋊C4×C53—24no—
268C22⋊Dic53—24no—
269C22⋊Dic53—24no—
270C22⋊Dic53—24no—
271C22⋊Dic53C2×D414yes—
272#11719923—28no—
273#11719922—44no—
274#11719921—24no—
275#11719921—24no—
276#11719921C2×D414yes—
277C4⋊Dic53—21no—
278C4⋊Dic53—21no—
279C4⋊Dic53C2412yes—
280C4⋊Dic53C2412yes—
281#11719919—24no—
282#11719919—24no—
283#11719919C2×D414yes—
284C4×Dic53—24no—
285C4×Dic53—24no—
286C4×Dic53—24no—
287C4×Dic53C2×D412yes—
288C4×Dic53C2412yes—
289C2×#88322—22no—
290C2×#88322—22no—
291C2×#88322C2412yes—
292C2×#88322C2412yes—
293C8×D53—44no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—42no—
300C23×C53—42no—
301C23×C53—42no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53C22×D412yes—
306C23×C53C22×D411yescharacteristic
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—42no—
312C22×D53—42no—
313C22×D53—42no—
314C22×D53C22×D412yes—
315D4×C53—22no—
316D4×C53—22no—
317D4×C53—22no—
318D4×C53—22no—
319D4×C53—42no—
320D4×C53—42no—
321D4×C53—84no—
322D4×C53—84no—
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×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53C22×D412yes—
332C2×C4×C53C22×D411yescharacteristic
333C2×C4×C53C2×#4112yes—
334C2×C4×C53H(5,𝔽2)12yes—
335C2×C4×C53C2511yescharacteristic
336C22⋊D53—28no—
337C22⋊D53—48no—
338C22⋊D53—48no—
339C22⋊D53—48no—
340C22⋊D53—84no—
341C22⋊D53—84no—
342C2×Dic53—24no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—48no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—48no—
352C2×Dic53#13514yes—
353C2×Dic53C22×D412yes—
354C2×Dic53C22×D412yes—
355C2×Dic53C22×D412yes—
356D212—22no—
357D212—22no—
358D212—42no—
359D212—84no—
360C4×D53—24no—
361C4×D53—22no—
362C4×D53—22no—
363C4×D53—48no—
364Dic106—24no—
365Dic106—22no—
366Dic106—84no—
367Dic106C2×#4114yes—
368C8×C53—22no—
369C8×C53—22no—
370#88322—22no—
371#88322—22no—
372C2×#3305—531nomaximal, Sylow
373C22×C53—22no—
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—44no—
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53—42no—
382C22×C53—42no—
383C22×C53—84no—
384C22×C53—84no—
385C22×C53#54612yes—
386C22×C53C2×#13512yes—
387C22×C53#57612yes—
388C22×C53C23×D411yescharacteristic
389C2×D53—22no—
390C2×D53—22no—
391C2×D53—22no—
392C2×D53—44no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—42no—
396C2×D53—84no—
397C4×C53—22no—
398C4×C53—42no—
399C4×C53—42no—
400C4×C53#54612yes—
401C4×C53C22×#4111yescharacteristic
402C4×C53C2×H(5,𝔽2)11yescharacteristic
403Dic53—24no—
404Dic53—22no—
405Dic53—22no—
406Dic53—42no—
407Dic53—42no—
408Dic53C2×#13514yes—
409C2×#555—531no—
410C2×#550—531no—
411#3305—5316no—
412C2×#486—531no—
413C2×#482—531no—
414C2×#482—531no—
415C2×#477—531no—
416C2×#466—531no—
417C2×#466D5311yescharacteristic, complemented
418C2×#459—531no—
419C2×#449—531no—
420C2×#449—531no—
421C2×C4×SD16—531no—
422C2×C8×D4—531no—
423C2×#416—531no—
424C2×#416—531no—
425C2×C53—42no—
426C2×C53—82no—
427C2×C53—82no—
428C2×C53#330514yescomplemented
429C2×C53C2×#54611yescharacteristic
430C2×C53C22×#13511yescharacteristic
431C2×C53C2×#57611yescharacteristic
432D53—42no—
433D53—82no—
434C22×#41—531no—
435C22×#41—531no—
436C22×SD16—531no—
437C22×D8—531no—
438C22×D8C2×D5311yescharacteristic
439C23×C8—531no—
440C23×C8C2×D5311yescharacteristic
441#555—538no—
442#555—1064no—
443#550—538no—
444#550—1064no—
445C2×C4⋊Q8—531no—
446C2×#127—531no—
447C2×#127—1061no—
448C2×#124—1061no—
449C2×#124—1061no—
450C2×#121—531no—
451C2×#121—531no—
452C2×#121—1061no—
453C2×#121—1061no—
454C2×#121—1061no—
455C2×#121C2×D5311yescharacteristic
456C2×#121C2×D5311yescharacteristic
457C2×C4×Q8—531no—
458C2×C4×D4—531no—
459C2×C4×D4—531no—
460C2×C4×D4—1061no—
461C2×#117—531no—
462C2×#117—531no—
463C2×#117—1061no—
464#486—538no—
465#482—538no—
466#482—538no—
467#477—538no—
468#466—538no—
469#466C2×D5318yescomplemented
470#459—538no—
471#449—538no—
472#449—538no—
473C4×SD16—538no—
474C8×D4—538no—
475C2×#107—531no—
476C2×#107C2×D5311yescharacteristic
477C2×#106—531no—
478C2×C4⋊C8—531no—
479#416—538no—
480#416—538no—
481C2×#103—531no—
482C2×#103—531no—
483C2×#103—531no—
484C2×#102—531no—
485C2×#102—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102C2×D5311yescharacteristic
490C2×#102C2×D5311yescharacteristic
491C2×C22⋊C8—531no—
492C2×C22⋊C8—531no—
493C2×C4×C8—531no—
494C53C2×#330511yescharacteristic, complemented, Sylow
495C2×#41—534no—
496C2×#41—534no—
497C2×#41—1064no—
498C2×#41—1062no—
499C2×#41—1062no—
500C2×#41—1064no—
501C2×#41—2122no—
502C2×#41—2122no—
503C22×Q8—531no—
504C22×Q8—1061no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—531no—
508C22×D4—531no—
509C22×D4—1061no—
510C22×D4—1061no—
511C22×D4—1061no—
512C22×D4—1061no—
513C22×D4—1061no—
514C22×D4—1061no—
515C22×D4C22×D5311yescharacteristic
516C22×D4C22×D5311yescharacteristic
517C23×C4—531no—
518C23×C4—1061no—
519C23×C4—1061no—
520C23×C4—1061no—
521C23×C4C22×D5311yescharacteristic
522C2×SD16—534no—
523C2×SD16—1064no—
524C2×D8—42no—
525C2×D8—534no—
526C2×D8—2122no—
527C2×D8C22×D5314yes—
528C22×C8—42no—
529C22×C8—531no—
530C22×C8—531no—
531C22×C8—534no—
532C22×C8—2122no—
533C22×C8C22×D5311yescharacteristic
534C22×C8C22×D5311yescharacteristic
535C22×C8C22×D5314yes—
536C4⋊Q8—534no—
537C4⋊Q8—1062no—
538#127—534no—
539#127—1062no—
540#127—1068no—
541#124—1068no—
542#124—1068no—
543#121—22no—
544#121—22no—
545#121—534no—
546#121—534no—
547#121—1068no—
548#121—1068no—
549#121—1062no—
550#121—1062no—
551#121—1068no—
552#121C22×D5314yes—
553#121C22×D5314yes—
554C4×Q8—534no—
555C4×Q8—1062no—
556C4×D4—534no—
557C4×D4—534no—
558C4×D4—534no—
559C4×D4—1062no—
560C4×D4—1068no—
561#117—534no—
562#117—534no—
563#117—1068no—
564#117—1062no—
565#117—1062no—
566C2×C4⋊C4—531no—
567C2×C4⋊C4—531no—
568C2×C4⋊C4—531no—
569C2×C4⋊C4—1061no—
570C2×C4⋊C4—1061no—
571C2×C4⋊C4C22×D5311yescharacteristic
572C2×C4⋊C4C22×D5311yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—531no—
576C2×C22⋊C4—531no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1061no—
579C2×C22⋊C4—1061no—
580C2×C22⋊C4—1061no—
581C2×C22⋊C4—1061no—
582C2×C42—531no—
583C2×C42—1061no—
584C2×C42—1061no—
585C2×C42—1061no—
586#107—534no—
587#107C22×D5314yes—
588#106—534no—
589C4⋊C8—534no—
590#103—534no—
591#103—534no—
592#103—534no—
593#102—534no—
594#102—534no—
595#102—534no—
596#102—534no—
597#102—534no—
598#102C22×D5314yes—
599#102C22×D5314yes—
600C22⋊C8—534no—
601C22⋊C8—534no—
602C4×C8—534no—
603C24—21no—
604C24—21no—
605C24—531no—
606C24—1061no—
607C24D4×D5311yescharacteristic
608#41—1068no—
609#41—1068no—
610#41—2124no—
611#41—2128no—
612#41—2124no—
613#41—2128no—
614C2×Q8—534no—
615C2×Q8—532no—
616C2×Q8—1064no—
617C2×Q8—1061no—
618C2×Q8—1062no—
619C2×Q8—4242no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—82no—
629C2×D4—82no—
630C2×D4—534no—
631C2×D4—532no—
632C2×D4—1064no—
633C2×D4—1064no—
634C2×D4—1064no—
635C2×D4—1064no—
636C2×D4—1064no—
637C2×D4—1064no—
638C2×D4—1064no—
639C2×D4—1061no—
640C2×D4—1062no—
641C2×D4—1062no—
642C2×D4—4242no—
643C2×D4—4242no—
644C2×D4—4242no—
645C2×D4—2124no—
646C2×D4—2124no—
647C2×D4—2124no—
648C2×D4C23×D5312yes—
649C2×D4C23×D5312yes—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—531no—
655C22×C4—531no—
656C22×C4—531no—
657C22×C4—532no—
658C22×C4—532no—
659C22×C4—1064no—
660C22×C4—1064no—
661C22×C4—1061no—
662C22×C4—1062no—
663C22×C4—1062no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—1064no—
667C22×C4—2124no—
668C22×C4—2124no—
669C22×C4—2124no—
670C22×C4D4×D5312yes—
671C22×C4D4×D5311yescharacteristic
672C22×C4C23×D5312yes—
673C22×C4C23×D5311yescharacteristic
674SD16—1068no—
675D8—44no—
676D8—2124no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—44no—
680C2×C8—532no—
681C2×C8—532no—
682C2×C8—1062no—
683C2×C8—1062no—
684C2×C8—2124no—
685C2×C8C23×D5312yes—
686C2×C8C23×D5312yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—534no—
690C4⋊C4—532no—
691C4⋊C4—532no—
692C4⋊C4—1064no—
693C4⋊C4—1064no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4C23×D5312yes—
697C4⋊C4C23×D5312yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—534no—
701C22⋊C4—534no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C22⋊C4—1064no—
706C22⋊C4—1064no—
707C42—532no—
708C42—532no—
709C42—1064no—
710C42—1064no—
711C42—1064no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—532no—
724C23—1062no—
725C23—1062no—
726C23—1062no—
727C23—1062no—
728C23—2122no—
729C23—2122no—
730C23—2122no—
731C23C2×D4×D5312yes—
732C23C2×D4×D5311yescharacteristic
733Q8—534no—
734Q8—1062no—
735Q8—1064no—
736Q8—4244no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—42no—
742D4—42no—
743D4—84no—
744D4—84no—
745D4—1068no—
746D4—1062no—
747D4—1062no—
748D4—4244no—
749D4—4244no—
750D4—4244no—
751D4—2128no—
752D4—2128no—
753D4—2128no—
754D4—2122no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—534no—
764C2×C4—532no—
765C2×C4—532no—
766C2×C4—532no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—1064no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—1064no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—2128no—
777C2×C4—2128no—
778C2×C4—2128no—
779C2×C4—2122no—
780C2×C4—2122no—
781C2×C4C2×D4×D5312yes—
782C2×C4C2×D4×D5311yescharacteristic
783C2×C4#41×D5312yes—
784C2×C4#1313326212yes—
785C2×C4C24×D5311yescharacteristic
786C8—22no—
787C8—22no—
788C8—1062no—
789C8—1062no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—84no—
802C22—1062no—
803C22—1062no—
804C22—1062no—
805C22—4244no—
806C22—2122no—
807C22—2122no—
808C22—2122no—
809C22—2124no—
810C22#1681126212yes—
811C22#135×D5312yes—
812C22#1681142412yes—
813C22C22×D4×D5311yescharacteristic
814C4—22no—
815C4—42no—
816C4—42no—
817C4—534no—
818C4—1062no—
819C4—1064no—
820C4—1062no—
821C4—2122no—
822C4—2122no—
823C4#1681126212yes—
824C4C2×#41×D5311yescharacteristic
825C4C2×#1313326211yescharacteristic
826C2—42no—
827C2—82no—
828C2—82no—
829C2—4242no—
830C2—2122no—
831C2#2028666014yesdirect product factor
832C2C2×#1681126211yescharacteristic
833C2C2×#135×D5311yescharacteristic
834C2C2×#1681142411yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#466C2
socleC23×C53C22×D4
hypercenterC2×#466D53
hypocenterC53C2×#3305
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#16811337C2semidirect
2. C2×#16811291C2semidirect
3. #20286660C2direct (N × H)
4. C2×#16810968C2semidirect
5. C2×#16810950C2semidirect
6. C2×#16810944C2semidirect
7. C2×#16810917C2semidirect
8. C2×#16810858C2semidirect
9. C2×#16810816C2semidirect
10. C2×#16810766C2semidirect
11. C2×#16810765C2semidirect
12. C2×#16810714C2semidirect
13. C2×C8×C22⋊D53C2semidirect
14. C2×#16810620C2semidirect
15. C2×#16810616C2semidirect
16. C2×C53×#466C2semidirect
23. #16811337C22semidirect
25. #16811291C22semidirect
43. #16810968C22semidirect
44. #16810950C22semidirect
45. #16810944C22semidirect
46. #16810917C22semidirect
47. #16810858C22semidirect
48. #16810816C22semidirect
49. #16810766C22semidirect
50. #16810765C22semidirect
51. #16810714C22semidirect
52. C8×C22⋊D53C22semidirect
56. #16810620C22semidirect
57. #16810616C22semidirect
73. C53×#466C22semidirect
417. C2×#466D53semidirect
428. C2×C53#3305semidirect
469. #466C2×D53semidirect
494. C53C2×#3305semidirect
831. C2#20286660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113372
C2×#168112912
#202866602
C2×#168109682
C2×#168109502
C2×#168109442
C2×#168109172
C2×#168108582
C2×#168108162
C2×#168107662
C2×#168107652
C2×#168107142
C2×C8×C22⋊D532
C2×#168106202
C2×#168106162
C2×C53×#4662
C2×#330553