Finite Group Databasebeta

← C2×#20286663 #28260565

Subgroups — C2×#20286663 #28260565

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×#16811336C211yesmaximal, characteristic, complemented
2C2×#16811291C211yesmaximal, characteristic, complemented
3#20286663C2116yesmaximal, direct product factor
4C2×#16810968C211yesmaximal, characteristic, complemented
5C2×#16810949C211yesmaximal, characteristic, complemented
6C2×#16810917C211yesmaximal, characteristic, complemented
7C2×#16810860C211yesmaximal, characteristic, complemented
8C2×#16810857C211yesmaximal, characteristic, complemented
9C2×#16810817C211yesmaximal, characteristic, complemented
10C2×#16810770C211yesmaximal, characteristic, complemented
11C2×#16810769C211yesmaximal, characteristic, complemented
12C2×#16810710C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic, complemented
14C2×#16810617C211yesmaximal, characteristic, complemented
15C2×#16810616C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C23×#88322C2211yescharacteristic
23C22×C8×D53C2211yescharacteristic
24#16811336—24no—
25#16811336C2218yescomplemented
26#16811291—24no—
27#16811291C2218yescomplemented
28C2×#13133216C2211yescharacteristic
29C2×#13133213—21no—
30C2×#13133213C2211yescharacteristic
31C2×#13133205—21no—
32C2×#13133203—21no—
33C2×#13133192C2211yescharacteristic
34C2×#13133192C2211yescharacteristic
35C2×#13133191C2211yescharacteristic
36C2×#13133190—21no—
37C2×#13133190—21no—
38C2×#13133189—21no—
39C2×#13133182C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53C2211yescharacteristic
42C2×#13133177—21no—
43C2×#13133175C2211yescharacteristic
44C2×#13133174—21no—
45#16810968C2218yescomplemented
46#16810949C2218yescomplemented
47#16810917C2218yescomplemented
48#16810860C2218yescomplemented
49#16810857C2218yescomplemented
50#16810817C2218yescomplemented
51#16810770C2218yescomplemented
52#16810769C2218yescomplemented
53#16810710C2218yescomplemented
54#16810686C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810617C2218yescomplemented
58#16810616C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×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×D212—21no—
89C22×D212C2311yescharacteristic
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C22⋊D53D411yescharacteristic
97C23×Dic53—21no—
98C22×C4×D53—21no—
99C22×C4×D53—21no—
100C22×C4×D53C2311yescharacteristic
101C2×#11719913—24no—
102C2×#11719913C2314yes—
103C2×D424—42no—
104C2×D424C2314yes—
105C2×#11719922—42no—
106C2×#11719922C2314yes—
107C22×#88322—42no—
108C22×#88322C2311yescharacteristic
109C22×#88322C2311yescharacteristic
110C22×#88322C2314yes—
111C2×C8×D53—42no—
112C2×C8×D53C2314yes—
113#13133216—22no—
114#13133216C2314yes—
115#13133213—22no—
116#13133213—28no—
117#13133213C2314yes—
118#13133205—28no—
119#13133203—28no—
120#13133192—22no—
121#13133192—22no—
122#13133192C2314yes—
123#13133192C2314yes—
124#13133191—22no—
125#13133191C2314yes—
126#13133190—28no—
127#13133190—28no—
128#13133189—28no—
129#13133182—22no—
130#13133182C2314yes—
131#13133179—22no—
132#13133179C2314yes—
133C4×C22⋊D53D414yes—
134C4×C22⋊D53C2314yes—
135#13133177—28no—
136#13133175—22no—
137#13133175C2314yes—
138#13133174—28no—
139C2×C4⋊Dic53C2311yescharacteristic
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919D411yescharacteristic
143C2×C22⋊Dic53D411yescharacteristic
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133139C2314yes—
159#13133138C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133137C2314yes—
163#13133129C2314yes—
164C8×Dic53C2314yes—
165C22×D4×C53—21no—
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170#121×C53—22no—
171#121×C53C2314yes—
172#117×C53—22no—
173#117×C53C2314yes—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180#107×C53C2314yes—
181#106×C53C2314yes—
182#102×C53C2314yes—
183#102×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53—21no—
189C23×D53C2×D411yescharacteristic
190C2×D4×C53—24no—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53—82no—
195C2×D4×C53C2412yes—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—44no—
213C2×C22⋊D53—44no—
214C2×C22⋊D53—82no—
215C2×C22⋊D53—82no—
216C2×C22⋊D53C2×D414yes—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—24no—
220C22×Dic53—44no—
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224#11719947—28no—
225#11719947—44no—
226#11719947—48no—
227#11719945—28no—
228#11719945—44no—
229#11719945—48no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—22no—
234C2×D212—21no—
235C2×D212—21no—
236C2×D212—24no—
237C2×D212—24no—
238C2×D212—82no—
239C2×D212—82no—
240C2×D212C2412yes—
241C2×D212C2412yes—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—24no—
245C2×C4×D53—24no—
246C2×C4×D53—44no—
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—
256C2×C8×C53—22no—
257C2×C8×C53—22no—
258C2×C8×C53C2412yes—
259C2×C8×C53C2412yes—
260C4⋊C4×C53—21no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53C2412yes—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C22⋊C4×C53—24no—
267C22⋊C4×C53—24no—
268C42×C53—24no—
269C22⋊Dic53C2×D414yes—
270#11719922—44no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921C2×D414yes—
277C4⋊Dic53—21no—
278C4⋊Dic53C2412yes—
279#11719919—24no—
280#11719919—24no—
281#11719919C2×D414yes—
282C4×Dic53—24no—
283C4×Dic53—24no—
284C4×Dic53C2×D412yes—
285C4×Dic53C2412yes—
286C2×#88322—22no—
287C2×#88322—22no—
288C2×#88322—44no—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291D424—44no—
292#11719913—28no—
293C8×D53—44no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53—42no—
301C23×C53C22×D412yes—
302C23×C53C22×D411yescharacteristic
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—42no—
312C22×D53—42no—
313C22×D53—42no—
314C22×D53C22×D412yes—
315D4×C53—22no—
316D4×C53—22no—
317D4×C53—42no—
318D4×C53—84no—
319C2×C4×C53—22no—
320C2×C4×C53—24no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—42no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53C22×D412yes—
330C2×C4×C53C22×D411yescharacteristic
331C2×C4×C53C2×#4112yes—
332C2×C4×C53H(5,𝔽2)12yes—
333C2×C4×C53C2511yescharacteristic
334C22⋊D53—28no—
335C22⋊D53—48no—
336C22⋊D53—48no—
337C22⋊D53—48no—
338C22⋊D53—84no—
339C22⋊D53—84no—
340C2×Dic53—24no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—48no—
346C2×Dic53—42no—
347C2×Dic53#13514yes—
348C2×Dic53C22×D412yes—
349C2×Dic53C22×D412yes—
350C2×Dic53C22×D412yes—
351D212—22no—
352D212—22no—
353D212—22no—
354D212—22no—
355D212—42no—
356D212—42no—
357D212—84no—
358D212—84no—
359C4×D53—24no—
360C4×D53—22no—
361C4×D53—22no—
362C4×D53—48no—
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—84no—
381C22×C53#54612yes—
382C22×C53C2×#13512yes—
383C22×C53#57612yes—
384C22×C53C23×D411yescharacteristic
385C2×D53—22no—
386C2×D53—22no—
387C2×D53—22no—
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—22no—
398C4×C53—42no—
399C4×C53—42no—
400C4×C53—42no—
401C4×C53#54612yes—
402C4×C53C22×#4111yescharacteristic
403C4×C53C2×H(5,𝔽2)11yescharacteristic
404Dic53—24no—
405Dic53—22no—
406Dic53—22no—
407Dic53—42no—
408Dic53C2×#13514yes—
409C2×#555—531no—
410C2×#550—531no—
411#3305—5316no—
412C2×#486—531no—
413C2×#482—531no—
414C2×#482D5311yescharacteristic, complemented
415C2×#477—531no—
416C2×#466—531no—
417C2×#466—531no—
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#330514yescomplemented
428C2×C53C2×#54611yescharacteristic
429C2×C53C22×#13511yescharacteristic
430C2×C53C2×#57611yescharacteristic
431D53—42no—
432D53—82no—
433D53—82no—
434C22×#41—531no—
435C22×#41—531no—
436C22×SD16—531no—
437C22×D8—531no—
438C22×D8—531no—
439C23×C8—531no—
440C23×C8—531no—
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—531no—
453C2×#121—1061no—
454C2×#121—1061no—
455C2×#121—1061no—
456C2×#121C2×D5311yescharacteristic
457C2×C4×Q8—531no—
458C2×C4×D4—531no—
459C2×C4×D4—531no—
460C2×C4×D4—1061no—
461C2×#117—531no—
462C2×#117—1061no—
463C2×#117C2×D5311yescharacteristic
464#486—538no—
465#482—538no—
466#482C2×D5318yescomplemented
467#477—538no—
468#466—538no—
469#466—538no—
470#459—538no—
471#449—538no—
472#449—538no—
473C4×SD16—538no—
474C8×D4—538no—
475C2×#107—531no—
476C2×#107C2×D5311yescharacteristic
477C2×#106C2×D5311yescharacteristic
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⋊C8C2×D5311yescharacteristic
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—531no—
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×D4—1061no—
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—534no—
525C2×D8—534no—
526C2×D8—2122no—
527C2×D8—2122no—
528C22×C8—531no—
529C22×C8—531no—
530C22×C8—534no—
531C22×C8—534no—
532C22×C8—2122no—
533C22×C8—2122no—
534C22×C8C22×D5311yescharacteristic
535C22×C8C22×D5311yescharacteristic
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—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#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—22no—
562#117—534no—
563#117—1068no—
564#117—1062no—
565#117C22×D5314yes—
566C2×C4⋊C4—531no—
567C2×C4⋊C4—531no—
568C2×C4⋊C4—1061no—
569C2×C4⋊C4—1061no—
570C2×C4⋊C4C22×D5311yescharacteristic
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—21no—
583C2×C42—531no—
584C2×C42—1061no—
585C2×C42—1061no—
586#107—534no—
587#107C22×D5314yes—
588#106C22×D5314yes—
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⋊C8C22×D5314yes—
602C4×C8—534no—
603C24—21no—
604C24—531no—
605C24—1061no—
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—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—82no—
625C2×D4—534no—
626C2×D4—532no—
627C2×D4—532no—
628C2×D4—1064no—
629C2×D4—1064no—
630C2×D4—1064no—
631C2×D4—1064no—
632C2×D4—1064no—
633C2×D4—1064no—
634C2×D4—1064no—
635C2×D4—1064no—
636C2×D4—1061no—
637C2×D4—1061no—
638C2×D4—1062no—
639C2×D4—1062no—
640C2×D4—1062no—
641C2×D4—1062no—
642C2×D4—4242no—
643C2×D4—4242no—
644C2×D4—4242no—
645C2×D4—4242no—
646C2×D4—2124no—
647C2×D4—2124no—
648C2×D4—2124no—
649C2×D4C23×D5312yes—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—531no—
656C22×C4—531no—
657C22×C4—531no—
658C22×C4—532no—
659C22×C4—532no—
660C22×C4—1064no—
661C22×C4—1064no—
662C22×C4—1061no—
663C22×C4—1062no—
664C22×C4—1062no—
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—2124no—
676D8—2124no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—532no—
680C2×C8—532no—
681C2×C8—1062no—
682C2×C8—1062no—
683C2×C8—2124no—
684C2×C8—2124no—
685C2×C8C23×D5312yes—
686C2×C8C23×D5312yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—534no—
691C4⋊C4—532no—
692C4⋊C4—1064no—
693C4⋊C4—1064no—
694C4⋊C4—1061no—
695C4⋊C4C23×D5312yes—
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—24no—
708C42—532no—
709C42—532no—
710C42—1064no—
711C42—1064no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—532no—
720C23—1062no—
721C23—1062no—
722C23—1062no—
723C23—1062no—
724C23—1062no—
725C23—2122no—
726C23—2122no—
727C23—2122no—
728C23—2122no—
729C23—2122no—
730C23—2122no—
731C23C2×D4×D5312yes—
732C23C2×D4×D5311yescharacteristic
733Q8—534no—
734Q8—1064no—
735Q8—1062no—
736Q8—4244no—
737D4—22no—
738D4—22no—
739D4—42no—
740D4—84no—
741D4—1068no—
742D4—1062no—
743D4—1062no—
744D4—1062no—
745D4—1062no—
746D4—4244no—
747D4—4244no—
748D4—4244no—
749D4—4244no—
750D4—2128no—
751D4—2128no—
752D4—2128no—
753D4—2122no—
754D4—2122no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—534no—
766C2×C4—532no—
767C2×C4—532no—
768C2×C4—532no—
769C2×C4—1062no—
770C2×C4—1064no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—1064no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—2128no—
778C2×C4—2128no—
779C2×C4—2128no—
780C2×C4—2122no—
781C2×C4C2×D4×D5312yes—
782C2×C4C2×D4×D5311yescharacteristic
783C2×C4#41×D5312yes—
784C2×C4#1313326312yes—
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—84no—
798C22—1062no—
799C22—1062no—
800C22—1062no—
801C22—4244no—
802C22—4244no—
803C22—2122no—
804C22—2122no—
805C22—2122no—
806C22—2122no—
807C22—2122no—
808C22—2122no—
809C22—2124no—
810C22#1681126512yes—
811C22#135×D5312yes—
812C22#1681142712yes—
813C22C22×D4×D5311yescharacteristic
814C4—22no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—534no—
819C4—1062no—
820C4—1064no—
821C4—1062no—
822C4—2122no—
823C4#1681126512yes—
824C4C2×#41×D5311yescharacteristic
825C4C2×#1313326311yescharacteristic
826C2—42no—
827C2—82no—
828C2—4242no—
829C2—4242no—
830C2—2122no—
831C2#2028666314yesdirect product factor
832C2C2×#1681126511yescharacteristic
833C2C2×#135×D5311yescharacteristic
834C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
hypercenterC2×#482D53
hypocenterC53C2×#3305
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16811336C2semidirect
2. C2×#16811291C2semidirect
3. #20286663C2direct (N × H)
4. C2×#16810968C2semidirect
5. C2×#16810949C2semidirect
6. C2×#16810917C2semidirect
7. C2×#16810860C2semidirect
8. C2×#16810857C2semidirect
9. C2×#16810817C2semidirect
10. C2×#16810770C2semidirect
11. C2×#16810769C2semidirect
12. C2×#16810710C2semidirect
13. C2×#16810686C2semidirect
14. C2×#16810617C2semidirect
15. C2×#16810616C2semidirect
16. C2×C53×#482C2semidirect
25. #16811336C22semidirect
27. #16811291C22semidirect
45. #16810968C22semidirect
46. #16810949C22semidirect
47. #16810917C22semidirect
48. #16810860C22semidirect
49. #16810857C22semidirect
50. #16810817C22semidirect
51. #16810770C22semidirect
52. #16810769C22semidirect
53. #16810710C22semidirect
54. #16810686C22semidirect
57. #16810617C22semidirect
58. #16810616C22semidirect
71. C53×#482C22semidirect
414. C2×#482D53semidirect
427. C2×C53#3305semidirect
466. #482C2×D53semidirect
494. C53C2×#3305semidirect
831. C2#20286663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113362
C2×#168112912
#202866632
C2×#168109682
C2×#168109492
C2×#168109172
C2×#168108602
C2×#168108572
C2×#168108172
C2×#168107702
C2×#168107692
C2×#168107102
C2×#168106862
C2×#168106172
C2×#168106162
C2×C53×#4822
C2×#330553