Finite Group Databasebeta

← C2×#20286714 #28260787

Subgroups — C2×#20286714 #28260787

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×#16811325C211yesmaximal, characteristic, complemented
2C2×#16811292C211yesmaximal, characteristic, complemented
3#20286714C2116yesmaximal, direct product factor
4C2×#16810986C211yesmaximal, characteristic, complemented
5C2×#16810945C211yesmaximal, characteristic, complemented
6C2×#16810937C211yesmaximal, characteristic, complemented
7C2×#16810932C211yesmaximal, characteristic, complemented
8C2×#16810874C211yesmaximal, characteristic, complemented
9C2×#16810856C211yesmaximal, characteristic, complemented
10C2×#16810816C211yesmaximal, characteristic, complemented
11C2×#16810767C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×#16810697C211yesmaximal, characteristic, complemented
14C2×#16810624C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C2×C53×#449C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811325—24no—
22#16811325C2218yescomplemented
23#16811292—24no—
24#16811292C2218yescomplemented
25C2×#13133213—21no—
26C2×#13133213C2211yescharacteristic
27C2×#13133210—21no—
28C2×#13133208C2211yescharacteristic
29C2×#13133201—21no—
30C2×#13133191—21no—
31C2×#13133191C2211yescharacteristic
32C2×#13133189—21no—
33C2×#13133188—21no—
34C2×#13133188C2211yescharacteristic
35C2×#13133188C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×D4×Dic53—21no—
38C2×D4×Dic53C2211yescharacteristic
39C2×C4×C22⋊D53—21no—
40C2×C4×C22⋊D53C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42C22×C4⋊Dic53C2211yescharacteristic
43#16810986C2218yescomplemented
44#16810945C2218yescomplemented
45#16810937C2218yescomplemented
46#16810932C2218yescomplemented
47#16810874C2218yescomplemented
48#16810856C2218yescomplemented
49#16810816C2218yescomplemented
50#16810767C2218yescomplemented
51#16810724C2218yescomplemented
52#16810697C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810624C2218yescomplemented
58#16810618C2218yescomplemented
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C22×D8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#449C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C22×D212—21no—
82C22×D212C2311yescharacteristic
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53D411yescharacteristic
89C23×Dic53—21no—
90C23×Dic53—21no—
91C22×C4×D53—21no—
92C22×C4×D53C2311yescharacteristic
93C2×#11719922—42no—
94C2×#11719922C2314yes—
95C2×#11719917—42no—
96C2×#11719917C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C2×C8×D53—42no—
100C2×C8×D53C2314yes—
101#13133213—22no—
102#13133213—28no—
103#13133213C2314yes—
104#13133210—28no—
105#13133208—22no—
106#13133208C2314yes—
107#13133201—28no—
108#13133191—28no—
109#13133191—22no—
110#13133191C2314yes—
111#13133189—28no—
112#13133188—28no—
113#13133188—22no—
114#13133188—22no—
115#13133188C2314yes—
116#13133188C2314yes—
117Q8×Dic53—22no—
118Q8×Dic53C2314yes—
119D4×Dic53—28no—
120D4×Dic53—22no—
121D4×Dic53C2314yes—
122C4×C22⋊D53—28no—
123C4×C22⋊D53D414yes—
124C4×C22⋊D53C2314yes—
125#13133175—22no—
126#13133175C2314yes—
127C2×C4⋊Dic53—22no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2314yes—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53D411yescharacteristic
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921D411yescharacteristic
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yes—
148#13133151C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133139C2314yes—
154#13133139C2314yes—
155#13133138C2314yes—
156#13133138C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133129C2314yes—
160#13133127C2314yes—
161C2×#41×C53—22no—
162C2×#41×C53—24no—
163C2×#41×C53—42no—
164C2×#41×C53C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C22×D4×C53—21no—
167C22×D4×C53—21no—
168C22×D4×C53C2311yescharacteristic
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53C2311yescharacteristic
172C2×SD16×C53—24no—
173C2×SD16×C53C2314yes—
174C2×D8×C53—42no—
175C2×D8×C53C2314yes—
176C22×C8×C53C2311yescharacteristic
177C22×C8×C53C2311yescharacteristic
178#121×C53—22no—
179#121×C53C2314yes—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182#103×C53C2314yes—
183#102×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C23×D53—21no—
189C23×D53C2×D411yescharacteristic
190#41×C53—28no—
191#41×C53—44no—
192#41×C53—48no—
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53#4114yes—
196C2×Q8×C53C2412yes—
197C2×D4×C53—24no—
198C2×D4×C53—24no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—22no—
202C2×D4×C53—22no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—44no—
206C2×D4×C53—44no—
207C2×D4×C53C2412yes—
208C2×D4×C53C2412yes—
209C22×C4×C53—21no—
210C22×C4×C53—22no—
211C22×C4×C53—22no—
212C22×C4×C53—21no—
213C22×C4×C53—24no—
214C22×C4×C53—44no—
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D412yes—
217C22×C4×C53C2412yes—
218C22×C4×C53C2411yescharacteristic
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—24no—
223C2×C22⋊D53—24no—
224C2×C22⋊D53—42no—
225C2×C22⋊D53—44no—
226C2×C22⋊D53—82no—
227C2×C22⋊D53—82no—
228C2×C22⋊D53—82no—
229C2×C22⋊D53—82no—
230C2×C22⋊D53C2×D414yes—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—24no—
235C22×Dic53—24no—
236C22×Dic53—82no—
237C22×Dic53—82no—
238C22×Dic53C2×D411yescharacteristic
239C22×Dic53C2×D411yescharacteristic
240C22×Dic53C2×D411yescharacteristic
241#11719949—28no—
242#11719949—44no—
243#11719949—48no—
244C2×D212—22no—
245C2×D212—22no—
246C2×D212—24no—
247C2×D212—21no—
248C2×D212—44no—
249C2×D212C2412yes—
250C2×C4×D53—22no—
251C2×C4×D53—22no—
252C2×C4×D53—24no—
253C2×C4×D53—44no—
254C2×C4×D53C2×D412yes—
255C2×C4×D53C2412yes—
256SD16×C53—28no—
257D8×C53—44no—
258C2×C8×C53—22no—
259C2×C8×C53—22no—
260C2×C8×C53C2412yes—
261C2×C8×C53C2412yes—
262C4⋊C4×C53—21no—
263C4⋊C4×C53C2412yes—
264C22⋊C4×C53—24no—
265C22⋊Dic53—24no—
266C22⋊Dic53—24no—
267C22⋊Dic53—24no—
268C22⋊Dic53C2×D414yes—
269#11719922—44no—
270#11719921—24no—
271#11719921—24no—
272#11719921C2×D414yes—
273C4⋊Dic53—21no—
274C4⋊Dic53—21no—
275C4⋊Dic53—24no—
276C4⋊Dic53—21no—
277C4⋊Dic53—24no—
278C4⋊Dic53—24no—
279C4⋊Dic53C2412yes—
280C4⋊Dic53C2412yes—
281C4⋊Dic53C2412yes—
282#11719919—24no—
283#11719919C2×D414yes—
284C4×Dic53—24no—
285C4×Dic53—24no—
286C4×Dic53C2×D412yes—
287C4×Dic53C2412yes—
288#11719917—44no—
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—
315Q8×C53—24no—
316Q8×C53—22no—
317Q8×C53C2×#4114yes—
318D4×C53—22no—
319D4×C53—22no—
320D4×C53—22no—
321D4×C53—22no—
322D4×C53—48no—
323D4×C53—48no—
324D4×C53—42no—
325D4×C53—42no—
326C2×C4×C53—24no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—24no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—48no—
334C2×C4×C53—42no—
335C2×C4×C53C22×D412yes—
336C2×C4×C53C22×D411yescharacteristic
337C2×C4×C53C2×#4112yes—
338C2×C4×C53H(5,𝔽2)12yes—
339C2×C4×C53C2511yescharacteristic
340C22⋊D53—44no—
341C22⋊D53—48no—
342C22⋊D53—84no—
343C22⋊D53—84no—
344C22⋊D53—84no—
345C22⋊D53—84no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—42no—
353C2×Dic53—42no—
354C2×Dic53—42no—
355C2×Dic53—84no—
356C2×Dic53—84no—
357C2×Dic53C22×D412yes—
358C2×Dic53C22×D412yes—
359C2×Dic53C22×D412yes—
360D212—22no—
361D212—22no—
362D212—48no—
363D212—42no—
364C4×D53—24no—
365C4×D53—22no—
366C4×D53—22no—
367C4×D53—48no—
368C8×C53—22no—
369C8×C53—22no—
370#88322—22no—
371#88322—22no—
372C2×#3309—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×C53#57512yes—
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—24no—
398C4×C53—22no—
399C4×C53—42no—
400C4×C53#54612yes—
401C4×C53C22×#4111yescharacteristic
402C4×C53C2×H(5,𝔽2)11yescharacteristic
403Dic53—22no—
404Dic53—22no—
405Dic53—22no—
406Dic53—42no—
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×#449D5311yescharacteristic, complemented
421C2×#440—531no—
422C2×#435—531no—
423C2×#417—531no—
424C2×#416—531no—
425C2×C53—42no—
426C2×C53—82no—
427C2×C53—82no—
428C2×C53#330914yescomplemented
429C2×C53C2×#54611yescharacteristic
430C2×C53C2×#57511yescharacteristic
431C2×C53C2×#57611yescharacteristic
432D53—42no—
433D53—82no—
434C22×#41—531no—
435C22×#41C2×D5311yescharacteristic
436C22×SD16C2×D5311yescharacteristic
437C22×D8—531no—
438C22×D8C2×D5311yescharacteristic
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—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×C4×D4—1061no—
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#449C2×D5318yescomplemented
473#440—538no—
474#435—538no—
475C2×#107—531no—
476C2×#107—531no—
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⋊C8C2×D5311yescharacteristic
493C2×#97—531no—
494C53C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—22no—
496C2×#41—24no—
497C2×#41—42no—
498C2×#41—534no—
499C2×#41—1062no—
500C2×#41—1064no—
501C2×#41—2122no—
502C2×#41C22×D5314yes—
503C22×Q8C22×D5311yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—531no—
507C22×D4—531no—
508C22×D4—1061no—
509C22×D4—1061no—
510C22×D4—1061no—
511C22×D4—1061no—
512C22×D4—1061no—
513C22×D4—1061no—
514C22×D4C22×D5311yescharacteristic
515C22×D4C22×D5311yescharacteristic
516C23×C4—21no—
517C23×C4—531no—
518C23×C4—1061no—
519C23×C4—1061no—
520C23×C4—1061no—
521C23×C4C22×D5311yescharacteristic
522C2×SD16—24no—
523C2×SD16C22×D5314yes—
524C2×D8—42no—
525C2×D8—534no—
526C2×D8—2122no—
527C2×D8C22×D5314yes—
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—1062no—
538#127—1068no—
539#126—1068no—
540#125—534no—
541#125—1062no—
542#123—1068no—
543#121—22no—
544#121—534no—
545#121—534no—
546#121—534no—
547#121—1068no—
548#121—1068no—
549#121—1062no—
550#121—1062no—
551#121—1068no—
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—
561C4×D4—1068no—
562#117—534no—
563#117—1062no—
564C2×C4⋊C4—531no—
565C2×C4⋊C4—531no—
566C2×C4⋊C4—531no—
567C2×C4⋊C4—534no—
568C2×C4⋊C4—531no—
569C2×C4⋊C4—1061no—
570C2×C4⋊C4—1061no—
571C2×C4⋊C4—1061no—
572C2×C4⋊C4—1061no—
573C2×C4⋊C4—1062no—
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—531no—
584C2×C42—1061no—
585C2×C42—1061no—
586#107—534no—
587#107—534no—
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⋊C8C22×D5314yes—
602#97—534no—
603C24—21no—
604C24—21no—
605C24—531no—
606C24—1061no—
607C24D4×D5311yescharacteristic
608#41—28no—
609#41—44no—
610#41—48no—
611#41—1068no—
612#41—2124no—
613#41—2128no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8#1171994714yes—
617C2×Q8C23×D5312yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—534no—
629C2×D4—532no—
630C2×D4—1064no—
631C2×D4—1064no—
632C2×D4—1064no—
633C2×D4—1064no—
634C2×D4—1064no—
635C2×D4—1064no—
636C2×D4—1061no—
637C2×D4—1062no—
638C2×D4—1062no—
639C2×D4—4242no—
640C2×D4—4242no—
641C2×D4—4242no—
642C2×D4—4242no—
643C2×D4—2124no—
644C2×D4—2122no—
645C2×D4—2124no—
646C2×D4C23×D5312yes—
647C2×D4C23×D5312yes—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—44no—
654C22×C4—531no—
655C22×C4—531no—
656C22×C4—531no—
657C22×C4—532no—
658C22×C4—532no—
659C22×C4—1064no—
660C22×C4—1064no—
661C22×C4—1062no—
662C22×C4—1062no—
663C22×C4—1064no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—1061no—
667C22×C4—4242no—
668C22×C4—4242no—
669C22×C4—2124no—
670C22×C4D4×D5312yes—
671C22×C4D4×D5311yescharacteristic
672C22×C4C23×D5312yes—
673C22×C4C23×D5311yescharacteristic
674SD16—28no—
675D8—44no—
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—21no—
688C4⋊C4—534no—
689C4⋊C4—532no—
690C4⋊C4—532no—
691C4⋊C4—532no—
692C4⋊C4—1064no—
693C4⋊C4—1064no—
694C4⋊C4—1064no—
695C4⋊C4—1061no—
696C4⋊C4—1061no—
697C4⋊C4—1064no—
698C4⋊C4—1061no—
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—532no—
709C42—532no—
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—22no—
734Q8—24no—
735Q8C2×#1171994714yes—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—48no—
742D4—42no—
743D4—42no—
744D4—1062no—
745D4—1062no—
746D4—4244no—
747D4—4244no—
748D4—4244no—
749D4—4244no—
750D4—2128no—
751D4—2124no—
752D4—2128no—
753D4—2122no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—48no—
762C2×C4—42no—
763C2×C4—532no—
764C2×C4—532no—
765C2×C4—532no—
766C2×C4—1062no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—1062no—
771C2×C4—1064no—
772C2×C4—1062no—
773C2×C4—1062no—
774C2×C4—1062no—
775C2×C4—4244no—
776C2×C4—4244no—
777C2×C4—2128no—
778C2×C4—2122no—
779C2×C4—2122no—
780C2×C4—2122no—
781C2×C4C2×D4×D5312yes—
782C2×C4C2×D4×D5311yescharacteristic
783C2×C4C2×#1171994712yes—
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#1681126012yes—
811C22#1681141912yes—
812C22#1681142512yes—
813C22C22×D4×D5311yescharacteristic
814C4—22no—
815C4—24no—
816C4—42no—
817C4—1062no—
818C4—1062no—
819C4—1062no—
820C4—2122no—
821C4—2122no—
822C4—2122no—
823C4#1681126012yes—
824C4C22×#1171994711yescharacteristic
825C4C2×#1313326211yescharacteristic
826C2—42no—
827C2—82no—
828C2—82no—
829C2—4242no—
830C2—2122no—
831C2#2028671414yesdirect product factor
832C2C2×#1681126011yescharacteristic
833C2C2×#1681141911yescharacteristic
834C2C2×#1681142511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#449C2
socleC23×C53C22×D4
hypercenterC2×#449D53
hypocenterC53C2×#3309
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16811325C2semidirect
2. C2×#16811292C2semidirect
3. #20286714C2direct (N × H)
4. C2×#16810986C2semidirect
5. C2×#16810945C2semidirect
6. C2×#16810937C2semidirect
7. C2×#16810932C2semidirect
8. C2×#16810874C2semidirect
9. C2×#16810856C2semidirect
10. C2×#16810816C2semidirect
11. C2×#16810767C2semidirect
12. C2×#16810724C2semidirect
13. C2×#16810697C2semidirect
14. C2×#16810624C2semidirect
15. C2×#16810618C2semidirect
16. C2×C53×#449C2semidirect
22. #16811325C22semidirect
24. #16811292C22semidirect
43. #16810986C22semidirect
44. #16810945C22semidirect
45. #16810937C22semidirect
46. #16810932C22semidirect
47. #16810874C22semidirect
48. #16810856C22semidirect
49. #16810816C22semidirect
50. #16810767C22semidirect
51. #16810724C22semidirect
52. #16810697C22semidirect
57. #16810624C22semidirect
58. #16810618C22semidirect
73. C53×#449C22semidirect
420. C2×#449D53semidirect
428. C2×C53#3309semidirect
472. #449C2×D53semidirect
494. C53C2×#3309semidirect
831. C2#20286714direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113252
C2×#168112922
#202867142
C2×#168109862
C2×#168109452
C2×#168109372
C2×#168109322
C2×#168108742
C2×#168108562
C2×#168108162
C2×#168107672
C2×#168107242
C2×#168106972
C2×#168106242
C2×#168106182
C2×C53×#4492
C2×#330953