Finite Group Databasebeta

← C2×#20285763 #28255421

Subgroups — C2×#20285763 #28255421

Order 13568.

2342 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811226C211yesmaximal, characteristic, complemented
2C2×#16811187C211yesmaximal, characteristic, complemented
3#20285763C2116yesmaximal, direct product factor
4C2×#16811009C211yesmaximal, characteristic, complemented
5C2×#16810998C211yesmaximal, characteristic, complemented
6C2×#16810986C211yesmaximal, characteristic, complemented
7C2×#16810979C211yesmaximal, characteristic, complemented
8C2×#16810841C211yesmaximal, characteristic, complemented
9C2×#16810840C211yesmaximal, characteristic, complemented
10C2×#16810817C211yesmaximal, characteristic, complemented
11C2×#16810816C211yesmaximal, characteristic, complemented
12C2×#16810768C211yesmaximal, characteristic, complemented
13C2×#16810759C211yesmaximal, characteristic, complemented
14C2×#16810756C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#449C211yesmaximal, characteristic, complemented
17C23×D212C2211yescharacteristic
18C22×#11719924C2211yescharacteristic, complemented
19C22×D424C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23C22×#11719922C2211yescharacteristic, complemented
24#16811226—24no—
25#16811226C2218yescomplemented
26#16811187—24no—
27#16811187C2218yescomplemented
28C2×#13133213C2211yescharacteristic
29C2×#13133213C2211yescharacteristic
30C2×#13133213C2211yescharacteristic, complemented
31C2×#13133208C2211yescharacteristic, complemented
32C2×#13133206C2211yescharacteristic
33C2×#13133206C2211yescharacteristic
34C2×#13133201—21no—
35C2×#13133199—21no—
36C2×#13133191—21no—
37C2×#13133191—21no—
38C2×#13133191C2211yescharacteristic
39C2×#13133189—21no—
40C2×#13133188—21no—
41C2×#13133185—21no—
42C2×#13133185—21no—
43C2×D4×Dic53C2211yescharacteristic, complemented
44C2×#13133179C2211yescharacteristic, complemented
45C2×#13133176C2211yescharacteristic
46#16811009C2218yescomplemented
47#16810998C2218yescomplemented
48#16810986C2218yescomplemented
49#16810979C2218yescomplemented
50#16810841C2218yescomplemented
51#16810840C2218yescomplemented
52#16810817C2218yescomplemented
53#16810816C2218yescomplemented
54#16810768C2218yescomplemented
55#16810759C2218yescomplemented
56#16810756C2218yescomplemented
57#16810681C2218yescomplemented
58C2×#13133146C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133141C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic, complemented
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C22×#41×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic, complemented
71C22×D8×C53C2211yescharacteristic, complemented
72C2×#121×C53C2211yescharacteristic
73C53×#449C2218yescomplemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C24×D53—21no—
78C22×D212—21no—
79C22×D212—22no—
80C22×D212—42no—
81C22×D212—42no—
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×D212C2314yes—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C23×Dic53—21no—
94C22×C4×D53—21no—
95C2×#11719924—42no—
96C2×#11719924C2314yescomplemented
97C2×D424—42no—
98C2×D424—42no—
99C2×D424C2314yes—
100C2×D424C2314yes—
101C2×#11719922—42no—
102C2×#11719922—42no—
103C2×#11719922—42no—
104C2×#11719922C2314yes—
105C2×#11719922C2314yes—
106C2×#11719922C2314yescomplemented
107C22×#88322C2311yescharacteristic
108C22×#88322C2311yescharacteristic
109#13133213—22no—
110#13133213—22no—
111#13133213—22no—
112#13133213C2314yes—
113#13133213C2314yes—
114#13133213C2314yescomplemented
115#13133208—22no—
116#13133208C2314yescomplemented
117#13133206—22no—
118#13133206—22no—
119#13133206C2314yes—
120#13133206C2314yes—
121#13133201—28no—
122#13133199—28no—
123#13133191—28no—
124#13133191—28no—
125#13133191—22no—
126#13133191C2314yes—
127#13133189—28no—
128#13133188—28no—
129#13133185—28no—
130#13133185—28no—
131D4×Dic53—22no—
132D4×Dic53C2314yescomplemented
133#13133179—22no—
134#13133179C2314yescomplemented
135#13133176D414yes—
136#13133176C2314yes—
137C2×C4⋊Dic53—21no—
138C2×C4⋊Dic53D411yescharacteristic
139C2×C4⋊Dic53D411yescharacteristic
140C2×C4⋊Dic53C2311yescharacteristic
141C2×#11719919—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53D411yescharacteristic
144C2×C22⋊Dic53D411yescharacteristic
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×C4×Dic53C2311yescharacteristic
152C2×C4×Dic53C2311yescharacteristic
153#13133146C2314yescomplemented
154#13133146C2314yescomplemented
155#13133141C2314yescomplemented
156#13133139C2314yes—
157#13133139C2314yes—
158#13133138C2314yescomplemented
159#13133137C2314yes—
160#13133137C2314yes—
161C22⋊#88322C2314yes—
162#13133127C2314yescomplemented
163C8×Dic53C2314yescomplemented
164C2×#41×C53—22no—
165C2×#41×C53—42no—
166C2×#41×C53—42no—
167C2×#41×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C22×D4×C53—21no—
170C22×D4×C53—21no—
171C22×D4×C53C2311yescharacteristic
172C22×D4×C53C2311yescharacteristic
173C23×C4×C53—21no—
174C23×C4×C53C2311yescharacteristic
175C2×SD16×C53—42no—
176C2×SD16×C53C2314yescomplemented
177C2×D8×C53—42no—
178C2×D8×C53C2314yescomplemented
179C22×C8×C53C2311yescharacteristic
180C22×C8×C53C2311yescharacteristic
181#121×C53—22no—
182#121×C53C2314yes—
183C2×C4⋊C4×C53C2311yescharacteristic
184C2×C22⋊C4×C53—21no—
185#103×C53C2314yescomplemented
186#102×C53C2314yescomplemented
187C22⋊C8×C53C2314yes—
188C24×C53—21no—
189C24×C53—21no—
190C24×C53C2×D411yescharacteristic
191C23×D53—21no—
192C23×D53—21no—
193C23×D53—21no—
194C23×D53—24no—
195C23×D53—44no—
196C23×D53—82no—
197C23×D53—82no—
198#41×C53—44no—
199#41×C53—44no—
200#41×C53—48no—
201C2×Q8×C53—21no—
202C2×Q8×C53—22no—
203C2×Q8×C53—22no—
204C2×Q8×C53C2412yes—
205C2×D4×C53—24no—
206C2×D4×C53—24no—
207C2×D4×C53—21no—
208C2×D4×C53—21no—
209C2×D4×C53—22no—
210C2×D4×C53—22no—
211C2×D4×C53—22no—
212C2×D4×C53—22no—
213C2×D4×C53—44no—
214C2×D4×C53—82no—
215C2×D4×C53C2412yes—
216C2×D4×C53C2412yes—
217C22×C4×C53—22no—
218C22×C4×C53—22no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—24no—
222C22×C4×C53—44no—
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D412yes—
225C22×C4×C53C2412yes—
226C22×C4×C53C2411yescharacteristic
227C2×C22⋊D53—24no—
228C2×C22⋊D53—24no—
229C2×C22⋊D53—24no—
230C2×C22⋊D53—24no—
231C2×C22⋊D53—24no—
232C2×C22⋊D53—24no—
233C2×C22⋊D53—24no—
234C2×C22⋊D53—82no—
235C2×C22⋊D53—82no—
236C2×C22⋊D53—82no—
237C2×C22⋊D53—82no—
238C2×C22⋊D53—82no—
239C2×C22⋊D53—82no—
240C2×C22⋊D53—82no—
241C22×Dic53—21no—
242C22×Dic53—24no—
243C22×Dic53—82no—
244C22×Dic53C2×D411yescharacteristic
245C22×Dic53C2×D411yescharacteristic
246C22×Dic53C2×D411yescharacteristic
247C22×Dic53C2×D411yescharacteristic
248C2×D212—22no—
249C2×D212—22no—
250C2×D212—22no—
251C2×D212—22no—
252C2×D212—22no—
253C2×D212—22no—
254C2×D212—21no—
255C2×D212—24no—
256C2×D212—21no—
257C2×D212—21no—
258C2×D212—44no—
259C2×D212—44no—
260C2×D212—44no—
261C2×D212—48no—
262C2×D212C2412yes—
263C2×D212C2412yes—
264C2×D212C2412yes—
265C2×C4×D53—24no—
266C2×C4×D53—82no—
267SD16×C53—44no—
268D8×C53—44no—
269C2×C8×C53—22no—
270C2×C8×C53—22no—
271C2×C8×C53C2412yes—
272C2×C8×C53C2412yes—
273C4⋊C4×C53—21no—
274C4⋊C4×C53C2412yes—
275C22⋊C4×C53—24no—
276C22⋊Dic53—24no—
277C22⋊Dic53C2×D414yes—
278C22⋊Dic53C2×D414yes—
279#11719924—44no—
280#11719922—44no—
281#11719922—44no—
282#11719922—44no—
283#11719921—24no—
284#11719921—24no—
285#11719921—24no—
286#11719921—24no—
287#11719921—24no—
288#11719921—24no—
289C4⋊Dic53—21no—
290C4⋊Dic53—24no—
291C4⋊Dic53C2×D414yes—
292C4⋊Dic53C2×D414yes—
293C4⋊Dic53C2412yes—
294#11719919—24no—
295C4×Dic53C2×D412yes—
296C4×Dic53C2×D412yes—
297C4×Dic53C2412yes—
298C4×Dic53C2412yes—
299C2×#88322—22no—
300C2×#88322—22no—
301C2×#88322C2412yes—
302C2×#88322C2412yes—
303D424—44no—
304D424—44no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—42no—
311C23×C53—42no—
312C23×C53—42no—
313C23×C53—42no—
314C23×C53—42no—
315C23×C53—42no—
316C23×C53C22×D412yes—
317C23×C53C22×D411yescharacteristic
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—48no—
322C22×D53—42no—
323C22×D53—42no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53—42no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53—84no—
332C22×D53—84no—
333C22×D53—816no—
334Q8×C53—22no—
335Q8×C53—22no—
336Q8×C53—42no—
337D4×C53—22no—
338D4×C53—22no—
339D4×C53—22no—
340D4×C53—22no—
341D4×C53—48no—
342D4×C53—42no—
343D4×C53—42no—
344D4×C53—84no—
345C2×C4×C53—22no—
346C2×C4×C53—24no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—48no—
352C2×C4×C53—42no—
353C2×C4×C53—42no—
354C2×C4×C53C22×D412yes—
355C2×C4×C53C22×D411yescharacteristic
356C2×C4×C53H(5,𝔽2)12yes—
357C2×C4×C53H(5,𝔽2)12yes—
358C2×C4×C53C2511yescharacteristic
359C22⋊D53—84no—
360C22⋊D53—84no—
361C22⋊D53—84no—
362C22⋊D53—84no—
363C22⋊D53—84no—
364C22⋊D53—84no—
365C22⋊D53—84no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—42no—
372C2×Dic53—84no—
373C2×Dic53C22×D412yes—
374C2×Dic53C22×D412yes—
375C2×Dic53C22×D412yes—
376C2×Dic53C22×D412yes—
377D212—22no—
378D212—22no—
379D212—22no—
380D212—22no—
381D212—22no—
382D212—22no—
383D212—48no—
384D212—42no—
385D212—42no—
386D212—42no—
387C4×D53—84no—
388C8×C53—22no—
389C8×C53—22no—
390#88322—22no—
391#88322—22no—
392C2×#3220—531nomaximal, Sylow
393C22×C53—22no—
394C22×C53—22no—
395C22×C53—22no—
396C22×C53—44no—
397C22×C53—42no—
398C22×C53—42no—
399C22×C53—42no—
400C22×C53—42no—
401C22×C53—42no—
402C22×C53—42no—
403C22×C53—84no—
404C22×C53—84no—
405C22×C53#53512yes—
406C22×C53#57612yes—
407C22×C53#57612yes—
408C22×C53C23×D411yescharacteristic
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—42no—
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—42no—
415C2×D53—42no—
416C2×D53—42no—
417C2×D53—42no—
418C2×D53—816no—
419C2×D53—84no—
420C2×D53—84no—
421C2×D53—84no—
422C4×C53—22no—
423C4×C53—42no—
424C4×C53—42no—
425C4×C53#53512yes—
426C4×C53C2×H(5,𝔽2)11yescharacteristic
427C4×C53C2×H(5,𝔽2)11yescharacteristic
428Dic53—22no—
429Dic53—22no—
430Dic53—22no—
431Dic53—22no—
432Dic53—42no—
433C2×#540—531no—
434C2×#535—531no—
435#3220—5316no—
436C2×#496—531no—
437C2×#493—531no—
438C2×#490—531no—
439C2×#488—531no—
440C2×#463—531no—
441C2×#463—531no—
442C2×#459—531no—
443C2×#459—531no—
444C2×#449—531no—
445C2×#449D5311yescharacteristic, complemented
446C2×#447—531no—
447C2×#447—531no—
448C2×#433—531no—
449C2×C53—42no—
450C2×C53—82no—
451C2×C53—82no—
452C2×C53#322014yescomplemented
453C2×C53C2×#53511yescharacteristic
454C2×C53C2×#57611yescharacteristic
455C2×C53C2×#57611yescharacteristic
456D53—82no—
457D53—82no—
458D53—82no—
459C22×#41C2×D5311yescharacteristic
460C23×D4—531no—
461C22×SD16—531no—
462C22×SD16C2×D5311yescharacteristic, complemented
463C22×D8—531no—
464C22×D8—531no—
465C22×D8—531no—
466C22×D8—531no—
467C22×D8—531no—
468C22×D8C2×D5311yescharacteristic, complemented
469#540—538no—
470#540—1064no—
471#535—538no—
472#535—1064no—
473C2×#127—531no—
474C2×#127—531no—
475C2×#127—531no—
476C2×#125—531no—
477C2×#124—531no—
478C2×#124—531no—
479C2×#123—1061no—
480C2×#123—1061no—
481C2×#121—531no—
482C2×#121—1061no—
483C2×#121—1061no—
484C2×#121—1061no—
485C2×#121—1061no—
486C2×#121C2×D5311yescharacteristic
487C2×#120—1061no—
488C2×#120—1061no—
489C2×C4×D4—531no—
490C2×C4×D4—531no—
491C2×#117—531no—
492#496—538no—
493#493—538no—
494#490—538no—
495#488—538no—
496#463—538no—
497#463—538no—
498#459—538no—
499#459—538no—
500#449—538no—
501#449C2×D5318yescomplemented
502#447—538no—
503#447—538no—
504#433—538no—
505C2×C4⋊C8—531no—
506C2×C4⋊C8—531no—
507C2×#103—531no—
508C2×#103C2×D5311yescharacteristic, complemented
509C2×#102—531no—
510C2×#102—531no—
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102C2×D5311yescharacteristic, complemented
515C2×C22⋊C8—531no—
516C2×C22⋊C8C2×D5311yescharacteristic
517C2×#97—531no—
518C2×C4×C8—531no—
519C53C2×#322011yescharacteristic, complemented, Sylow
520C25—1061no—
521C2×#41—22no—
522C2×#41—42no—
523C2×#41—42no—
524C2×#41C22×D5314yes—
525C22×Q8C22×D5311yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—531no—
529C22×D4—531no—
530C22×D4—531no—
531C22×D4—534no—
532C22×D4—1061no—
533C22×D4—1061no—
534C22×D4—1061no—
535C22×D4—1061no—
536C22×D4—1061no—
537C22×D4—1061no—
538C22×D4—1061no—
539C22×D4—1061no—
540C22×D4—1062no—
541C22×D4—2122no—
542C22×D4—2122no—
543C22×D4C22×D5311yescharacteristic
544C22×D4C22×D5311yescharacteristic
545C23×C4—21no—
546C23×C4—1061no—
547C23×C4—1061no—
548C23×C4C22×D5311yescharacteristic
549C2×SD16—42no—
550C2×SD16—534no—
551C2×SD16—2122no—
552C2×SD16C22×D5314yescomplemented
553C2×D8—42no—
554C2×D8—534no—
555C2×D8—534no—
556C2×D8—534no—
557C2×D8—534no—
558C2×D8—534no—
559C2×D8—2122no—
560C2×D8—2122no—
561C2×D8—2122no—
562C2×D8—2122no—
563C2×D8—2122no—
564C2×D8C22×D5314yescomplemented
565C22×C8—531no—
566C22×C8—531no—
567C22×C8C22×D5311yescharacteristic
568C22×C8C22×D5311yescharacteristic
569#127—534no—
570#127—534no—
571#127—534no—
572#127—1062no—
573#127—1062no—
574#127—1062no—
575#125—534no—
576#125—1062no—
577#124—534no—
578#124—534no—
579#124—1062no—
580#124—1062no—
581#123—1068no—
582#123—1068no—
583#121—22no—
584#121—534no—
585#121—1068no—
586#121—1068no—
587#121—1068no—
588#121—1068no—
589#121—1062no—
590#121C22×D5314yes—
591#120—1068no—
592#120—1068no—
593C4×D4—534no—
594C4×D4—534no—
595C4×D4—1062no—
596C4×D4—1062no—
597#117—534no—
598#117—534no—
599C2×C4⋊C4—531no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—1061no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4C22×D5311yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—531no—
607C2×C22⋊C4—531no—
608C2×C22⋊C4—1061no—
609C2×C22⋊C4—1061no—
610C2×C22⋊C4—1061no—
611C2×C22⋊C4—1061no—
612C2×C22⋊C4—1061no—
613C2×C22⋊C4—1061no—
614C2×C22⋊C4—1061no—
615C2×C42—531no—
616C2×C42—531no—
617C4⋊C8—534no—
618C4⋊C8—534no—
619#103—534no—
620#103C22×D5314yescomplemented
621#102—534no—
622#102—534no—
623#102—534no—
624#102—534no—
625#102—534no—
626#102C22×D5314yescomplemented
627C22⋊C8—534no—
628C22⋊C8C22×D5314yes—
629#97—534no—
630C4×C8—534no—
631C24—21no—
632C24—21no—
633C24—1064no—
634C24—1061no—
635C24—1061no—
636C24—1061no—
637C24—4242no—
638C24—4242no—
639C24—2124no—
640C24D4×D5311yescharacteristic
641#41—44no—
642#41—44no—
643#41—48no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8C23×D5312yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—44no—
657C2×D4—82no—
658C2×D4—532no—
659C2×D4—532no—
660C2×D4—532no—
661C2×D4—1064no—
662C2×D4—1064no—
663C2×D4—1064no—
664C2×D4—1064no—
665C2×D4—1064no—
666C2×D4—1064no—
667C2×D4—1064no—
668C2×D4—1061no—
669C2×D4—1064no—
670C2×D4—1061no—
671C2×D4—1061no—
672C2×D4—1062no—
673C2×D4—1062no—
674C2×D4—1062no—
675C2×D4—1062no—
676C2×D4—1062no—
677C2×D4—1062no—
678C2×D4—4242no—
679C2×D4—4242no—
680C2×D4—4242no—
681C2×D4—4242no—
682C2×D4—4242no—
683C2×D4—4242no—
684C2×D4—4242no—
685C2×D4—2124no—
686C2×D4—2124no—
687C2×D4—2124no—
688C2×D4—2128no—
689C2×D4C23×D5312yes—
690C2×D4C23×D5312yes—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—24no—
696C22×C4—44no—
697C22×C4—531no—
698C22×C4—531no—
699C22×C4—531no—
700C22×C4—531no—
701C22×C4—1064no—
702C22×C4—1064no—
703C22×C4—1061no—
704C22×C4—4242no—
705C22×C4—4242no—
706C22×C4D4×D5312yes—
707C22×C4D4×D5311yescharacteristic
708C22×C4C23×D5312yes—
709C22×C4C23×D5311yescharacteristic
710SD16—44no—
711SD16—2124no—
712D8—44no—
713D8—2124no—
714D8—2124no—
715D8—2124no—
716D8—2124no—
717D8—2124no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—532no—
721C2×C8—532no—
722C2×C8—1062no—
723C2×C8—1062no—
724C2×C8C23×D5312yes—
725C2×C8C23×D5312yes—
726C4⋊C4—21no—
727C4⋊C4—534no—
728C4⋊C4—534no—
729C4⋊C4—532no—
730C4⋊C4—1064no—
731C4⋊C4—1064no—
732C4⋊C4—1061no—
733C4⋊C4C23×D5312yes—
734C22⋊C4—24no—
735C22⋊C4—534no—
736C22⋊C4—534no—
737C22⋊C4—1064no—
738C22⋊C4—1064no—
739C22⋊C4—1064no—
740C22⋊C4—1064no—
741C22⋊C4—1064no—
742C22⋊C4—1064no—
743C22⋊C4—1064no—
744C42—532no—
745C42—532no—
746C42—532no—
747C42—532no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—1062no—
760C23—1062no—
761C23—1062no—
762C23—4244no—
763C23—4244no—
764C23—42416no—
765C23—2128no—
766C23—2122no—
767C23—2122no—
768C23—2122no—
769C23—2122no—
770C23—2122no—
771C23—2122no—
772C23—2122no—
773C23—2122no—
774C23—2122no—
775C23C2×D4×D5312yes—
776C23C2×D4×D5311yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—42no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—42no—
786D4—42no—
787D4—84no—
788D4—1062no—
789D4—1062no—
790D4—1062no—
791D4—1062no—
792D4—1062no—
793D4—1062no—
794D4—4244no—
795D4—4244no—
796D4—4244no—
797D4—4244no—
798D4—4244no—
799D4—4244no—
800D4—4244no—
801D4—2128no—
802D4—2122no—
803D4—2122no—
804D4—2122no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—48no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—532no—
815C2×C4—532no—
816C2×C4—532no—
817C2×C4—532no—
818C2×C4—1062no—
819C2×C4—1062no—
820C2×C4—1062no—
821C2×C4—1062no—
822C2×C4—1062no—
823C2×C4—4244no—
824C2×C4—4244no—
825C2×C4—2122no—
826C2×C4C2×D4×D5312yes—
827C2×C4C2×D4×D5311yescharacteristic
828C2×C4#1313326212yes—
829C2×C4#1313326212yes—
830C2×C4C24×D5311yescharacteristic
831C8—22no—
832C8—22no—
833C8—1062no—
834C8—1062no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—44no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—84no—
846C22—84no—
847C22—42416no—
848C22—4244no—
849C22—4244no—
850C22—4244no—
851C22—2122no—
852C22—2122no—
853C22—2122no—
854C22—2122no—
855C22—2122no—
856C22—2122no—
857C22—2122no—
858C22—2122no—
859C22—2122no—
860C22#1681118812yes—
861C22#1681142512yes—
862C22#1681142712yes—
863C22C22×D4×D5311yescharacteristic
864C4—22no—
865C4—42no—
866C4—42no—
867C4—1062no—
868C4—1062no—
869C4—1062no—
870C4—1062no—
871C4—2122no—
872C4#1681118812yes—
873C4C2×#1313326211yescharacteristic
874C4C2×#1313326211yescharacteristic
875C2—42no—
876C2—82no—
877C2—82no—
878C2—4242no—
879C2—4242no—
880C2—4242no—
881C2#2028576314yesdirect product factor
882C2C2×#1681118811yescharacteristic
883C2C2×#1681142511yescharacteristic
884C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#449C2
socleC23×C53C22×D4
hypercenterC2×#449D53
hypocenterC53C2×#3220
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×#16811226C2semidirect
2. C2×#16811187C2semidirect
3. #20285763C2direct (N × H)
4. C2×#16811009C2semidirect
5. C2×#16810998C2semidirect
6. C2×#16810986C2semidirect
7. C2×#16810979C2semidirect
8. C2×#16810841C2semidirect
9. C2×#16810840C2semidirect
10. C2×#16810817C2semidirect
11. C2×#16810816C2semidirect
12. C2×#16810768C2semidirect
13. C2×#16810759C2semidirect
14. C2×#16810756C2semidirect
15. C2×#16810681C2semidirect
16. C2×C53×#449C2semidirect
18. C22×#11719924C22semidirect
23. C22×#11719922C22semidirect
25. #16811226C22semidirect
27. #16811187C22semidirect
30. C2×#13133213C22semidirect
31. C2×#13133208C22semidirect
43. C2×D4×Dic53C22semidirect
44. C2×#13133179C22semidirect
46. #16811009C22semidirect
47. #16810998C22semidirect
48. #16810986C22semidirect
49. #16810979C22semidirect
50. #16810841C22semidirect
51. #16810840C22semidirect
52. #16810817C22semidirect
53. #16810816C22semidirect
54. #16810768C22semidirect
55. #16810759C22semidirect
56. #16810756C22semidirect
57. #16810681C22semidirect
58. C2×#13133146C22semidirect
59. C2×#13133146C22semidirect
60. C2×#13133141C22semidirect
63. C2×#13133138C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
70. C22×SD16×C53C22semidirect
71. C22×D8×C53C22semidirect
73. C53×#449C22semidirect
74. C2×#103×C53C22semidirect
75. C2×#102×C53C22semidirect
96. C2×#11719924C23semidirect
106. C2×#11719922C23semidirect
114. #13133213C23semidirect
116. #13133208C23semidirect
132. D4×Dic53C23semidirect
134. #13133179C23semidirect
153. #13133146C23semidirect
154. #13133146C23semidirect
155. #13133141C23semidirect
158. #13133138C23semidirect
162. #13133127C23semidirect
163. C8×Dic53C23semidirect
176. C2×SD16×C53C23semidirect
178. C2×D8×C53C23semidirect
185. #103×C53C23semidirect
186. #102×C53C23semidirect
445. C2×#449D53semidirect
452. C2×C53#3220semidirect
462. C22×SD16C2×D53semidirect
468. C22×D8C2×D53semidirect
501. #449C2×D53semidirect
508. C2×#103C2×D53semidirect
514. C2×#102C2×D53semidirect
519. C53C2×#3220semidirect
552. C2×SD16C22×D53semidirect
564. C2×D8C22×D53semidirect
620. #103C22×D53semidirect
626. #102C22×D53semidirect
881. C2#20285763direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112262
C2×#168111872
#202857632
C2×#168110092
C2×#168109982
C2×#168109862
C2×#168109792
C2×#168108412
C2×#168108402
C2×#168108172
C2×#168108162
C2×#168107682
C2×#168107592
C2×#168107562
C2×#168106812
C2×C53×#4492
C2×#322053