Finite Group Databasebeta

← C2×#20284960 #28252388

Subgroups — C2×#20284960 #28252388

Order 13568.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811229C211yesmaximal, characteristic, complemented
2C2×#16811095C211yesmaximal, characteristic, complemented
3#20284960C2116yesmaximal, direct product factor
4C2×#16810950C211yesmaximal, characteristic, complemented
5C2×#16810949C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810819C211yesmaximal, characteristic, complemented
8C2×#16810818C211yesmaximal, characteristic, complemented
9C2×#16810758C211yesmaximal, characteristic, complemented
10C2×#16810758C211yesmaximal, characteristic, complemented
11C2×#16810734C211yesmaximal, characteristic, complemented
12C2×#16810732C211yesmaximal, characteristic, complemented
13C2×#16810705C211yesmaximal, characteristic, complemented
14C2×#16810703C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C22×D424C2211yescharacteristic
19C22×D424C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22#16811229—24no—
23#16811229C2218yescomplemented
24C2×#13133214C2211yescharacteristic, complemented
25C2×#13133202—21no—
26C2×#13133202—21no—
27C2×#13133192—21no—
28C2×#13133192—21no—
29C2×#13133192C2211yescharacteristic
30C2×#13133192C2211yescharacteristic
31#16811095—24no—
32#16811095C2218yescomplemented
33C2×C4×D212C2211yescharacteristic
34C2×D4×Dic53C2211yescharacteristic
35C2×#13133179C2211yescharacteristic
36C2×#13133179C2211yescharacteristic, complemented
37C2×#13133179C2211yescharacteristic, complemented
38C2×C4×C22⋊D53—21no—
39C2×#13133177—21no—
40C2×#13133175C2211yescharacteristic
41C2×#13133174C2211yescharacteristic
42C22×#11719921—21no—
43C2×C22⋊C4×D53—21no—
44#16810950C2218yescomplemented
45#16810949C2218yescomplemented
46#16810920C2218yescomplemented
47#16810819C2218yescomplemented
48#16810818C2218yescomplemented
49#16810758C2218yescomplemented
50#16810758C2218yescomplemented
51#16810734C2218yescomplemented
52#16810732C2218yescomplemented
53#16810705C2218yescomplemented
54#16810703C2218yescomplemented
55#16810683C2218yescomplemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133139C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic, complemented
61C2×#13133137C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic, complemented
64C2×#13133137C2211yescharacteristic, complemented
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C2×#125×C53C2211yescharacteristic, complemented
70C2×C4×D4×C53C2211yescharacteristic
71C53×#478C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C22×D212—21no—
79C22×D212—21no—
80C22×D212—21no—
81C22×D212—21no—
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C2×D4×D53—24no—
87C2×D4×D53—24no—
88C2×D4×D53—22no—
89C2×D4×D53C2314yes—
90C23×Dic53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53C2311yescharacteristic
96C2×D424—24no—
97C2×D424—24no—
98C2×D424C2314yes—
99C2×D424C2314yes—
100C2×#11719922—24no—
101C2×#11719922—24no—
102C2×#11719922C2314yes—
103C2×#11719922C2314yes—
104C22×#88322C2311yescharacteristic
105C22×#88322C2311yescharacteristic
106#13133214—22no—
107#13133214C2314yescomplemented
108#13133202—28no—
109#13133202—28no—
110#13133192—28no—
111#13133192—28no—
112#13133192—22no—
113#13133192—22no—
114#13133192C2314yes—
115#13133192C2314yes—
116C4×D212—22no—
117C4×D212C2314yes—
118D4×Dic53—22no—
119D4×Dic53C2314yes—
120#13133179—22no—
121#13133179—22no—
122#13133179—22no—
123#13133179C2314yes—
124#13133179C2314yescomplemented
125#13133179C2314yescomplemented
126C4×C22⋊D53—28no—
127#13133177—28no—
128#13133175—22no—
129#13133175C2314yes—
130#13133174D414yes—
131#13133174C2314yes—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919D411yescharacteristic
134C2×#11719919D411yescharacteristic
135C2×C22⋊Dic53—21no—
136C2×#11719921—28no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921D411yescharacteristic
145C2×#11719921D411yescharacteristic
146C22⋊C4×D53—28no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yescomplemented
150#13133148C2314yescomplemented
151C4⋊#88322C2314yescomplemented
152#13133139C2314yescomplemented
153#13133139C2314yescomplemented
154#13133137C2314yes—
155#13133137C2314yes—
156#13133137C2314yescomplemented
157#13133137C2314yescomplemented
158#13133129C2314yes—
159#13133129C2314yes—
160#13133127C2314yescomplemented
161C8×Dic53C2314yescomplemented
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166#125×C53—22no—
167#125×C53C2314yescomplemented
168C4×D4×C53—22no—
169C4×D4×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yescomplemented
178#106×C53C2314yescomplemented
179C4⋊C8×C53C2314yescomplemented
180#102×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C23×D53—21no—
184C23×D53—28no—
185C23×D53—24no—
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—82no—
189C23×D53—82no—
190C23×D53C2×D411yescharacteristic
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53#4114yes—
194C2×D4×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—24no—
199C22×C4×C53—82no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—28no—
204C2×C22⋊D53—24no—
205C22×Dic53—21no—
206C22×Dic53—24no—
207C22×Dic53—82no—
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211D4×D53—216no—
212D4×D53—28no—
213D4×D53—28no—
214C2×D212—21no—
215C2×D212—22no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—22no—
219C2×D212—22no—
220C2×D212—21no—
221C2×D212—21no—
222C2×D212—24no—
223C2×D212—24no—
224C2×D212—24no—
225C2×D212—24no—
226C2×D212—82no—
227C2×D212—82no—
228C2×D212—82no—
229C2×D212—82no—
230C2×D212#4114yes—
231C2×D212C2412yes—
232C2×D212C2412yes—
233C2×D212C2412yes—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53—24no—
239C2×C4×D53—24no—
240C2×C4×D53—82no—
241C2×C4×D53—82no—
242C2×C4×D53—82no—
243C2×C4×D53—82no—
244C2×C4×D53C2×D412yes—
245C2×C4×D53C2412yes—
246C2×C8×C53—22no—
247C2×C8×C53—22no—
248C2×C8×C53C2412yes—
249C2×C8×C53C2412yes—
250C4⋊C4×C53—24no—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C2412yes—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C42×C53C2×D412yes—
260C42×C53C2412yes—
261C22⋊Dic53—24no—
262#11719922—28no—
263#11719922—28no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921C2×D414yes—
272#11719921C2×D414yes—
273C4⋊Dic53—21no—
274C4⋊Dic53C2412yes—
275#11719919C2×D414yes—
276#11719919C2×D414yes—
277C4×Dic53—24no—
278C4×Dic53C2×D412yes—
279C4×Dic53C2412yes—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322C2412yes—
283C2×#88322C2412yes—
284D424—28no—
285D424—28no—
286C23×C53—24no—
287C23×C53—22no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53C22×D411yescharacteristic
291C22×D53—22no—
292C22×D53—24no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—216no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—42no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—84no—
308C22×D53—84no—
309C22×D53—816no—
310C22×D53C22×D412yes—
311D4×C53—24no—
312D4×C53—22no—
313D4×C53C2×#4114yes—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—84no—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C2×#4112yes—
327C2×C4×C53C2×#4112yes—
328C2×C4×C53C2511yescharacteristic
329C22⋊D53—216no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—42no—
335C2×Dic53—84no—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338C2×Dic53C22×D412yes—
339D212—24no—
340D212—22no—
341D212—22no—
342D212—22no—
343D212—22no—
344D212—22no—
345D212—42no—
346D212—42no—
347D212—84no—
348D212—84no—
349D212—84no—
350D212—84no—
351D212C2×#4114yes—
352C4×D53—24no—
353C4×D53—22no—
354C4×D53—22no—
355C4×D53—84no—
356C4×D53—84no—
357C4×D53—84no—
358C4×D53—84no—
359C8×C53—22no—
360C8×C53—22no—
361#88322—22no—
362#88322—22no—
363C2×#3122—531nomaximal, Sylow
364C22×C53—24no—
365C22×C53—48no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53#52512yes—
369C22×C53#57612yes—
370C22×C53#57612yes—
371C22×C53C23×D411yescharacteristic
372C2×D53—22no—
373C2×D53—24no—
374C2×D53—22no—
375C2×D53—22no—
376C2×D53—44no—
377C2×D53—48no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—816no—
387C2×D53—84no—
388C2×D53—84no—
389C4×C53—22no—
390C4×C53—22no—
391C4×C53—42no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53#52512yes—
395C4×C53C22×#4111yescharacteristic
396C4×C53C22×#4111yescharacteristic
397Dic53—22no—
398Dic53—22no—
399Dic53—22no—
400Dic53—42no—
401C2×#540—531no—
402C2×#518—531no—
403#3122—5316no—
404C2×#482—531no—
405C2×#482—531no—
406C2×#478—531no—
407C2×#478D5311yescharacteristic, complemented
408C2×#459—531no—
409C2×#459—531no—
410C2×#447—531no—
411C2×#447—531no—
412C2×#442—531no—
413C2×#442—531no—
414C2×C4×D8—531no—
415C2×C4×D8—531no—
416C2×#433—531no—
417C2×C53—44no—
418C2×C53#312214yescomplemented
419C2×C53C2×#52511yescharacteristic
420C2×C53C2×#57611yescharacteristic
421C2×C53C2×#57611yescharacteristic
422D53—42no—
423D53—44no—
424D53—82no—
425D53—82no—
426C23×D4—531no—
427C22×D8—531no—
428C22×D8—531no—
429C22×D8—531no—
430C22×D8—531no—
431#540—538no—
432#540—1064no—
433C2×#127—531no—
434C2×#125C2×D5311yescharacteristic, complemented
435C2×#123—1061no—
436C2×#123—1061no—
437C2×#121—531no—
438C2×#121—531no—
439C2×#121—1061no—
440C2×#121—1061no—
441#518—538no—
442#518—1064no—
443C2×C4×D4—531no—
444C2×C4×D4—531no—
445C2×C4×D4—531no—
446C2×C4×D4—531no—
447C2×C4×D4—531no—
448C2×C4×D4—1061no—
449C2×C4×D4—1061no—
450C2×C4×D4C2×D5311yescharacteristic
451C2×#117—531no—
452C2×#117—531no—
453C22×C22⋊C4—1061no—
454C22×C22⋊C4—1061no—
455#482—538no—
456#482—538no—
457#478—538no—
458#478C2×D5318yescomplemented
459#459—538no—
460#459—538no—
461#447—538no—
462#447—538no—
463#442—538no—
464#442—538no—
465C4×D8—538no—
466C4×D8—538no—
467#433—538no—
468C2×#107—531no—
469C2×#107C2×D5311yescharacteristic, complemented
470C2×#106—531no—
471C2×#106C2×D5311yescharacteristic, complemented
472C2×C4⋊C8—531no—
473C2×C4⋊C8C2×D5311yescharacteristic, complemented
474C2×#102—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102C2×D5311yescharacteristic
481C2×#102C2×D5311yescharacteristic
482C2×C22⋊C8—531no—
483C2×C22⋊C8—531no—
484C2×#97—531no—
485C2×C4×C8—531no—
486C53C2×#312211yescharacteristic, complemented, Sylow
487C25—1061no—
488C22×D4—534no—
489C22×D4—531no—
490C22×D4—531no—
491C22×D4—531no—
492C22×D4—1061no—
493C22×D4—1061no—
494C22×D4—1062no—
495C22×D4—1061no—
496C22×D4—1064no—
497C22×D4—1064no—
498C22×D4—1061no—
499C22×D4—1061no—
500C22×D4C22×D5311yescharacteristic
501C23×C4—21no—
502C23×C4—531no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4—1061no—
507C23×C4—1061no—
508C2×D8—534no—
509C2×D8—534no—
510C2×D8—534no—
511C2×D8—534no—
512C2×D8—1064no—
513C2×D8—1064no—
514C2×D8—1064no—
515C2×D8—1064no—
516C22×C8—531no—
517C22×C8—531no—
518C22×C8C22×D5311yescharacteristic
519C22×C8C22×D5311yescharacteristic
520#127—534no—
521#127—1062no—
522#125—22no—
523#125C22×D5314yescomplemented
524#123—1068no—
525#123—1068no—
526#121—534no—
527#121—534no—
528#121—1068no—
529#121—1068no—
530#121—1062no—
531#121—1062no—
532C4×D4—22no—
533C4×D4—534no—
534C4×D4—534no—
535C4×D4—534no—
536C4×D4—534no—
537C4×D4—534no—
538C4×D4—1062no—
539C4×D4—1062no—
540C4×D4—1062no—
541C4×D4—1062no—
542C4×D4—1068no—
543C4×D4—1068no—
544C4×D4—1062no—
545C4×D4C22×D5314yes—
546#117—534no—
547#117—534no—
548#117—534no—
549#117—1062no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4C22×D5311yescharacteristic
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C4⋊C4C22×D5311yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—531no—
560C2×C22⋊C4—531no—
561C2×C22⋊C4—1068no—
562C2×C22⋊C4—1068no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C42—531no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575#107C22×D5314yescomplemented
576#106—534no—
577#106C22×D5314yescomplemented
578C4⋊C8—534no—
579C4⋊C8C22×D5314yescomplemented
580#102—534no—
581#102—534no—
582#102—534no—
583#102—534no—
584#102—534no—
585#102—534no—
586#102C22×D5314yes—
587#102C22×D5314yes—
588C22⋊C8—534no—
589C22⋊C8—534no—
590#97—534no—
591C4×C8—534no—
592C24—21no—
593C24—531no—
594C24—1064no—
595C24—1068no—
596C24—1061no—
597C24—1061no—
598C24—1061no—
599C24—4242no—
600C24—4242no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—534no—
604C2×D4—532no—
605C2×D4—532no—
606C2×D4—532no—
607C2×D4—1064no—
608C2×D4—1064no—
609C2×D4—1064no—
610C2×D4—1068no—
611C2×D4—10616no—
612C2×D4—1068no—
613C2×D4—1068no—
614C2×D4—1061no—
615C2×D4—1064no—
616C2×D4—1064no—
617C2×D4—1061no—
618C2×D4—1061no—
619C2×D4—1062no—
620C2×D4—1062no—
621C2×D4—1062no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—4242no—
625C2×D4—4242no—
626C2×D4—4242no—
627C2×D4—4242no—
628C2×D4#1171994914yes—
629C2×D4C23×D5312yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—531no—
636C22×C4—531no—
637C22×C4—531no—
638C22×C4—532no—
639C22×C4—532no—
640C22×C4—1064no—
641C22×C4—1064no—
642C22×C4—1064no—
643C22×C4—1064no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1061no—
647C22×C4—1064no—
648C22×C4—4242no—
649C22×C4—4242no—
650C22×C4—4242no—
651C22×C4—4242no—
652C22×C4—4242no—
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4C23×D5311yescharacteristic
656D8—1068no—
657D8—1068no—
658D8—1068no—
659D8—1068no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8C23×D5312yes—
667C2×C8C23×D5312yes—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—534no—
674C4⋊C4—534no—
675C4⋊C4—532no—
676C4⋊C4—1061no—
677C4⋊C4C23×D5312yes—
678C4⋊C4C23×D5312yes—
679C4⋊C4C23×D5312yes—
680C22⋊C4—24no—
681C22⋊C4—534no—
682C22⋊C4—534no—
683C22⋊C4—1064no—
684C22⋊C4—1064no—
685C22⋊C4—1064no—
686C22⋊C4—1064no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C42—532no—
692C42—532no—
693C42—1064no—
694C42D4×D5312yes—
695C42C23×D5312yes—
696C23—24no—
697C23—22no—
698C23—42no—
699C23—42no—
700C23—532no—
701C23—10616no—
702C23—1062no—
703C23—1064no—
704C23—1062no—
705C23—1062no—
706C23—1062no—
707C23—1062no—
708C23—1062no—
709C23—4244no—
710C23—4244no—
711C23—42416no—
712C23—2122no—
713C23—2122no—
714C23—2122no—
715C23—2122no—
716C23—2122no—
717C23—2122no—
718C23—2122no—
719C23—2122no—
720C23C2×D4×D5311yescharacteristic
721D4—24no—
722D4—22no—
723D4—534no—
724D4—10616no—
725D4—1064no—
726D4—1062no—
727D4—1062no—
728D4—1062no—
729D4—1062no—
730D4—1062no—
731D4—4244no—
732D4—4244no—
733D4—4244no—
734D4—4244no—
735D4—2122no—
736D4—2122no—
737D4C2×#1171994914yes—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—84no—
747C2×C4—532no—
748C2×C4—532no—
749C2×C4—532no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1064no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—4244no—
758C2×C4—4244no—
759C2×C4—4244no—
760C2×C4—4244no—
761C2×C4—4244no—
762C2×C4—2122no—
763C2×C4C2×D4×D5312yes—
764C2×C4C2×D4×D5312yes—
765C2×C4C2×D4×D5311yescharacteristic
766C2×C4#41×D5312yes—
767C2×C4C2×#1171994912yes—
768C2×C4C24×D5311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1062no—
772C8—1062no—
773C22—24no—
774C22—48no—
775C22—42no—
776C22—42no—
777C22—1062no—
778C22—1062no—
779C22—1062no—
780C22—1064no—
781C22—42416no—
782C22—4244no—
783C22—4244no—
784C22—2122no—
785C22—2122no—
786C22—2122no—
787C22—2122no—
788C22—2122no—
789C22—2122no—
790C22—2124no—
791C22—2128no—
792C22—2122no—
793C22—2122no—
794C22#1681113612yes—
795C22#1681142512yes—
796C22#1681142712yes—
797C22C22×D4×D5311yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—1062no—
804C4—1062no—
805C4—1062no—
806C4—2122no—
807C4#1681113612yes—
808C4C2×#41×D5311yescharacteristic
809C4C22×#1171994911yescharacteristic
810C2—44no—
811C2—4242no—
812C2—4242no—
813C2—2122no—
814C2—2124no—
815C2#2028496014yesdirect product factor
816C2C2×#1681113611yescharacteristic
817C2C2×#1681142511yescharacteristic
818C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
hypercenterC2×#478D53
hypocenterC53C2×#3122
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16811229C2semidirect
2. C2×#16811095C2semidirect
3. #20284960C2direct (N × H)
4. C2×#16810950C2semidirect
5. C2×#16810949C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810819C2semidirect
8. C2×#16810818C2semidirect
9. C2×#16810758C2semidirect
10. C2×#16810758C2semidirect
11. C2×#16810734C2semidirect
12. C2×#16810732C2semidirect
13. C2×#16810705C2semidirect
14. C2×#16810703C2semidirect
15. C2×#16810683C2semidirect
16. C2×C53×#478C2semidirect
23. #16811229C22semidirect
24. C2×#13133214C22semidirect
32. #16811095C22semidirect
36. C2×#13133179C22semidirect
37. C2×#13133179C22semidirect
44. #16810950C22semidirect
45. #16810949C22semidirect
46. #16810920C22semidirect
47. #16810819C22semidirect
48. #16810818C22semidirect
49. #16810758C22semidirect
50. #16810758C22semidirect
51. #16810734C22semidirect
52. #16810732C22semidirect
53. #16810705C22semidirect
54. #16810703C22semidirect
55. #16810683C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133148C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133139C22semidirect
60. C2×#13133139C22semidirect
63. C2×#13133137C22semidirect
64. C2×#13133137C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
69. C2×#125×C53C22semidirect
71. C53×#478C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×C4⋊C8×C53C22semidirect
107. #13133214C23semidirect
124. #13133179C23semidirect
125. #13133179C23semidirect
149. #13133150C23semidirect
150. #13133148C23semidirect
151. C4⋊#88322C23semidirect
152. #13133139C23semidirect
153. #13133139C23semidirect
156. #13133137C23semidirect
157. #13133137C23semidirect
160. #13133127C23semidirect
161. C8×Dic53C23semidirect
167. #125×C53C23semidirect
177. #107×C53C23semidirect
178. #106×C53C23semidirect
179. C4⋊C8×C53C23semidirect
407. C2×#478D53semidirect
418. C2×C53#3122semidirect
434. C2×#125C2×D53semidirect
458. #478C2×D53semidirect
469. C2×#107C2×D53semidirect
471. C2×#106C2×D53semidirect
473. C2×C4⋊C8C2×D53semidirect
486. C53C2×#3122semidirect
523. #125C22×D53semidirect
575. #107C22×D53semidirect
577. #106C22×D53semidirect
579. C4⋊C8C22×D53semidirect
815. C2#20284960direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112292
C2×#168110952
#202849602
C2×#168109502
C2×#168109492
C2×#168109202
C2×#168108192
C2×#168108182
C2×#168107582
C2×#168107342
C2×#168107322
C2×#168107052
C2×#168107032
C2×#168106832
C2×C53×#4782
C2×#312253