Finite Group Databasebeta

← C2×#20286898 #28260839

Subgroups — C2×#20286898 #28260839

Order 13568.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811339C211yesmaximal, characteristic, complemented
2C2×#16811285C211yesmaximal, characteristic, complemented
3#20286898C2116yesmaximal, direct product factor
4C2×#16810985C211yesmaximal, characteristic, complemented
5C2×#16810967C211yesmaximal, characteristic, complemented
6C2×#16810949C211yesmaximal, characteristic, complemented
7C2×#16810877C211yesmaximal, characteristic, complemented
8C2×#16810853C211yesmaximal, characteristic, complemented
9C2×#16810839C211yesmaximal, characteristic, complemented
10C2×#16810771C211yesmaximal, characteristic, complemented
11C2×#16810763C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×#16810693C211yesmaximal, characteristic, complemented
14C2×#16810630C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C2×C53×#475C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×D424C2211yescharacteristic
22C22×#11719912C2211yescharacteristic
23C22×C8×D53C2211yescharacteristic
24#16811339—24no—
25#16811339C2218yescomplemented
26#16811285—24no—
27#16811285C2218yescomplemented
28C2×#13133206—21no—
29C2×#13133206—21no—
30C2×#13133205—21no—
31C2×#13133205C2211yescharacteristic
32C2×#13133197—21no—
33C2×#13133197C2211yescharacteristic
34C2×#13133192—21no—
35C2×#13133192—21no—
36C2×#13133192C2211yescharacteristic
37C2×#13133192C2211yescharacteristic
38C2×#13133192C2211yescharacteristic
39C2×C4×D212—21no—
40C2×C4×D212C2211yescharacteristic
41C2×C4×D212C2211yescharacteristic
42C2×#13133175—21no—
43C2×#13133175C2211yescharacteristic
44C2×#13133175C2211yescharacteristic
45#16810985C2218yescomplemented
46#16810967C2218yescomplemented
47#16810949C2218yescomplemented
48#16810877C2218yescomplemented
49#16810853C2218yescomplemented
50#16810839C2218yescomplemented
51#16810771C2218yescomplemented
52#16810763C2218yescomplemented
53#16810721C2218yescomplemented
54#16810693C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56#16810630C2218yescomplemented
57#16810618C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C53×#475C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C22×Dic106—21no—
82C22×Dic106C2311yescharacteristic
83C2×Q8×D53—22no—
84C2×Q8×D53—24no—
85C2×Q8×D53—42no—
86C2×Q8×D53C2314yes—
87C22×D212—21no—
88C22×D212—21no—
89C22×D212—21no—
90C22×D212—21no—
91C22×D212D411yescharacteristic
92C22×D212C2311yescharacteristic
93C22×D212C2311yescharacteristic
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53C2311yescharacteristic
98C22×C4×D53C2311yescharacteristic
99C2×#11719913—42no—
100C2×#11719913C2314yes—
101C2×#11719924—24no—
102C2×#11719924C2314yes—
103C2×D424—42no—
104C2×D424C2314yes—
105C2×#11719912—42no—
106C2×#11719912C2314yes—
107C22×#88322C2311yescharacteristic
108C22×#88322C2311yescharacteristic
109C2×C8×D53—42no—
110C2×C8×D53C2314yes—
111#13133206—28no—
112#13133206—28no—
113#13133205—22no—
114#13133205—28no—
115#13133205C2314yes—
116#13133197—28no—
117#13133197—22no—
118#13133197C2314yes—
119#13133192—28no—
120#13133192—28no—
121#13133192—22no—
122#13133192—22no—
123#13133192—22no—
124#13133192C2314yes—
125#13133192C2314yes—
126#13133192C2314yes—
127C4×D212—22no—
128C4×D212—28no—
129C4×D212D414yes—
130C4×D212C2314yes—
131C4×D212C2314yes—
132#13133175—28no—
133#13133175—22no—
134#13133175—22no—
135#13133175C2314yes—
136#13133175C2314yes—
137C2×C4⋊Dic53—21no—
138C2×C4⋊Dic53D411yescharacteristic
139C2×C4⋊Dic53C2311yescharacteristic
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C2×#11719921D411yescharacteristic
151C2×C4×Dic53—21no—
152C2×C4×Dic53—21no—
153#13133150C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133139C2314yes—
159#13133137C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133129C2314yes—
163#13133129C2314yes—
164#13133128C2314yes—
165C22×Q8×C53—21no—
166C22×Q8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4⋊Q8×C53—22no—
170C4⋊Q8×C53C2314yes—
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C42×C53—21no—
179C2×C42×C53C2311yescharacteristic
180#106×C53C2314yes—
181#106×C53C2314yes—
182C4⋊C8×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C23×D53—21no—
186C23×D53—21no—
187C23×D53C2×D411yescharacteristic
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—24no—
191C2×Q8×C53—22no—
192C2×Q8×C53—82no—
193C2×Q8×C53#4114yes—
194C2×Q8×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2411yescharacteristic
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206#11719949—28no—
207#11719949—44no—
208#11719949—48no—
209Q8×D53—28no—
210Q8×D53—44no—
211Q8×D53—48no—
212C2×D212—22no—
213C2×D212—22no—
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—24no—
217C2×D212—24no—
218C2×D212—21no—
219C2×D212—21no—
220C2×D212—24no—
221C2×D212—24no—
222C2×D212—42no—
223C2×D212—44no—
224C2×D212—44no—
225C2×D212—82no—
226C2×D212—82no—
227C2×D212C2×D414yes—
228C2×D212C2412yes—
229C2×D212C2412yes—
230C2×C4×D53—22no—
231C2×C4×D53—22no—
232C2×C4×D53—22no—
233C2×C4×D53—22no—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—24no—
237C2×C4×D53—44no—
238C2×C4×D53—44no—
239C2×C4×D53—44no—
240C2×C4×D53C2×D412yes—
241C2×C4×D53C2×D412yes—
242C2×C4×D53C2412yes—
243C2×C4×D53C2412yes—
244C2×Dic106—22no—
245C2×Dic106—22no—
246C2×Dic106—21no—
247C2×Dic106—24no—
248C2×Dic106—44no—
249C2×Dic106C2412yes—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53C2412yes—
253C2×C8×C53C2412yes—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—24no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53C2412yes—
260C4⋊C4×C53C2412yes—
261C4⋊C4×C53C2412yes—
262C42×C53—24no—
263C42×C53C2×D412yes—
264C42×C53C2412yes—
265#11719924—28no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921C2×D414yes—
276#11719921C2×D414yes—
277C4⋊Dic53—21no—
278C4⋊Dic53—24no—
279C4⋊Dic53C2×D414yes—
280C4⋊Dic53C2412yes—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322C2412yes—
286C2×#88322C2412yes—
287D424—44no—
288#11719913—44no—
289#11719912—44no—
290C8×D53—44no—
291C23×C53C22×D411yescharacteristic
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53C22×D412yes—
307C22×D53C22×D412yes—
308Q8×C53—24no—
309Q8×C53—22no—
310Q8×C53—84no—
311Q8×C53C2×#4114yes—
312C2×C4×C53—24no—
313C2×C4×C53—22no—
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×C53C22×D412yes—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C2×#4112yes—
326C2×C4×C53H(5,𝔽2)12yes—
327C2×C4×C53C2511yescharacteristic
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53C22×D412yes—
335C2×Dic53C22×D412yes—
336D212—22no—
337D212—22no—
338D212—22no—
339D212—22no—
340D212—44no—
341D212—48no—
342D212—48no—
343D212—42no—
344D212—42no—
345D212—84no—
346D212—84no—
347C4×D53—24no—
348C4×D53—24no—
349C4×D53—22no—
350C4×D53—22no—
351C4×D53—22no—
352C4×D53—22no—
353C4×D53—48no—
354C4×D53—48no—
355C4×D53—48no—
356Dic106—22no—
357Dic106—22no—
358Dic106—48no—
359Dic106—42no—
360C8×C53—22no—
361C8×C53—22no—
362#88322—22no—
363#88322—22no—
364C2×#3321—531nomaximal, Sylow
365C22×C53#54612yes—
366C22×C53#57512yes—
367C22×C53#57712yes—
368C22×C53C23×D411yescharacteristic
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—22no—
372C2×D53—22no—
373C2×D53—22no—
374C2×D53—22no—
375C2×D53—44no—
376C2×D53—44no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—84no—
384C2×D53—84no—
385C4×C53—24no—
386C4×C53—22no—
387C4×C53—22no—
388C4×C53—42no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53#54612yes—
392C4×C53C22×#4111yescharacteristic
393C4×C53C2×H(5,𝔽2)11yescharacteristic
394Dic53—22no—
395Dic53—22no—
396Dic53—42no—
397Dic53—42no—
398C2×#555—531no—
399C2×#548—531no—
400#3321—5316no—
401C2×#489—531no—
402C2×#485—531no—
403C2×#482—531no—
404C2×#475D5311yescharacteristic, complemented
405C2×#469—531no—
406C2×#465—531no—
407C2×#463—531no—
408C2×#449—531no—
409C2×#448—531no—
410C2×#440—531no—
411C2×#435—531no—
412C2×#419—531no—
413C2×#416—531no—
414C2×C53#332114yescomplemented
415C2×C53C2×#54611yescharacteristic
416C2×C53C2×#57511yescharacteristic
417C2×C53C2×#57711yescharacteristic
418D53—42no—
419D53—42no—
420D53—82no—
421D53—82no—
422C22×#41—531no—
423C23×Q8—531no—
424C22×SD16—531no—
425C22×SD16—531no—
426C22×D8—531no—
427C22×M16—531no—
428C23×C8—531no—
429#555—538no—
430#555—1064no—
431#548—538no—
432#548—1064no—
433C2×C4⋊Q8C2×D5311yescharacteristic
434C2×#124—531no—
435C2×#124—1061no—
436C2×#124—1061no—
437C2×#124—1061no—
438C2×C22⋊Q8—531no—
439C2×C22⋊Q8—1061no—
440C2×#121—531no—
441C2×#121—531no—
442C2×#121—531no—
443C2×#121—1061no—
444C2×#121—1061no—
445C2×C4×Q8C2×D5311yescharacteristic
446C2×C4×D4—531no—
447C2×C4×D4—531no—
448C2×C4×D4—1061no—
449C2×#117—531no—
450C2×#117—531no—
451C2×#117—1061no—
452#489—538no—
453#485—538no—
454#482—538no—
455#475C2×D5318yescomplemented
456#469—538no—
457#465—538no—
458#463—538no—
459#449—538no—
460#448—538no—
461#440—538no—
462#435—538no—
463C2×#107—531no—
464C2×#106C2×D5311yescharacteristic
465C2×#106C2×D5311yescharacteristic
466C2×C4⋊C8C2×D5311yescharacteristic
467#419—538no—
468#416—538no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103C2×D5311yescharacteristic
474C2×#103C2×D5311yescharacteristic
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×C22⋊C8—531no—
480C2×C22⋊C8—531no—
481C2×#97—531no—
482C53C2×#332111yescharacteristic, complemented, Sylow
483C2×#41—534no—
484C2×#41—1062no—
485C2×#41—1064no—
486C2×#41—2122no—
487C22×Q8—21no—
488C22×Q8—534no—
489C22×Q8—531no—
490C22×Q8—1061no—
491C22×Q8—1062no—
492C22×Q8—1064no—
493C22×Q8—2122no—
494C22×Q8C22×D5311yescharacteristic
495C22×D4—531no—
496C22×D4—531no—
497C22×D4—531no—
498C22×D4—1061no—
499C22×D4—1061no—
500C22×D4—1061no—
501C22×D4—1061no—
502C23×C4—531no—
503C23×C4—531no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4—1061no—
507C2×SD16—534no—
508C2×SD16—534no—
509C2×SD16—1064no—
510C2×SD16—2122no—
511C2×D8—534no—
512C2×D8—2122no—
513C2×M16—534no—
514C2×M16—2122no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—534no—
518C22×C8—2122no—
519C22×C8C22×D5311yescharacteristic
520C22×C8C22×D5311yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8C22×D5314yes—
523#124—534no—
524#124—1068no—
525#124—1068no—
526#124—1068no—
527#124—1062no—
528C22⋊Q8—534no—
529C22⋊Q8—1068no—
530C22⋊Q8—1062no—
531#121—534no—
532#121—534no—
533#121—534no—
534#121—1062no—
535#121—1062no—
536#121—1062no—
537#121—1068no—
538#121—1068no—
539C4×Q8—22no—
540C4×Q8C22×D5314yes—
541C4×D4—534no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—1068no—
545C4×D4—1062no—
546#117—534no—
547#117—534no—
548#117—1068no—
549#117—1062no—
550#117—1062no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C4⋊C4C22×D5311yescharacteristic
558C2×C4⋊C4C22×D5311yescharacteristic
559C2×C22⋊C4—531no—
560C2×C22⋊C4—531no—
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
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×C42—21no—
571C2×C42—1061no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575#106C22×D5314yes—
576#106C22×D5314yes—
577C4⋊C8C22×D5314yes—
578#103—534no—
579#103—534no—
580#103—534no—
581#103—534no—
582#103C22×D5314yes—
583#103C22×D5314yes—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588C22⋊C8—534no—
589C22⋊C8—534no—
590#97—534no—
591C24—531no—
592C24—531no—
593C24—1061no—
594C24—1061no—
595#41—1068no—
596#41—2124no—
597#41—2128no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—22no—
601C2×Q8—82no—
602C2×Q8—532no—
603C2×Q8—1064no—
604C2×Q8—1061no—
605C2×Q8—1068no—
606C2×Q8—1062no—
607C2×Q8—1062no—
608C2×Q8—2124no—
609C2×Q8—2124no—
610C2×Q8—2128no—
611C2×Q8#1171994914yes—
612C2×Q8C23×D5312yes—
613C2×D4—534no—
614C2×D4—532no—
615C2×D4—532no—
616C2×D4—1064no—
617C2×D4—1064no—
618C2×D4—1064no—
619C2×D4—1064no—
620C2×D4—1061no—
621C2×D4—1061no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—1062no—
625C2×D4—1062no—
626C2×D4—4242no—
627C2×D4—4242no—
628C2×D4—2122no—
629C2×D4—2124no—
630C2×D4—2124no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—531no—
636C22×C4—531no—
637C22×C4—532no—
638C22×C4—532no—
639C22×C4—532no—
640C22×C4—532no—
641C22×C4—1064no—
642C22×C4—1064no—
643C22×C4—1062no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1064no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4—2124no—
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4C23×D5311yescharacteristic
656SD16—1068no—
657SD16—2124no—
658D8—2124no—
659M16—2124no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—2124no—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—534no—
675C4⋊C4—532no—
676C4⋊C4—1064no—
677C4⋊C4—1061no—
678C4⋊C4C23×D5312yes—
679C4⋊C4C23×D5312yes—
680C4⋊C4C23×D5312yes—
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—
691C22⋊C4—1064no—
692C42—24no—
693C42—1064no—
694C42—1064no—
695C42D4×D5312yes—
696C42C23×D5312yes—
697C23—532no—
698C23—532no—
699C23—1062no—
700C23—1062no—
701C23—1062no—
702C23—1062no—
703C23—1062no—
704C23—1062no—
705C23—1062no—
706C23—1062no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23—2122no—
711C23—2122no—
712C23—2122no—
713C23C2×D4×D5311yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—84no—
717Q8—1062no—
718Q8—1062no—
719Q8—2128no—
720Q8—2122no—
721Q8C2×#1171994914yes—
722D4—1062no—
723D4—1062no—
724D4—1062no—
725D4—1062no—
726D4—4244no—
727D4—4244no—
728D4—2124no—
729D4—2128no—
730D4—2128no—
731D4—2122no—
732D4—2122no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—532no—
744C2×C4—532no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1064no—
748C2×C4—1064no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—2128no—
756C2×C4—2128no—
757C2×C4—2128no—
758C2×C4—2122no—
759C2×C4—2122no—
760C2×C4C2×D4×D5312yes—
761C2×C4C2×D4×D5312yes—
762C2×C4C2×D4×D5311yescharacteristic
763C2×C4C2×#1171994912yes—
764C2×C4#1313326312yes—
765C2×C4C24×D5311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1062no—
769C8—1062no—
770C22—1062no—
771C22—1062no—
772C22—1062no—
773C22—1062no—
774C22—1062no—
775C22—1062no—
776C22—4244no—
777C22—4244no—
778C22—2122no—
779C22—2122no—
780C22—2122no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22—2124no—
785C22—2124no—
786C22#1681126412yes—
787C22#1681142212yes—
788C22#1681142912yes—
789C22C22×D4×D5311yescharacteristic
790C4—24no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—1062no—
797C4—1062no—
798C4—2122no—
799C4—2122no—
800C4#1681126412yes—
801C4C22×#1171994911yescharacteristic
802C4C2×#1313326311yescharacteristic
803C2—4242no—
804C2—4242no—
805C2—2122no—
806C2—2122no—
807C2#2028689814yesdirect product factor
808C2C2×#1681126411yescharacteristic
809C2C2×#1681142211yescharacteristic
810C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#475C2
socleC23×C53C22×D4
hypercenterC2×#475D53
hypocenterC53C2×#3321
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#16811339C2semidirect
2. C2×#16811285C2semidirect
3. #20286898C2direct (N × H)
4. C2×#16810985C2semidirect
5. C2×#16810967C2semidirect
6. C2×#16810949C2semidirect
7. C2×#16810877C2semidirect
8. C2×#16810853C2semidirect
9. C2×#16810839C2semidirect
10. C2×#16810771C2semidirect
11. C2×#16810763C2semidirect
12. C2×#16810721C2semidirect
13. C2×#16810693C2semidirect
14. C2×#16810630C2semidirect
15. C2×#16810618C2semidirect
16. C2×C53×#475C2semidirect
25. #16811339C22semidirect
27. #16811285C22semidirect
45. #16810985C22semidirect
46. #16810967C22semidirect
47. #16810949C22semidirect
48. #16810877C22semidirect
49. #16810853C22semidirect
50. #16810839C22semidirect
51. #16810771C22semidirect
52. #16810763C22semidirect
53. #16810721C22semidirect
54. #16810693C22semidirect
56. #16810630C22semidirect
57. #16810618C22semidirect
71. C53×#475C22semidirect
404. C2×#475D53semidirect
414. C2×C53#3321semidirect
455. #475C2×D53semidirect
482. C53C2×#3321semidirect
807. C2#20286898direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113392
C2×#168112852
#202868982
C2×#168109852
C2×#168109672
C2×#168109492
C2×#168108772
C2×#168108532
C2×#168108392
C2×#168107712
C2×#168107632
C2×#168107212
C2×#168106932
C2×#168106302
C2×#168106182
C2×C53×#4752
C2×#332153