Finite Group Databasebeta

← C2×#20287306 #28262804

Subgroups — C2×#20287306 #28262804

Order 13568.

2146 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811336C211yesmaximal, characteristic, complemented
2C2×#16811274C211yesmaximal, characteristic, complemented
3#20287306C2116yesmaximal, direct product factor
4C2×#16811020C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810941C211yesmaximal, characteristic, complemented
7C2×#16810950C211yesmaximal, characteristic, complemented
8C2×#16810947C211yesmaximal, characteristic, complemented
9C2×#16810912C211yesmaximal, characteristic, complemented
10C2×#16810902C211yesmaximal, characteristic, complemented
11C2×#16810877C211yesmaximal, characteristic, complemented
12C2×#16810876C211yesmaximal, characteristic, complemented
13C2×#16810705C211yesmaximal, characteristic, complemented
14C2×#16810699C211yesmaximal, characteristic, complemented
15C2×#16810664C211yesmaximal, characteristic, complemented
16C2×C53×#428C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×D424C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20#16811336—24no—
21#16811336C2218yescomplemented
22#16811274—24no—
23#16811274C2218yescomplemented
24C2×#13133216C2211yescharacteristic
25C2×#13133216C2211yescharacteristic
26C2×#13133205—21no—
27C2×#13133203—21no—
28C2×#13133202—21no—
29C2×#13133200—21no—
30C2×#13133195—21no—
31C2×#13133192C2211yescharacteristic
32C2×#13133192C2211yescharacteristic
33C2×#13133191C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35C2×#13133190—21no—
36C2×#13133179C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133175C2211yescharacteristic
40C2×#13133174—21no—
41C2×C4⋊C4×D53C2211yescharacteristic
42#16811020C2218yescomplemented
43#16810950C2218yescomplemented
44#16810947C2218yescomplemented
45#16810943C2218yescomplemented
46#16810941C2218yescomplemented
47#16810912C2218yescomplemented
48#16810902C2218yescomplemented
49#16810877C2218yescomplemented
50#16810876C2218yescomplemented
51#16810705C2218yescomplemented
52#16810699C2218yescomplemented
53#16810664C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C53×#428C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#107×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#106×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×D212—21no—
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53D411yescharacteristic
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53C2311yescharacteristic
92C2×D424—24no—
93C2×D424C2314yes—
94C2×#11719912—24no—
95C2×#11719912C2314yes—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98#13133216—22no—
99#13133216—22no—
100#13133216C2314yes—
101#13133216C2314yes—
102#13133205—28no—
103#13133203—28no—
104#13133202—28no—
105#13133200—28no—
106#13133195—28no—
107#13133192—22no—
108#13133192—22no—
109#13133192C2314yes—
110#13133192C2314yes—
111#13133191—22no—
112#13133191—22no—
113#13133191C2314yes—
114#13133191C2314yes—
115#13133190—28no—
116#13133179—22no—
117#13133179—22no—
118#13133179C2314yes—
119#13133179C2314yes—
120C4×C22⋊D53D414yes—
121C4×C22⋊D53C2314yes—
122#13133175—22no—
123#13133175C2314yes—
124#13133174—28no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C2×C22⋊Dic53D411yescharacteristic
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×C4×Dic53—21no—
143C2×C4×Dic53C2311yescharacteristic
144#13133150C2314yes—
145#13133149C2314yes—
146#13133148C2314yes—
147#13133148C2314yes—
148#13133148C2314yes—
149#13133146C2314yes—
150#13133139C2314yes—
151#13133139C2314yes—
152#13133137C2314yes—
153#13133137C2314yes—
154#13133137C2314yes—
155#13133137C2314yes—
156C22⋊#88322C2314yes—
157#13133129C2314yes—
158C8×Dic53C2314yes—
159C23×C4×C53—21no—
160C23×C4×C53C2311yescharacteristic
161C2×M16×C53—24no—
162C2×M16×C53C2314yes—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165#117×C53—22no—
166#117×C53C2314yes—
167C2×C4⋊C4×C53—22no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2314yes—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C42×C53—21no—
176#107×C53C2314yes—
177#107×C53C2314yes—
178#106×C53C2314yes—
179#106×C53C2314yes—
180C24×C53C2×D411yescharacteristic
181C23×D53—21no—
182C23×D53—21no—
183C23×D53C2×D411yescharacteristic
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—24no—
191C22×C4×C53—44no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D412yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2411yescharacteristic
196C2×C22⋊D53—24no—
197C2×C22⋊D53—24no—
198C2×C22⋊D53—24no—
199C2×C22⋊D53—44no—
200C2×C22⋊D53—82no—
201C2×C22⋊D53C2×D414yes—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207#11719945—432no—
208C2×D212—22no—
209C2×D212—22no—
210C2×D212—22no—
211C2×D212—22no—
212C2×D212—24no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—24no—
216C2×D212—44no—
217C2×D212—82no—
218C2×D212C2412yes—
219C2×D212C2412yes—
220C2×C4×D53—22no—
221C2×C4×D53—22no—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—44no—
226C2×C4×D53—44no—
227C2×C4×D53—44no—
228C2×C4×D53C2×D412yes—
229C2×C4×D53C2412yes—
230C2×Dic106—24no—
231C2×Dic106—24no—
232C2×Dic106—44no—
233C2×Dic106—82no—
234M16×C53—28no—
235C2×C8×C53—22no—
236C2×C8×C53#4114yescomplemented
237C2×C8×C53C2412yes—
238C2×C8×C53C2412yes—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—24no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53C2412yes—
245C4⋊C4×C53C2412yes—
246C4⋊C4×C53C2412yes—
247C4⋊C4×C53C2412yes—
248C22⋊C4×C53—24no—
249C42×C53—24no—
250C22⋊Dic53C2×D414yes—
251#11719921—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921C2×D414yes—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4⋊Dic53C2412yes—
262C4⋊Dic53C2412yes—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919C2×D414yes—
267C4×Dic53—24no—
268C4×Dic53C2×D412yes—
269C4×Dic53C2412yes—
270C2×#88322—22no—
271C2×#88322—22no—
272C2×#88322C2412yes—
273C2×#88322C2412yes—
274D424—28no—
275#11719912—28no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53C22×D412yes—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53C22×D412yes—
293C2×C4×C53—22no—
294C2×C4×C53—24no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—48no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C2×#4112yes—
309C2×C4×C532−1+412yes—
310C2×C4×C53C2511yescharacteristic
311C22⋊D53—28no—
312C22⋊D53—48no—
313C22⋊D53—84no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53AGL(1,ℤ/8)14yes—
321C2×Dic53C22×D412yes—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324D212—22no—
325D212—22no—
326D212—22no—
327D212—22no—
328D212—48no—
329D212—42no—
330D212—42no—
331D212—84no—
332C4×D53—24no—
333C4×D53—22no—
334C4×D53—22no—
335C4×D53—48no—
336C4×D53—48no—
337C4×D53—48no—
338Dic106—48no—
339Dic106—84no—
340C8×C53—22no—
341C8×C53C2×#4114yescomplemented
342#88322—22no—
343#88322—22no—
344C2×#3354—531nomaximal, Sylow
345C22×C53—22no—
346C22×C53—22no—
347C22×C53—22no—
348C22×C53—44no—
349C22×C53#54712yes—
350C22×C53C2×AGL(1,ℤ/8)12yes—
351C22×C53#57712yes—
352C22×C53C23×D411yescharacteristic
353C2×D53—22no—
354C2×D53—22no—
355C2×D53—22no—
356C2×D53—44no—
357C2×D53—42no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—84no—
364C2×D53—84no—
365C4×C53—22no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53#54712yes—
371C4×C53C22×#4111yescharacteristic
372C4×C53C2×2−1+411yescharacteristic
373Dic53—22no—
374Dic53—22no—
375Dic53—42no—
376Dic53—42no—
377Dic53C2×AGL(1,ℤ/8)14yes—
378C2×#555—531no—
379C2×#547—531no—
380#3354—5316no—
381C2×#498—531no—
382C2×#481—531no—
383C2×#481—531no—
384C2×#482—531no—
385C2×#482—531no—
386C2×#476—531no—
387C2×#474—531no—
388C2×#469—531no—
389C2×#469—531no—
390C2×C4×D8—531no—
391C2×#436—531no—
392C2×#428—531no—
393C2×#428D5311yescharacteristic, complemented
394C2×C53—42no—
395C2×C53#335414yescomplemented
396C2×C53C2×#54711yescharacteristic
397C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
398C2×C53C2×#57711yescharacteristic
399D53—42no—
400D53—82no—
401D53—82no—
402C22×#41—1061no—
403C22×D8—531no—
404C22×M16—531no—
405C22×M16C2×D5311yescharacteristic
406#555—538no—
407#555—1064no—
408#547—538no—
409#547—1064no—
410C2×C4⋊Q8—531no—
411C2×C4⋊Q8—531no—
412C2×#124—1061no—
413C2×#124—1061no—
414C2×#123—1061no—
415C2×#123—1061no—
416C2×C22⋊Q8—1061no—
417C2×#121—531no—
418C2×#121—531no—
419C2×#121—531no—
420C2×#121—531no—
421C2×#121—1061no—
422C2×C4×D4—531no—
423C2×C4×D4—531no—
424C2×C4×D4—531no—
425C2×#117—531no—
426C2×#117—1061no—
427C2×#117C2×D5311yescharacteristic
428C22×C4⋊C4—531no—
429C22×C4⋊C4C2×D5311yescharacteristic
430#498—538no—
431#482—538no—
432#482—538no—
433#481—538no—
434#481—538no—
435#476—538no—
436#474—538no—
437#469—538no—
438#469—538no—
439C4×D8—538no—
440#436—538no—
441#428—538no—
442#428C2×D5318yescomplemented
443C2×#107—531no—
444C2×#107C2×D5311yescharacteristic
445C2×#107C2×D5311yescharacteristic
446C2×#106—531no—
447C2×#106—531no—
448C2×#106—531no—
449C2×#106—531no—
450C2×#106C2×D5311yescharacteristic
451C2×#106C2×D5311yescharacteristic
452C2×C4⋊C8—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×#102—531no—
457C2×#102—531no—
458C2×#102—531no—
459C2×C22⋊C8—531no—
460C2×C22⋊C8—531no—
461C2×C4×C8—531no—
462C53C2×#335411yescharacteristic, complemented, Sylow
463C2×#41—1068no—
464C2×#41—2128no—
465C22×Q8—1061no—
466C22×Q8—1061no—
467C22×D4—531no—
468C22×D4—531no—
469C22×D4—531no—
470C22×D4—1061no—
471C22×D4—1061no—
472C22×D4—1061no—
473C22×D4—1061no—
474C23×C4—21no—
475C23×C4—531no—
476C23×C4—1061no—
477C23×C4—1061no—
478C23×C4—1061no—
479C23×C4C22×D5311yescharacteristic
480C2×D8—534no—
481C2×D8—1064no—
482C2×M16—24no—
483C2×M16—534no—
484C2×M16—1064no—
485C2×M16C22×D5314yes—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490C4⋊Q8—534no—
491C4⋊Q8—534no—
492C4⋊Q8—1062no—
493C4⋊Q8—1062no—
494#124—1068no—
495#124—1068no—
496#123—1068no—
497#123—1068no—
498C22⋊Q8—1068no—
499#121—534no—
500#121—534no—
501#121—534no—
502#121—534no—
503#121—1068no—
504#121—1062no—
505#121—1062no—
506#121—1062no—
507#121—1062no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—534no—
511C4×D4—534no—
512C4×D4—1062no—
513C4×D4—1062no—
514#117—22no—
515#117—534no—
516#117—1068no—
517#117—1062no—
518#117C22×D5314yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—534no—
525C2×C4⋊C4—1062no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4C22×D5311yescharacteristic
530C2×C4⋊C4C22×D5311yescharacteristic
531C2×C4⋊C4C22×D5314yes—
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C22⋊C4—1061no—
544C2×C42—21no—
545C2×C42—531no—
546C2×C42—1061no—
547#107—534no—
548#107C22×D5314yes—
549#107C22×D5314yes—
550#106—534no—
551#106—534no—
552#106—534no—
553#106—534no—
554#106C22×D5314yes—
555#106C22×D5314yes—
556C4⋊C8—534no—
557#102—534no—
558#102—534no—
559#102—534no—
560#102—534no—
561#102—534no—
562#102—534no—
563C22⋊C8—534no—
564C22⋊C8—534no—
565C4×C8—534no—
566C24—531no—
567C24—1061no—
568C24—1061no—
569C24D4×D5311yescharacteristic
570#41—21232no—
571C2×Q8—1064no—
572C2×Q8—1064no—
573C2×Q8—4242no—
574C2×Q8—2124no—
575C2×D4—534no—
576C2×D4—532no—
577C2×D4—532no—
578C2×D4—1064no—
579C2×D4—1064no—
580C2×D4—1064no—
581C2×D4—1064no—
582C2×D4—1064no—
583C2×D4—1061no—
584C2×D4—1061no—
585C2×D4—1062no—
586C2×D4—1062no—
587C2×D4—1062no—
588C2×D4—1062no—
589C2×D4—4242no—
590C2×D4—4242no—
591C2×D4—2124no—
592C2×D4—2124no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—44no—
601C22×C4—531no—
602C22×C4—531no—
603C22×C4—531no—
604C22×C4—532no—
605C22×C4—532no—
606C22×C4—1064no—
607C22×C4—1064no—
608C22×C4—1064no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—2124no—
614C22×C4—2124no—
615C22×C4—2124no—
616C22×C4D4×D5312yes—
617C22×C4D4×D5311yescharacteristic
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620D8—1068no—
621M16—28no—
622M16—1068no—
623C2×C8—22no—
624C2×C8—532no—
625C2×C8—532no—
626C2×C8—1062no—
627C2×C8—1062no—
628C2×C8#1171994514yescomplemented
629C2×C8C23×D5312yes—
630C2×C8C23×D5312yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—534no—
637C4⋊C4—532no—
638C4⋊C4—532no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1061no—
643C4⋊C4—1061no—
644C4⋊C4C23×D5312yes—
645C4⋊C4C23×D5312yes—
646C4⋊C4C23×D5312yes—
647C4⋊C4C23×D5312yes—
648C22⋊C4—24no—
649C22⋊C4—534no—
650C22⋊C4—534no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4—1064no—
658C42—24no—
659C42—532no—
660C42—532no—
661C42—1064no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—532no—
666C23—1062no—
667C23—1062no—
668C23—1062no—
669C23—1062no—
670C23—1062no—
671C23—2122no—
672C23—2122no—
673C23—2122no—
674C23—2122no—
675C23—2122no—
676C23—2122no—
677C23C2×D4×D5312yes—
678C23C2×D4×D5311yescharacteristic
679Q8—4244no—
680Q8—2128no—
681D4—1068no—
682D4—1062no—
683D4—1062no—
684D4—1062no—
685D4—1062no—
686D4—4244no—
687D4—4244no—
688D4—2128no—
689D4—2128no—
690D4—2122no—
691D4—2122no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—48no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—534no—
706C2×C4—532no—
707C2×C4—532no—
708C2×C4—532no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1064no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—2128no—
717C2×C4—2128no—
718C2×C4—2128no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4C2×D4×D5312yes—
722C2×C4C2×D4×D5311yescharacteristic
723C2×C4C2×#1171994512yes—
724C2×C4#1313326512yes—
725C2×C4C24×D5311yescharacteristic
726C8—22no—
727C8—1062no—
728C8—1062no—
729C8C2×#1171994514yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—1062no—
735C22—1062no—
736C22—1062no—
737C22—4244no—
738C22—4244no—
739C22—2122no—
740C22—2122no—
741C22—2122no—
742C22—2122no—
743C22—2122no—
744C22—2122no—
745C22—2124no—
746C22#1681127412yes—
747C22AGL(1,ℤ/8)×D5312yes—
748C22#1681143212yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—534no—
756C4—1062no—
757C4—1062no—
758C4—2122no—
759C4—2122no—
760C4#1681127412yes—
761C4C22×#1171994511yescharacteristic
762C4C2×#1313326511yescharacteristic
763C2—42no—
764C2—4242no—
765C2—4242no—
766C2—2122no—
767C2#2028730614yesdirect product factor
768C2C2×#1681127411yescharacteristic
769C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
770C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#428C2
socleC23×C53C22×D4
hypercenterC2×#428D53
hypocenterC53C2×#3354
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#16811336C2semidirect
2. C2×#16811274C2semidirect
3. #20287306C2direct (N × H)
4. C2×#16811020C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810941C2semidirect
7. C2×#16810950C2semidirect
8. C2×#16810947C2semidirect
9. C2×#16810912C2semidirect
10. C2×#16810902C2semidirect
11. C2×#16810877C2semidirect
12. C2×#16810876C2semidirect
13. C2×#16810705C2semidirect
14. C2×#16810699C2semidirect
15. C2×#16810664C2semidirect
16. C2×C53×#428C2semidirect
21. #16811336C22semidirect
23. #16811274C22semidirect
42. #16811020C22semidirect
43. #16810950C22semidirect
44. #16810947C22semidirect
45. #16810943C22semidirect
46. #16810941C22semidirect
47. #16810912C22semidirect
48. #16810902C22semidirect
49. #16810877C22semidirect
50. #16810876C22semidirect
51. #16810705C22semidirect
52. #16810699C22semidirect
53. #16810664C22semidirect
72. C53×#428C22semidirect
236. C2×C8×C53#41semidirect
341. C8×C53C2×#41semidirect
393. C2×#428D53semidirect
395. C2×C53#3354semidirect
442. #428C2×D53semidirect
462. C53C2×#3354semidirect
628. C2×C8#11719945semidirect
729. C8C2×#11719945semidirect
767. C2#20287306direct (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×#168112742
#202873062
C2×#168110202
C2×#168109432
C2×#168109412
C2×#168109502
C2×#168109472
C2×#168109122
C2×#168109022
C2×#168108772
C2×#168108762
C2×#168107052
C2×#168106992
C2×#168106642
C2×C53×#4282
C2×#335453