Finite Group Databasebeta

← C2×#20287184 #28262654

Subgroups — C2×#20287184 #28262654

Order 13568.

2158 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×#16811326C211yesmaximal, characteristic, complemented
2C2×#16811276C211yesmaximal, characteristic, complemented
3#20287184C2116yesmaximal, direct product factor
4C2×#16810943C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810950C211yesmaximal, characteristic, complemented
7C2×#16810938C211yesmaximal, characteristic, complemented
8C2×#16810920C211yesmaximal, characteristic, complemented
9C2×#16810910C211yesmaximal, characteristic, complemented
10C2×#16810877C211yesmaximal, characteristic, complemented
11C2×#16810860C211yesmaximal, characteristic, complemented
12C2×#16810736C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810664C211yesmaximal, characteristic, complemented
15C2×#106×D53C211yesmaximal, characteristic, complemented
16C2×C53×#501C211yesmaximal, characteristic, complemented
17C22×#11719949—21no—
18C22×D424C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811326—24no—
22#16811326C2218yescomplemented
23#16811276—24no—
24#16811276C2218yescomplemented
25C2×#13133212—21no—
26C2×#13133202—21no—
27C2×#13133202—21no—
28C2×#13133202—21no—
29C2×#13133193—21no—
30C2×#13133192—21no—
31C2×#13133192C2211yescharacteristic
32C2×#13133192C2211yescharacteristic
33C2×#13133192C2211yescharacteristic
34C2×#13133192C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×C4×D212C2211yescharacteristic
38C2×#13133179—21no—
39C2×#13133175C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810950C2218yescomplemented
44#16810943C2218yescomplemented
45#16810943C2218yescomplemented
46#16810938C2218yescomplemented
47#16810920C2218yescomplemented
48#16810910C2218yescomplemented
49#16810877C2218yescomplemented
50#16810860C2218yescomplemented
51#16810736C2218yescomplemented
52#16810696C2218yescomplemented
53#16810664C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59#106×D53C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#125×C53C2211yescharacteristic
71C53×#501C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#106×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719949—28no—
78C2×#11719949—48no—
79C22×D212—21no—
80C22×D212—21no—
81C22×D212—21no—
82C22×D212—21no—
83C22×D212D411yescharacteristic
84C22×D212C2311yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53C2311yescharacteristic
92C22×C4×D53C2311yescharacteristic
93C2×D424—24no—
94C2×D424C2314yes—
95C2×#11719912—24no—
96C2×#11719912C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C2×C8×D53—24no—
100C2×C8×D53C2314yes—
101#13133212—28no—
102#13133202—28no—
103#13133202—28no—
104#13133202—28no—
105#13133193—28no—
106#13133192—28no—
107#13133192—22no—
108#13133192—22no—
109#13133192—22no—
110#13133192—22no—
111#13133192C2314yes—
112#13133192C2314yes—
113#13133192C2314yes—
114#13133192C2314yes—
115C4×D212—22no—
116C4×D212—22no—
117C4×D212D414yes—
118C4×D212C2314yes—
119C4×D212C2314yes—
120C4×D212C2314yes—
121#13133179—28no—
122#13133175—22no—
123#13133175C2314yes—
124C2×C4⋊Dic53D411yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C4⋊C4×D53—22no—
131C4⋊C4×D53—22no—
132C4⋊C4×D53—22no—
133C4⋊C4×D53C2314yes—
134C4⋊C4×D53C2314yes—
135C4⋊C4×D53C2314yes—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921D411yescharacteristic
144C2×#11719921D411yescharacteristic
145C2×C4×Dic53—21no—
146#13133150C2314yes—
147#13133149C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150#13133148C2314yes—
151C4⋊#88322C2314yes—
152#13133139C2314yes—
153#13133139C2314yes—
154#13133137C2314yes—
155#13133137C2314yes—
156#13133137C2314yes—
157#13133137C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160C22×Q8×C53—21no—
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C4⋊Q8×C53—22no—
164C4⋊Q8×C53C2314yes—
165#125×C53—22no—
166#125×C53C2314yes—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C42×C53C2311yescharacteristic
175#107×C53C2314yes—
176#107×C53C2314yes—
177#106×C53C2314yes—
178#106×C53C2314yes—
179#97×C53C2314yes—
180C23×D53—21no—
181C23×D53—21no—
182C23×D53C2×D411yescharacteristic
183C23×D53C2×D411yescharacteristic
184C2×Q8×C53—24no—
185C2×Q8×C53—44no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2411yescharacteristic
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53C2×D411yescharacteristic
196C22×Dic53C2×D411yescharacteristic
197#11719949—432no—
198C2×D212—24no—
199C2×D212—22no—
200C2×D212—22no—
201C2×D212—22no—
202C2×D212—22no—
203C2×D212—24no—
204C2×D212—24no—
205C2×D212—24no—
206C2×D212—21no—
207C2×D212—21no—
208C2×D212—24no—
209C2×D212—44no—
210C2×D212—44no—
211C2×D212—44no—
212C2×D212—82no—
213C2×D212C2×D414yes—
214C2×D212C2412yes—
215C2×D212C2412yes—
216C2×C4×D53—22no—
217C2×C4×D53—22no—
218C2×C4×D53—22no—
219C2×C4×D53—22no—
220C2×C4×D53—24no—
221C2×C4×D53—24no—
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×D53—82no—
229C2×C4×D53—82no—
230C2×C4×D53C2×D412yes—
231C2×C4×D53C2×D412yes—
232C2×C4×D53C2412yes—
233C2×C4×D53C2412yes—
234C2×C8×C53—22no—
235C2×C8×C53#4114yescomplemented
236C2×C8×C53C2412yes—
237C2×C8×C53C2412yes—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—24no—
240C4⋊C4×C53—24no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—21no—
245C4⋊C4×C53C2412yes—
246C4⋊C4×C53C2412yes—
247C4⋊C4×C53C2412yes—
248C4⋊C4×C53C2412yes—
249C42×C53C2×D412yes—
250C42×C53C2412yes—
251#11719921—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921C2×D414yes—
259#11719921C2×D414yes—
260C4⋊Dic53—21no—
261C4⋊Dic53—21no—
262C4⋊Dic53C2×D414yes—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268C4×Dic53—24no—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273D424—28no—
274#11719912—28no—
275C8×D53—28no—
276C23×C53C22×D411yescharacteristic
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—42no—
285C22×D53—42no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53AGL(1,ℤ/8)14yes—
291C22×D53C22×D412yes—
292C22×D53C22×D412yes—
293Q8×C53—48no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D411yescharacteristic
307C2×C4×C53C2×#4112yes—
308C2×C4×C532−1+412yes—
309C2×C4×C53C2511yescharacteristic
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53C22×D412yes—
317C2×Dic53C22×D412yes—
318D212—28no—
319D212—22no—
320D212—22no—
321D212—22no—
322D212—22no—
323D212—48no—
324D212—48no—
325D212—48no—
326D212—42no—
327D212—42no—
328D212—84no—
329C4×D53—24no—
330C4×D53—24no—
331C4×D53—22no—
332C4×D53—22no—
333C4×D53—22no—
334C4×D53—22no—
335C4×D53—48no—
336C4×D53—48no—
337C4×D53—48no—
338C4×D53—84no—
339C4×D53—84no—
340C8×C53—22no—
341C8×C53C2×#4114yescomplemented
342#88322—22no—
343#88322—22no—
344C2×#3345—531nomaximal, Sylow
345C22×C53#54712yes—
346C22×C53C2×AGL(1,ℤ/8)12yes—
347C22×C53#57712yes—
348C22×C53C23×D411yescharacteristic
349C2×D53—28no—
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—22no—
353C2×D53—22no—
354C2×D53—22no—
355C2×D53—44no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—84no—
363C2×D53—84no—
364C2×D53C2×AGL(1,ℤ/8)14yes—
365C4×C53—22no—
366C4×C53—22no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53—42no—
371C4×C53#54712yes—
372C4×C53C22×#4111yescharacteristic
373C4×C53C2×2−1+411yescharacteristic
374Dic53—22no—
375Dic53—22no—
376Dic53—42no—
377Dic53—42no—
378C2×#553—531no—
379C2×#547—531no—
380#3345—5316no—
381C2×#501D5311yescharacteristic, complemented
382C2×#481—531no—
383C2×#481—531no—
384C2×#482—531no—
385C2×#480—531no—
386C2×#478—531no—
387C2×#476—531no—
388C2×#469—531no—
389C2×#466—531no—
390C2×#442—531no—
391C2×#435—531no—
392C2×#428—531no—
393C22×#106—531no—
394C2×C53#334514yescomplemented
395C2×C53C2×#54711yescharacteristic
396C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
397C2×C53C2×#57711yescharacteristic
398D53—24no—
399D53—42no—
400D53—82no—
401D53—82no—
402C22×#41—1061no—
403C22×D8—531no—
404C22×M16—531no—
405C23×C8—531no—
406#553—538no—
407#553—1064no—
408#547—538no—
409#547—1064no—
410C2×C4⋊Q8C2×D5311yescharacteristic
411C2×#126—1061no—
412C2×#125C2×D5311yescharacteristic
413C2×#123—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×C4×D4—1061no—
426C2×#117—531no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4—531no—
430#501C2×D5318yescomplemented
431#482—538no—
432#481—538no—
433#481—538no—
434#480—538no—
435#478—538no—
436#476—538no—
437#469—538no—
438#466—538no—
439#442—538no—
440#435—538no—
441#428—538no—
442C2×#107—531no—
443C2×#107C2×D5311yescharacteristic
444C2×#107C2×D5311yescharacteristic
445C2×#106—531no—
446C2×#106—531no—
447C2×#106—531no—
448C2×#106—531no—
449C2×#106—538no—
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×#97C2×D5311yescharacteristic
462C53C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—1068no—
464C2×#41—2128no—
465C22×Q8—21no—
466C22×D4—531no—
467C22×D4—531no—
468C22×D4—531no—
469C22×D4—1061no—
470C22×D4—1061no—
471C22×D4—1061no—
472C22×D4—1061no—
473C23×C4—531no—
474C23×C4—531no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4—1061no—
478C23×C4—1061no—
479C23×C4—1061no—
480C2×D8—534no—
481C2×D8—1064no—
482C2×M16—534no—
483C2×M16—1064no—
484C22×C8—531no—
485C22×C8—531no—
486C22×C8—534no—
487C22×C8—1064no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490C4⋊Q8—22no—
491C4⋊Q8C22×D5314yes—
492#126—1068no—
493#125—22no—
494#125C22×D5314yes—
495#123—1068no—
496#123—1068no—
497#123—1068no—
498C22⋊Q8—1068no—
499#121—534no—
500#121—534no—
501#121—534no—
502#121—534no—
503#121—1062no—
504#121—1062no—
505#121—1062no—
506#121—1062no—
507#121—1068no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—534no—
511C4×D4—534no—
512C4×D4—1068no—
513C4×D4—1062no—
514C4×D4—1062no—
515#117—534no—
516#117—1062no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—534no—
524C2×C4⋊C4—534no—
525C2×C4⋊C4—534no—
526C2×C4⋊C4—1062no—
527C2×C4⋊C4—1062no—
528C2×C4⋊C4—1062no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C4⋊C4C22×D5311yescharacteristic
535C2×C4⋊C4C22×D5311yescharacteristic
536C2×C22⋊C4—531no—
537C2×C22⋊C4—531no—
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×C22⋊C4—1061no—
545C2×C42—1061no—
546C2×C42C22×D5311yescharacteristic
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—
565#97C22×D5314yes—
566C24—531no—
567C24—531no—
568C24—1061no—
569C24—1061no—
570#41—21232no—
571C2×Q8—24no—
572C2×Q8—44no—
573C2×D4—534no—
574C2×D4—532no—
575C2×D4—532no—
576C2×D4—1064no—
577C2×D4—1064no—
578C2×D4—1064no—
579C2×D4—1064no—
580C2×D4—1064no—
581C2×D4—1061no—
582C2×D4—1061no—
583C2×D4—1062no—
584C2×D4—1062no—
585C2×D4—1062no—
586C2×D4—1062no—
587C2×D4—4242no—
588C2×D4—2124no—
589C2×D4—2124no—
590C2×D4—2124no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—531no—
596C22×C4—531no—
597C22×C4—532no—
598C22×C4—532no—
599C22×C4—532no—
600C22×C4—532no—
601C22×C4—1064no—
602C22×C4—1064no—
603C22×C4—1064no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1064no—
611C22×C4—1064no—
612C22×C4—4242no—
613C22×C4—4242no—
614C22×C4—2124no—
615C22×C4—2124no—
616C22×C4—2124no—
617C22×C4D4×D5311yescharacteristic
618C22×C4D4×D5311yescharacteristic
619C22×C4C23×D5311yescharacteristic
620D8—1068no—
621M16—1068no—
622C2×C8—22no—
623C2×C8—532no—
624C2×C8—532no—
625C2×C8—1062no—
626C2×C8—1062no—
627C2×C8—1068no—
628C2×C8#1171994914yescomplemented
629C2×C8C23×D5312yes—
630C2×C8C23×D5312yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—534no—
639C4⋊C4—532no—
640C4⋊C4—532no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4—1061no—
645C4⋊C4—1061no—
646C4⋊C4C23×D5312yes—
647C4⋊C4C23×D5312yes—
648C4⋊C4C23×D5312yes—
649C4⋊C4C23×D5312yes—
650C22⋊C4—534no—
651C22⋊C4—534no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C42—1064no—
660C42D4×D5312yes—
661C42C23×D5312yes—
662C23—534no—
663C23—532no—
664C23—532no—
665C23—1062no—
666C23—1062no—
667C23—1062no—
668C23—1062no—
669C23—1062no—
670C23—1062no—
671C23—1062no—
672C23—2122no—
673C23—2122no—
674C23—2122no—
675C23—2122no—
676C23—2122no—
677C23—2122no—
678C23C2×D4×D5311yescharacteristic
679Q8—48no—
680D4—1068no—
681D4—1062no—
682D4—1062no—
683D4—1062no—
684D4—1062no—
685D4—4244no—
686D4—2128no—
687D4—2128no—
688D4—2128no—
689D4—2122no—
690D4—2122no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—532no—
702C2×C4—532no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1064no—
706C2×C4—1064no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—4244no—
714C2×C4—4244no—
715C2×C4—2128no—
716C2×C4—2128no—
717C2×C4—2128no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4C2×D4×D5312yes—
721C2×C4C2×D4×D5312yes—
722C2×C4C2×D4×D5311yescharacteristic
723C2×C4C2×#1171994912yes—
724C2×C4#1313326512yes—
725C2×C4C24×D5311yescharacteristic
726C8—22no—
727C8—1062no—
728C8—1062no—
729C8C2×#1171994914yescomplemented
730C22—534no—
731C22—1062no—
732C22—1062no—
733C22—1068no—
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#1681127612yes—
747C22AGL(1,ℤ/8)×D5312yes—
748C22#1681143212yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—1062no—
757C4—1062no—
758C4—2122no—
759C4—2122no—
760C4#1681127612yes—
761C4C22×#1171994911yescharacteristic
762C4C2×#1313326511yescharacteristic
763C2—1064no—
764C2—4242no—
765C2—4242no—
766C2—2122no—
767C2#2028718414yesdirect product factor
768C2C2×#1681127611yescharacteristic
769C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
770C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#501C2
socleC23×C53C22×D4
hypercenterC2×#501D53
hypocenterC53C2×#3345
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16811326C2semidirect
2. C2×#16811276C2semidirect
3. #20287184C2direct (N × H)
4. C2×#16810943C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810950C2semidirect
7. C2×#16810938C2semidirect
8. C2×#16810920C2semidirect
9. C2×#16810910C2semidirect
10. C2×#16810877C2semidirect
11. C2×#16810860C2semidirect
12. C2×#16810736C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810664C2semidirect
15. C2×#106×D53C2semidirect
16. C2×C53×#501C2semidirect
22. #16811326C22semidirect
24. #16811276C22semidirect
43. #16810950C22semidirect
44. #16810943C22semidirect
45. #16810943C22semidirect
46. #16810938C22semidirect
47. #16810920C22semidirect
48. #16810910C22semidirect
49. #16810877C22semidirect
50. #16810860C22semidirect
51. #16810736C22semidirect
52. #16810696C22semidirect
53. #16810664C22semidirect
59. #106×D53C22semidirect
71. C53×#501C22semidirect
235. C2×C8×C53#41semidirect
341. C8×C53C2×#41semidirect
381. C2×#501D53semidirect
394. C2×C53#3345semidirect
430. #501C2×D53semidirect
462. C53C2×#3345semidirect
628. C2×C8#11719949semidirect
729. C8C2×#11719949semidirect
767. C2#20287184direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113262
C2×#168112762
#202871842
C2×#168109432
C2×#168109502
C2×#168109382
C2×#168109202
C2×#168109102
C2×#168108772
C2×#168108602
C2×#168107362
C2×#168106962
C2×#168106642
C2×#106×D532
C2×C53×#5012
C2×#334553