Finite Group Databasebeta

← C2×#20287510 #28263782

Subgroups — C2×#20287510 #28263782

Order 13568.

2134 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811356C211yesmaximal, characteristic, complemented
2C2×#16811288C211yesmaximal, characteristic, complemented
3#20287510C2116yesmaximal, direct product factor
4C2×#16810985C211yesmaximal, characteristic, complemented
5C2×#16810981C211yesmaximal, characteristic, complemented
6C2×#16810968C211yesmaximal, characteristic, complemented
7C2×#16810907C211yesmaximal, characteristic, complemented
8C2×#16810912C211yesmaximal, characteristic, complemented
9C2×#16810839C211yesmaximal, characteristic, complemented
10C2×#16810837C211yesmaximal, characteristic, complemented
11C2×#16810817C211yesmaximal, characteristic
12C2×#16810752C211yesmaximal, characteristic, complemented
13C2×#16810734C211yesmaximal, characteristic, complemented
14C2×#16810733C211yesmaximal, characteristic, complemented
15C2×#16810710C211yesmaximal, characteristic, complemented
16C2×C53×#476C211yesmaximal, characteristic, complemented
17C22×Q8×D53—21no—
18C22×#11719913C2211yescharacteristic
19C22×D424C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21#16811356—24no—
22#16811356C2218yescomplemented
23#16811288—24no—
24#16811288C2218yescomplemented
25C2×#13133216C2211yescharacteristic
26C2×#13133216C2211yescharacteristic
27C2×#13133213C2211yescharacteristic
28C2×#13133205C2211yescharacteristic
29C2×#13133204C2211yescharacteristic
30C2×#13133203—21no—
31C2×#13133200—21no—
32C2×#13133199—21no—
33C2×#13133195—21no—
34C2×#13133195—21no—
35C2×#13133193—21no—
36C2×C4×Dic106C2211yescharacteristic
37C2×#13133182C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×#13133179C2211yescharacteristic
42C2×C4×C22⋊D53—21no—
43#16810985C2218yescomplemented
44#16810981C2218yescomplemented
45#16810968C2218yescomplemented
46#16810912C2218yescomplemented
47#16810907C2218yescomplemented
48#16810839C2218yescomplemented
49#16810837C2218yescomplemented
50#16810817C2218yes—
51#16810752C2218yescomplemented
52#16810734C2218yescomplemented
53#16810733C2218yescomplemented
54#16810710C2218yescomplemented
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133128C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C53×#476C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106D411yescharacteristic
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—28no—
82C2×Q8×D53—48no—
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C2×#11719913—24no—
92C2×#11719913C2314yes—
93C2×D424—24no—
94C2×D424C2314yes—
95C2×#11719922—24no—
96C2×#11719922C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99#13133216—22no—
100#13133216—22no—
101#13133216C2314yes—
102#13133216C2314yes—
103#13133213—22no—
104#13133213C2314yes—
105#13133205—22no—
106#13133205C2314yes—
107#13133204—22no—
108#13133204C2314yes—
109#13133203—28no—
110#13133200—28no—
111#13133199—28no—
112#13133195—28no—
113#13133195—28no—
114#13133193—28no—
115C4×Dic106D414yes—
116C4×Dic106C2314yes—
117#13133182—22no—
118#13133182C2314yes—
119C4×D212—22no—
120C4×D212C2314yes—
121#13133179—22no—
122#13133179—22no—
123#13133179—22no—
124#13133179C2314yes—
125#13133179C2314yes—
126#13133179C2314yes—
127C4×C22⋊D53—28no—
128C2×C4⋊Dic53D411yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919D411yescharacteristic
134C2×#11719919D411yescharacteristic
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145C2×C4×Dic53C2311yescharacteristic
146#13133148C2314yes—
147#13133146C2314yes—
148#13133146C2314yes—
149#13133142C2314yes—
150#13133140C2314yes—
151#13133140C2314yes—
152#13133139C2314yes—
153#13133138C2314yes—
154#13133137C2314yes—
155#13133137C2314yes—
156#13133137C2314yes—
157#13133128C2314yes—
158#13133127C2314yes—
159C8×Dic53C2314yes—
160C22×Q8×C53—21no—
161C22×D4×C53C2311yescharacteristic
162C23×C4×C53—21no—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C4⋊Q8×C53—22no—
166C4⋊Q8×C53C2314yes—
167C4×D4×C53—22no—
168C4×D4×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#106×C53C2314yes—
176#106×C53C2314yes—
177C4⋊C8×C53C2314yes—
178#102×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C23×D53—21no—
182C23×D53—21no—
183C2×Q8×C53—24no—
184C2×Q8×C53—44no—
185C2×D4×C53—21no—
186C2×D4×C53—22no—
187C2×D4×C53—22no—
188C2×D4×C53C2412yes—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—24no—
193C22×C4×C53—82no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2411yescharacteristic
197C2×C22⋊D53—24no—
198C2×C22⋊D53—24no—
199C2×C22⋊D53—44no—
200C2×C22⋊D53—82no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207Q8×D53—432no—
208C2×D212—21no—
209C2×D212—22no—
210C2×D212—22no—
211C2×D212—22no—
212C2×D212—21no—
213C2×D212#4114yes—
214C2×D212C2412yes—
215C2×D212C2412yes—
216C2×C4×D53—24no—
217C2×C4×D53—24no—
218C2×C4×D53—24no—
219C2×C4×D53—24no—
220C2×C4×D53—44no—
221C2×C4×D53—44no—
222C2×C4×D53—44no—
223C2×C4×D53—82no—
224C2×Dic106—24no—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—21no—
228C2×Dic106—24no—
229C2×Dic106—24no—
230C2×Dic106—44no—
231C2×Dic106—44no—
232C2×Dic106C2×D414yes—
233C2×Dic106C2412yes—
234C2×C8×C53—22no—
235C2×C8×C53—22no—
236C2×C8×C53C2412yes—
237C2×C8×C53C2412yes—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C4⋊C4×C53C2412yes—
245C22⋊C4×C53—24no—
246C42×C53C2×D412yes—
247C42×C53C2412yes—
248C22⋊Dic53—24no—
249C22⋊Dic53—24no—
250#11719922—28no—
251#11719921—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257C4⋊Dic53—21no—
258C4⋊Dic53C2×D414yes—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919C2×D414yes—
264#11719919C2×D414yes—
265C4×Dic53—24no—
266C4×Dic53C2×D412yes—
267C4×Dic53C2×D412yes—
268C4×Dic53C2412yes—
269C4×Dic53C2412yes—
270C2×#88322—22no—
271C2×#88322—22no—
272C2×#88322C2412yes—
273C2×#88322C2412yes—
274D424—28no—
275#11719913—28no—
276C23×C53—22no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53C22×D411yescharacteristic
281C22×D53—24no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—42no—
285C22×D53—42no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289Q8×C53—48no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—42no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—84no—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C532−1+412yes—
307C2×C4×C53C2511yescharacteristic
308C22⋊D53—48no—
309C22⋊D53—84no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53AGL(1,ℤ/8)14yes—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322D212—24no—
323D212—22no—
324D212—22no—
325D212—22no—
326D212—42no—
327D212C2×#4114yes—
328C4×D53—48no—
329C4×D53—48no—
330C4×D53—48no—
331C4×D53—84no—
332Dic106—28no—
333Dic106—22no—
334Dic106—22no—
335Dic106—48no—
336Dic106—42no—
337Dic106—48no—
338C8×C53—22no—
339C8×C53—22no—
340#88322—22no—
341#88322—22no—
342C2×#3373—531nomaximal, Sylow
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—84no—
347C22×C53#54812yes—
348C22×C53C2×AGL(1,ℤ/8)12yes—
349C22×C53#57712yes—
350C22×C53C23×D411yescharacteristic
351C2×D53—24no—
352C2×D53—48no—
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—84no—
359C4×C53—22no—
360C4×C53—22no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53—42no—
364C4×C53#54812yes—
365C4×C53C22×#4111yescharacteristic
366C4×C53C2×2−1+411yescharacteristic
367Dic53—22no—
368Dic53—22no—
369Dic53—22no—
370Dic53—42no—
371Dic53—42no—
372Dic53C2×AGL(1,ℤ/8)14yes—
373C2×#559—531no—
374C2×D4×Q8—531no—
375#3373—5316no—
376C2×#489—531no—
377C2×#489—531no—
378C2×#486—531no—
379C2×#475—531no—
380C2×#476—531no—
381C2×#476D5311yescharacteristic, complemented
382C2×#463—531no—
383C2×#463—531no—
384C2×#459—531no—
385C2×#446—531no—
386C2×#442—531no—
387C2×#442—531no—
388C2×C4×SD16—531no—
389C2×C53—82no—
390C2×C53#337314yescomplemented
391C2×C53C2×#54811yescharacteristic
392C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
393C2×C53C2×#57711yescharacteristic
394D53—44no—
395D53—82no—
396C23×Q8—1061no—
397C22×SD16—531no—
398C22×D8—531no—
399C22×D8—531no—
400#559—538no—
401#559—1064no—
402D4×Q8—538no—
403D4×Q8—1064no—
404C2×C4⋊Q8—531no—
405C2×C4⋊Q8—531no—
406C2×C4⋊Q8C2×D5311yescharacteristic
407C2×#127—531no—
408C2×#124—531no—
409C2×#124—531no—
410C2×#124—1061no—
411C2×#123—1061no—
412C2×#123—1061no—
413C2×C22⋊Q8—1061no—
414C2×C22⋊Q8—1061no—
415C2×C22⋊Q8—1061no—
416C2×C4×Q8—531no—
417C2×C4×Q8—531no—
418C2×C4×D4—531no—
419C2×C4×D4—531no—
420C2×C4×D4—531no—
421C2×C4×D4—531no—
422C2×C4×D4—1061no—
423C2×C4×D4C2×D5311yescharacteristic
424#489—538no—
425#489—538no—
426#486—538no—
427#476—538no—
428#476C2×D5318yescomplemented
429#475—538no—
430#463—538no—
431#463—538no—
432#459—538no—
433#446—538no—
434#442—538no—
435#442—538no—
436C4×SD16—538no—
437C2×#106—531no—
438C2×#106C2×D5311yescharacteristic
439C2×#106C2×D5311yescharacteristic
440C2×C4⋊C8—531no—
441C2×C4⋊C8—531no—
442C2×C4⋊C8C2×D5311yescharacteristic
443C2×#103—531no—
444C2×#103—531no—
445C2×#103—531no—
446C2×#102—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102C2×D5311yescharacteristic
452C2×#102C2×D5311yescharacteristic
453C2×#97—531no—
454C2×#97—531no—
455C2×C4×C8—531no—
456C53C2×#337311yescharacteristic, complemented, Sylow
457C22×Q8—21no—
458C22×Q8—531no—
459C22×Q8—531no—
460C22×Q8—1061no—
461C22×Q8—1061no—
462C22×Q8—1068no—
463C22×Q8—2128no—
464C22×D4—531no—
465C22×D4—531no—
466C22×D4—1061no—
467C22×D4—1061no—
468C22×D4C22×D5311yescharacteristic
469C23×C4—21no—
470C23×C4—1061no—
471C23×C4—1061no—
472C23×C4—1061no—
473C23×C4—1061no—
474C2×SD16—534no—
475C2×SD16—1064no—
476C2×D8—534no—
477C2×D8—534no—
478C2×D8—1064no—
479C2×D8—1064no—
480C22×C8—531no—
481C22×C8—531no—
482C22×C8C22×D5311yescharacteristic
483C22×C8C22×D5311yescharacteristic
484C4⋊Q8—22no—
485C4⋊Q8—534no—
486C4⋊Q8—534no—
487C4⋊Q8—1062no—
488C4⋊Q8—1062no—
489C4⋊Q8C22×D5314yes—
490#127—534no—
491#127—1062no—
492#124—534no—
493#124—534no—
494#124—1062no—
495#124—1068no—
496#124—1062no—
497#123—1068no—
498#123—1068no—
499C22⋊Q8—1068no—
500C22⋊Q8—1068no—
501C22⋊Q8—1068no—
502C4×Q8—534no—
503C4×Q8—534no—
504C4×Q8—534no—
505C4×Q8—1062no—
506C4×D4—22no—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—534no—
511C4×D4—1062no—
512C4×D4—1062no—
513C4×D4—1062no—
514C4×D4—1068no—
515C4×D4—1062no—
516C4×D4C22×D5314yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—531no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C42—531no—
538C2×C42—531no—
539C2×C42—1061no—
540C2×C42C22×D5311yescharacteristic
541#106—534no—
542#106C22×D5314yes—
543#106C22×D5314yes—
544C4⋊C8—534no—
545C4⋊C8—534no—
546C4⋊C8C22×D5314yes—
547#103—534no—
548#103—534no—
549#103—534no—
550#102—534no—
551#102—534no—
552#102—534no—
553#102—534no—
554#102—534no—
555#102C22×D5314yes—
556#102C22×D5314yes—
557#97—534no—
558#97—534no—
559C4×C8—534no—
560C24—21no—
561C24—1061no—
562C24—1061no—
563C2×Q8—24no—
564C2×Q8—44no—
565C2×Q8—534no—
566C2×Q8—532no—
567C2×Q8—1064no—
568C2×Q8—1064no—
569C2×Q8—1064no—
570C2×Q8—1061no—
571C2×Q8—1062no—
572C2×Q8—1062no—
573C2×Q8—2124no—
574C2×Q8—2124no—
575C2×Q8—21232no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—534no—
580C2×D4—532no—
581C2×D4—532no—
582C2×D4—1064no—
583C2×D4—1064no—
584C2×D4—1061no—
585C2×D4—1061no—
586C2×D4—1062no—
587C2×D4—1062no—
588C2×D4—1062no—
589C2×D4—4242no—
590C2×D4—2124no—
591C2×D4C23×D5312yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—82no—
597C22×C4—531no—
598C22×C4—531no—
599C22×C4—531no—
600C22×C4—531no—
601C22×C4—1064no—
602C22×C4—1064no—
603C22×C4—1064no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1064no—
607C22×C4—4242no—
608C22×C4—2124no—
609C22×C4—2124no—
610C22×C4—2124no—
611C22×C4D4×D5311yescharacteristic
612C22×C4D4×D5311yescharacteristic
613C22×C4C23×D5311yescharacteristic
614SD16—1068no—
615D8—1068no—
616D8—1068no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—532no—
620C2×C8—532no—
621C2×C8—1062no—
622C2×C8—1062no—
623C2×C8C23×D5312yes—
624C2×C8C23×D5312yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—534no—
630C4⋊C4—534no—
631C4⋊C4—534no—
632C4⋊C4—532no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4—1061no—
637C4⋊C4C23×D5312yes—
638C4⋊C4C23×D5312yes—
639C4⋊C4C23×D5312yes—
640C22⋊C4—24no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C42—532no—
650C42—532no—
651C42—532no—
652C42—532no—
653C42—1064no—
654C42D4×D5312yes—
655C42C23×D5312yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—1064no—
661C23—1062no—
662C23—1062no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669Q8—48no—
670Q8—1068no—
671Q8—1062no—
672Q8—1062no—
673Q8—2128no—
674Q8—2128no—
675Q8—2122no—
676D4—22no—
677D4—22no—
678D4—42no—
679D4—534no—
680D4—1064no—
681D4—1062no—
682D4—1062no—
683D4—1062no—
684D4—4244no—
685D4—2128no—
686D4—2122no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—84no—
696C2×C4—534no—
697C2×C4—532no—
698C2×C4—532no—
699C2×C4—532no—
700C2×C4—532no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—4244no—
707C2×C4—2128no—
708C2×C4—2128no—
709C2×C4—2128no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4C2×D4×D5312yes—
713C2×C4C2×D4×D5312yes—
714C2×C4C2×D4×D5311yescharacteristic
715C2×C4#41×D5312yes—
716C2×C4#1313326512yes—
717C2×C4C24×D5311yescharacteristic
718C8—22no—
719C8—22no—
720C8—1062no—
721C8—1062no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—1064no—
727C22—4244no—
728C22—2122no—
729C22—2122no—
730C22—2122no—
731C22—2128no—
732C22—2122no—
733C22—2122no—
734C22#1681128312yes—
735C22AGL(1,ℤ/8)×D5312yes—
736C22#1681142912yes—
737C22C22×D4×D5311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—534no—
744C4—1062no—
745C4—1062no—
746C4—1062no—
747C4—2122no—
748C4—2122no—
749C4#1681128312yes—
750C4C2×#41×D5311yescharacteristic
751C4C2×#1313326511yescharacteristic
752C2—82no—
753C2—4242no—
754C2—2124no—
755C2#2028751014yesdirect product factor
756C2C2×#1681128311yescharacteristic
757C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
758C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#476C2
socleC23×C53C22×D4
prime radicalC2×#16810817C2
hypercenterC2×#476D53
hypocenterC53C2×#3373
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16811356C2semidirect
2. C2×#16811288C2semidirect
3. #20287510C2direct (N × H)
4. C2×#16810985C2semidirect
5. C2×#16810981C2semidirect
6. C2×#16810968C2semidirect
7. C2×#16810907C2semidirect
8. C2×#16810912C2semidirect
9. C2×#16810839C2semidirect
10. C2×#16810837C2semidirect
12. C2×#16810752C2semidirect
13. C2×#16810734C2semidirect
14. C2×#16810733C2semidirect
15. C2×#16810710C2semidirect
16. C2×C53×#476C2semidirect
22. #16811356C22semidirect
24. #16811288C22semidirect
43. #16810985C22semidirect
44. #16810981C22semidirect
45. #16810968C22semidirect
46. #16810912C22semidirect
47. #16810907C22semidirect
48. #16810839C22semidirect
49. #16810837C22semidirect
51. #16810752C22semidirect
52. #16810734C22semidirect
53. #16810733C22semidirect
54. #16810710C22semidirect
71. C53×#476C22semidirect
381. C2×#476D53semidirect
390. C2×C53#3373semidirect
428. #476C2×D53semidirect
456. C53C2×#3373semidirect
755. C2#20287510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113562
C2×#168112882
#202875102
C2×#168109852
C2×#168109812
C2×#168109682
C2×#168109072
C2×#168109122
C2×#168108392
C2×#168108372
C2×#168108172
C2×#168107522
C2×#168107342
C2×#168107332
C2×#168107102
C2×C53×#4762
C2×#337353