Finite Group Databasebeta

← C2×#20284744 #28252119

Subgroups — C2×#20284744 #28252119

Order 13568.

2418 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811170C211yesmaximal, characteristic
2C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
3#20284744C2116yesmaximal, direct product factor
4C2×#16810943C211yesmaximal, characteristic, complemented
5C2×#16810940C211yesmaximal, characteristic, complemented
6C2×#16810907C211yesmaximal, characteristic, complemented
7C2×#16810906C211yesmaximal, characteristic, complemented
8C2×#16810822C211yesmaximal, characteristic, complemented
9C2×#16810821C211yesmaximal, characteristic, complemented
10C2×#16810763C211yesmaximal, characteristic, complemented
11C2×#16810760C211yesmaximal, characteristic, complemented
12C2×C4×#11719913C211yesmaximal, characteristic, complemented
13C2×C4×#11719924C211yesmaximal, characteristic, complemented
14C2×C4×#11719923C211yesmaximal, characteristic, complemented
15C2×#16810674C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C53C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×Q8×D53C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22#16811170—24no—
23#16811170C2218yes—
24C2×#13133216C2211yescharacteristic
25C2×#13133213C2211yescharacteristic
26C2×#13133203—21no—
27C2×#13133192C2211yescharacteristic
28C2×#13133190—21no—
29C2×#13133188C2211yescharacteristic
30C2×Q8×Dic53C2211yescharacteristic
31C2×C4×Dic106—21no—
32C2×C4×Dic106C2211yescharacteristic
33C2×#13133182—21no—
34C2×#13133182C2211yescharacteristic
35C4×Q8×D53—24no—
36C4×Q8×D53C2218yescomplemented
37C2×C4×D212C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×C4⋊C4×D53—21no—
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C42×D53—21no—
42C2×C42×D53C2211yescharacteristic
43#16810943C2218yescomplemented
44#16810940C2218yescomplemented
45#16810907C2218yescomplemented
46#16810906C2218yescomplemented
47#16810822C2218yescomplemented
48#16810821C2218yescomplemented
49#16810763C2218yescomplemented
50#16810760C2218yescomplemented
51C4×#11719913C2218yescomplemented
52C4×#11719924C2218yescomplemented
53C4×#11719923C2218yescomplemented
54#16810674C2218yescomplemented
55C2×#13133149C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C4×SD16×C53C2218yescomplemented
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106C2311yescharacteristic
82C2×Q8×D53—24no—
83C2×Q8×D53—22no—
84C2×Q8×D53—24no—
85C2×Q8×D53C2314yes—
86C22×D212—21no—
87C22×D212C2311yescharacteristic
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53D411yescharacteristic
95C22×C4×D53D411yescharacteristic
96C22×C4×D53C2311yescharacteristic
97C2×#11719913—24no—
98C2×#11719913C2314yes—
99C2×#11719923—24no—
100C2×#11719923C2314yes—
101C2×#11719924—24no—
102C2×#11719924C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133216—22no—
106#13133216C2314yes—
107#13133213—22no—
108#13133213C2314yes—
109#13133203—28no—
110#13133192—22no—
111#13133192C2314yes—
112#13133190—28no—
113#13133188—22no—
114#13133188C2314yes—
115Q8×Dic53—22no—
116Q8×Dic53C2314yes—
117C4×Dic106—22no—
118C4×Dic106—28no—
119C4×Dic106C2314yes—
120#13133182—22no—
121#13133182—28no—
122#13133182C2314yes—
123C4×D212—22no—
124C4×D212C2314yes—
125C4×C22⋊D53—28no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C4⋊C4×D53—28no—
134C4⋊C4×D53—22no—
135C4⋊C4×D53C2314yes—
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53D411yescharacteristic
144C2×C4×Dic53C2311yescharacteristic
145C42×D53—28no—
146C42×D53D414yes—
147C42×D53C2314yes—
148#13133149C2314yes—
149#13133148C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133140C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133129C2314yes—
160#13133129C2314yes—
161C4×#88322C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C2×SD16×C53—24no—
166C2×SD16×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4×Q8×C53—22no—
170C4×Q8×C53C2314yes—
171C4×D4×C53—22no—
172C4×D4×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179#106×C53C2314yes—
180#103×C53C2314yes—
181#102×C53C2314yes—
182C4×C8×C53C2314yes—
183C24×C53—21no—
184C23×D53—21no—
185C23×D53C2×D411yescharacteristic
186C2×Q8×C53—21no—
187C2×Q8×C53—22no—
188C2×Q8×C53#4114yescomplemented
189C2×Q8×C53C2412yes—
190C2×D4×C53—21no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53C2412yes—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—24no—
198C22×C4×C53—44no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—24no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—44no—
206C2×C22⋊D53—44no—
207C2×C22⋊D53—44no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214Q8×D53—216no—
215Q8×D53—28no—
216Q8×D53—28no—
217#11719945—432no—
218C2×D212—22no—
219C2×D212—22no—
220C2×D212—24no—
221C2×D212—21no—
222C2×D212—44no—
223C2×D212C2412yes—
224C2×C4×D53—28no—
225C2×C4×D53—24no—
226C2×C4×D53—22no—
227C2×C4×D53—22no—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—42no—
231C2×C4×D53—44no—
232C2×C4×D53—44no—
233C2×C4×D53SD1618yescomplemented
234C2×C4×D53C2×D412yes—
235C2×C4×D53C2×D414yes—
236C2×C4×D53C2×D414yes—
237C2×C4×D53C2412yes—
238C2×Dic106—28no—
239C2×Dic106—21no—
240C2×Dic106—22no—
241C2×Dic106—24no—
242C2×Dic106—24no—
243C2×Dic106—44no—
244C2×Dic106#4114yescomplemented
245C2×Dic106C2412yes—
246SD16×C53—28no—
247C2×C8×C53—22no—
248C2×C8×C53—22no—
249C2×C8×C53C2412yes—
250C2×C8×C53C2412yes—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53C2412yes—
255C4⋊C4×C53C2412yes—
256C22⋊C4×C53—24no—
257C42×C53—24no—
258C42×C53C2×D412yes—
259C42×C53C2412yes—
260C22⋊Dic53—24no—
261#11719924—28no—
262#11719923—28no—
263#11719921—24no—
264#11719921—24no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274C4×Dic53—24no—
275C4×Dic53—24no—
276C4×Dic53—24no—
277C4×Dic53C2×D412yes—
278C4×Dic53C2×D414yes—
279C4×Dic53C2×D414yes—
280C4×Dic53C2412yes—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322C2412yes—
284C2×#88322C2412yes—
285#11719913—28no—
286C23×C53—22no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53C22×D411yescharacteristic
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53C2×SD1614yes—
298C22×D53C22×D412yes—
299Q8×C53—24no—
300Q8×C53—22no—
301Q8×C53C2×#4114yescomplemented
302D4×C53—22no—
303D4×C53—22no—
304D4×C53—42no—
305C2×C4×C53—24no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—48no—
313C2×C4×C53C2×SD1614yes—
314C2×C4×C53C22×D412yes—
315C2×C4×C53C22×D411yescharacteristic
316C2×C4×C53C22×D412yes—
317C2×C4×C53C2×#4112yes—
318C2×C4×C53C2×#4112yes—
319C2×C4×C53C2511yescharacteristic
320C22⋊D53—48no—
321C22⋊D53—48no—
322C22⋊D53—48no—
323C2×Dic53—22no—
324C2×Dic53—24no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53C2×SD1614yes—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334C2×Dic53C22×D412yes—
335D212—22no—
336D212—22no—
337D212—48no—
338D212—42no—
339C4×D53—216no—
340C4×D53—24no—
341C4×D53—22no—
342C4×D53—22no—
343C4×D53—44no—
344C4×D53—48no—
345C4×D53—48no—
346C4×D53C2×SD16116yescomplemented
347Dic106—216no—
348Dic106—24no—
349Dic106—22no—
350Dic106—48no—
351Dic106C2×#4114yescomplemented
352C8×C53—22no—
353C8×C53—22no—
354#88322—22no—
355#88322—22no—
356C2×#3103—531nomaximal, Sylow
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—84no—
361C22×C53#52512yes—
362C22×C53C22×SD1612yes—
363C22×C53#57512yes—
364C22×C53C23×D411yescharacteristic
365C2×D53—28no—
366C2×D53—22no—
367C2×D53—22no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—84no—
372C2×D53C22×SD1614yes—
373C4×C53—24no—
374C4×C53—22no—
375C4×C53—42no—
376C4×C53—42no—
377C4×C53#52512yes—
378C4×C53C22×SD1614yes—
379C4×C53C22×#4111yescharacteristic
380C4×C53C22×#4111yescharacteristic
381Dic53—22no—
382Dic53—24no—
383Dic53—22no—
384Dic53—42no—
385Dic53—42no—
386Dic53C22×SD1614yes—
387C2×#532—531no—
388C22×C4×Q8—531no—
389#3103—5316no—
390C2×#481—531no—
391C2×#481—531no—
392C2×#475—531no—
393C2×#475—531no—
394C2×#460—531no—
395C2×#460—531no—
396C2×#448—531no—
397C2×#448—531no—
398C2×C4×SD16—531no—
399C2×C4×SD16—531no—
400C2×C4×SD16—531no—
401C2×C4×SD16D5311yescharacteristic, complemented
402C2×#431—531no—
403C2×C53—82no—
404C2×C53#310314yescomplemented
405C2×C53C2×#52511yescharacteristic
406C2×C53C23×SD1611yescharacteristic
407C2×C53C2×#57511yescharacteristic
408D53—24no—
409D53—82no—
410C22×#41—1061no—
411C23×Q8—531no—
412C22×SD16—531no—
413C22×SD16—531no—
414C22×SD16—531no—
415C22×SD16C2×D5311yescharacteristic
416#532—538no—
417#532—1064no—
418C2×C4⋊Q8—531no—
419C2×#127—531no—
420C2×#124—1061no—
421C2×#121—531no—
422C2×#121—531no—
423C2×#121—1061no—
424C2×C4×Q8—531no—
425C2×C4×Q8—538no—
426C2×C4×Q8—531no—
427C2×C4×Q8—531no—
428C2×C4×Q8—1061no—
429C2×C4×Q8—1061no—
430C2×C4×Q8—1064no—
431C2×C4×Q8C2×D5311yescharacteristic
432C2×C4×D4—531no—
433C2×C4×D4—1061no—
434C2×C4×D4C2×D5311yescharacteristic
435C22×C4⋊C4—531no—
436C22×C4⋊C4—1061no—
437C22×C42—531no—
438C22×C42—1061no—
439#481—538no—
440#481—538no—
441#475—538no—
442#475—538no—
443#460—538no—
444#460—538no—
445#448—538no—
446#448—538no—
447C4×SD16—538no—
448C4×SD16—538no—
449C4×SD16—538no—
450C4×SD16C2×D5318yescomplemented
451#431—538no—
452C2×#106—531no—
453C2×#106—531no—
454C2×#106—531no—
455C2×#106C2×D5311yescharacteristic
456C2×C4⋊C8—531no—
457C2×C4⋊C8—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103C2×D5311yescharacteristic
462C2×#102—531no—
463C2×#102—531no—
464C2×#102—531no—
465C2×#102C2×D5311yescharacteristic
466C2×C22⋊C8—531no—
467C2×C22⋊C8—531no—
468C2×C4×C8—531no—
469C2×C4×C8C2×D5311yescharacteristic
470C53C2×#310311yescharacteristic, complemented, Sylow
471C2×#41—1068no—
472C2×#41—2128no—
473C22×Q8—534no—
474C22×Q8—531no—
475C22×Q8—1061no—
476C22×Q8—1061no—
477C22×Q8—1062no—
478C22×Q8—1064no—
479C22×Q8—1064no—
480C22×Q8C22×D5311yescharacteristic
481C22×D4—531no—
482C22×D4—1061no—
483C22×D4—1061no—
484C22×D4—1061no—
485C22×D4—1061no—
486C22×D4C22×D5311yescharacteristic
487C23×C4—21no—
488C23×C4—531no—
489C23×C4—531no—
490C23×C4—531no—
491C23×C4—1061no—
492C23×C4—1061no—
493C23×C4—1061no—
494C2×SD16—24no—
495C2×SD16—534no—
496C2×SD16—534no—
497C2×SD16—534no—
498C2×SD16—1064no—
499C2×SD16—1064no—
500C2×SD16—1064no—
501C2×SD16C22×D5314yes—
502C22×C8—531no—
503C22×C8—531no—
504C22×C8C22×D5311yescharacteristic
505C22×C8C22×D5311yescharacteristic
506C4⋊Q8—534no—
507C4⋊Q8—1062no—
508#127—534no—
509#127—1062no—
510#124—1068no—
511#121—534no—
512#121—534no—
513#121—1068no—
514#121—1062no—
515#121—1062no—
516C4×Q8—22no—
517C4×Q8—534no—
518C4×Q8—534no—
519C4×Q8—534no—
520C4×Q8—1068no—
521C4×Q8—1068no—
522C4×Q8—1062no—
523C4×Q8—1062no—
524C4×Q8—1062no—
525C4×Q8C22×D5314yes—
526C4×D4—22no—
527C4×D4—534no—
528C4×D4—1068no—
529C4×D4—1062no—
530C4×D4C22×D5314yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—534no—
535C2×C4⋊C4—1062no—
536C2×C4⋊C4—1068no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4C22×D5311yescharacteristic
543C2×C4⋊C4C22×D5311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C42—21no—
549C2×C42—531no—
550C2×C42—531no—
551C2×C42—531no—
552C2×C42—534no—
553C2×C42—534no—
554C2×C42—1068no—
555C2×C42—1061no—
556C2×C42—1061no—
557C2×C42—1061no—
558C2×C42C22×D5311yescharacteristic
559#106—534no—
560#106—534no—
561#106—534no—
562#106C22×D5314yes—
563C4⋊C8—534no—
564C4⋊C8—534no—
565#103—534no—
566#103—534no—
567#103—534no—
568#103C22×D5314yes—
569#102—534no—
570#102—534no—
571#102—534no—
572#102C22×D5314yes—
573C22⋊C8—534no—
574C22⋊C8—534no—
575C4×C8—534no—
576C4×C8C22×D5314yes—
577C24—21no—
578C24—531no—
579C24—1061no—
580#41—21232no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—534no—
584C2×Q8—532no—
585C2×Q8—1064no—
586C2×Q8—1064no—
587C2×Q8—1068no—
588C2×Q8—1068no—
589C2×Q8—10616no—
590C2×Q8—1068no—
591C2×Q8—1061no—
592C2×Q8—1062no—
593C2×Q8—2124no—
594C2×Q8#1171994514yescomplemented
595C2×Q8C23×D5312yes—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—532no—
600C2×D4—1064no—
601C2×D4—1064no—
602C2×D4—1064no—
603C2×D4—1064no—
604C2×D4—1061no—
605C2×D4—1062no—
606C2×D4—1062no—
607C2×D4—2124no—
608C2×D4—2124no—
609C2×D4—2124no—
610C2×D4—2124no—
611C2×D4C23×D5312yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—531no—
618C22×C4—538no—
619C22×C4—534no—
620C22×C4—531no—
621C22×C4—531no—
622C22×C4—532no—
623C22×C4—532no—
624C22×C4—534no—
625C22×C4—1064no—
626C22×C4—1068no—
627C22×C4—1064no—
628C22×C4—1061no—
629C22×C4—1062no—
630C22×C4—1062no—
631C22×C4—1061no—
632C22×C4—1061no—
633C22×C4—1064no—
634C22×C4—2122no—
635C22×C4—2124no—
636C22×C4—2124no—
637C22×C4D4×D5311yescharacteristic
638C22×C4D4×D5311yescharacteristic
639C22×C4C23×D5311yescharacteristic
640SD16—28no—
641SD16—1068no—
642SD16—1068no—
643SD16—1068no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—532no—
647C2×C8—532no—
648C2×C8—1062no—
649C2×C8—1062no—
650C2×C8C23×D5312yes—
651C2×C8C23×D5312yes—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—532no—
656C4⋊C4—532no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1061no—
662C4⋊C4—1061no—
663C4⋊C4—1064no—
664C4⋊C4C23×D5312yes—
665C4⋊C4C23×D5312yes—
666C22⋊C4—24no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C42—24no—
671C42—534no—
672C42—534no—
673C42—532no—
674C42—532no—
675C42—1064no—
676C42—1064no—
677C42—1064no—
678C42D4×D5312yes—
679C42C23×D5312yes—
680C23—22no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—534no—
685C23—532no—
686C23—1062no—
687C23—1062no—
688C23—1062no—
689C23—2122no—
690C23—2122no—
691C23—2122no—
692C23C2×D4×D5311yescharacteristic
693Q8—24no—
694Q8—22no—
695Q8—534no—
696Q8—10616no—
697Q8—1064no—
698Q8—1062no—
699Q8—2128no—
700Q8C2×#1171994514yescomplemented
701D4—22no—
702D4—22no—
703D4—42no—
704D4—1062no—
705D4—1062no—
706D4—2128no—
707D4—2128no—
708D4—2128no—
709D4—2128no—
710D4—2122no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—48no—
719C2×C4—534no—
720C2×C4—532no—
721C2×C4—5316no—
722C2×C4—532no—
723C2×C4—532no—
724C2×C4—10616no—
725C2×C4—1062no—
726C2×C4—1064no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1064no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—2124no—
735C2×C4—2128no—
736C2×C4—2122no—
737C2×C4—2122no—
738C2×C4—2128no—
739C2×C4SD16×D5314yes—
740C2×C4C2×D4×D5312yes—
741C2×C4C2×D4×D5311yescharacteristic
742C2×C4C2×D4×D5312yes—
743C2×C4#41×D5312yes—
744C2×C4C2×#1171994512yes—
745C2×C4C24×D5311yescharacteristic
746C8—22no—
747C8—22no—
748C8—1062no—
749C8—1062no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22—534no—
755C22—1068no—
756C22—1062no—
757C22—1062no—
758C22—4244no—
759C22—2122no—
760C22—2122no—
761C22—2122no—
762C22#1681113212yes—
763C22C2×SD16×D5312yes—
764C22#1681142012yes—
765C22C22×D4×D5311yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—534no—
771C4—1062no—
772C4—1062no—
773C4—1064no—
774C4—2122no—
775C4—2122no—
776C4#1681113212yes—
777C4C2×SD16×D5314yes—
778C4C2×#41×D5311yescharacteristic
779C4C22×#1171994511yescharacteristic
780C2—82no—
781C2—1064no—
782C2—4242no—
783C2#2028474414yesdirect product factor
784C2C2×#1681113211yescharacteristic
785C2C22×SD16×D5311yescharacteristic
786C2C2×#1681142011yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×SD16×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811170C2
hypercenterC2×C4×SD16D53
hypocenterC53C2×#3103
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D53C2semidirect
3. #20284744C2direct (N × H)
4. C2×#16810943C2semidirect
5. C2×#16810940C2semidirect
6. C2×#16810907C2semidirect
7. C2×#16810906C2semidirect
8. C2×#16810822C2semidirect
9. C2×#16810821C2semidirect
10. C2×#16810763C2semidirect
11. C2×#16810760C2semidirect
12. C2×C4×#11719913C2semidirect
13. C2×C4×#11719924C2semidirect
14. C2×C4×#11719923C2semidirect
15. C2×#16810674C2semidirect
16. C2×C4×SD16×C53C2semidirect
36. C4×Q8×D53C22semidirect
43. #16810943C22semidirect
44. #16810940C22semidirect
45. #16810907C22semidirect
46. #16810906C22semidirect
47. #16810822C22semidirect
48. #16810821C22semidirect
49. #16810763C22semidirect
50. #16810760C22semidirect
51. C4×#11719913C22semidirect
52. C4×#11719924C22semidirect
53. C4×#11719923C22semidirect
54. #16810674C22semidirect
72. C4×SD16×C53C22semidirect
188. C2×Q8×C53#41semidirect
233. C2×C4×D53SD16semidirect
244. C2×Dic106#41semidirect
301. Q8×C53C2×#41semidirect
346. C4×D53C2×SD16semidirect
351. Dic106C2×#41semidirect
401. C2×C4×SD16D53semidirect
404. C2×C53#3103semidirect
450. C4×SD16C2×D53semidirect
470. C53C2×#3103semidirect
594. C2×Q8#11719945semidirect
700. Q8C2×#11719945semidirect
783. C2#20284744direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111702
C2×C4×Q8×D532
#202847442
C2×#168109432
C2×#168109402
C2×#168109072
C2×#168109062
C2×#168108222
C2×#168108212
C2×#168107632
C2×#168107602
C2×C4×#117199132
C2×C4×#117199242
C2×C4×#117199232
C2×#168106742
C2×C4×SD16×C532
C2×#310353