Finite Group Databasebeta

← C2×#20284721 #28252094

Subgroups — C2×#20284721 #28252094

Order 13568.

2570 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811177C211yesmaximal, characteristic, complemented
2C2×C4×D4×D53C211yesmaximal, characteristic
3#20284721C2116yesmaximal, direct product factor
4C2×#16810955C211yesmaximal, characteristic, complemented
5C2×#16810952C211yesmaximal, characteristic, complemented
6C2×#16810912C211yesmaximal, characteristic, complemented
7C2×#16810911C211yesmaximal, characteristic, complemented
8C2×#16810827C211yesmaximal, characteristic, complemented
9C2×#16810826C211yesmaximal, characteristic, complemented
10C2×#16810775C211yesmaximal, characteristic
11C2×#16810772C211yesmaximal, characteristic
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×D4×D53C2211yescharacteristic
18C23×C4×D53—21no—
19C22×#11719913C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22#16811177—24no—
23#16811177C2218yescomplemented
24C2×#13133216C2211yescharacteristic, complemented
25C2×#13133215C2211yescharacteristic, complemented
26C2×#13133207—21no—
27C2×#13133197C2211yescharacteristic
28C2×#13133195—21no—
29C2×#13133193C2211yescharacteristic
30C2×C4×Dic106—21no—
31C2×C4×Dic106C2211yescharacteristic, complemented
32C2×C4×D212C2211yescharacteristic
33C2×D4×Dic53C2211yescharacteristic
34C2×#13133179C2211yescharacteristic
35C2×C4×C22⋊D53—21no—
36C2×#13133177—21no—
37C4×D4×D53—24no—
38C4×D4×D53C2218yes—
39C2×#13133174—21no—
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C22⋊C4×D53—21no—
42C2×C42×D53C2211yescharacteristic
43#16810955C2218yescomplemented
44#16810952C2218yescomplemented
45#16810912C2218yescomplemented
46#16810911C2218yescomplemented
47#16810827C2218yescomplemented
48#16810826C2218yescomplemented
49#16810775C2218yes—
50#16810772C2218yes—
51C4×#11719913C2218yescomplemented
52C4×#11719924C2218yescomplemented
53C4×#11719923C2218yescomplemented
54#16810674C2218yescomplemented
55C2×#13133149C2211yescharacteristic, complemented
56C2×#13133148C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133146C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133142C2211yescharacteristic, complemented
61C2×#13133141C2211yescharacteristic, complemented
62C2×#13133140C2211yescharacteristic, complemented
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic, complemented
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic, complemented
71C2×C4×D4×C53C2211yescharacteristic
72C4×SD16×C53C2218yescomplemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C2×D4×D53—24no—
83C2×D4×D53—24no—
84C2×D4×D53—22no—
85C2×D4×D53C2314yes—
86C23×Dic53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—28no—
91C22×C4×D53—48no—
92C22×C4×D53D411yescharacteristic
93C22×C4×D53D411yescharacteristic
94C22×C4×D53C2311yescharacteristic
95C2×#11719913—24no—
96C2×#11719913C2314yes—
97C2×#11719923—24no—
98C2×#11719923C2314yes—
99C2×#11719924—24no—
100C2×#11719924C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133216—22no—
104#13133216C2314yescomplemented
105#13133215—22no—
106#13133215C2314yescomplemented
107#13133207—28no—
108#13133197—22no—
109#13133197C2314yes—
110#13133195—28no—
111#13133193—22no—
112#13133193C2314yes—
113C4×Dic106—22no—
114C4×Dic106—28no—
115C4×Dic106C2314yescomplemented
116C4×D212—22no—
117C4×D212C2314yes—
118D4×Dic53—22no—
119D4×Dic53C2314yes—
120#13133179—22no—
121#13133179C2314yes—
122C4×C22⋊D53—28no—
123#13133177—28no—
124#13133174—28no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C4⋊C4×D53—22no—
135C4⋊C4×D53C2314yes—
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C22⋊C4×D53—28no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53D411yescharacteristic
144C2×C4×Dic53D411yescharacteristic
145C2×C4×Dic53C2311yescharacteristic
146C42×D53D414yes—
147C42×D53C2314yes—
148#13133149C2314yescomplemented
149#13133148C2314yescomplemented
150#13133148C2314yescomplemented
151#13133146C2314yescomplemented
152#13133146C2314yescomplemented
153#13133142C2314yescomplemented
154#13133141C2314yescomplemented
155#13133140C2314yescomplemented
156#13133139C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133129C2314yes—
160#13133129C2314yes—
161C4×#88322C2314yescomplemented
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×C53C2314yescomplemented
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×C53C2314yescomplemented
180#103×C53C2314yescomplemented
181#102×C53C2314yes—
182C4×C8×C53C2314yescomplemented
183C24×C53—21no—
184C23×D53—28no—
185C23×D53—21no—
186C23×D53—24no—
187C23×D53—44no—
188C23×D53—44no—
189C23×D53C2×D411yescharacteristic
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53C2412yes—
194C2×D4×C53—21no—
195C2×D4×C53—22no—
196C2×D4×C53#4114yes—
197C2×D4×C53C2412yes—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—44no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—28no—
207C2×C22⋊D53—24no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—24no—
212C22×Dic53—44no—
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216D4×D53—216no—
217D4×D53—28no—
218D4×D53—28no—
219C2×D212—21no—
220C2×D212—22no—
221C2×D212#4114yes—
222C2×D212C2412yes—
223C2×C4×D53—22no—
224C2×C4×D53—22no—
225C2×C4×D53—24no—
226C2×C4×D53—24no—
227C2×C4×D53—24no—
228C2×C4×D53—42no—
229C2×C4×D53—44no—
230C2×C4×D53—44no—
231C2×C4×D53—44no—
232C2×C4×D53—432no—
233C2×C4×D53SD1618yescomplemented
234C2×C4×D53C2×D412yes—
235C2×C4×D53C2×D414yes—
236C2×C4×D53C2×D414yes—
237C2×C4×D53C2412yes—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—21no—
241C2×Dic106—24no—
242C2×Dic106—44no—
243C2×Dic106C2412yes—
244SD16×C53—28no—
245C2×C8×C53—22no—
246C2×C8×C53—22no—
247C2×C8×C53C2412yes—
248C2×C8×C53C2412yes—
249C4⋊C4×C53—24no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53C2412yes—
253C4⋊C4×C53C2412yes—
254C22⋊C4×C53—24no—
255C42×C53—24no—
256C42×C53C2×D412yes—
257C42×C53C2412yes—
258C22⋊Dic53—24no—
259#11719924—28no—
260#11719923—28no—
261#11719921—24no—
262#11719921—24no—
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—
274#11719919—24no—
275#11719919—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—24no—
287C23×C53—22no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53C22×D411yescharacteristic
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—216no—
294C22×D53—24no—
295C22×D53—22no—
296C22×D53—432no—
297C22×D53—48no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53—48no—
301C22×D53C2×SD1614yes—
302C22×D53C22×D412yes—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53—42no—
306D4×C53—24no—
307D4×C53—22no—
308D4×C53C2×#4114yes—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—48no—
317C2×C4×C53C2×SD1614yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53C22×D412yes—
321C2×C4×C53C2×#4112yes—
322C2×C4×C53C2×#4112yes—
323C2×C4×C53C2511yescharacteristic
324C22⋊D53—216no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—48no—
334C2×Dic53C2×SD1614yes—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338D212—24no—
339D212—22no—
340D212C2×#4114yes—
341C4×D53—24no—
342C4×D53—22no—
343C4×D53—22no—
344C4×D53—44no—
345C4×D53—48no—
346C4×D53—48no—
347C4×D53—48no—
348C4×D53C2×SD16116yescomplemented
349Dic106—22no—
350Dic106—22no—
351Dic106—48no—
352Dic106—42no—
353C8×C53—22no—
354C8×C53—22no—
355#88322—22no—
356#88322—22no—
357C2×#3101—531nomaximal, Sylow
358C22×C53—24no—
359C22×C53—48no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53#52512yes—
363C22×C53C22×SD1612yes—
364C22×C53#57512yes—
365C22×C53C23×D411yescharacteristic
366C2×D53—28no—
367C2×D53—22no—
368C2×D53—22no—
369C2×D53—24no—
370C2×D53—432no—
371C2×D53—48no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53C22×SD1614yes—
375C4×C53—22no—
376C4×C53—42no—
377C4×C53—42no—
378C4×C53—42no—
379C4×C53#52512yes—
380C4×C53C22×SD1614yes—
381C4×C53C22×#4111yescharacteristic
382C4×C53C22×#4111yescharacteristic
383Dic53—22no—
384Dic53—22no—
385Dic53—42no—
386Dic53—42no—
387Dic53—42no—
388Dic53C22×SD1614yes—
389C2×#533—531no—
390C22×C4×D4—531no—
391#3101—5316no—
392C2×#483—531no—
393C2×#483—531no—
394C2×#476—531no—
395C2×#476—531no—
396C2×#461—531no—
397C2×#461—531no—
398C2×#450—531no—
399C2×#450—531no—
400C2×C4×SD16—531no—
401C2×C4×SD16—531no—
402C2×C4×SD16—531no—
403C2×C4×SD16D5311yescharacteristic, complemented
404C2×#431—531no—
405C2×C53—44no—
406C2×C53#310114yescomplemented
407C2×C53C2×#52511yescharacteristic
408C2×C53C23×SD1611yescharacteristic
409C2×C53C2×#57511yescharacteristic
410D53—24no—
411D53—44no—
412C23×D4—531no—
413C24×C4—1061no—
414C22×SD16—531no—
415C22×SD16—531no—
416C22×SD16—531no—
417C22×SD16C2×D5311yescharacteristic
418#533—538no—
419#533—1064no—
420C2×C4⋊Q8—531no—
421C2×C4⋊Q8—531no—
422C2×#125—1061no—
423C2×C22⋊Q8—531no—
424C2×C22⋊Q8—531no—
425C2×C22⋊Q8—1061no—
426C2×C4×Q8—531no—
427C2×C4×Q8—1061no—
428C2×C4×Q8C2×D5311yescharacteristic, complemented
429C2×C4×D4—531no—
430C2×C4×D4—538no—
431C2×C4×D4—531no—
432C2×C4×D4—531no—
433C2×C4×D4—1061no—
434C2×C4×D4—1064no—
435C2×C4×D4—1061no—
436C2×C4×D4C2×D5311yescharacteristic
437C2×#117—1061no—
438C22×C4⋊C4—531no—
439C22×C22⋊C4—1061no—
440C22×C42—531no—
441#483—538no—
442#483—538no—
443#476—538no—
444#476—538no—
445#461—538no—
446#461—538no—
447#450—538no—
448#450—538no—
449C4×SD16—538no—
450C4×SD16—538no—
451C4×SD16—538no—
452C4×SD16C2×D5318yescomplemented
453#431—538no—
454C2×#106—531no—
455C2×#106—531no—
456C2×#106—531no—
457C2×#106C2×D5311yescharacteristic, complemented
458C2×C4⋊C8—531no—
459C2×C4⋊C8—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103C2×D5311yescharacteristic, complemented
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102C2×D5311yescharacteristic
468C2×C22⋊C8—531no—
469C2×C22⋊C8—531no—
470C2×C4×C8—531no—
471C2×C4×C8C2×D5311yescharacteristic, complemented
472C53C2×#310111yescharacteristic, complemented, Sylow
473C25—1061no—
474C22×Q8—531no—
475C22×Q8—1061no—
476C22×Q8C22×D5311yescharacteristic
477C22×D4—534no—
478C22×D4—531no—
479C22×D4—1062no—
480C22×D4—1061no—
481C22×D4—1064no—
482C22×D4—1064no—
483C22×D4C22×D5311yescharacteristic
484C23×C4—21no—
485C23×C4—531no—
486C23×C4—531no—
487C23×C4—531no—
488C23×C4—1061no—
489C23×C4—1068no—
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4—1061no—
493C23×C4—2128no—
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—534no—
508C4⋊Q8—1062no—
509C4⋊Q8—1062no—
510#125—1068no—
511C22⋊Q8—534no—
512C22⋊Q8—534no—
513C22⋊Q8—1062no—
514C22⋊Q8—1068no—
515C22⋊Q8—1062no—
516C4×Q8—22no—
517C4×Q8—534no—
518C4×Q8—1068no—
519C4×Q8—1062no—
520C4×Q8C22×D5314yescomplemented
521C4×D4—22no—
522C4×D4—534no—
523C4×D4—534no—
524C4×D4—534no—
525C4×D4—1068no—
526C4×D4—1062no—
527C4×D4—1068no—
528C4×D4—1062no—
529C4×D4—1062no—
530C4×D4C22×D5314yes—
531#117—1068no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—534no—
536C2×C4⋊C4—1062no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—1068no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C42—21no—
554C2×C42—531no—
555C2×C42—531no—
556C2×C42—531no—
557C2×C42—534no—
558C2×C42—534no—
559C2×C42—1061no—
560C2×C42C22×D5311yescharacteristic
561#106—534no—
562#106—534no—
563#106—534no—
564#106C22×D5314yescomplemented
565C4⋊C8—534no—
566C4⋊C8—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103C22×D5314yescomplemented
571#102—534no—
572#102—534no—
573#102—534no—
574#102C22×D5314yes—
575C22⋊C8—534no—
576C22⋊C8—534no—
577C4×C8—534no—
578C4×C8C22×D5314yescomplemented
579C24—21no—
580C24—531no—
581C24—1064no—
582C24—1068no—
583C24—1061no—
584C24—2124no—
585C24—2124no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—532no—
590C2×Q8—1064no—
591C2×Q8—1061no—
592C2×Q8—1062no—
593C2×Q8—1062no—
594C2×Q8—2124no—
595C2×Q8C23×D5312yes—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—534no—
599C2×D4—532no—
600C2×D4—1064no—
601C2×D4—1068no—
602C2×D4—10616no—
603C2×D4—1068no—
604C2×D4—1068no—
605C2×D4—1061no—
606C2×D4—1062no—
607C2×D4#1171994514yes—
608C2×D4C23×D5312yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—44no—
614C22×C4—531no—
615C22×C4—538no—
616C22×C4—534no—
617C22×C4—531no—
618C22×C4—531no—
619C22×C4—532no—
620C22×C4—532no—
621C22×C4—534no—
622C22×C4—1064no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1064no—
631C22×C4—2122no—
632C22×C4—2124no—
633C22×C4—21232no—
634C22×C4—2124no—
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—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1061no—
664C4⋊C4—1061no—
665C4⋊C4—1064no—
666C4⋊C4C23×D5312yes—
667C4⋊C4C23×D5312yes—
668C22⋊C4—24no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C42—24no—
675C42—534no—
676C42—534no—
677C42—532no—
678C42—532no—
679C42—1064no—
680C42D4×D5312yes—
681C42C23×D5312yes—
682C23—24no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—534no—
687C23—532no—
688C23—10616no—
689C23—1062no—
690C23—1062no—
691C23—1064no—
692C23—1062no—
693C23—2128no—
694C23—21232no—
695C23—2128no—
696C23—2122no—
697C23—2122no—
698C23C2×D4×D5311yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—42no—
702Q8—1062no—
703Q8—1062no—
704Q8—2128no—
705Q8—2122no—
706D4—24no—
707D4—22no—
708D4—534no—
709D4—10616no—
710D4—1064no—
711D4—1062no—
712D4C2×#1171994514yes—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—48no—
721C2×C4—534no—
722C2×C4—532no—
723C2×C4—5316no—
724C2×C4—532no—
725C2×C4—532no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1064no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—2124no—
735C2×C4—2128no—
736C2×C4—2128no—
737C2×C4—2128no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4—2128no—
742C2×C4SD16×D5314yes—
743C2×C4C2×D4×D5312yes—
744C2×C4C2×D4×D5311yescharacteristic
745C2×C4C2×D4×D5312yes—
746C2×C4#41×D5312yes—
747C2×C4C2×#1171994512yes—
748C2×C4C24×D5311yescharacteristic
749C8—22no—
750C8—22no—
751C8—1062no—
752C8—1062no—
753C22—24no—
754C22—48no—
755C22—42no—
756C22—42no—
757C22—534no—
758C22—1068no—
759C22—1062no—
760C22—1062no—
761C22—1064no—
762C22—21232no—
763C22—2128no—
764C22—2122no—
765C22—2122no—
766C22#1681113212yes—
767C22C2×SD16×D5312yes—
768C22#1681142012yes—
769C22C22×D4×D5311yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—534no—
775C4—1062no—
776C4—1062no—
777C4—2122no—
778C4—2122no—
779C4—2122no—
780C4#1681113212yes—
781C4C2×SD16×D5314yes—
782C4C2×#41×D5311yescharacteristic
783C4C22×#1171994511yescharacteristic
784C2—44no—
785C2—1064no—
786C2—2124no—
787C2#2028472114yesdirect product factor
788C2C2×#1681113211yescharacteristic
789C2C22×SD16×D5311yescharacteristic
790C2C2×#1681142011yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×SD16×C53C2
socleC23×C53C22×D4
prime radicalC22×D4×D53C22
hypercenterC2×C4×SD16D53
hypocenterC53C2×#3101
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
1. C2×#16811177C2semidirect
3. #20284721C2direct (N × H)
4. C2×#16810955C2semidirect
5. C2×#16810952C2semidirect
6. C2×#16810912C2semidirect
7. C2×#16810911C2semidirect
8. C2×#16810827C2semidirect
9. C2×#16810826C2semidirect
12. C2×C4×#11719913C2semidirect
13. C2×C4×#11719924C2semidirect
14. C2×C4×#11719923C2semidirect
15. C2×#16810674C2semidirect
16. C2×C4×SD16×C53C2semidirect
23. #16811177C22semidirect
24. C2×#13133216C22semidirect
25. C2×#13133215C22semidirect
31. C2×C4×Dic106C22semidirect
43. #16810955C22semidirect
44. #16810952C22semidirect
45. #16810912C22semidirect
46. #16810911C22semidirect
47. #16810827C22semidirect
48. #16810826C22semidirect
51. C4×#11719913C22semidirect
52. C4×#11719924C22semidirect
53. C4×#11719923C22semidirect
54. #16810674C22semidirect
55. C2×#13133149C22semidirect
56. C2×#13133148C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133146C22semidirect
59. C2×#13133146C22semidirect
60. C2×#13133142C22semidirect
61. C2×#13133141C22semidirect
62. C2×#13133140C22semidirect
68. C2×C4×#88322C22semidirect
70. C2×C4×Q8×C53C22semidirect
72. C4×SD16×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#103×C53C22semidirect
76. C2×C4×C8×C53C22semidirect
104. #13133216C23semidirect
106. #13133215C23semidirect
115. C4×Dic106C23semidirect
148. #13133149C23semidirect
149. #13133148C23semidirect
150. #13133148C23semidirect
151. #13133146C23semidirect
152. #13133146C23semidirect
153. #13133142C23semidirect
154. #13133141C23semidirect
155. #13133140C23semidirect
161. C4×#88322C23semidirect
170. C4×Q8×C53C23semidirect
179. #106×C53C23semidirect
180. #103×C53C23semidirect
182. C4×C8×C53C23semidirect
233. C2×C4×D53SD16semidirect
348. C4×D53C2×SD16semidirect
403. C2×C4×SD16D53semidirect
406. C2×C53#3101semidirect
428. C2×C4×Q8C2×D53semidirect
452. C4×SD16C2×D53semidirect
457. C2×#106C2×D53semidirect
463. C2×#103C2×D53semidirect
471. C2×C4×C8C2×D53semidirect
472. C53C2×#3101semidirect
520. C4×Q8C22×D53semidirect
564. #106C22×D53semidirect
570. #103C22×D53semidirect
578. C4×C8C22×D53semidirect
787. C2#20284721direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111772
C2×C4×D4×D532
#202847212
C2×#168109552
C2×#168109522
C2×#168109122
C2×#168109112
C2×#168108272
C2×#168108262
C2×#168107752
C2×#168107722
C2×C4×#117199132
C2×C4×#117199242
C2×C4×#117199232
C2×#168106742
C2×C4×SD16×C532
C2×#310153