Finite Group Databasebeta

← C2×#20284895 #28252319

Subgroups — C2×#20284895 #28252319

Order 13568.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811238C211yesmaximal, characteristic, complemented
2C2×#16811095C211yesmaximal, characteristic, complemented
3#20284895C2116yesmaximal, direct product factor
4C2×#16810966C211yesmaximal, characteristic, complemented
5C2×#16810946C211yesmaximal, characteristic, complemented
6C2×#16810911C211yesmaximal, characteristic, complemented
7C2×#16810902C211yesmaximal, characteristic, complemented
8C2×#16810837C211yesmaximal, characteristic, complemented
9C2×#16810836C211yesmaximal, characteristic, complemented
10C2×#16810775C211yesmaximal, characteristic, complemented
11C2×#16810755C211yesmaximal, characteristic
12C2×#16810733C211yesmaximal, characteristic, complemented
13C2×#16810723C211yesmaximal, characteristic, complemented
14C2×C4×#11719913C211yesmaximal, characteristic, complemented
15C2×#16810682C211yesmaximal, characteristic, complemented
16C2×C4×D8×C53C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21#16811238—24no—
22#16811238C2218yescomplemented
23C2×#13133216C2211yescharacteristic, complemented
24C2×#13133210—21no—
25C2×#13133204C2211yescharacteristic, complemented
26C2×#13133203—21no—
27C2×#13133200—21no—
28C2×#13133197C2211yescharacteristic
29C2×#13133196—21no—
30C2×#13133188C2211yescharacteristic
31#16811095—24no—
32#16811095C2218yescomplemented
33C2×C4×Dic106C2211yescharacteristic, complemented
34C2×C4×D212C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×C4×C22⋊D53—21no—
38C2×#13133177—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133174C2211yescharacteristic
41C22×#11719921—21no—
42C2×C22⋊C4×D53—21no—
43#16810966C2218yescomplemented
44#16810946C2218yescomplemented
45#16810911C2218yescomplemented
46#16810902C2218yescomplemented
47#16810837C2218yescomplemented
48#16810836C2218yescomplemented
49#16810775C2218yescomplemented
50#16810755C2218yes—
51#16810733C2218yescomplemented
52#16810723C2218yescomplemented
53C4×#11719913C2218yescomplemented
54#16810682C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133149C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133146C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133142C2211yescharacteristic, complemented
61C2×#13133140C2211yescharacteristic, complemented
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic, complemented
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic, complemented
69C22×D8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic, complemented
72C4×D8×C53C2218yescomplemented
73C2×#107×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C4×C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C2×D4×D53—24no—
84C2×D4×D53—24no—
85C2×D4×D53—22no—
86C2×D4×D53C2314yes—
87C23×Dic53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53C2311yescharacteristic
91C2×#11719913—24no—
92C2×#11719913C2314yes—
93C2×#11719923—24no—
94C2×#11719923C2314yes—
95C2×#11719922—24no—
96C2×#11719922C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99#13133216—22no—
100#13133216C2314yescomplemented
101#13133210—28no—
102#13133204—22no—
103#13133204C2314yescomplemented
104#13133203—28no—
105#13133200—28no—
106#13133197—22no—
107#13133197C2314yes—
108#13133196—28no—
109#13133188—22no—
110#13133188C2314yes—
111C4×Dic106—22no—
112C4×Dic106C2314yescomplemented
113C4×D212—22no—
114C4×D212C2314yes—
115D4×Dic53—22no—
116D4×Dic53C2314yes—
117#13133179—22no—
118#13133179C2314yes—
119C4×C22⋊D53—28no—
120#13133177—28no—
121#13133175—22no—
122#13133175C2314yes—
123#13133174D414yes—
124#13133174C2314yes—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C2×#11719919D411yescharacteristic
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×#11719921—28no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×#11719921D411yescharacteristic
143C22⋊C4×D53—28no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133150C2314yescomplemented
148#13133149C2314yescomplemented
149#13133148C2314yescomplemented
150#13133146C2314yescomplemented
151#13133146C2314yescomplemented
152#13133142C2314yescomplemented
153#13133140C2314yescomplemented
154#13133139C2314yes—
155#13133138C2314yes—
156#13133138C2314yescomplemented
157#13133137C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160#13133128C2314yescomplemented
161C22×D4×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C23×C4×C53—21no—
165C2×D8×C53—24no—
166C2×D8×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4×D4×C53—22no—
170C4×D4×C53—22no—
171C4×D4×C53C2314yes—
172C4×D4×C53C2314yescomplemented
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yescomplemented
179#102×C53C2314yes—
180#102×C53C2314yescomplemented
181C4×C8×C53C2314yescomplemented
182C24×C53—21no—
183C24×C53—21no—
184C23×D53—21no—
185C23×D53—28no—
186C23×D53—24no—
187C23×D53—82no—
188C23×D53—82no—
189C23×D53C2×D411yescharacteristic
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53#4114yes—
196C2×D4×C53C2412yes—
197C2×D4×C53C2412yes—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—24no—
201C22×C4×C53—24no—
202C22×C4×C53—82no—
203C22×C4×C53—82no—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2411yescharacteristic
207C2×C22⋊D53—28no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—82no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—82no—
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219D4×D53—216no—
220D4×D53—28no—
221D4×D53—28no—
222C2×D212—21no—
223C2×D212—22no—
224C2×D212#4114yes—
225C2×D212C2412yes—
226C2×C4×D53—22no—
227C2×C4×D53—22no—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—82no—
231C2×C4×D53—82no—
232C2×C4×D53C2×D412yes—
233C2×C4×D53C2412yes—
234C2×Dic106—22no—
235C2×Dic106—22no—
236C2×Dic106—21no—
237C2×Dic106—24no—
238C2×Dic106—82no—
239C2×Dic106C2412yes—
240D8×C53—28no—
241C2×C8×C53—22no—
242C2×C8×C53—22no—
243C2×C8×C53C2412yes—
244C2×C8×C53C2412yes—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53C2412yes—
248C4⋊C4×C53C2412yes—
249C22⋊C4×C53—24no—
250C22⋊C4×C53—24no—
251C42×C53C2×D412yes—
252C42×C53C2412yes—
253C22⋊Dic53—24no—
254C22⋊Dic53—24no—
255C22⋊Dic53—24no—
256C22⋊Dic53—24no—
257#11719923—28no—
258#11719922—28no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921C2×D414yes—
264#11719921C2×D414yes—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919—24no—
272#11719919C2×D414yes—
273#11719919C2×D414yes—
274C4×Dic53—24no—
275C4×Dic53—24no—
276C4×Dic53C2×D412yes—
277C4×Dic53C2412yes—
278C2×#88322—22no—
279C2×#88322—22no—
280C2×#88322C2412yes—
281C2×#88322C2412yes—
282#11719913—28no—
283C23×C53—24no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—42no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53C22×D411yescharacteristic
292C22×D53—22no—
293C22×D53—24no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—216no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53—84no—
301C22×D53—84no—
302C22×D53—816no—
303C22×D53C22×D412yes—
304D4×C53—24no—
305D4×C53—22no—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—42no—
309D4×C53C2×#4114yes—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—84no—
317C2×C4×C53—84no—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D411yescharacteristic
321C2×C4×C53C2×#4112yes—
322C2×C4×C53C2×#4112yes—
323C2×C4×C53C2511yescharacteristic
324C22⋊D53—216no—
325C22⋊D53—84no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—84no—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338C2×Dic53C22×D412yes—
339D212—24no—
340D212—22no—
341D212C2×#4114yes—
342C4×D53—24no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—84no—
346C4×D53—84no—
347Dic106—22no—
348Dic106—22no—
349Dic106—42no—
350Dic106—84no—
351C8×C53—22no—
352C8×C53—22no—
353#88322—22no—
354#88322—22no—
355C2×#3118—531nomaximal, Sylow
356C22×C53—24no—
357C22×C53—48no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—84no—
364C22×C53#52512yes—
365C22×C53#57612yes—
366C22×C53#57712yes—
367C22×C53C23×D411yescharacteristic
368C2×D53—22no—
369C2×D53—24no—
370C2×D53—22no—
371C2×D53—22no—
372C2×D53—44no—
373C2×D53—48no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—816no—
377C4×C53—22no—
378C4×C53—22no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53#52512yes—
382C4×C53C22×#4111yescharacteristic
383C4×C53C22×#4111yescharacteristic
384Dic53—22no—
385Dic53—22no—
386Dic53—22no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390C2×#542—531no—
391C2×#518—531no—
392#3118—5316no—
393C2×#485—531no—
394C2×#482—531no—
395C2×#476—531no—
396C2×#474—531no—
397C2×#463—531no—
398C2×#463—531no—
399C2×#450—531no—
400C2×#447—531no—
401C2×#442—531no—
402C2×#440—531no—
403C2×C4×SD16—531no—
404C2×C4×D8D5311yescharacteristic, complemented
405C2×#433—531no—
406C2×C53—44no—
407C2×C53—82no—
408C2×C53#311814yescomplemented
409C2×C53C2×#52511yescharacteristic
410C2×C53C2×#57611yescharacteristic
411C2×C53C2×#57711yescharacteristic
412D53—42no—
413D53—44no—
414C23×D4—531no—
415C22×SD16—531no—
416C22×SD16—531no—
417C22×D8—531no—
418C22×D8C2×D5311yescharacteristic
419#542—538no—
420#542—1064no—
421C2×C4⋊Q8—531no—
422C2×#126—1061no—
423C2×#124—531no—
424C2×#124—1061no—
425C2×#123—1061no—
426C2×C22⋊Q8—531no—
427C2×C22⋊Q8—1061no—
428C2×#121—531no—
429#518—538no—
430#518—1064no—
431C2×C4×Q8—531no—
432C2×C4×D4—531no—
433C2×C4×D4—531no—
434C2×C4×D4—531no—
435C2×C4×D4—1061no—
436C2×C4×D4—1061no—
437C2×C4×D4C2×D5311yescharacteristic
438C2×C4×D4C2×D5311yescharacteristic, complemented
439C2×#117—531no—
440C2×#117—531no—
441C22×C22⋊C4—1061no—
442C22×C22⋊C4—1061no—
443#485—538no—
444#482—538no—
445#476—538no—
446#474—538no—
447#463—538no—
448#463—538no—
449#450—538no—
450#447—538no—
451#442—538no—
452#440—538no—
453C4×SD16—538no—
454C4×D8C2×D5318yescomplemented
455#433—538no—
456C2×#107—531no—
457C2×#107C2×D5311yescharacteristic, complemented
458C2×#106—531no—
459C2×#106—531no—
460C2×C4⋊C8—531no—
461C2×C4⋊C8—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102—531no—
468C2×#102C2×D5311yescharacteristic
469C2×#102C2×D5311yescharacteristic, complemented
470C2×C22⋊C8—531no—
471C2×C22⋊C8—531no—
472C2×#97—531no—
473C2×C4×C8C2×D5311yescharacteristic, complemented
474C53C2×#311811yescharacteristic, complemented, Sylow
475C25—1061no—
476C22×Q8—531no—
477C22×Q8—1061no—
478C22×D4—534no—
479C22×D4—531no—
480C22×D4—1062no—
481C22×D4—1061no—
482C22×D4—1064no—
483C22×D4—1064no—
484C22×D4—1061no—
485C22×D4C22×D5311yescharacteristic
486C22×D4C22×D5311yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—531no—
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4—1061no—
493C2×SD16—534no—
494C2×SD16—534no—
495C2×SD16—1064no—
496C2×SD16—1064no—
497C2×D8—24no—
498C2×D8—534no—
499C2×D8—1064no—
500C2×D8C22×D5314yes—
501C22×C8—531no—
502C22×C8—531no—
503C22×C8C22×D5311yescharacteristic
504C22×C8C22×D5311yescharacteristic
505C4⋊Q8—534no—
506C4⋊Q8—1062no—
507#126—1068no—
508#124—534no—
509#124—1062no—
510#124—1068no—
511#123—1068no—
512C22⋊Q8—534no—
513C22⋊Q8—1062no—
514C22⋊Q8—1068no—
515#121—534no—
516#121—1062no—
517C4×Q8—534no—
518C4×Q8—1062no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—534no—
522C4×D4—534no—
523C4×D4—534no—
524C4×D4—1062no—
525C4×D4—1062no—
526C4×D4—1068no—
527C4×D4—1068no—
528C4×D4—1062no—
529C4×D4C22×D5314yes—
530C4×D4C22×D5314yescomplemented
531#117—534no—
532#117—534no—
533#117—534no—
534#117—1062no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
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—21no—
546C2×C22⋊C4—531no—
547C2×C22⋊C4—531no—
548C2×C22⋊C4—1068no—
549C2×C22⋊C4—1068no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C42—531no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42C22×D5311yescharacteristic
562#107—534no—
563#107C22×D5314yescomplemented
564#106—534no—
565#106—534no—
566C4⋊C8—534no—
567C4⋊C8—534no—
568#103—534no—
569#103—534no—
570#102—534no—
571#102—534no—
572#102—534no—
573#102—534no—
574#102C22×D5314yes—
575#102C22×D5314yescomplemented
576C22⋊C8—534no—
577C22⋊C8—534no—
578#97—534no—
579C4×C8C22×D5314yescomplemented
580C24—21no—
581C24—21no—
582C24—531no—
583C24—1064no—
584C24—1068no—
585C24—1061no—
586C24—4242no—
587C24—4242no—
588C2×Q8—532no—
589C2×Q8—1064no—
590C2×Q8—1061no—
591C2×Q8—1062no—
592C2×Q8—1062no—
593C2×Q8—4242no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—534no—
600C2×D4—532no—
601C2×D4—1064no—
602C2×D4—1068no—
603C2×D4—10616no—
604C2×D4—1068no—
605C2×D4—1068no—
606C2×D4—1064no—
607C2×D4—1061no—
608C2×D4—1062no—
609C2×D4—4242no—
610C2×D4#1171994514yes—
611C2×D4C23×D5312yes—
612C2×D4C23×D5312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—531no—
620C22×C4—531no—
621C22×C4—531no—
622C22×C4—532no—
623C22×C4—532no—
624C22×C4—1064no—
625C22×C4—1064no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1064no—
632C22×C4—4242no—
633C22×C4—4242no—
634C22×C4—4242no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638SD16—1068no—
639SD16—1068no—
640D8—28no—
641D8—1068no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8C23×D5312yes—
649C2×C8C23×D5312yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—534no—
653C4⋊C4—534no—
654C4⋊C4—532no—
655C4⋊C4—532no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1061no—
659C4⋊C4—1061no—
660C4⋊C4—1064no—
661C4⋊C4C23×D5312yes—
662C4⋊C4C23×D5312yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—534no—
666C22⋊C4—534no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C42—532no—
676C42—532no—
677C42—1064no—
678C42—1064no—
679C42D4×D5312yes—
680C42C23×D5312yes—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—532no—
690C23—10616no—
691C23—1062no—
692C23—1064no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—4244no—
697C23—4244no—
698C23—42416no—
699C23—2122no—
700C23—2122no—
701C23C2×D4×D5311yescharacteristic
702Q8—1062no—
703Q8—1062no—
704Q8—4244no—
705Q8—2122no—
706D4—24no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—42no—
711D4—534no—
712D4—10616no—
713D4—1064no—
714D4—1062no—
715D4—4244no—
716D4C2×#1171994514yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—532no—
726C2×C4—532no—
727C2×C4—532no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1064no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—4244no—
738C2×C4—4244no—
739C2×C4—4244no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4C2×D4×D5312yes—
744C2×C4C2×D4×D5312yes—
745C2×C4C2×D4×D5311yescharacteristic
746C2×C4#41×D5312yes—
747C2×C4C2×#1171994512yes—
748C2×C4C24×D5311yescharacteristic
749C8—22no—
750C8—22no—
751C8—1062no—
752C8—1062no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—1062no—
762C22—1062no—
763C22—1062no—
764C22—1064no—
765C22—42416no—
766C22—2122no—
767C22—2122no—
768C22—2124no—
769C22—2128no—
770C22#1681113212yes—
771C22#1681142412yes—
772C22#1681143012yes—
773C22C22×D4×D5311yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—1062no—
779C4—1062no—
780C4—1062no—
781C4—2122no—
782C4—2122no—
783C4—2122no—
784C4#1681113212yes—
785C4C2×#41×D5311yescharacteristic
786C4C22×#1171994511yescharacteristic
787C2—44no—
788C2—82no—
789C2—2122no—
790C2—2124no—
791C2#2028489514yesdirect product factor
792C2C2×#1681113211yescharacteristic
793C2C2×#1681142411yescharacteristic
794C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×D8×C53C2
socleC23×C53C22×D4
prime radicalC2×#16810755C2
hypercenterC2×C4×D8D53
hypocenterC53C2×#3118
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16811238C2semidirect
2. C2×#16811095C2semidirect
3. #20284895C2direct (N × H)
4. C2×#16810966C2semidirect
5. C2×#16810946C2semidirect
6. C2×#16810911C2semidirect
7. C2×#16810902C2semidirect
8. C2×#16810837C2semidirect
9. C2×#16810836C2semidirect
10. C2×#16810775C2semidirect
12. C2×#16810733C2semidirect
13. C2×#16810723C2semidirect
14. C2×C4×#11719913C2semidirect
15. C2×#16810682C2semidirect
16. C2×C4×D8×C53C2semidirect
22. #16811238C22semidirect
23. C2×#13133216C22semidirect
25. C2×#13133204C22semidirect
32. #16811095C22semidirect
33. C2×C4×Dic106C22semidirect
43. #16810966C22semidirect
44. #16810946C22semidirect
45. #16810911C22semidirect
46. #16810902C22semidirect
47. #16810837C22semidirect
48. #16810836C22semidirect
49. #16810775C22semidirect
51. #16810733C22semidirect
52. #16810723C22semidirect
53. C4×#11719913C22semidirect
54. #16810682C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133149C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133146C22semidirect
59. C2×#13133146C22semidirect
60. C2×#13133142C22semidirect
61. C2×#13133140C22semidirect
64. C2×#13133138C22semidirect
68. C2×#13133128C22semidirect
71. C2×C4×D4×C53C22semidirect
72. C4×D8×C53C22semidirect
73. C2×#107×C53C22semidirect
75. C2×#102×C53C22semidirect
76. C2×C4×C8×C53C22semidirect
100. #13133216C23semidirect
103. #13133204C23semidirect
112. C4×Dic106C23semidirect
147. #13133150C23semidirect
148. #13133149C23semidirect
149. #13133148C23semidirect
150. #13133146C23semidirect
151. #13133146C23semidirect
152. #13133142C23semidirect
153. #13133140C23semidirect
156. #13133138C23semidirect
160. #13133128C23semidirect
172. C4×D4×C53C23semidirect
178. #107×C53C23semidirect
180. #102×C53C23semidirect
181. C4×C8×C53C23semidirect
404. C2×C4×D8D53semidirect
408. C2×C53#3118semidirect
438. C2×C4×D4C2×D53semidirect
454. C4×D8C2×D53semidirect
457. C2×#107C2×D53semidirect
469. C2×#102C2×D53semidirect
473. C2×C4×C8C2×D53semidirect
474. C53C2×#3118semidirect
530. C4×D4C22×D53semidirect
563. #107C22×D53semidirect
575. #102C22×D53semidirect
579. C4×C8C22×D53semidirect
791. C2#20284895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112382
C2×#168110952
#202848952
C2×#168109662
C2×#168109462
C2×#168109112
C2×#168109022
C2×#168108372
C2×#168108362
C2×#168107752
C2×#168107552
C2×#168107332
C2×#168107232
C2×C4×#117199132
C2×#168106822
C2×C4×D8×C532
C2×#311853