Finite Group Databasebeta

← C2×#20286555 #28260448

Subgroups — C2×#20286555 #28260448

Order 13568.

2286 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811314C211yesmaximal, characteristic, complemented
2C2×#16811268C211yesmaximal, characteristic
3#20286555C2116yesmaximal, direct product factor
4C2×#16810978C211yesmaximal, characteristic, complemented
5C2×#16810949C211yesmaximal, characteristic, complemented
6C2×#16810955C211yesmaximal, characteristic, complemented
7C2×#16810923C211yesmaximal, characteristic, complemented
8C2×#16810863C211yesmaximal, characteristic, complemented
9C2×#16810855C211yesmaximal, characteristic, complemented
10C2×#16810845C211yesmaximal, characteristic, complemented
11C2×#16810782C211yesmaximal, characteristic, complemented
12C2×#16810772C211yesmaximal, characteristic, complemented
13C2×C8×D212C211yesmaximal, characteristic, complemented
14C2×#16810616C211yesmaximal, characteristic, complemented
15C2×#102×D53C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C53C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic, complemented
20C22×#11719924C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic, complemented
23#16811314—24no—
24#16811314C2218yescomplemented
25#16811268—24no—
26#16811268C2218yes—
27C2×#13133211—21no—
28C2×#13133209C2211yescharacteristic, complemented
29C2×#13133207—21no—
30C2×#13133205C2211yescharacteristic
31C2×#13133202—21no—
32C2×#13133201—21no—
33C2×#13133197C2211yescharacteristic
34C2×#13133193C2211yescharacteristic
35C2×#13133193C2211yescharacteristic, complemented
36C2×#13133192C2211yescharacteristic
37C2×#13133191—21no—
38C2×#13133187—21no—
39C2×C4×D212C2211yescharacteristic
40C2×#13133175C2211yescharacteristic, complemented
41C2×#13133174—21no—
42C2×C4⋊C4×D53C2211yescharacteristic
43C22×#11719921—21no—
44#16810978C2218yescomplemented
45#16810955C2218yescomplemented
46#16810949C2218yescomplemented
47#16810923C2218yescomplemented
48#16810863C2218yescomplemented
49#16810855C2218yescomplemented
50#16810845C2218yescomplemented
51#16810782C2218yescomplemented
52#16810772C2218yescomplemented
53C8×D212C2218yescomplemented
54C2×#13133150C2211yescharacteristic, complemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×C4⋊#88322C2211yescharacteristic, complemented
57#16810616C2218yescomplemented
58C2×#13133142C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66#102×D53C2218yescomplemented
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic, 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—
78C2×#11719947—24no—
79C2×#11719947—22no—
80C2×#11719947—42no—
81C2×#11719947C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×D212—21no—
84C22×D212D411yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C2×D4×D53—24no—
89C2×D4×D53—22no—
90C2×D4×D53—42no—
91C2×D4×D53C2314yes—
92C23×Dic53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C22×C4×D53C2311yescharacteristic
96C2×#11719925—42no—
97C2×#11719925C2314yescomplemented
98C2×#11719924—42no—
99C2×#11719924C2314yes—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C2×C8×D53—42no—
103C2×C8×D53—42no—
104C2×C8×D53C2314yes—
105C2×C8×D53C2314yescomplemented
106#13133211—28no—
107#13133209—22no—
108#13133209C2314yescomplemented
109#13133207—28no—
110#13133205—22no—
111#13133205C2314yes—
112#13133202—28no—
113#13133201—28no—
114#13133197—22no—
115#13133197C2314yes—
116#13133193—22no—
117#13133193—22no—
118#13133193C2314yes—
119#13133193C2314yescomplemented
120#13133192—22no—
121#13133192C2314yes—
122#13133191—28no—
123#13133187—28no—
124C4×D212D414yes—
125C4×D212C2314yes—
126#13133175—22no—
127#13133175C2314yescomplemented
128#13133174—28no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53D411yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C4⋊C4×D53—22no—
139C4⋊C4×D53C2314yes—
140C2×#11719921—28no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151#13133150C2314yescomplemented
152#13133148C2314yescomplemented
153C4⋊#88322C2314yescomplemented
154#13133142C2314yescomplemented
155#13133142C2314yescomplemented
156#13133140C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yes—
159#13133138C2314yes—
160#13133138C2314yes—
161#13133137C2314yes—
162#13133129C2314yes—
163#13133129C2314yescomplemented
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C2×SD16×C53—24no—
168C2×SD16×C53C2314yes—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yescomplemented
173C4×D4×C53—22no—
174C4×D4×C53C2314yes—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#106×C53C2314yescomplemented
182#103×C53C2314yescomplemented
183#102×C53C2314yes—
184C4×C8×C53C2314yescomplemented
185C24×C53—21no—
186C23×D53—21no—
187C23×D53—24no—
188C23×D53—44no—
189C23×D53—44no—
190C23×D53—82no—
191C23×D53C2×D411yescharacteristic
192C23×D53C2×D411yescharacteristic
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53C2412yes—
197C2×D4×C53—21no—
198C2×D4×C53—22no—
199C2×D4×C53#4114yes—
200C2×D4×C53C2412yes—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—24no—
205C22×C4×C53—82no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2411yescharacteristic
209C2×C22⋊D53—24no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—44no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—24no—
217C22×Dic53—44no—
218C22×Dic53C2×D411yescharacteristic
219C22×Dic53C2×D411yescharacteristic
220#11719947—28no—
221#11719947—44no—
222#11719947—48no—
223D4×D53—28no—
224D4×D53—44no—
225D4×D53—48no—
226C2×D212—24no—
227C2×D212—22no—
228C2×D212—22no—
229C2×D212—21no—
230C2×D212—24no—
231C2×D212—82no—
232C2×D212C2×D414yes—
233C2×D212C2412yes—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—24no—
239C2×C4×D53—44no—
240C2×C4×D53C2×D412yes—
241C2×C4×D53C2×D412yes—
242C2×C4×D53C2412yes—
243C2×C4×D53C2412yes—
244C2×Dic106—22no—
245C2×Dic106—22no—
246C2×Dic106—21no—
247C2×Dic106C2412yes—
248SD16×C53—28no—
249C2×C8×C53—22no—
250C2×C8×C53—22no—
251C2×C8×C53C2412yes—
252C2×C8×C53C2412yes—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C42×C53—24no—
260C42×C53C2×D412yes—
261C42×C53C2412yes—
262#11719925—44no—
263#11719924—44no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921C2×D414yes—
272#11719921C2×D414yes—
273C4⋊Dic53—21no—
274C4⋊Dic53—21no—
275C4⋊Dic53—24no—
276C4⋊Dic53C2×D414yes—
277C4⋊Dic53C2412yes—
278C4⋊Dic53C2412yes—
279#11719919—24no—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283#11719919—24no—
284C4×Dic53—24no—
285C2×#88322—22no—
286C2×#88322—22no—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289C8×D53—44no—
290C8×D53—44no—
291C23×C53—24no—
292C23×C53—22no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53C22×D411yescharacteristic
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—48no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—48no—
307C22×D53—84no—
308C22×D53—816no—
309C22×D53#13514yes—
310C22×D53C22×D412yes—
311C22×D53C22×D412yes—
312Q8×C53—22no—
313Q8×C53—22no—
314Q8×C53—42no—
315D4×C53—24no—
316D4×C53—22no—
317D4×C53C2×#4114yes—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53—42no—
326C2×C4×C53—84no—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D412yes—
329C2×C4×C53C22×D411yescharacteristic
330C2×C4×C53C2×#4112yes—
331C2×C4×C53H(5,𝔽2)12yes—
332C2×C4×C53C2511yescharacteristic
333C22⋊D53—48no—
334C22⋊D53—48no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—48no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346D212—28no—
347D212—22no—
348D212—22no—
349D212—42no—
350D212—84no—
351C4×D53—24no—
352C4×D53—24no—
353C4×D53—22no—
354C4×D53—22no—
355C4×D53—22no—
356C4×D53—22no—
357C4×D53—48no—
358Dic106—22no—
359Dic106—22no—
360Dic106—42no—
361C8×C53—22no—
362C8×C53—22no—
363#88322—22no—
364#88322—22no—
365C2×#3296—531nomaximal, Sylow
366C22×C53—24no—
367C22×C53—48no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53#54612yes—
371C22×C53C2×#13512yes—
372C22×C53#57712yes—
373C22×C53C23×D411yescharacteristic
374C2×D53—22no—
375C2×D53—28no—
376C2×D53—22no—
377C2×D53—22no—
378C2×D53—22no—
379C2×D53—22no—
380C2×D53—44no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—816no—
385C2×D53—84no—
386C2×D53C2×#13514yes—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53#54612yes—
393C4×C53C22×#4111yescharacteristic
394C4×C53C2×H(5,𝔽2)11yescharacteristic
395Dic53—22no—
396Dic53—22no—
397Dic53—42no—
398Dic53—42no—
399Dic53—42no—
400C2×#552—531no—
401C2×#546—531no—
402#3296—5316no—
403C2×#488—531no—
404C2×#482—531no—
405C2×#483—531no—
406C2×#478—531no—
407C2×#467—531no—
408C2×#465—531no—
409C2×#464—531no—
410C2×#452—531no—
411C2×#450—531no—
412C2×C4×SD16D5311yescharacteristic, complemented
413C2×C8×D4—531no—
414C2×#416—531no—
415C22×#102—531no—
416C2×C53—44no—
417C2×C53#329614yescomplemented
418C2×C53C2×#54611yescharacteristic
419C2×C53C22×#13511yescharacteristic
420C2×C53C2×#57711yescharacteristic
421D53—24no—
422D53—42no—
423D53—82no—
424C22×#41—531no—
425C23×D4—531no—
426C22×Q16—531no—
427C22×SD16—531no—
428C22×SD16C2×D5311yescharacteristic
429C23×C8—531no—
430C23×C8—531no—
431#552—538no—
432#552—1064no—
433#546—538no—
434#546—1064no—
435C2×#126—1061no—
436C2×#125—531no—
437C2×#125—1061no—
438C2×#124—531no—
439C2×#123—1061no—
440C2×#123—1061no—
441C2×C22⋊Q8—531no—
442C2×C22⋊Q8—531no—
443C2×C22⋊Q8—531no—
444C2×#121—531no—
445C2×#121—1061no—
446C2×#120—1061no—
447C2×C4×Q8C2×D5311yescharacteristic, complemented
448C2×C4×D4—531no—
449C2×C4×D4C2×D5311yescharacteristic
450C2×#117—531no—
451C2×#117—1061no—
452C22×C4⋊C4—531no—
453C22×C22⋊C4—1061no—
454#488—538no—
455#483—538no—
456#482—538no—
457#478—538no—
458#467—538no—
459#465—538no—
460#464—538no—
461#452—538no—
462#450—538no—
463C4×SD16C2×D5318yescomplemented
464C8×D4—538no—
465C2×#107—531no—
466C2×#106—531no—
467C2×#106C2×D5311yescharacteristic, complemented
468C2×C4⋊C8—531no—
469#416—538no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103C2×D5311yescharacteristic, complemented
474C2×#102—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—538no—
480C2×#102C2×D5311yescharacteristic
481C2×C22⋊C8—531no—
482C2×C22⋊C8—531no—
483C2×C4×C8C2×D5311yescharacteristic, complemented
484C53C2×#329611yescharacteristic, complemented, Sylow
485C25—1061no—
486C2×#41—534no—
487C2×#41—1062no—
488C2×#41—1064no—
489C2×#41—2122no—
490C22×Q8—531no—
491C22×Q8C22×D5311yescharacteristic
492C22×D4—534no—
493C22×D4—531no—
494C22×D4—531no—
495C22×D4—1061no—
496C22×D4—1062no—
497C22×D4—1061no—
498C22×D4—1064no—
499C22×D4—1061no—
500C22×D4—2122no—
501C22×D4C22×D5311yescharacteristic
502C23×C4—21no—
503C23×C4—531no—
504C23×C4—531no—
505C23×C4—1061no—
506C23×C4—1061no—
507C2×Q16—534no—
508C2×Q16—2122no—
509C2×SD16—24no—
510C2×SD16—534no—
511C2×SD16—2122no—
512C2×SD16C22×D5314yes—
513C22×C8—531no—
514C22×C8—531no—
515C22×C8—534no—
516C22×C8—534no—
517C22×C8—2122no—
518C22×C8—2122no—
519C22×C8C22×D5311yescharacteristic
520C22×C8C22×D5311yescharacteristic
521#126—1068no—
522#125—534no—
523#125—1068no—
524#125—1062no—
525#124—534no—
526#124—1062no—
527#123—1068no—
528#123—1068no—
529C22⋊Q8—534no—
530C22⋊Q8—534no—
531C22⋊Q8—534no—
532C22⋊Q8—1062no—
533C22⋊Q8—1062no—
534C22⋊Q8—1062no—
535#121—534no—
536#121—1068no—
537#121—1062no—
538#120—1068no—
539C4×Q8—22no—
540C4×Q8C22×D5314yescomplemented
541C4×D4—22no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4C22×D5314yes—
545#117—534no—
546#117—1068no—
547#117—1062no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—531no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—534no—
553C2×C4⋊C4—1062no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C4⋊C4C22×D5311yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—531no—
564C2×C22⋊C4—531no—
565C2×C22⋊C4—1068no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C42—21no—
574C2×C42—1061no—
575C2×C42C22×D5311yescharacteristic
576#107—534no—
577#106—534no—
578#106C22×D5314yescomplemented
579C4⋊C8—534no—
580#103—534no—
581#103—534no—
582#103—534no—
583#103C22×D5314yescomplemented
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588#102—534no—
589#102C22×D5314yes—
590C22⋊C8—534no—
591C22⋊C8—534no—
592C4×C8C22×D5314yescomplemented
593C24—21no—
594C24—531no—
595C24—531no—
596C24—1064no—
597C24—1061no—
598C24—4242no—
599C24—2124no—
600C24—2124no—
601#41—1068no—
602#41—2124no—
603#41—2128no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—532no—
608C2×Q8—1061no—
609C2×Q8—1062no—
610C2×Q8—1062no—
611C2×Q8C23×D5312yes—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—534no—
615C2×D4—532no—
616C2×D4—1064no—
617C2×D4—1064no—
618C2×D4—1064no—
619C2×D4—1068no—
620C2×D4—1064no—
621C2×D4—1061no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—4242no—
625C2×D4—2124no—
626C2×D4—2128no—
627C2×D4—2124no—
628C2×D4—2124no—
629C2×D4#1171994514yes—
630C2×D4C23×D5312yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—82no—
636C22×C4—531no—
637C22×C4—531no—
638C22×C4—532no—
639C22×C4—532no—
640C22×C4—532no—
641C22×C4—532no—
642C22×C4—1064no—
643C22×C4—1064no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1062no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—1061no—
651C22×C4—2124no—
652C22×C4—2124no—
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4C23×D5311yescharacteristic
656Q16—2124no—
657SD16—28no—
658SD16—2124no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—532no—
662C2×C8—532no—
663C2×C8—1062no—
664C2×C8—1062no—
665C2×C8—2124no—
666C2×C8—2124no—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—534no—
673C4⋊C4—532no—
674C4⋊C4—532no—
675C4⋊C4—1064no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1061no—
680C4⋊C4—1061no—
681C4⋊C4—1064no—
682C4⋊C4—1064no—
683C4⋊C4C23×D5312yes—
684C4⋊C4C23×D5312yes—
685C22⋊C4—24no—
686C22⋊C4—534no—
687C22⋊C4—534no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C22⋊C4—1064no—
695C42—24no—
696C42—1064no—
697C42D4×D5312yes—
698C42C23×D5312yes—
699C23—24no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—534no—
704C23—532no—
705C23—532no—
706C23—1062no—
707C23—1062no—
708C23—1062no—
709C23—1062no—
710C23—1062no—
711C23—1062no—
712C23—42416no—
713C23—4244no—
714C23—2128no—
715C23—2128no—
716C23—2122no—
717C23—2122no—
718C23—2122no—
719C23C2×D4×D5311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—1062no—
724Q8—1062no—
725Q8—2122no—
726D4—24no—
727D4—22no—
728D4—1068no—
729D4—1062no—
730D4—1062no—
731D4—4244no—
732D4—2128no—
733D4—2128no—
734D4—2122no—
735D4C2×#1171994514yes—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—532no—
746C2×C4—532no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1064no—
750C2×C4—1064no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—2128no—
759C2×C4—2128no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4C2×D4×D5312yes—
764C2×C4C2×D4×D5312yes—
765C2×C4C2×D4×D5311yescharacteristic
766C2×C4C2×#1171994512yes—
767C2×C4#1313326312yes—
768C2×C4C24×D5311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1062no—
772C8—1062no—
773C22—24no—
774C22—48no—
775C22—42no—
776C22—42no—
777C22—534no—
778C22—1068no—
779C22—1062no—
780C22—1062no—
781C22—1062no—
782C22—1062no—
783C22—1062no—
784C22—42416no—
785C22—4244no—
786C22—2122no—
787C22—2122no—
788C22—2122no—
789C22—2124no—
790C22#1681126912yes—
791C22#135×D5312yes—
792C22#1681142912yes—
793C22C22×D4×D5311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—1062no—
800C4—1062no—
801C4—2122no—
802C4—2122no—
803C4—2122no—
804C4#1681126912yes—
805C4C22×#1171994511yescharacteristic
806C4C2×#1313326311yescharacteristic
807C2—44no—
808C2—1064no—
809C2—4242no—
810C2—2122no—
811C2#2028655514yesdirect product factor
812C2C2×#1681126911yescharacteristic
813C2C2×#135×D5311yescharacteristic
814C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×SD16×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811268C2
hypercenterC2×C4×SD16D53
hypocenterC53C2×#3296
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16811314C2semidirect
3. #20286555C2direct (N × H)
4. C2×#16810978C2semidirect
5. C2×#16810949C2semidirect
6. C2×#16810955C2semidirect
7. C2×#16810923C2semidirect
8. C2×#16810863C2semidirect
9. C2×#16810855C2semidirect
10. C2×#16810845C2semidirect
11. C2×#16810782C2semidirect
12. C2×#16810772C2semidirect
13. C2×C8×D212C2semidirect
14. C2×#16810616C2semidirect
15. C2×#102×D53C2semidirect
16. C2×C4×SD16×C53C2semidirect
19. C22×#11719925C22semidirect
22. C22×C8×D53C22semidirect
24. #16811314C22semidirect
28. C2×#13133209C22semidirect
35. C2×#13133193C22semidirect
40. C2×#13133175C22semidirect
44. #16810978C22semidirect
45. #16810955C22semidirect
46. #16810949C22semidirect
47. #16810923C22semidirect
48. #16810863C22semidirect
49. #16810855C22semidirect
50. #16810845C22semidirect
51. #16810782C22semidirect
52. #16810772C22semidirect
53. C8×D212C22semidirect
54. C2×#13133150C22semidirect
55. C2×#13133148C22semidirect
56. C2×C4⋊#88322C22semidirect
57. #16810616C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133140C22semidirect
66. #102×D53C22semidirect
68. C2×#13133129C22semidirect
70. C2×C4×Q8×C53C22semidirect
72. C4×SD16×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#103×C53C22semidirect
76. C2×C4×C8×C53C22semidirect
97. C2×#11719925C23semidirect
105. C2×C8×D53C23semidirect
108. #13133209C23semidirect
119. #13133193C23semidirect
127. #13133175C23semidirect
151. #13133150C23semidirect
152. #13133148C23semidirect
153. C4⋊#88322C23semidirect
154. #13133142C23semidirect
155. #13133142C23semidirect
156. #13133140C23semidirect
163. #13133129C23semidirect
172. C4×Q8×C53C23semidirect
181. #106×C53C23semidirect
182. #103×C53C23semidirect
184. C4×C8×C53C23semidirect
412. C2×C4×SD16D53semidirect
417. C2×C53#3296semidirect
447. C2×C4×Q8C2×D53semidirect
463. C4×SD16C2×D53semidirect
467. C2×#106C2×D53semidirect
473. C2×#103C2×D53semidirect
483. C2×C4×C8C2×D53semidirect
484. C53C2×#3296semidirect
540. C4×Q8C22×D53semidirect
578. #106C22×D53semidirect
583. #103C22×D53semidirect
592. C4×C8C22×D53semidirect
811. C2#20286555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113142
C2×#168112682
#202865552
C2×#168109782
C2×#168109492
C2×#168109552
C2×#168109232
C2×#168108632
C2×#168108552
C2×#168108452
C2×#168107822
C2×#168107722
C2×C8×D2122
C2×#168106162
C2×#102×D532
C2×C4×SD16×C532
C2×#329653