Finite Group Databasebeta

← C2×#20286543 #28260436

Subgroups — C2×#20286543 #28260436

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×#16811307C211yesmaximal, characteristic, complemented
2C2×#16811261C211yesmaximal, characteristic
3#20286543C2116yesmaximal, direct product factor
4C2×#16810979C211yesmaximal, characteristic, complemented
5C2×#16810948C211yesmaximal, characteristic, complemented
6C2×#16810952C211yesmaximal, characteristic, complemented
7C2×#16810921C211yesmaximal, characteristic, complemented
8C2×#16810861C211yesmaximal, characteristic, complemented
9C2×#16810854C211yesmaximal, characteristic, complemented
10C2×#16810847C211yesmaximal, characteristic, complemented
11C2×#16810772C211yesmaximal, characteristic, complemented
12C2×SD16×Dic53C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic, complemented
14C2×#16810619C211yesmaximal, characteristic, complemented
15C2×#102×D53C211yesmaximal, characteristic, complemented
16C2×C53×#452C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C23×#88322C2211yescharacteristic, complemented
20C22×C8×D53C2211yescharacteristic
21#16811307—24no—
22#16811307C2218yescomplemented
23#16811261—24no—
24#16811261C2218yes—
25C2×#13133210—21no—
26C2×#13133208C2211yescharacteristic, complemented
27C2×#13133207—21no—
28C2×#13133206C2211yescharacteristic
29C2×#13133200—21no—
30C2×#13133199—21no—
31C2×#13133193C2211yescharacteristic
32C2×#13133193C2211yescharacteristic
33C2×#13133191C2211yescharacteristic
34C2×#13133189—21no—
35C2×#13133185—21no—
36C2×Q8×Dic53C2211yescharacteristic, complemented
37C2×D4×Dic53C2211yescharacteristic
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133176C2211yescharacteristic, complemented
40C2×#13133175—21no—
41C2×C4⋊C4×D53C2211yescharacteristic
42C22×#11719921—21no—
43#16810979C2218yescomplemented
44#16810952C2218yescomplemented
45#16810948C2218yescomplemented
46#16810921C2218yescomplemented
47#16810861C2218yescomplemented
48#16810854C2218yescomplemented
49#16810847C2218yescomplemented
50#16810772C2218yescomplemented
51SD16×Dic53C2218yescomplemented
52#16810686C2218yescomplemented
53C2×#13133151C2211yescharacteristic, complemented
54C2×#13133149C2211yescharacteristic, complemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133146C2211yescharacteristic, complemented
57#16810619C2218yescomplemented
58C2×#13133141C2211yescharacteristic, complemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133141C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66#102×D53C2218yescomplemented
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic, complemented
69C22×#41×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic, complemented
71C22×SD16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic, complemented
73C53×#452C2218yescomplemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C22×D212C2311yescharacteristic
79C22×C22⋊D53—21no—
80C22×C22⋊D53—21no—
81C22×C22⋊D53D411yescharacteristic
82C2×D4×D53—24no—
83C2×D4×D53—22no—
84C2×D4×D53—42no—
85C2×D4×D53C2314yes—
86C23×Dic53—21no—
87C22×C4×D53—21no—
88C22×C4×D53C2311yescharacteristic
89C2×#11719924—42no—
90C2×#11719924C2314yes—
91C22×#88322—42no—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2314yescomplemented
95C2×C8×D53—42no—
96C2×C8×D53C2314yes—
97#13133210—28no—
98#13133208—22no—
99#13133208C2314yescomplemented
100#13133207—28no—
101#13133206—22no—
102#13133206C2314yes—
103#13133200—28no—
104#13133199—28no—
105#13133193—22no—
106#13133193—22no—
107#13133193C2314yes—
108#13133193C2314yes—
109#13133191—22no—
110#13133191C2314yes—
111#13133189—28no—
112#13133185—28no—
113Q8×Dic53—22no—
114Q8×Dic53C2314yescomplemented
115D4×Dic53—22no—
116D4×Dic53C2314yes—
117C4×C22⋊D53D414yes—
118C4×C22⋊D53C2314yes—
119#13133176—22no—
120#13133176C2314yescomplemented
121#13133175—28no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919D411yescharacteristic
132C4⋊C4×D53—22no—
133C4⋊C4×D53C2314yes—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53D411yescharacteristic
137C2×#11719921—28no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921D411yescharacteristic
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yescomplemented
148#13133149C2314yescomplemented
149#13133148C2314yescomplemented
150#13133146C2314yescomplemented
151#13133141C2314yescomplemented
152#13133141C2314yescomplemented
153#13133141C2314yescomplemented
154#13133139C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133129C2314yes—
160C8×Dic53C2314yescomplemented
161C2×#41×C53—22no—
162C2×#41×C53—24no—
163C2×#41×C53—42no—
164C2×#41×C53C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53—21no—
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53C2311yescharacteristic
171C2×Q16×C53—42no—
172C2×Q16×C53C2314yescomplemented
173C2×SD16×C53—24no—
174C2×SD16×C53C2314yes—
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53C2314yescomplemented
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182#103×C53C2314yescomplemented
183#102×C53C2314yes—
184C22⋊C8×C53C2314yescomplemented
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53—24no—
189C23×D53—44no—
190C23×D53—44no—
191C23×D53—82no—
192C23×D53C2×D411yescharacteristic
193#41×C53—28no—
194#41×C53—44no—
195#41×C53—48no—
196C2×Q8×C53—21no—
197C2×Q8×C53—21no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53—22no—
202C2×Q8×C53C2412yes—
203C2×Q8×C53C2412yes—
204C2×D4×C53—24no—
205C2×D4×C53—21no—
206C2×D4×C53—22no—
207C2×D4×C53—44no—
208C2×D4×C53#4114yes—
209C2×D4×C53C2412yes—
210C22×C4×C53—22no—
211C22×C4×C53—22no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—24no—
216C22×C4×C53—44no—
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D412yes—
219C22×C4×C53C2412yes—
220C22×C4×C53C2411yescharacteristic
221C2×C22⋊D53—24no—
222C2×C22⋊D53—24no—
223C2×C22⋊D53—24no—
224C2×C22⋊D53—44no—
225C2×C22⋊D53—82no—
226C2×C22⋊D53C2×D414yes—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—24no—
231C22×Dic53—82no—
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234C22×Dic53C2×D411yescharacteristic
235D4×D53—28no—
236D4×D53—44no—
237D4×D53—48no—
238C2×D212—22no—
239C2×D212—22no—
240C2×D212—21no—
241C2×D212C2412yes—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—24no—
245C2×C4×D53—44no—
246C2×C4×D53C2×D412yes—
247C2×C4×D53C2412yes—
248Q16×C53—44no—
249SD16×C53—28no—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53C2412yes—
253C2×C8×C53C2412yes—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C22⋊C4×C53—24no—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53C2×D414yes—
261#11719924—44no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921C2×D414yes—
268C4⋊Dic53—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—24no—
272C4⋊Dic53—24no—
273C4⋊Dic53C2412yes—
274C4⋊Dic53C2412yes—
275C4⋊Dic53C2412yes—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919C2×D414yes—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C4×Dic53C2×D412yes—
284C4×Dic53C2412yes—
285C2×#88322—22no—
286C2×#88322—22no—
287C2×#88322—44no—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290C8×D53—44no—
291C23×C53—24no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53C22×D412yes—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—48no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—48no—
308C22×D53—84no—
309C22×D53—816no—
310C22×D53#13514yes—
311C22×D53C22×D412yes—
312Q8×C53—22no—
313Q8×C53—22no—
314Q8×C53—22no—
315Q8×C53—22no—
316Q8×C53—42no—
317Q8×C53—42no—
318D4×C53—24no—
319D4×C53—22no—
320D4×C53—48no—
321D4×C53C2×#4114yes—
322C2×C4×C53—22no—
323C2×C4×C53—24no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—48no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53—42no—
333C2×C4×C53C22×D412yes—
334C2×C4×C53C22×D411yescharacteristic
335C2×C4×C53C2×#4112yes—
336C2×C4×C53H(5,𝔽2)12yes—
337C2×C4×C53C2511yescharacteristic
338C22⋊D53—28no—
339C22⋊D53—48no—
340C22⋊D53—84no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—84no—
351C2×Dic53C22×D412yes—
352C2×Dic53C22×D412yes—
353C2×Dic53C22×D412yes—
354D212—22no—
355D212—22no—
356D212—42no—
357C4×D53—24no—
358C4×D53—22no—
359C4×D53—22no—
360C4×D53—48no—
361C8×C53—22no—
362C8×C53—22no—
363#88322—22no—
364#88322—22no—
365C2×#3296—531nomaximal, Sylow
366C22×C53—24no—
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—48no—
371C22×C53—44no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53#54612yes—
375C22×C53C2×#13512yes—
376C22×C53#57712yes—
377C22×C53C23×D411yescharacteristic
378C2×D53—22no—
379C2×D53—28no—
380C2×D53—22no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—816no—
385C2×D53—84no—
386C2×D53C2×#13514yes—
387C4×C53—22no—
388C4×C53—42no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53#54612yes—
392C4×C53C22×#4111yescharacteristic
393C4×C53C2×H(5,𝔽2)11yescharacteristic
394Dic53—22no—
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×#452D5311yescharacteristic, complemented
411C2×#450—531no—
412C2×C4×SD16—531no—
413C2×C8×D4—531no—
414C2×#416—531no—
415C22×#102—531no—
416C2×C53—44no—
417C2×C53—42no—
418C2×C53#329614yescomplemented
419C2×C53C2×#54611yescharacteristic
420C2×C53C22×#13511yescharacteristic
421C2×C53C2×#57711yescharacteristic
422D53—24no—
423D53—82no—
424C22×#41C2×D5311yescharacteristic
425C23×D4—531no—
426C22×Q16C2×D5311yescharacteristic, complemented
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⋊Q8C2×D5311yescharacteristic, complemented
444C2×#121—531no—
445C2×#121—1061no—
446C2×#120—1061no—
447C2×C4×Q8—531no—
448C2×C4×D4—531no—
449C2×C4×D4—531no—
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#452C2×D5318yescomplemented
462#450—538no—
463C4×SD16—538no—
464C8×D4—538no—
465C2×#107—531no—
466C2×#106—531no—
467C2×#106—531no—
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⋊C8C2×D5311yescharacteristic, complemented
483C2×C4×C8—531no—
484C53C2×#329611yescharacteristic, complemented, Sylow
485C25—1061no—
486C2×#41—22no—
487C2×#41—24no—
488C2×#41—42no—
489C2×#41C22×D5314yes—
490C22×Q8C22×D5311yescharacteristic
491C22×Q8C22×D5311yescharacteristic
492C22×D4—21no—
493C22×D4—531no—
494C22×D4—534no—
495C22×D4—531no—
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—1061no—
505C23×C4—1061no—
506C23×C4C22×D5311yescharacteristic
507C2×Q16—42no—
508C2×Q16C22×D5314yescomplemented
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—1062no—
524#125—1068no—
525#124—534no—
526#124—1062no—
527#123—1068no—
528#123—1068no—
529C22⋊Q8—22no—
530C22⋊Q8—534no—
531C22⋊Q8—534no—
532C22⋊Q8—1062no—
533C22⋊Q8—1062no—
534C22⋊Q8C22×D5314yescomplemented
535#121—534no—
536#121—1068no—
537#121—1062no—
538#120—1068no—
539C4×Q8—534no—
540C4×Q8—1062no—
541C4×D4—534no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—1062no—
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—531no—
553C2×C4⋊C4—534no—
554C2×C4⋊C4—1062no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
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—531no—
574C2×C42—1061no—
575C2×C42—1061no—
576#107—534no—
577#106—534no—
578#106—534no—
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⋊C8C22×D5314yescomplemented
592C4×C8—534no—
593C24—21no—
594C24—531no—
595C24—1064no—
596C24—1061no—
597C24—4242no—
598C24—2124no—
599C24—2124no—
600C24D4×D5311yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8C23×D5312yes—
611C2×Q8C23×D5312yes—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—44no—
616C2×D4—534no—
617C2×D4—532no—
618C2×D4—1064no—
619C2×D4—1064no—
620C2×D4—1068no—
621C2×D4—1064no—
622C2×D4—1061no—
623C2×D4—1062no—
624C2×D4—1062no—
625C2×D4—4242no—
626C2×D4—2124no—
627C2×D4—2128no—
628C2×D4—2124no—
629C2×D4#1171994714yes—
630C2×D4C23×D5312yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—44no—
638C22×C4—531no—
639C22×C4—531no—
640C22×C4—531no—
641C22×C4—532no—
642C22×C4—532no—
643C22×C4—1064no—
644C22×C4—1064no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—4242no—
651C22×C4—2124no—
652C22×C4D4×D5312yes—
653C22×C4D4×D5311yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—44no—
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—534no—
672C4⋊C4—532no—
673C4⋊C4—532no—
674C4⋊C4—532no—
675C4⋊C4—1064no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1061no—
682C4⋊C4—1061no—
683C4⋊C4—1061no—
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—532no—
696C42—532no—
697C42—1064no—
698C42—1064no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—42no—
705C23—42no—
706C23—534no—
707C23—532no—
708C23—1062no—
709C23—1062no—
710C23—1062no—
711C23—42416no—
712C23—4244no—
713C23—2128no—
714C23—2128no—
715C23—2122no—
716C23—2122no—
717C23—2122no—
718C23C2×D4×D5312yes—
719C23C2×D4×D5311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726D4—22no—
727D4—24no—
728D4—48no—
729D4—1068no—
730D4—1062no—
731D4—1062no—
732D4—4244no—
733D4—2128no—
734D4—2122no—
735D4C2×#1171994714yes—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—532no—
748C2×C4—532no—
749C2×C4—532no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1064no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—4244no—
760C2×C4—2128no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4C2×D4×D5312yes—
765C2×C4C2×D4×D5311yescharacteristic
766C2×C4C2×#1171994712yes—
767C2×C4#1313326212yes—
768C2×C4C24×D5311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1062no—
772C8—1062no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—22no—
777C22—44no—
778C22—48no—
779C22—42no—
780C22—42no—
781C22—534no—
782C22—1068no—
783C22—1062no—
784C22—1062no—
785C22—42416no—
786C22—4244no—
787C22—2122no—
788C22—2122no—
789C22—2122no—
790C22#1681126012yes—
791C22#135×D5312yes—
792C22#1681143212yes—
793C22C22×D4×D5311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—1062no—
799C4—1062no—
800C4—1062no—
801C4—2122no—
802C4—2122no—
803C4—2122no—
804C4#1681126012yes—
805C4C22×#1171994711yescharacteristic
806C4C2×#1313326211yescharacteristic
807C2—42no—
808C2—44no—
809C2—1064no—
810C2—4242no—
811C2#2028654314yesdirect product factor
812C2C2×#1681126011yescharacteristic
813C2C2×#135×D5311yescharacteristic
814C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC2×#16811261C2
hypercenterC2×#452D53
hypocenterC53C2×#3296
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16811307C2semidirect
3. #20286543C2direct (N × H)
4. C2×#16810979C2semidirect
5. C2×#16810948C2semidirect
6. C2×#16810952C2semidirect
7. C2×#16810921C2semidirect
8. C2×#16810861C2semidirect
9. C2×#16810854C2semidirect
10. C2×#16810847C2semidirect
11. C2×#16810772C2semidirect
12. C2×SD16×Dic53C2semidirect
13. C2×#16810686C2semidirect
14. C2×#16810619C2semidirect
15. C2×#102×D53C2semidirect
16. C2×C53×#452C2semidirect
19. C23×#88322C22semidirect
22. #16811307C22semidirect
26. C2×#13133208C22semidirect
36. C2×Q8×Dic53C22semidirect
39. C2×#13133176C22semidirect
43. #16810979C22semidirect
44. #16810952C22semidirect
45. #16810948C22semidirect
46. #16810921C22semidirect
47. #16810861C22semidirect
48. #16810854C22semidirect
49. #16810847C22semidirect
50. #16810772C22semidirect
51. SD16×Dic53C22semidirect
52. #16810686C22semidirect
53. C2×#13133151C22semidirect
54. C2×#13133149C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133146C22semidirect
57. #16810619C22semidirect
58. C2×#13133141C22semidirect
59. C2×#13133141C22semidirect
60. C2×#13133141C22semidirect
66. #102×D53C22semidirect
68. C2×C8×Dic53C22semidirect
70. C22×Q16×C53C22semidirect
72. C2×C22⋊Q8×C53C22semidirect
73. C53×#452C22semidirect
74. C2×#103×C53C22semidirect
76. C2×C22⋊C8×C53C22semidirect
94. C22×#88322C23semidirect
99. #13133208C23semidirect
114. Q8×Dic53C23semidirect
120. #13133176C23semidirect
147. #13133151C23semidirect
148. #13133149C23semidirect
149. #13133148C23semidirect
150. #13133146C23semidirect
151. #13133141C23semidirect
152. #13133141C23semidirect
153. #13133141C23semidirect
160. C8×Dic53C23semidirect
172. C2×Q16×C53C23semidirect
178. C22⋊Q8×C53C23semidirect
182. #103×C53C23semidirect
184. C22⋊C8×C53C23semidirect
410. C2×#452D53semidirect
418. C2×C53#3296semidirect
426. C22×Q16C2×D53semidirect
443. C2×C22⋊Q8C2×D53semidirect
461. #452C2×D53semidirect
473. C2×#103C2×D53semidirect
482. C2×C22⋊C8C2×D53semidirect
484. C53C2×#3296semidirect
508. C2×Q16C22×D53semidirect
534. C22⋊Q8C22×D53semidirect
583. #103C22×D53semidirect
591. C22⋊C8C22×D53semidirect
811. C2#20286543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113072
C2×#168112612
#202865432
C2×#168109792
C2×#168109482
C2×#168109522
C2×#168109212
C2×#168108612
C2×#168108542
C2×#168108472
C2×#168107722
C2×SD16×Dic532
C2×#168106862
C2×#168106192
C2×#102×D532
C2×C53×#4522
C2×#329653