Finite Group Databasebeta

← C2×#20284344 #28251249

Subgroups — C2×#20284344 #28251249

Order 13568.

2898 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C22×M16×D53C211yesmaximal, characteristic, complemented
3C2×#16811136C211yesmaximal, characteristic
4C2×C22⋊Q8×D53C211yesmaximal, characteristic, complemented
5#20284344C2116yesmaximal, direct product factor
6C2×#16810879C211yesmaximal, characteristic, complemented
7C2×#16810871C211yesmaximal, characteristic, complemented
8C2×#16810869C211yesmaximal, characteristic, complemented
9C2×#16810863C211yesmaximal, characteristic, complemented
10C2×#16810861C211yesmaximal, characteristic, complemented
11C2×#16810855C211yesmaximal, characteristic, complemented
12C2×#16810853C211yesmaximal, characteristic, complemented
13C2×#16810662C211yesmaximal, characteristic, complemented
14C2×#16810623C211yesmaximal, characteristic, complemented
15C2×#16810630C211yesmaximal, characteristic, complemented
16C2×C53×#470C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×#13133249—28no—
21C2×#13133249C2218yescomplemented
22C22×#11719925C2211yescharacteristic, complemented
23C22×#11719913C2211yescharacteristic, complemented
24C22×#11719924C2211yescharacteristic, complemented
25C22×#11719917C2211yescharacteristic
26C22×#11719912C2211yescharacteristic
27C22×#11719912C2211yescharacteristic
28C2×M16×D53—28no—
29C2×M16×D53C2218yescomplemented
30C22×C8×D53C2211yescharacteristic
31C22×C8×D53C2211yescharacteristic
32#16811136—24no—
33#16811136C2218yes—
34C2×#13133202—21no—
35C2×#13133197C2211yescharacteristic
36C2×#13133196C2211yescharacteristic
37C2×#13133195—21no—
38C2×#13133194—21no—
39C2×#13133193C2211yescharacteristic
40C2×#13133193C2211yescharacteristic
41C22⋊Q8×D53—24no—
42C22⋊Q8×D53C2218yescomplemented
43C2×#13133192C2211yescharacteristic
44C2×#13133191C2211yescharacteristic
45C2×#13133187—21no—
46C2×#13133179—21no—
47C2×#13133177—21no—
48C2×#13133175C2211yescharacteristic
49C2×C4⋊C4×D53—21no—
50C2×C4⋊C4×D53C2211yescharacteristic
51C2×C22⋊C4×D53—21no—
52#16810879C2218yescomplemented
53#16810871C2218yescomplemented
54#16810869C2218yescomplemented
55#16810863C2218yescomplemented
56#16810861C2218yescomplemented
57#16810855C2218yescomplemented
58#16810853C2218yescomplemented
59#16810662C2218yescomplemented
60C2×#13133151C2211yescharacteristic, complemented
61C2×#13133150C2211yescharacteristic, complemented
62C2×#13133148C2211yescharacteristic, complemented
63#16810630C2218yescomplemented
64#16810623C2218yescomplemented
65C2×#13133142C2211yescharacteristic, complemented
66C2×#13133141C2211yescharacteristic, complemented
67C2×#13133141C2211yescharacteristic, complemented
68C2×#13133140C2211yescharacteristic, complemented
69C2×#13133139C2211yescharacteristic, complemented
70C2×#13133137C2211yescharacteristic, complemented
71C22×Q16×C53C2211yescharacteristic, complemented
72C22×M16×C53C2211yescharacteristic
73C2×C22⋊Q8×C53C2211yescharacteristic
74C2×C22⋊Q8×C53C2211yescharacteristic
75C53×#470C2218yescomplemented
76C2×#106×C53C2211yescharacteristic, complemented
77C2×#103×C53C2211yescharacteristic, complemented
78C2×#103×C53C2211yescharacteristic, complemented
79C24×D53D411yescharacteristic
80C2×#11719949—22no—
81C2×#11719949—24no—
82C2×#11719949—24no—
83C2×#11719949C2314yes—
84C22×Dic106—21no—
85C22×Dic106C2311yescharacteristic
86C2×Q8×D53—22no—
87C2×Q8×D53—24no—
88C2×Q8×D53—24no—
89C2×Q8×D53C2314yes—
90C22×D212—21no—
91C22×D212—21no—
92C22×D212C2311yescharacteristic
93C22×C22⋊D53—21no—
94C23×Dic53D411yescharacteristic
95C22×C4×D53—24no—
96C22×C4×D53—24no—
97C22×C4×D53—21no—
98C22×C4×D53—21no—
99C22×C4×D53—21no—
100C22×C4×D53D411yescharacteristic
101C22×C4×D53D411yescharacteristic
102C22×C4×D53D414yes—
103C22×C4×D53C2311yescharacteristic
104C22×C4×D53C2314yes—
105C22×C4×D53C2311yescharacteristic
106#13133249—232no—
107C2×#11719925—24no—
108C2×#11719925C2314yescomplemented
109C2×#11719913—24no—
110C2×#11719913C2314yescomplemented
111C2×#11719924—24no—
112C2×#11719924C2314yescomplemented
113C2×#11719917—24no—
114C2×#11719917C2314yes—
115C2×#11719912—24no—
116C2×#11719912D418yescomplemented
117C2×#11719912C2314yes—
118C2×#11719912C2314yes—
119M16×D53—232no—
120C22×#88322C2311yescharacteristic
121C22×#88322C2311yescharacteristic
122C2×C8×D53—24no—
123C2×C8×D53—24no—
124C2×C8×D53C2314yes—
125C2×C8×D53C2314yes—
126#13133202—28no—
127#13133197—22no—
128#13133197C2314yes—
129#13133196—22no—
130#13133196C2314yes—
131#13133195—28no—
132#13133194—28no—
133#13133193—22no—
134#13133193—22no—
135#13133193C2314yes—
136#13133193C2314yes—
137#13133192—22no—
138#13133192C2314yes—
139#13133191—22no—
140#13133191C2314yes—
141#13133187—28no—
142#13133179—28no—
143#13133177—28no—
144#13133175—22no—
145#13133175C2314yes—
146C2×C4⋊Dic53—21no—
147C2×C4⋊Dic53C2311yescharacteristic
148C2×C4⋊Dic53C2311yescharacteristic
149C2×#11719919—21no—
150C2×#11719919—21no—
151C2×#11719919—21no—
152C2×#11719919—21no—
153C4⋊C4×D53—28no—
154C4⋊C4×D53—22no—
155C4⋊C4×D53C2314yes—
156C2×C22⋊Dic53—21no—
157C2×#11719921—21no—
158C2×#11719921—21no—
159C2×#11719921—21no—
160C2×#11719921—21no—
161C2×#11719921—21no—
162C2×#11719921—21no—
163C22⋊C4×D53—28no—
164C2×C4×Dic53—21no—
165#13133151C2314yescomplemented
166#13133150C2314yescomplemented
167#13133148C2314yescomplemented
168#13133142C2314yescomplemented
169#13133141C2314yescomplemented
170#13133141C2314yescomplemented
171#13133140C2314yescomplemented
172#13133139C2314yescomplemented
173#13133137C2314yescomplemented
174C22×Q8×C53C2311yescharacteristic
175C22×Q8×C53C2311yescharacteristic
176C23×C4×C53C2311yescharacteristic
177C2×Q16×C53—24no—
178C2×Q16×C53C2314yescomplemented
179C2×M16×C53—24no—
180C2×M16×C53C2314yes—
181C22×C8×C53C2311yescharacteristic
182C22×C8×C53C2311yescharacteristic
183C22⋊Q8×C53—22no—
184C22⋊Q8×C53—22no—
185C22⋊Q8×C53C2314yes—
186C22⋊Q8×C53C2314yes—
187C2×C4⋊C4×C53—21no—
188C2×C4⋊C4×C53—21no—
189C2×C4⋊C4×C53C2311yescharacteristic
190C2×C4⋊C4×C53C2311yescharacteristic
191C2×C22⋊C4×C53—21no—
192C2×C22⋊C4×C53—21no—
193#106×C53C2314yescomplemented
194#103×C53C2314yescomplemented
195#103×C53C2314yescomplemented
196C24×C53C2×D411yescharacteristic
197C23×D53—24no—
198C23×D53—24no—
199C23×D53—21no—
200C23×D53—42no—
201C23×D53C2×D414yes—
202C23×D53C2×D411yescharacteristic
203C23×D53C2×D411yescharacteristic
204C2×Q8×C53—21no—
205C2×Q8×C53—21no—
206C2×Q8×C53—22no—
207C2×Q8×C53—22no—
208C2×Q8×C53—22no—
209C2×Q8×C53—22no—
210C2×Q8×C53C2412yes—
211C2×Q8×C53C2412yes—
212C22×C4×C53—22no—
213C22×C4×C53—22no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D412yes—
220C22×C4×C53C2412yes—
221C22×C4×C53C2411yescharacteristic
222C2×C22⋊D53—24no—
223C2×C22⋊D53—44no—
224C22×Dic53—24no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D414yes—
230C22×Dic53C2×D411yescharacteristic
231#11719949—28no—
232#11719949—28no—
233#11719949—48no—
234Q8×D53—28no—
235Q8×D53—28no—
236Q8×D53—48no—
237C2×D212—22no—
238C2×D212—22no—
239C2×D212—24no—
240C2×D212—24no—
241C2×D212—21no—
242C2×D212—44no—
243C2×D212—44no—
244C2×D212C2412yes—
245C2×C4×D53—24no—
246C2×C4×D53—22no—
247C2×C4×D53—22no—
248C2×C4×D53—24no—
249C2×C4×D53—216no—
250C2×C4×D53—28no—
251C2×C4×D53—28no—
252C2×C4×D53—24no—
253C2×C4×D53—24no—
254C2×C4×D53—24no—
255C2×C4×D53—44no—
256C2×C4×D53—44no—
257C2×C4×D53—44no—
258C2×C4×D53C2×D414yes—
259C2×C4×D53C2×D414yes—
260C2×C4×D53C2×D412yes—
261C2×C4×D53C2×D412yes—
262C2×C4×D53C2×D414yes—
263C2×C4×D53#4114yes—
264C2×C4×D53C2412yes—
265C2×C4×D53C2412yes—
266C2×Dic106—22no—
267C2×Dic106—22no—
268C2×Dic106—21no—
269C2×Dic106—24no—
270C2×Dic106—44no—
271C2×Dic106C2412yes—
272Q16×C53—28no—
273M16×C53—28no—
274C2×C8×C53—22no—
275C2×C8×C53C2×D414yes—
276C2×C8×C53C2412yes—
277C2×C8×C53C2412yes—
278C4⋊C4×C53—24no—
279C4⋊C4×C53—24no—
280C4⋊C4×C53—21no—
281C4⋊C4×C53—21no—
282C4⋊C4×C53C2412yes—
283C4⋊C4×C53C2412yes—
284C22⋊C4×C53—24no—
285C22⋊C4×C53—24no—
286C22⋊Dic53—24no—
287#11719925—28no—
288#11719924—28no—
289#11719921—24no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293#11719921—24no—
294#11719921—24no—
295C4⋊Dic53—21no—
296C4⋊Dic53—21no—
297C4⋊Dic53—24no—
298C4⋊Dic53C2412yes—
299C4⋊Dic53C2412yes—
300#11719919—24no—
301#11719919—24no—
302#11719919—24no—
303#11719919—24no—
304C4×Dic53—24no—
305#11719917—28no—
306C2×#88322—22no—
307C2×#88322C2×D414yes—
308C2×#88322C2412yes—
309C2×#88322C2412yes—
310#11719913—28no—
311#11719912—28no—
312#11719912C2×D4116yescomplemented
313C8×D53—28no—
314C8×D53—28no—
315C23×C53—22no—
316C23×C53—22no—
317C23×C53—22no—
318C23×C53C22×D412yes—
319C23×C53C22×D411yescharacteristic
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—28no—
325C22×D53—28no—
326C22×D53—22no—
327C22×D53—44no—
328C22×D53—416no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53—42no—
332C22×D53#12114yes—
333C22×D53#13714yescomplemented
334C22×D53C22×D412yes—
335C22×D53C22×D412yes—
336Q8×C53—22no—
337Q8×C53—22no—
338Q8×C53—22no—
339Q8×C53—22no—
340Q8×C53—42no—
341Q8×C53—42no—
342C2×C4×C53—22no—
343C2×C4×C53—24no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—42no—
351C2×C4×C53—42no—
352C2×C4×C53—42no—
353C2×C4×C53—42no—
354C2×C4×C53C22×D412yes—
355C2×C4×C53C22×D411yescharacteristic
356C2×C4×C53C22×D412yes—
357C2×C4×C53C2×#4112yes—
358C2×C4×C53C2511yescharacteristic
359C22⋊D53—48no—
360C2×Dic53—22no—
361C2×Dic53—28no—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—42no—
366C2×Dic53—42no—
367C2×Dic53—42no—
368C2×Dic53#12114yes—
369C2×Dic53C22×D412yes—
370C2×Dic53C22×D412yes—
371D212—22no—
372D212—22no—
373D212—48no—
374D212—48no—
375D212—42no—
376C4×D53—28no—
377C4×D53—24no—
378C4×D53—22no—
379C4×D53—22no—
380C4×D53—28no—
381C4×D53—48no—
382C4×D53—48no—
383C4×D53—48no—
384C4×D53#12118yes—
385C4×D53C22×D414yes—
386C4×D53C2×#4114yes—
387Dic106—22no—
388Dic106—22no—
389Dic106—42no—
390Dic106—48no—
391C8×C53—22no—
392C8×C53C22×D414yes—
393#88322—22no—
394#88322C22×D414yes—
395C2×#3056—531nomaximal, Sylow
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—44no—
400C22×C53C2×#12112yes—
401C22×C53C2×#13712yes—
402C22×C53#57512yes—
403C22×C53C23×D411yescharacteristic
404C2×D53—22no—
405C2×D53—28no—
406C2×D53—28no—
407C2×D53—22no—
408C2×D53—22no—
409C2×D53—22no—
410C2×D53—416no—
411C2×D53—42no—
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—84no—
415C2×D53C2×#12114yes—
416C2×D53C2×#13714yescomplemented
417C4×C53—22no—
418C4×C53—42no—
419C4×C53—42no—
420C4×C53—42no—
421C4×C53—42no—
422C4×C53C2×#12112yes—
423C4×C53C23×D411yescharacteristic
424C4×C53C22×#4111yescharacteristic
425Dic53—22no—
426Dic53—42no—
427Dic53—42no—
428Dic53—42no—
429Dic53C2×#12114yes—
430C22×#137—531no—
431C23×M16—531no—
432C2×#525—531no—
433C22×C22⋊Q8—531no—
434#3056—5316no—
435C2×#470—531no—
436C2×#470D5311yescharacteristic, complemented
437C2×#468—531no—
438C2×#468—531no—
439C2×#467—531no—
440C2×#467—531no—
441C2×#465—531no—
442C2×#465—531no—
443C2×#428—531no—
444C2×#417—531no—
445C2×#419—531no—
446C2×C53—42no—
447C2×C53#305614yescomplemented
448C2×C53C22×#12111yescharacteristic
449C2×C53C22×#13711yescharacteristic
450C2×C53C2×#57511yescharacteristic
451D53—24no—
452D53—24no—
453D53—82no—
454C22×#41—531no—
455C23×Q8—531no—
456C24×C4—531no—
457C2×#137—538no—
458C2×#137—1068no—
459C22×Q16—531no—
460C22×Q16C2×D5311yescharacteristic, complemented
461C22×SD16—531no—
462C22×SD16—531no—
463C22×M16—531no—
464C22×M16—538no—
465C22×M16—531no—
466C22×M16—531no—
467C22×M16—1068no—
468C22×M16C2×D5311yescharacteristic
469C23×C8—531no—
470C23×C8—531no—
471#525—538no—
472#525—1064no—
473C2×#123—1061no—
474C2×C22⋊Q8—531no—
475C2×C22⋊Q8—531no—
476C2×C22⋊Q8—531no—
477C2×C22⋊Q8—538no—
478C2×C22⋊Q8—531no—
479C2×C22⋊Q8—1061no—
480C2×C22⋊Q8—1061no—
481C2×C22⋊Q8—1064no—
482C2×C22⋊Q8C2×D5311yescharacteristic
483C2×C22⋊Q8C2×D5311yescharacteristic
484C2×#121—531no—
485C2×#121—531no—
486C2×#120—1061no—
487C2×C4×D4—1061no—
488C2×C4×D4—1061no—
489C2×#117—531no—
490C22×C4⋊C4—531no—
491C22×C4⋊C4—1061no—
492C22×C22⋊C4—1061no—
493#470—538no—
494#470C2×D5318yescomplemented
495#468—538no—
496#468—538no—
497#467—538no—
498#467—538no—
499#465—538no—
500#465—538no—
501#428—538no—
502C2×#107—531no—
503C2×#107—531no—
504C2×#106—531no—
505C2×#106C2×D5311yescharacteristic, complemented
506#419—538no—
507#417—538no—
508C2×#103—531no—
509C2×#103—531no—
510C2×#103—531no—
511C2×#103—531no—
512C2×#103C2×D5311yescharacteristic, complemented
513C2×#103C2×D5311yescharacteristic, complemented
514C2×#102—531no—
515C2×#102—531no—
516C53C2×#305611yescharacteristic, complemented, Sylow
517C25—531no—
518C2×#41—534no—
519C2×#41—1062no—
520C2×#41—1064no—
521C2×#41—1064no—
522C22×Q8—534no—
523C22×Q8—531no—
524C22×Q8—1061no—
525C22×Q8—1062no—
526C22×Q8—1064no—
527C22×Q8—1064no—
528C22×Q8C22×D5311yescharacteristic
529C22×Q8C22×D5311yescharacteristic
530C22×D4—531no—
531C22×D4—1061no—
532C22×D4—1061no—
533C22×D4—1061no—
534C23×C4—531no—
535C23×C4—531no—
536C23×C4—531no—
537C23×C4—531no—
538C23×C4—534no—
539C23×C4—531no—
540C23×C4—534no—
541C23×C4—1064no—
542C23×C4—1064no—
543C23×C4—1061no—
544C23×C4—1061no—
545C23×C4—1061no—
546C23×C4C22×D5311yescharacteristic
547#137—10632no—
548C2×Q16—24no—
549C2×Q16—534no—
550C2×Q16—1064no—
551C2×Q16C22×D5314yescomplemented
552C2×SD16—534no—
553C2×SD16—534no—
554C2×SD16—1064no—
555C2×SD16—1064no—
556C2×M16—24no—
557C2×M16—534no—
558C2×M16—538no—
559C2×M16—534no—
560C2×M16—534no—
561C2×M16—1064no—
562C2×M16—1064no—
563C2×M16—10632no—
564C2×M16C22×D5314yes—
565C22×C8—531no—
566C22×C8—531no—
567C22×C8—534no—
568C22×C8—534no—
569C22×C8—1064no—
570C22×C8—1064no—
571C22×C8C22×D5311yescharacteristic
572C22×C8C22×D5311yescharacteristic
573#123—1068no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—534no—
577C22⋊Q8—534no—
578C22⋊Q8—534no—
579C22⋊Q8—534no—
580C22⋊Q8—1068no—
581C22⋊Q8—1068no—
582C22⋊Q8—1062no—
583C22⋊Q8—1062no—
584C22⋊Q8—1062no—
585C22⋊Q8—1062no—
586C22⋊Q8C22×D5314yes—
587C22⋊Q8C22×D5314yes—
588#121—534no—
589#121—534no—
590#121—1062no—
591#121—1062no—
592#120—1068no—
593C4×D4—1068no—
594C4×D4—1068no—
595#117—534no—
596#117—1062no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—531no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—534no—
602C2×C4⋊C4—1062no—
603C2×C4⋊C4—1068no—
604C2×C4⋊C4—1061no—
605C2×C4⋊C4—1061no—
606C2×C4⋊C4—1061no—
607C2×C4⋊C4—1061no—
608C2×C4⋊C4—1061no—
609C2×C4⋊C4C22×D5311yescharacteristic
610C2×C4⋊C4C22×D5311yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—1068no—
614C2×C22⋊C4—1061no—
615C2×C22⋊C4—1061no—
616C2×C22⋊C4—1061no—
617C2×C22⋊C4—1061no—
618C2×C22⋊C4—1061no—
619C2×C22⋊C4—1061no—
620C2×C22⋊C4—1061no—
621C2×C42—1061no—
622#107—534no—
623#107—534no—
624#106—534no—
625#106C22×D5314yescomplemented
626#103—534no—
627#103—534no—
628#103—534no—
629#103—534no—
630#103C22×D5314yescomplemented
631#103C22×D5314yescomplemented
632#102—534no—
633#102—534no—
634C24—531no—
635C24—531no—
636C24—534no—
637C24—1064no—
638C24—1064no—
639C24—1061no—
640C24—2122no—
641C24D4×D5311yescharacteristic
642#41—1068no—
643#41—1068no—
644#41—2128no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—532no—
652C2×Q8—1064no—
653C2×Q8—1068no—
654C2×Q8—1068no—
655C2×Q8—1061no—
656C2×Q8—1062no—
657C2×Q8—1062no—
658C2×Q8—2124no—
659C2×Q8—2128no—
660C2×Q8C23×D5312yes—
661C2×Q8C23×D5312yes—
662C2×D4—532no—
663C2×D4—1064no—
664C2×D4—1064no—
665C2×D4—1064no—
666C2×D4—1062no—
667C2×D4—1061no—
668C2×D4—1062no—
669C2×D4—2124no—
670C2×D4—2124no—
671C2×D4—2124no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—531no—
679C22×C4—532no—
680C22×C4—534no—
681C22×C4—534no—
682C22×C4—532no—
683C22×C4—534no—
684C22×C4—531no—
685C22×C4—534no—
686C22×C4—534no—
687C22×C4—532no—
688C22×C4—532no—
689C22×C4—1068no—
690C22×C4—1064no—
691C22×C4—10616no—
692C22×C4—1068no—
693C22×C4—1064no—
694C22×C4—1064no—
695C22×C4—1064no—
696C22×C4—1064no—
697C22×C4—1064no—
698C22×C4—1062no—
699C22×C4—1062no—
700C22×C4—1061no—
701C22×C4—1061no—
702C22×C4—1061no—
703C22×C4—2124no—
704C22×C4—2124no—
705C22×C4—2124no—
706C22×C4D4×D5312yes—
707C22×C4D4×D5311yescharacteristic
708C22×C4C23×D5312yes—
709C22×C4C23×D5311yescharacteristic
710Q16—28no—
711Q16—1068no—
712SD16—1068no—
713SD16—1068no—
714M16—28no—
715M16—5316no—
716M16—1068no—
717M16—1068no—
718C2×C8—22no—
719C2×C8—534no—
720C2×C8—532no—
721C2×C8—532no—
722C2×C8—1068no—
723C2×C8—1062no—
724C2×C8—1068no—
725C2×C8D4×D5314yes—
726C2×C8C23×D5312yes—
727C2×C8C23×D5312yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—532no—
733C4⋊C4—532no—
734C4⋊C4—1064no—
735C4⋊C4—1064no—
736C4⋊C4—1064no—
737C4⋊C4—1064no—
738C4⋊C4—1061no—
739C4⋊C4—1061no—
740C4⋊C4—1064no—
741C4⋊C4C23×D5312yes—
742C4⋊C4C23×D5312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—1064no—
746C22⋊C4—1064no—
747C22⋊C4—1064no—
748C22⋊C4—1064no—
749C22⋊C4—1064no—
750C22⋊C4—1064no—
751C22⋊C4—1064no—
752C42—1064no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—534no—
757C23—534no—
758C23—532no—
759C23—532no—
760C23—1068no—
761C23—1068no—
762C23—1062no—
763C23—1062no—
764C23—1062no—
765C23—1062no—
766C23—1062no—
767C23—2124no—
768C23—21216no—
769C23—2122no—
770C23—2122no—
771C23—2122no—
772C23C2×D4×D5312yes—
773C23C2×D4×D5311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—42no—
779Q8—42no—
780Q8—1062no—
781Q8—1062no—
782Q8—2128no—
783Q8—2122no—
784D4—1062no—
785D4—1062no—
786D4—2128no—
787D4—2128no—
788D4—2128no—
789D4—2122no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—534no—
803C2×C4—532no—
804C2×C4—538no—
805C2×C4—534no—
806C2×C4—534no—
807C2×C4—532no—
808C2×C4—1068no—
809C2×C4—1068no—
810C2×C4—1068no—
811C2×C4—1062no—
812C2×C4—1064no—
813C2×C4—1062no—
814C2×C4—1062no—
815C2×C4—1062no—
816C2×C4—1062no—
817C2×C4—1062no—
818C2×C4—2128no—
819C2×C4—2128no—
820C2×C4—2128no—
821C2×C4—2122no—
822C2×C4—2122no—
823C2×C4—2122no—
824C2×C4C2×D4×D5312yes—
825C2×C4C2×D4×D5311yescharacteristic
826C2×C4C2×D4×D5312yes—
827C2×C4#41×D5312yes—
828C2×C4C24×D5311yescharacteristic
829C8—22no—
830C8—534no—
831C8—1062no—
832C8C2×D4×D5314yes—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—534no—
838C22—534no—
839C22—1062no—
840C22—1062no—
841C22—1062no—
842C22—1068no—
843C22—1068no—
844C22—1062no—
845C22—4244no—
846C22—21216no—
847C22—2122no—
848C22—2122no—
849C22—2122no—
850C22#121×D5312yes—
851C22#137×D5312yes—
852C22#1681142212yes—
853C22C22×D4×D5311yescharacteristic
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—534no—
860C4—1062no—
861C4—2122no—
862C4—2122no—
863C4—2122no—
864C4#121×D5312yes—
865C4C22×D4×D5311yescharacteristic
866C4C2×#41×D5311yescharacteristic
867C2—42no—
868C2—1064no—
869C2—1064no—
870C2—4242no—
871C2#2028434414yesdirect product factor
872C2C2×#121×D5311yescharacteristic
873C2C2×#137×D5311yescharacteristic
874C2C2×#1681142211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#470C2
socleC23×C53C22×D4
prime radicalC2×#16811136C2
hypercenterC2×#470D53
hypocenterC53C2×#3056
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C22×#13133249C2semidirect
2. C22×M16×D53C2semidirect
4. C2×C22⋊Q8×D53C2semidirect
5. #20284344C2direct (N × H)
6. C2×#16810879C2semidirect
7. C2×#16810871C2semidirect
8. C2×#16810869C2semidirect
9. C2×#16810863C2semidirect
10. C2×#16810861C2semidirect
11. C2×#16810855C2semidirect
12. C2×#16810853C2semidirect
13. C2×#16810662C2semidirect
14. C2×#16810623C2semidirect
15. C2×#16810630C2semidirect
16. C2×C53×#470C2semidirect
21. C2×#13133249C22semidirect
22. C22×#11719925C22semidirect
23. C22×#11719913C22semidirect
24. C22×#11719924C22semidirect
29. C2×M16×D53C22semidirect
42. C22⋊Q8×D53C22semidirect
52. #16810879C22semidirect
53. #16810871C22semidirect
54. #16810869C22semidirect
55. #16810863C22semidirect
56. #16810861C22semidirect
57. #16810855C22semidirect
58. #16810853C22semidirect
59. #16810662C22semidirect
60. C2×#13133151C22semidirect
61. C2×#13133150C22semidirect
62. C2×#13133148C22semidirect
63. #16810630C22semidirect
64. #16810623C22semidirect
65. C2×#13133142C22semidirect
66. C2×#13133141C22semidirect
67. C2×#13133141C22semidirect
68. C2×#13133140C22semidirect
69. C2×#13133139C22semidirect
70. C2×#13133137C22semidirect
71. C22×Q16×C53C22semidirect
75. C53×#470C22semidirect
76. C2×#106×C53C22semidirect
77. C2×#103×C53C22semidirect
78. C2×#103×C53C22semidirect
108. C2×#11719925C23semidirect
110. C2×#11719913C23semidirect
112. C2×#11719924C23semidirect
116. C2×#11719912D4semidirect
165. #13133151C23semidirect
166. #13133150C23semidirect
167. #13133148C23semidirect
168. #13133142C23semidirect
169. #13133141C23semidirect
170. #13133141C23semidirect
171. #13133140C23semidirect
172. #13133139C23semidirect
173. #13133137C23semidirect
178. C2×Q16×C53C23semidirect
193. #106×C53C23semidirect
194. #103×C53C23semidirect
195. #103×C53C23semidirect
312. #11719912C2×D4semidirect
333. C22×D53#137semidirect
416. C2×D53C2×#137semidirect
436. C2×#470D53semidirect
447. C2×C53#3056semidirect
460. C22×Q16C2×D53semidirect
494. #470C2×D53semidirect
505. C2×#106C2×D53semidirect
512. C2×#103C2×D53semidirect
513. C2×#103C2×D53semidirect
516. C53C2×#3056semidirect
551. C2×Q16C22×D53semidirect
625. #106C22×D53semidirect
630. #103C22×D53semidirect
631. #103C22×D53semidirect
871. C2#20284344direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332492
C22×M16×D532
C2×#168111362
C2×C22⋊Q8×D532
#202843442
C2×#168108792
C2×#168108712
C2×#168108692
C2×#168108632
C2×#168108612
C2×#168108552
C2×#168108532
C2×#168106622
C2×#168106232
C2×#168106302
C2×C53×#4702
C2×#305653