Finite Group Databasebeta

← C2×#20284405 #28251338

Subgroups — C2×#20284405 #28251338

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C22×#13133223C211yesmaximal, characteristic, complemented
3C2×#16811203C211yesmaximal, characteristic
4C2×#16811196C211yesmaximal, characteristic, complemented
5#20284405C2116yesmaximal, direct product factor
6C2×#16810879C211yesmaximal, characteristic, complemented
7C2×#16810878C211yesmaximal, characteristic, complemented
8C2×#16810871C211yesmaximal, characteristic, complemented
9C2×#16810870C211yesmaximal, characteristic, complemented
10C2×#16810863C211yesmaximal, characteristic, complemented
11C2×#16810855C211yesmaximal, characteristic, complemented
12C2×#16810852C211yesmaximal, characteristic, complemented
13C2×#16810664C211yesmaximal, characteristic, complemented
14C2×#16810618C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#467C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20C2×#13133249—28no—
21C2×#13133249C2218yescomplemented
22C22×#11719925C2211yescharacteristic
23C22×#11719913C2211yescharacteristic
24C22×#11719924C2211yescharacteristic
25C2×#13133223—28no—
26C2×#13133223C2218yescomplemented
27C22×#11719917C2211yescharacteristic
28C22×#11719912C2211yescharacteristic
29C22×#11719912C2211yescharacteristic
30C22×C8×D53C2211yescharacteristic
31C22×C8×D53C2211yescharacteristic
32#16811203—24no—
33#16811203C2218yes—
34#16811196—24no—
35#16811196C2218yescomplemented
36C2×#13133216—21no—
37C2×#13133203—21no—
38C2×#13133202—21no—
39C2×#13133199—21no—
40C2×#13133197C2211yescharacteristic
41C2×#13133196C2211yescharacteristic
42C2×#13133195—21no—
43C2×#13133193C2211yescharacteristic
44C2×#13133193C2211yescharacteristic
45C2×#13133192—21no—
46C2×#13133192C2211yescharacteristic
47C2×#13133191C2211yescharacteristic
48C2×#13133190—21no—
49C2×#13133190—21no—
50C2×#13133175C2211yescharacteristic
51C2×C4⋊C4×D53C2211yescharacteristic
52#16810879C2218yescomplemented
53#16810878C2218yescomplemented
54#16810871C2218yescomplemented
55#16810870C2218yescomplemented
56#16810863C2218yescomplemented
57#16810855C2218yescomplemented
58#16810852C2218yescomplemented
59#16810664C2218yescomplemented
60C2×#13133150C2211yescharacteristic
61C2×#13133149C2211yescharacteristic
62C2×#13133148C2211yescharacteristic
63#16810618C2218yescomplemented
64C2×#13133142C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×#13133141C2211yescharacteristic
67C2×#13133140C2211yescharacteristic
68#103×D53C2218yescomplemented
69C2×#13133139C2211yescharacteristic
70C2×#13133137C2211yescharacteristic
71C22×Q16×C53C2211yescharacteristic
72C23×C8×C53C2211yescharacteristic
73C2×C22⋊Q8×C53C2211yescharacteristic
74C2×C22⋊Q8×C53C2211yescharacteristic
75C53×#467C2218yescomplemented
76C2×#107×C53C2211yescharacteristic
77C2×#103×C53C2211yescharacteristic
78C2×#103×C53C2211yescharacteristic
79C2×#11719949—22no—
80C2×#11719949—24no—
81C2×#11719949—24no—
82C2×#11719949C2314yes—
83C2×#11719945—24no—
84C2×#11719945—24no—
85C2×#11719945D414yes—
86C2×#11719945C2314yes—
87C22×Dic106—21no—
88C22×Dic106D411yescharacteristic
89C22×Dic106C2311yescharacteristic
90C2×Q8×D53—22no—
91C2×Q8×D53—24no—
92C2×Q8×D53—24no—
93C2×Q8×D53C2314yes—
94C22×D212—21no—
95C22×D212—21no—
96C22×D212D411yescharacteristic
97C22×D212C2311yescharacteristic
98C22×C22⋊D53—21no—
99C22×C22⋊D53D411yescharacteristic
100C22×C22⋊D53D411yescharacteristic
101C22×C4×D53—21no—
102C22×C4×D53—21no—
103C22×C4×D53—21no—
104C22×C4×D53C2311yescharacteristic
105C22×C4×D53C2311yescharacteristic
106#13133249—232no—
107C2×#11719925—24no—
108C2×#11719925C2314yes—
109C2×#11719913—24no—
110C2×#11719913C2314yes—
111C2×#11719924—24no—
112C2×#11719924C2314yes—
113#13133223—232no—
114C2×#11719917—24no—
115C2×#11719917C2314yes—
116C2×#11719912—24no—
117C2×#11719912D418yescomplemented
118C2×#11719912C2314yes—
119C2×#11719912C2314yes—
120C22×#88322C2311yescharacteristic
121C22×#88322C2311yescharacteristic
122C2×C8×D53—24no—
123C2×C8×D53—24no—
124C2×C8×D53C2314yes—
125C2×C8×D53C2314yes—
126#13133216—28no—
127#13133203—28no—
128#13133202—28no—
129#13133199—28no—
130#13133197—22no—
131#13133197C2314yes—
132#13133196—22no—
133#13133196C2314yes—
134#13133195—28no—
135#13133193—22no—
136#13133193—22no—
137#13133193C2314yes—
138#13133193C2314yes—
139#13133192—28no—
140#13133192—22no—
141#13133192C2314yes—
142#13133191—22no—
143#13133191C2314yes—
144#13133190—28no—
145#13133190—28no—
146#13133175—22no—
147#13133175C2314yes—
148C2×C4⋊Dic53—21no—
149C2×C4⋊Dic53C2311yescharacteristic
150C2×C4⋊Dic53C2311yescharacteristic
151C2×#11719919—21no—
152C2×#11719919—21no—
153C2×#11719919—21no—
154C2×#11719919—21no—
155C4⋊C4×D53—22no—
156C4⋊C4×D53C2314yes—
157C2×C22⋊Dic53—21no—
158C2×#11719921—21no—
159C2×#11719921—21no—
160C2×#11719921—21no—
161C2×#11719921—21no—
162C2×#11719921—21no—
163C2×#11719921—21no—
164C2×C4×Dic53—21no—
165#13133150C2314yes—
166#13133149C2314yes—
167#13133148C2314yes—
168#13133142C2314yes—
169#13133141C2314yes—
170#13133141C2314yes—
171#13133140C2314yes—
172#13133139C2314yes—
173#13133137C2314yes—
174C22×Q8×C53C2311yescharacteristic
175C22×Q8×C53C2311yescharacteristic
176C23×C4×C53C2311yescharacteristic
177C2×Q16×C53—24no—
178C2×Q16×C53C2314yes—
179C22×C8×C53—24no—
180C22×C8×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#107×C53C2314yes—
194#103×C53C2314yes—
195#103×C53C2314yes—
196C24×C53C2×D411yescharacteristic
197C23×D53—21no—
198C23×D53C2×D411yescharacteristic
199C23×D53C2×D411yescharacteristic
200C2×Q8×C53—21no—
201C2×Q8×C53—21no—
202C2×Q8×C53—22no—
203C2×Q8×C53—22no—
204C2×Q8×C53—22no—
205C2×Q8×C53—22no—
206C2×Q8×C53C2412yes—
207C2×Q8×C53C2412yes—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2412yes—
217C22×C4×C53C2411yescharacteristic
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—82no—
222C2×C22⋊D53C2×D414yes—
223C2×C22⋊D53C2×D414yes—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53C2×D411yescharacteristic
228C22×Dic53C2×D411yescharacteristic
229#11719949—28no—
230#11719949—28no—
231#11719949—48no—
232Q8×D53—28no—
233Q8×D53—28no—
234Q8×D53—48no—
235#11719945—216no—
236#11719945—28no—
237#11719945—28no—
238C2×D212—24no—
239C2×D212—22no—
240C2×D212—22no—
241C2×D212—24no—
242C2×D212—21no—
243C2×D212—24no—
244C2×D212—44no—
245C2×D212—82no—
246C2×D212C2×D414yes—
247C2×D212C2412yes—
248C2×C4×D53—22no—
249C2×C4×D53—22no—
250C2×C4×D53—24no—
251C2×C4×D53—24no—
252C2×C4×D53—24no—
253C2×C4×D53—44no—
254C2×C4×D53—44no—
255C2×C4×D53—82no—
256C2×C4×D53C2×D412yes—
257C2×C4×D53C2×D412yes—
258C2×C4×D53C2×D414yes—
259C2×C4×D53#4114yes—
260C2×C4×D53C2412yes—
261C2×C4×D53C2412yes—
262C2×Dic106—24no—
263C2×Dic106—22no—
264C2×Dic106—22no—
265C2×Dic106—21no—
266C2×Dic106—24no—
267C2×Dic106—44no—
268C2×Dic106C2×D414yes—
269C2×Dic106C2412yes—
270Q16×C53—28no—
271C2×C8×C53—22no—
272C2×C8×C53—28no—
273C2×C8×C53C2×D414yes—
274C2×C8×C53C2412yes—
275C2×C8×C53C2412yes—
276C4⋊C4×C53—24no—
277C4⋊C4×C53—24no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53C2412yes—
281C4⋊C4×C53C2412yes—
282C22⋊C4×C53—24no—
283C22⋊C4×C53—24no—
284C22⋊Dic53—24no—
285#11719925—28no—
286#11719924—28no—
287#11719921—24no—
288#11719921—24no—
289#11719921—24no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293C4⋊Dic53—21no—
294C4⋊Dic53—21no—
295C4⋊Dic53—24no—
296C4⋊Dic53C2412yes—
297C4⋊Dic53C2412yes—
298#11719919—24no—
299#11719919—24no—
300#11719919—24no—
301#11719919—24no—
302C4×Dic53—24no—
303#11719917—28no—
304C2×#88322—22no—
305C2×#88322C2×D414yes—
306C2×#88322C2412yes—
307C2×#88322C2412yes—
308#11719913—28no—
309#11719912—28no—
310#11719912C2×D4116yescomplemented
311C8×D53—28no—
312C8×D53—28no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53C22×D412yes—
317C23×C53C22×D411yescharacteristic
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53#12114yes—
328C22×D53C22×D412yes—
329C22×D53C22×D412yes—
330Q8×C53—22no—
331Q8×C53—22no—
332Q8×C53—22no—
333Q8×C53—22no—
334Q8×C53—42no—
335Q8×C53—42no—
336C2×C4×C53—22no—
337C2×C4×C53—24no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—42no—
345C2×C4×C53—42no—
346C2×C4×C53—42no—
347C2×C4×C53—42no—
348C2×C4×C53C22×D412yes—
349C2×C4×C53C22×D411yescharacteristic
350C2×C4×C53C22×D412yes—
351C2×C4×C53C2×#4112yes—
352C2×C4×C53C2511yescharacteristic
353C22⋊D53—28no—
354C22⋊D53—28no—
355C22⋊D53—84no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—42no—
361C2×Dic53—42no—
362C2×Dic53—42no—
363C2×Dic53#12114yes—
364C2×Dic53C22×D412yes—
365C2×Dic53C22×D412yes—
366D212—28no—
367D212—22no—
368D212—22no—
369D212—48no—
370D212—42no—
371D212—84no—
372C4×D53—24no—
373C4×D53—22no—
374C4×D53—22no—
375C4×D53—48no—
376C4×D53—48no—
377C4×D53—84no—
378C4×D53#12118yes—
379C4×D53C22×D414yes—
380C4×D53C2×#4114yes—
381Dic106—28no—
382Dic106—22no—
383Dic106—22no—
384Dic106—42no—
385Dic106—48no—
386C8×C53—22no—
387C8×C53C22×D414yes—
388#88322—22no—
389#88322C22×D414yes—
390C2×#3063—531nomaximal, Sylow
391C22×C53—22no—
392C22×C53—22no—
393C22×C53—22no—
394C22×C53—44no—
395C22×C53C2×#12112yes—
396C22×C53#57712yes—
397C22×C53#57812yes—
398C22×C53C23×D411yescharacteristic
399C2×D53—28no—
400C2×D53—22no—
401C2×D53—22no—
402C2×D53—22no—
403C2×D53—22no—
404C2×D53—22no—
405C2×D53—44no—
406C2×D53—42no—
407C2×D53—42no—
408C2×D53—42no—
409C2×D53—84no—
410C2×D53C2×#12114yes—
411C4×C53—22no—
412C4×C53—42no—
413C4×C53—42no—
414C4×C53—42no—
415C4×C53—42no—
416C4×C53C2×#12112yes—
417C4×C53C23×D411yescharacteristic
418C4×C53C22×#4111yescharacteristic
419Dic53—22no—
420Dic53—42no—
421Dic53—42no—
422Dic53—42no—
423Dic53C2×#12114yes—
424C22×#137—531no—
425C22×#131—531no—
426C2×#537—531no—
427C2×#536—531no—
428#3063—5316no—
429C2×#470—531no—
430C2×#470—531no—
431C2×#468—531no—
432C2×#468—531no—
433C2×#467—531no—
434C2×#467D5311yescharacteristic, complemented
435C2×#465—531no—
436C2×#465—531no—
437C2×#428—531no—
438C2×#416—531no—
439C22×#103—531no—
440C2×C53—42no—
441C2×C53#306314yescomplemented
442C2×C53C22×#12111yescharacteristic
443C2×C53C2×#57711yescharacteristic
444C2×C53C2×#57811yescharacteristic
445D53—24no—
446D53—42no—
447D53—82no—
448C22×#41—531no—
449C22×#41—531no—
450C23×Q8—531no—
451C2×#137—538no—
452C2×#137—1068no—
453C22×Q16—531no—
454C22×Q16C2×D5311yescharacteristic
455C22×SD16—531no—
456C22×SD16—531no—
457C2×#131—538no—
458C2×#131—1068no—
459C22×M16—531no—
460C22×M16—531no—
461C22×M16—531no—
462C23×C8—531no—
463C23×C8—531no—
464C23×C8C2×D5311yescharacteristic
465#537—538no—
466#537—1064no—
467#536—538no—
468#536—1064no—
469C2×C4⋊Q8—1061no—
470C2×#124—1061no—
471C2×#123—1061no—
472C2×#123—1061no—
473C2×C22⋊Q8—531no—
474C2×C22⋊Q8—531no—
475C2×C22⋊Q8—531no—
476C2×C22⋊Q8—531no—
477C2×C22⋊Q8—1061no—
478C2×C22⋊Q8C2×D5311yescharacteristic
479C2×C22⋊Q8C2×D5311yescharacteristic
480C2×#121—531no—
481C2×#121—531no—
482C2×#121—1061no—
483C2×#121—1061no—
484C2×#121—1061no—
485C2×#117—531no—
486C22×C4⋊C4—531no—
487#470—538no—
488#470—538no—
489#468—538no—
490#468—538no—
491#467—538no—
492#467C2×D5318yescomplemented
493#465—538no—
494#465—538no—
495#428—538no—
496C2×#107—531no—
497C2×#107C2×D5311yescharacteristic
498C2×#106—531no—
499C2×#106—531no—
500#416—538no—
501C2×#103—531no—
502C2×#103—531no—
503C2×#103—531no—
504C2×#103—531no—
505C2×#103—538no—
506C2×#103C2×D5311yescharacteristic
507C2×#103C2×D5311yescharacteristic
508C2×#102—531no—
509C2×#102—531no—
510C53C2×#306311yescharacteristic, complemented, Sylow
511C2×#41—534no—
512C2×#41—534no—
513C2×#41—534no—
514C2×#41—1064no—
515C2×#41—1064no—
516C2×#41—1062no—
517C2×#41—1064no—
518C2×#41—1064no—
519C22×Q8—531no—
520C22×Q8—534no—
521C22×Q8—531no—
522C22×Q8—1061no—
523C22×Q8—1062no—
524C22×Q8—1064no—
525C22×Q8—1064no—
526C22×Q8C22×D5311yescharacteristic
527C22×Q8C22×D5311yescharacteristic
528C22×D4—531no—
529C22×D4—531no—
530C22×D4—531no—
531C22×D4—531no—
532C22×D4—1061no—
533C22×D4—1061no—
534C22×D4—1061no—
535C23×C4—531no—
536C23×C4—531no—
537C23×C4—1061no—
538C23×C4—1061no—
539C23×C4—1061no—
540C23×C4C22×D5311yescharacteristic
541#137—10632no—
542C2×Q16—24no—
543C2×Q16—534no—
544C2×Q16—1064no—
545C2×Q16C22×D5314yes—
546C2×SD16—534no—
547C2×SD16—534no—
548C2×SD16—1064no—
549C2×SD16—1064no—
550#131—10632no—
551C2×M16—534no—
552C2×M16—538no—
553C2×M16—534no—
554C2×M16—534no—
555C2×M16—1064no—
556C2×M16—1064no—
557C22×C8—24no—
558C22×C8—531no—
559C22×C8—531no—
560C22×C8—534no—
561C22×C8—534no—
562C22×C8—1064no—
563C22×C8—1064no—
564C22×C8C22×D5311yescharacteristic
565C22×C8C22×D5314yes—
566C22×C8C22×D5311yescharacteristic
567C4⋊Q8—1068no—
568#124—1068no—
569#123—1068no—
570#123—1068no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—534no—
574C22⋊Q8—534no—
575C22⋊Q8—534no—
576C22⋊Q8—534no—
577C22⋊Q8—1062no—
578C22⋊Q8—1068no—
579C22⋊Q8—1062no—
580C22⋊Q8—1062no—
581C22⋊Q8—1062no—
582C22⋊Q8C22×D5314yes—
583C22⋊Q8C22×D5314yes—
584#121—534no—
585#121—534no—
586#121—1068no—
587#121—1068no—
588#121—1062no—
589#121—1068no—
590#121—1062no—
591#117—534no—
592#117—1062no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—531no—
596C2×C4⋊C4—531no—
597C2×C4⋊C4—534no—
598C2×C4⋊C4—1062no—
599C2×C4⋊C4—1061no—
600C2×C4⋊C4—1061no—
601C2×C4⋊C4—1061no—
602C2×C4⋊C4—1061no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4C22×D5311yescharacteristic
605C2×C4⋊C4C22×D5311yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—1061no—
609C2×C22⋊C4—1061no—
610C2×C22⋊C4—1061no—
611C2×C22⋊C4—1061no—
612C2×C22⋊C4—1061no—
613C2×C22⋊C4—1061no—
614C2×C22⋊C4—1061no—
615C2×C42—1061no—
616#107—534no—
617#107C22×D5314yes—
618#106—534no—
619#106—534no—
620#103—534no—
621#103—534no—
622#103—534no—
623#103—534no—
624#103C22×D5314yes—
625#103C22×D5314yes—
626#102—534no—
627#102—534no—
628C24—531no—
629C24—531no—
630C24—1061no—
631C24D4×D5311yescharacteristic
632#41—1068no—
633#41—10616no—
634#41—1068no—
635#41—1068no—
636#41—1068no—
637#41—2128no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8—22no—
644C2×Q8—534no—
645C2×Q8—532no—
646C2×Q8—1064no—
647C2×Q8—1064no—
648C2×Q8—1068no—
649C2×Q8—1068no—
650C2×Q8—1061no—
651C2×Q8—1062no—
652C2×Q8—1062no—
653C2×Q8—2124no—
654C2×Q8—2128no—
655C2×Q8C23×D5312yes—
656C2×Q8C23×D5312yes—
657C2×D4—534no—
658C2×D4—534no—
659C2×D4—534no—
660C2×D4—532no—
661C2×D4—1064no—
662C2×D4—1064no—
663C2×D4—1064no—
664C2×D4—1064no—
665C2×D4—1064no—
666C2×D4—1064no—
667C2×D4—1062no—
668C2×D4—1061no—
669C2×D4—1062no—
670C2×D4—4242no—
671C2×D4—4242no—
672C2×D4—2124no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—531no—
680C22×C4—532no—
681C22×C4—534no—
682C22×C4—534no—
683C22×C4—532no—
684C22×C4—531no—
685C22×C4—532no—
686C22×C4—532no—
687C22×C4—1064no—
688C22×C4—1064no—
689C22×C4—1064no—
690C22×C4—1062no—
691C22×C4—1062no—
692C22×C4—1061no—
693C22×C4—1061no—
694C22×C4—1061no—
695C22×C4—4242no—
696C22×C4—2124no—
697C22×C4—2124no—
698C22×C4D4×D5312yes—
699C22×C4D4×D5311yescharacteristic
700C22×C4C23×D5312yes—
701C22×C4C23×D5311yescharacteristic
702Q16—28no—
703Q16—1068no—
704SD16—1068no—
705SD16—1068no—
706M16—5316no—
707M16—1068no—
708M16—1068no—
709C2×C8—22no—
710C2×C8—28no—
711C2×C8—534no—
712C2×C8—532no—
713C2×C8—532no—
714C2×C8—1068no—
715C2×C8—1068no—
716C2×C8—1062no—
717C2×C8D4×D5314yes—
718C2×C8C23×D5312yes—
719C2×C8C23×D5312yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—532no—
725C4⋊C4—532no—
726C4⋊C4—1064no—
727C4⋊C4—1064no—
728C4⋊C4—1064no—
729C4⋊C4—1064no—
730C4⋊C4—1061no—
731C4⋊C4—1061no—
732C4⋊C4—1064no—
733C4⋊C4C23×D5312yes—
734C4⋊C4C23×D5312yes—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—1064no—
738C22⋊C4—1064no—
739C22⋊C4—1064no—
740C22⋊C4—1064no—
741C22⋊C4—1064no—
742C22⋊C4—1064no—
743C22⋊C4—1064no—
744C42—1064no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—534no—
749C23—532no—
750C23—532no—
751C23—1062no—
752C23—1062no—
753C23—1062no—
754C23—1062no—
755C23—1062no—
756C23—1062no—
757C23—2122no—
758C23—2122no—
759C23—2122no—
760C23C2×D4×D5312yes—
761C23C2×D4×D5311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—42no—
767Q8—42no—
768Q8—1068no—
769Q8—1062no—
770Q8—1062no—
771Q8—2128no—
772Q8—2122no—
773D4—1068no—
774D4—1068no—
775D4—1068no—
776D4—1062no—
777D4—1062no—
778D4—4244no—
779D4—4244no—
780D4—2128no—
781D4—2122no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—534no—
795C2×C4—532no—
796C2×C4—538no—
797C2×C4—534no—
798C2×C4—534no—
799C2×C4—532no—
800C2×C4—1062no—
801C2×C4—1064no—
802C2×C4—1062no—
803C2×C4—1062no—
804C2×C4—1062no—
805C2×C4—1062no—
806C2×C4—1062no—
807C2×C4—4244no—
808C2×C4—2128no—
809C2×C4—2128no—
810C2×C4—2122no—
811C2×C4—2122no—
812C2×C4—2122no—
813C2×C4C2×D4×D5312yes—
814C2×C4C2×D4×D5311yescharacteristic
815C2×C4C2×D4×D5312yes—
816C2×C4#41×D5312yes—
817C2×C4C24×D5311yescharacteristic
818C8—22no—
819C8—534no—
820C8—1062no—
821C8C2×D4×D5314yes—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—44no—
826C22—534no—
827C22—1062no—
828C22—1062no—
829C22—1068no—
830C22—1062no—
831C22—1062no—
832C22—1062no—
833C22—4244no—
834C22—2122no—
835C22—2122no—
836C22—2122no—
837C22—2124no—
838C22#121×D5312yes—
839C22#1681143012yes—
840C22#1681143612yes—
841C22C22×D4×D5311yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—534no—
848C4—1062no—
849C4—2122no—
850C4—2122no—
851C4—2122no—
852C4#121×D5312yes—
853C4C22×D4×D5311yescharacteristic
854C4C2×#41×D5311yescharacteristic
855C2—42no—
856C2—1064no—
857C2—4242no—
858C2—2122no—
859C2#2028440514yesdirect product factor
860C2C2×#121×D5311yescharacteristic
861C2C2×#1681143011yescharacteristic
862C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#467C2
socleC23×C53C22×D4
prime radicalC2×#16811203C2
hypercenterC2×#467D53
hypocenterC53C2×#3063
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#13133249C2semidirect
2. C22×#13133223C2semidirect
4. C2×#16811196C2semidirect
5. #20284405C2direct (N × H)
6. C2×#16810879C2semidirect
7. C2×#16810878C2semidirect
8. C2×#16810871C2semidirect
9. C2×#16810870C2semidirect
10. C2×#16810863C2semidirect
11. C2×#16810855C2semidirect
12. C2×#16810852C2semidirect
13. C2×#16810664C2semidirect
14. C2×#16810618C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#467C2semidirect
21. C2×#13133249C22semidirect
26. C2×#13133223C22semidirect
35. #16811196C22semidirect
52. #16810879C22semidirect
53. #16810878C22semidirect
54. #16810871C22semidirect
55. #16810870C22semidirect
56. #16810863C22semidirect
57. #16810855C22semidirect
58. #16810852C22semidirect
59. #16810664C22semidirect
63. #16810618C22semidirect
68. #103×D53C22semidirect
75. C53×#467C22semidirect
117. C2×#11719912D4semidirect
310. #11719912C2×D4semidirect
434. C2×#467D53semidirect
441. C2×C53#3063semidirect
492. #467C2×D53semidirect
510. C53C2×#3063semidirect
859. C2#20284405direct (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×#131332232
C2×#168112032
C2×#168111962
#202844052
C2×#168108792
C2×#168108782
C2×#168108712
C2×#168108702
C2×#168108632
C2×#168108552
C2×#168108522
C2×#168106642
C2×#168106182
C2×#103×D532
C2×C53×#4672
C2×#306353