Finite Group Databasebeta

← C2×#20284670 #28251916

Subgroups — C2×#20284670 #28251916

Order 13568.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811189C211yesmaximal, characteristic
2C2×#16811103C211yesmaximal, characteristic, complemented
3#20284670C2116yesmaximal, direct product factor
4C2×#16810943C211yesmaximal, characteristic, complemented
5C2×#16810939C211yesmaximal, characteristic, complemented
6C2×#16810950C211yesmaximal, characteristic, complemented
7C2×#16810947C211yesmaximal, characteristic, complemented
8C2×#16810945C211yesmaximal, characteristic, complemented
9C2×#16810937C211yesmaximal, characteristic, complemented
10C2×#16810935C211yesmaximal, characteristic, complemented
11C2×#16810662C211yesmaximal, characteristic, complemented
12C2×#16810660C211yesmaximal, characteristic, complemented
13C2×#16810626C211yesmaximal, characteristic, complemented
14C2×#102×D53C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811189—24no—
22#16811189C2218yes—
23C2×#13133213—21no—
24C2×#13133203—21no—
25C2×#13133192C2211yescharacteristic
26C2×#13133191C2211yescharacteristic
27C2×#13133188C2211yescharacteristic
28C2×#13133187—21no—
29C2×#13133185—21no—
30#16811103—24no—
31#16811103C2218yescomplemented
32C2×C4×Dic106—21no—
33C2×C4×D212—21no—
34C2×#13133177—21no—
35C2×#13133177—21no—
36C2×#13133175C2211yescharacteristic
37C2×#13133175C2211yescharacteristic
38C2×#13133175C2211yescharacteristic, complemented
39C22×C4⋊Dic53C2211yescharacteristic, complemented
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic, complemented
42#16810950C2218yescomplemented
43#16810947C2218yescomplemented
44#16810945C2218yescomplemented
45#16810943C2218yescomplemented
46#16810939C2218yescomplemented
47#16810937C2218yescomplemented
48#16810935C2218yescomplemented
49#16810662C2218yescomplemented
50#16810660C2218yescomplemented
51C2×#13133151C2211yescharacteristic, complemented
52C2×#13133151C2211yescharacteristic, complemented
53C2×#13133150C2211yescharacteristic, complemented
54C2×#13133148C2211yescharacteristic, complemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133148C2211yescharacteristic, complemented
57#16810626C2218yescomplemented
58C2×#13133139C2211yescharacteristic
59C2×#13133139C2211yescharacteristic
60C2×#13133138C2211yescharacteristic
61C2×#13133138C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64#102×D53C2218yescomplemented
65#16810588C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic, complemented
67C2×#13133129C2211yescharacteristic, complemented
68C2×#13133129C2211yescharacteristic, complemented
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic, complemented
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—24no—
79C2×#11719945—24no—
80C2×#11719945D414yes—
81C2×#11719945C2314yes—
82C22×Dic106D411yescharacteristic
83C22×D212—21no—
84C22×D212D411yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53D411yescharacteristic
90C22×C22⋊D53D411yescharacteristic
91C2×D4×D53—22no—
92C2×D4×D53—24no—
93C2×D4×D53—24no—
94C2×D4×D53C2314yes—
95C23×Dic53—21no—
96C22×C4×D53—21no—
97C22×C4×D53—21no—
98C22×C4×D53C2311yescharacteristic
99C22×C4×D53C2311yescharacteristic
100C2×#11719912—24no—
101C2×#11719912C2314yes—
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C2×C8×D53—24no—
105C2×C8×D53C2314yes—
106#13133213—28no—
107#13133203—28no—
108#13133192—22no—
109#13133192C2314yes—
110#13133191—22no—
111#13133191C2314yes—
112#13133188—22no—
113#13133188C2314yes—
114#13133187—28no—
115#13133185—28no—
116C4×Dic106—28no—
117C4×D212—28no—
118#13133177—28no—
119#13133177—28no—
120#13133175—22no—
121#13133175—22no—
122#13133175—22no—
123#13133175C2314yes—
124#13133175C2314yes—
125#13133175C2314yescomplemented
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—22no—
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2314yescomplemented
132C2×#11719919—21no—
133C2×#11719919—21no—
134C4⋊C4×D53—22no—
135C4⋊C4×D53—22no—
136C4⋊C4×D53C2314yes—
137C4⋊C4×D53C2314yescomplemented
138C2×C22⋊Dic53—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147#13133151C2314yescomplemented
148#13133151C2314yescomplemented
149#13133150C2314yescomplemented
150#13133148C2314yescomplemented
151#13133148C2314yescomplemented
152#13133148C2314yescomplemented
153#13133139C2314yes—
154#13133139C2314yes—
155#13133138C2314yes—
156#13133138C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yescomplemented
160#13133129C2314yescomplemented
161#13133129C2314yescomplemented
162C22×D4×C53—21no—
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167#121×C53—22no—
168#121×C53C2314yes—
169#117×C53—22no—
170#117×C53C2314yescomplemented
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177#107×C53C2314yescomplemented
178#106×C53C2314yescomplemented
179#102×C53C2314yes—
180#102×C53C2314yes—
181C22⋊C8×C53C2314yescomplemented
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185C23×D53—24no—
186C23×D53—44no—
187C23×D53—82no—
188C23×D53—82no—
189C23×D53C2×D411yescharacteristic
190C23×D53C2×D411yescharacteristic
191C2×D4×C53—24no—
192C2×D4×C53—21no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53—82no—
196C2×D4×C53C2412yes—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D412yes—
204C22×C4×C53C2412yes—
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—82no—
213C2×C22⋊D53—82no—
214C2×C22⋊D53C2×D414yes—
215C2×C22⋊D53C2×D414yes—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—24no—
220C22×Dic53—82no—
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223D4×D53—28no—
224D4×D53—28no—
225D4×D53—48no—
226#11719945—216no—
227#11719945—28no—
228#11719945—28no—
229C2×D212—24no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—21no—
233C2×D212—24no—
234C2×D212—82no—
235C2×D212C2×D414yes—
236C2×D212C2412yes—
237C2×C4×D53—22no—
238C2×C4×D53—22no—
239C2×C4×D53—24no—
240C2×C4×D53—24no—
241C2×C4×D53—82no—
242C2×C4×D53—82no—
243C2×C4×D53C2×D412yes—
244C2×C4×D53C2×D412yes—
245C2×C4×D53#4114yes—
246C2×C4×D53#4114yes—
247C2×C4×D53C2412yes—
248C2×C4×D53C2412yes—
249C2×Dic106—24no—
250C2×Dic106C2×D414yes—
251C2×C8×C53—22no—
252C2×C8×C53—22no—
253C2×C8×C53C2412yes—
254C2×C8×C53C2412yes—
255C4⋊C4×C53—21no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53C2412yes—
259C4⋊C4×C53C2412yes—
260C4⋊C4×C53C2412yes—
261C22⋊C4×C53—24no—
262C22⋊C4×C53—24no—
263C42×C53—24no—
264C22⋊Dic53—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—24no—
273C4⋊Dic53—21no—
274C4⋊Dic53C2412yes—
275C4⋊Dic53C2412yes—
276C4⋊Dic53C2412yes—
277#11719919—24no—
278#11719919—24no—
279C4×Dic53—24no—
280C4×Dic53—24no—
281C4×Dic53—24no—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286#11719912—28no—
287C8×D53—28no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—42no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53C22×D412yes—
296C23×C53C22×D411yescharacteristic
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—48no—
307C22×D53—84no—
308C22×D53—84no—
309C22×D53—816no—
310C22×D53#12314yes—
311C22×D53C22×D412yes—
312C22×D53C22×D412yes—
313D4×C53—22no—
314D4×C53—22no—
315D4×C53—42no—
316D4×C53—84no—
317C2×C4×C53—22no—
318C2×C4×C53—24no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—42no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C2×#4112yes—
330C2×C4×C53C2×#4112yes—
331C2×C4×C53C2511yescharacteristic
332C22⋊D53—28no—
333C22⋊D53—28no—
334C22⋊D53—48no—
335C22⋊D53—84no—
336C22⋊D53—84no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—84no—
345C2×Dic53#12314yes—
346C2×Dic53C22×D412yes—
347C2×Dic53C22×D412yes—
348D212—28no—
349D212—22no—
350D212—22no—
351D212—42no—
352D212—84no—
353C4×D53—24no—
354C4×D53—22no—
355C4×D53—22no—
356C4×D53—84no—
357C4×D53—84no—
358C4×D53#12318yes—
359C4×D53C2×#4114yes—
360C4×D53C2×#4114yes—
361Dic106—28no—
362C8×C53—22no—
363C8×C53—22no—
364#88322—22no—
365#88322—22no—
366C2×#3096—531nomaximal, Sylow
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—44no—
371C22×C53—42no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—84no—
375C22×C53C2×#12312yes—
376C22×C53#57612yes—
377C22×C53#57712yes—
378C22×C53C23×D411yescharacteristic
379C2×D53—28no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—22no—
385C2×D53—44no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—816no—
390C2×D53—84no—
391C2×D53C2×#12314yes—
392C4×C53—22no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53—42no—
396C4×C53C2×#12312yes—
397C4×C53C22×#4111yescharacteristic
398C4×C53C22×#4111yescharacteristic
399Dic53—22no—
400Dic53—42no—
401Dic53—42no—
402Dic53—42no—
403Dic53C2×#12314yes—
404C2×#535—531no—
405C2×#520—531no—
406#3096—5316no—
407C2×#481—531no—
408C2×#481—531no—
409C2×#482—531no—
410C2×#482—531no—
411C2×#482—531no—
412C2×#482D5311yescharacteristic, complemented
413C2×#480—531no—
414C2×#480—531no—
415C2×#428—531no—
416C2×#427—531no—
417C2×#418—531no—
418C22×#102—531no—
419C2×#408—531no—
420C2×C53—42no—
421C2×C53—82no—
422C2×C53#309614yescomplemented
423C2×C53C22×#12311yescharacteristic
424C2×C53C2×#57611yescharacteristic
425C2×C53C2×#57711yescharacteristic
426D53—24no—
427D53—42no—
428D53—82no—
429C22×#41—531no—
430C23×D4—531no—
431C22×M16—531no—
432C23×C8—531no—
433#535—538no—
434#535—1064no—
435C2×#127—1061no—
436C2×#124—1061no—
437C2×#121—531no—
438C2×#121—531no—
439C2×#121—531no—
440C2×#121C2×D5311yescharacteristic
441C2×#120—1061no—
442C2×#120—1061no—
443#520—538no—
444#520—1064no—
445C2×C4×Q8—1061no—
446C2×C4×D4—1061no—
447C2×C4×D4—1061no—
448C2×C4×D4—1061no—
449C2×#117—531no—
450C2×#117—531no—
451C2×#117—531no—
452C2×#117C2×D5311yescharacteristic, complemented
453C22×C4⋊C4—531no—
454C22×C4⋊C4—531no—
455C22×C4⋊C4—531no—
456#482—538no—
457#482—538no—
458#482—538no—
459#482C2×D5318yescomplemented
460#481—538no—
461#481—538no—
462#480—538no—
463#480—538no—
464#428—538no—
465#427—538no—
466C2×#107—531no—
467C2×#107—531no—
468C2×#107—531no—
469C2×#107C2×D5311yescharacteristic, complemented
470C2×#106—531no—
471C2×#106—531no—
472C2×#106—531no—
473C2×#106C2×D5311yescharacteristic, complemented
474#418—538no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102—531no—
481C2×#102—538no—
482C2×#102C2×D5311yescharacteristic
483C2×#102C2×D5311yescharacteristic
484#408—538no—
485C2×C22⋊C8—531no—
486C2×C22⋊C8—531no—
487C2×C22⋊C8—531no—
488C2×C22⋊C8C2×D5311yescharacteristic, complemented
489C53C2×#309611yescharacteristic, complemented, Sylow
490C25—1061no—
491C2×#41—534no—
492C2×#41—534no—
493C2×#41—1064no—
494C2×#41—1064no—
495C22×Q8—531no—
496C22×D4—21no—
497C22×D4—531no—
498C22×D4—531no—
499C22×D4—534no—
500C22×D4—531no—
501C22×D4—531no—
502C22×D4—1061no—
503C22×D4—1064no—
504C22×D4—1064no—
505C22×D4—1062no—
506C22×D4—1061no—
507C22×D4—1061no—
508C22×D4—1061no—
509C22×D4C22×D5311yescharacteristic
510C23×C4—531no—
511C23×C4—531no—
512C23×C4—1061no—
513C23×C4—1061no—
514C23×C4—1061no—
515C23×C4C22×D5311yescharacteristic
516C2×M16—534no—
517C2×M16—1064no—
518C22×C8—531no—
519C22×C8—531no—
520C22×C8—534no—
521C22×C8—1064no—
522C22×C8C22×D5311yescharacteristic
523C22×C8C22×D5311yescharacteristic
524#127—1068no—
525#124—1068no—
526#121—22no—
527#121—534no—
528#121—534no—
529#121—534no—
530#121—1062no—
531#121—1062no—
532#121—1062no—
533#121C22×D5314yes—
534#120—1068no—
535#120—1068no—
536C4×Q8—1068no—
537C4×D4—1068no—
538C4×D4—1068no—
539C4×D4—1068no—
540#117—22no—
541#117—534no—
542#117—534no—
543#117—534no—
544#117—1062no—
545#117—1062no—
546#117—1062no—
547#117C22×D5314yescomplemented
548C2×C4⋊C4—531no—
549C2×C4⋊C4—531no—
550C2×C4⋊C4—534no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—534no—
553C2×C4⋊C4—534no—
554C2×C4⋊C4—1062no—
555C2×C4⋊C4—1062no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1062no—
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C4⋊C4C22×D5311yescharacteristic
562C2×C4⋊C4C22×D5311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C42—21no—
572C2×C42—1061no—
573C2×C42—1061no—
574C2×C42—1061no—
575#107—534no—
576#107—534no—
577#107—534no—
578#107C22×D5314yescomplemented
579#106—534no—
580#106—534no—
581#106—534no—
582#106C22×D5314yescomplemented
583#102—534no—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588#102—534no—
589#102C22×D5314yes—
590#102C22×D5314yes—
591C22⋊C8—534no—
592C22⋊C8—534no—
593C22⋊C8—534no—
594C22⋊C8C22×D5314yescomplemented
595C24—21no—
596C24—531no—
597C24—531no—
598C24—1064no—
599C24—1061no—
600C24—4242no—
601C24—4242no—
602C24—2124no—
603C24D4×D5311yescharacteristic
604#41—10616no—
605#41—1068no—
606#41—1068no—
607C2×Q8—534no—
608C2×Q8—1064no—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—82no—
614C2×D4—534no—
615C2×D4—534no—
616C2×D4—534no—
617C2×D4—532no—
618C2×D4—1064no—
619C2×D4—1064no—
620C2×D4—1068no—
621C2×D4—1068no—
622C2×D4—1064no—
623C2×D4—1064no—
624C2×D4—1064no—
625C2×D4—1064no—
626C2×D4—1064no—
627C2×D4—1061no—
628C2×D4—1062no—
629C2×D4—1062no—
630C2×D4—4242no—
631C2×D4—4242no—
632C2×D4—4242no—
633C2×D4—2128no—
634C2×D4—2124no—
635C2×D4C23×D5312yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—531no—
642C22×C4—532no—
643C22×C4—534no—
644C22×C4—534no—
645C22×C4—532no—
646C22×C4—531no—
647C22×C4—532no—
648C22×C4—532no—
649C22×C4—1064no—
650C22×C4—1064no—
651C22×C4—1062no—
652C22×C4—1062no—
653C22×C4—1064no—
654C22×C4—1061no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—4242no—
658C22×C4—4242no—
659C22×C4—4242no—
660C22×C4D4×D5312yes—
661C22×C4D4×D5311yescharacteristic
662C22×C4C23×D5312yes—
663C22×C4C23×D5311yescharacteristic
664M16—1068no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—532no—
668C2×C8—532no—
669C2×C8—1068no—
670C2×C8—1062no—
671C2×C8—1062no—
672C2×C8C23×D5312yes—
673C2×C8C23×D5312yes—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—532no—
678C4⋊C4—532no—
679C4⋊C4—532no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4—1061no—
683C4⋊C4—1061no—
684C4⋊C4—1064no—
685C4⋊C4—1061no—
686C4⋊C4C23×D5312yes—
687C4⋊C4C23×D5312yes—
688C4⋊C4C23×D5312yes—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C22⋊C4—1064no—
695C22⋊C4—1064no—
696C22⋊C4—1064no—
697C42—24no—
698C42—1064no—
699C42—1064no—
700C42—1064no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—534no—
709C23—532no—
710C23—532no—
711C23—1062no—
712C23—1062no—
713C23—1062no—
714C23—1062no—
715C23—1062no—
716C23—1062no—
717C23—4244no—
718C23—4244no—
719C23—42416no—
720C23—2128no—
721C23—2122no—
722C23—2122no—
723C23—2122no—
724C23C2×D4×D5312yes—
725C23C2×D4×D5311yescharacteristic
726Q8—1068no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—1068no—
732D4—1068no—
733D4—1068no—
734D4—1062no—
735D4—1062no—
736D4—4244no—
737D4—4244no—
738D4—4244no—
739D4—2128no—
740D4—2122no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—534no—
752C2×C4—532no—
753C2×C4—538no—
754C2×C4—534no—
755C2×C4—534no—
756C2×C4—532no—
757C2×C4—1062no—
758C2×C4—1064no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—4244no—
765C2×C4—4244no—
766C2×C4—4244no—
767C2×C4—2122no—
768C2×C4—2122no—
769C2×C4—2122no—
770C2×C4C2×D4×D5312yes—
771C2×C4C2×D4×D5311yescharacteristic
772C2×C4#41×D5312yes—
773C2×C4#41×D5312yes—
774C2×C4C24×D5311yescharacteristic
775C8—22no—
776C8—22no—
777C8—1062no—
778C8—1062no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—534no—
788C22—1062no—
789C22—1062no—
790C22—1068no—
791C22—1062no—
792C22—1062no—
793C22—1062no—
794C22—42416no—
795C22—4244no—
796C22—2122no—
797C22—2122no—
798C22—2122no—
799C22—2124no—
800C22#123×D5312yes—
801C22#1681142512yes—
802C22#1681143312yes—
803C22C22×D4×D5311yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—534no—
809C4—1062no—
810C4—2122no—
811C4—2122no—
812C4—2122no—
813C4#123×D5312yes—
814C4C2×#41×D5311yescharacteristic
815C4C2×#41×D5311yescharacteristic
816C2—42no—
817C2—82no—
818C2—1064no—
819C2—4242no—
820C2—2122no—
821C2#2028467014yesdirect product factor
822C2C2×#123×D5311yescharacteristic
823C2C2×#1681142511yescharacteristic
824C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
prime radicalC2×#16811189C2
hypercenterC2×#482D53
hypocenterC53C2×#3096
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#16811103C2semidirect
3. #20284670C2direct (N × H)
4. C2×#16810943C2semidirect
5. C2×#16810939C2semidirect
6. C2×#16810950C2semidirect
7. C2×#16810947C2semidirect
8. C2×#16810945C2semidirect
9. C2×#16810937C2semidirect
10. C2×#16810935C2semidirect
11. C2×#16810662C2semidirect
12. C2×#16810660C2semidirect
13. C2×#16810626C2semidirect
14. C2×#102×D53C2semidirect
15. C2×#16810588C2semidirect
16. C2×C53×#482C2semidirect
31. #16811103C22semidirect
38. C2×#13133175C22semidirect
39. C22×C4⋊Dic53C22semidirect
41. C2×C4⋊C4×D53C22semidirect
42. #16810950C22semidirect
43. #16810947C22semidirect
44. #16810945C22semidirect
45. #16810943C22semidirect
46. #16810939C22semidirect
47. #16810937C22semidirect
48. #16810935C22semidirect
49. #16810662C22semidirect
50. #16810660C22semidirect
51. C2×#13133151C22semidirect
52. C2×#13133151C22semidirect
53. C2×#13133150C22semidirect
54. C2×#13133148C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133148C22semidirect
57. #16810626C22semidirect
64. #102×D53C22semidirect
65. #16810588C22semidirect
66. C2×C22⋊#88322C22semidirect
67. C2×#13133129C22semidirect
68. C2×#13133129C22semidirect
70. C2×#117×C53C22semidirect
71. C53×#482C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
76. C2×C22⋊C8×C53C22semidirect
125. #13133175C23semidirect
131. C2×C4⋊Dic53C23semidirect
137. C4⋊C4×D53C23semidirect
147. #13133151C23semidirect
148. #13133151C23semidirect
149. #13133150C23semidirect
150. #13133148C23semidirect
151. #13133148C23semidirect
152. #13133148C23semidirect
159. C22⋊#88322C23semidirect
160. #13133129C23semidirect
161. #13133129C23semidirect
170. #117×C53C23semidirect
177. #107×C53C23semidirect
178. #106×C53C23semidirect
181. C22⋊C8×C53C23semidirect
412. C2×#482D53semidirect
422. C2×C53#3096semidirect
452. C2×#117C2×D53semidirect
459. #482C2×D53semidirect
469. C2×#107C2×D53semidirect
473. C2×#106C2×D53semidirect
488. C2×C22⋊C8C2×D53semidirect
489. C53C2×#3096semidirect
547. #117C22×D53semidirect
578. #107C22×D53semidirect
582. #106C22×D53semidirect
594. C22⋊C8C22×D53semidirect
821. C2#20284670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111892
C2×#168111032
#202846702
C2×#168109432
C2×#168109392
C2×#168109502
C2×#168109472
C2×#168109452
C2×#168109372
C2×#168109352
C2×#168106622
C2×#168106602
C2×#168106262
C2×#102×D532
C2×#168105882
C2×C53×#4822
C2×#309653