Finite Group Databasebeta

← D53×#1866 #27385138

Subgroups — D53×#1866 #27385138

Order 13568.

1398 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#131×D53C211yesmaximal, characteristic
2C2×#108×D53C211yesmaximal, characteristic, complemented
3#424×D53C211yesmaximal, characteristic, complemented
4C2×#104×D53C211yesmaximal, characteristic
5#416×D53C211yesmaximal, characteristic
6#20274993C211yesmaximal, characteristic, complemented
7#20274992C211yesmaximal, characteristic, complemented
8#20274991C211yesmaximal, characteristic, complemented
9#20274990C211yesmaximal, characteristic, complemented
10#20274989C211yesmaximal, characteristic, complemented
11#20274988C211yesmaximal, characteristic, complemented
12#20274987C211yesmaximal, characteristic, complemented
13#339×D53C211yesmaximal, characteristic, complemented
14#336×D53C211yesmaximal, characteristic, complemented
15C53×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D53C2211yescharacteristic
17C2×#13133225—21no—
18C2×#13133225C2211yescharacteristic
19C2×#13133224C2211yescharacteristic
20C2×#13133223—21no—
21C2×#13133223C2211yescharacteristic
22#131×D53—24no—
23#131×D53—24no—
24C2×M16×D53—21no—
25C2×M16×D53C2211yescharacteristic
26C2×M16×D53C2211yescharacteristic
27C22×C8×D53—21no—
28C22×C8×D53C2211yescharacteristic
29C22×C8×D53C2211yescharacteristic
30#117×D53C2211yescharacteristic
31C2×C42×D53C2211yescharacteristic
32C2×#13133153C2211yescharacteristic, complemented
33C2×#13133152C2211yescharacteristic, complemented
34C2×#13133152C2211yescharacteristic, complemented
35#108×D53—24no—
36#16810651C2211yescharacteristic, complemented
37#16810650C2211yescharacteristic, complemented
38#16810649C2211yescharacteristic, complemented
39#16810648—21no—
40#16810648—21no—
41C4⋊C8×D53—21no—
42C4⋊C8×D53—21no—
43C2×#13133145C2211yescharacteristic
44C2×#13133144C2211yescharacteristic
45C2×#13133143C2211yescharacteristic
46#104×D53—24no—
47#16810620C2211yescharacteristic
48#16810619C2211yescharacteristic
49#16810618C411yescharacteristic, complemented
50#16810618C411yescharacteristic, complemented
51#16810617C2211yescharacteristic
52#16810616C411yescharacteristic, complemented
53#16810616C411yescharacteristic, complemented
54#103×D53C411yescharacteristic, complemented
55#103×D53C411yescharacteristic, complemented
56#102×D53C411yescharacteristic, complemented
57#102×D53C411yescharacteristic, complemented
58#16810384C2211yescharacteristic, complemented
59#16810383C2211yescharacteristic, complemented
60#16810382C2211yescharacteristic, complemented
61#16810378C2211yescharacteristic, complemented
62#16810377C2211yescharacteristic, complemented
63#16810377C2211yescharacteristic, complemented
64C2×#131×C53C2211yescharacteristic
65C2×#108×C53C2211yescharacteristic, complemented
66C53×#424C2211yescharacteristic, complemented
67C2×#104×C53C2211yescharacteristic
68C53×#416C2211yescharacteristic
69C53×#339C2211yescharacteristic, complemented
70C53×#336C2211yescharacteristic, complemented
71C2×#11719949C2×C411yescharacteristic
72C2×#11719945—21no—
73C2×#11719945C2311yescharacteristic
74C2×#11719947—21no—
75C2×#11719947C2×C411yescharacteristic
76#41×D53—22no—
77#41×D53—22no—
78#41×D53D414yes—
79#41×D53Q814yes—
80C2×Q8×D53C2×C411yescharacteristic
81C2×D4×D53—21no—
82C2×D4×D53C2×C411yescharacteristic
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53C2311yescharacteristic
86#13133225—28no—
87#13133225—22no—
88#13133225—22no—
89#13133224—22no—
90#13133224—22no—
91#13133223—28no—
92#13133223—22no—
93#13133223—22no—
94C2×#11719917—21no—
95C2×#11719917C2311yescharacteristic
96C2×#11719917C2311yescharacteristic
97C2×#11719912—21no—
98C2×#11719912—21no—
99C2×#11719912—21no—
100C2×#11719912—21no—
101M16×D53—28no—
102M16×D53—22no—
103M16×D53—22no—
104M16×D53—22no—
105M16×D53D414yes—
106C22×#88322—21no—
107C22×#88322C2311yescharacteristic
108C22×#88322C2311yescharacteristic
109C2×C8×D53—28no—
110C2×C8×D53—21no—
111C2×C8×D53—21no—
112C2×C8×D53—21no—
113C2×C8×D53—22no—
114C2×C8×D53—22no—
115C2×C8×D53—22no—
116C2×C8×D53—21no—
117C2×C8×D53—22no—
118C2×C8×D53C2×C411yescharacteristic
119C2×C8×D53C2×C411yescharacteristic
120C2×C8×D53C2×C411yescharacteristic
121C2×C8×D53C2×C411yescharacteristic
122C2×C8×D53D411yescharacteristic
123C2×C8×D53D411yescharacteristic
124C2×C8×D53D411yescharacteristic
125C2×C8×D53D411yescharacteristic
126#13133176C2311yescharacteristic
127#13133175C2×C411yescharacteristic
128#13133175C2×C411yescharacteristic
129#13133174—21no—
130#13133173—21no—
131C4⋊C4×D53C2×C411yescharacteristic
132C4⋊C4×D53C2×C411yescharacteristic
133C22⋊C4×D53—21no—
134C2×C4×Dic53—21no—
135C2×C4×Dic53C2311yescharacteristic
136C42×D53—21no—
137C42×D53—22no—
138C42×D53—22no—
139#13133153—22no—
140#13133152—22no—
141#13133152—22no—
142C4⋊#88322—21no—
143C4⋊#88322—21no—
144#13133146—21no—
145#13133146—21no—
146#13133146—21no—
147#13133146—21no—
148#13133145—22no—
149#13133144—22no—
150#13133143—22no—
151#13133142C2×C411yescharacteristic, complemented
152#13133142C2×C411yescharacteristic, complemented
153#13133141C2×C411yescharacteristic, complemented
154#13133141C2×C411yescharacteristic, complemented
155#13133140C2×C411yescharacteristic, complemented
156#13133140C2×C411yescharacteristic, complemented
157#13133139C2×C411yescharacteristic, complemented
158#13133139C2×C411yescharacteristic, complemented
159#13133138C2×C411yescharacteristic, complemented
160#13133138C2×C411yescharacteristic, complemented
161#13133137C2×C411yescharacteristic, complemented
162#13133137C2×C411yescharacteristic, complemented
163C2×#41×C53C2311yescharacteristic
164#131×C53—22no—
165#131×C53—22no—
166C2×M16×C53—21no—
167C2×M16×C53C2311yescharacteristic
168C2×M16×C53C2311yescharacteristic
169C22×C8×C53—21no—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172#117×C53C2311yescharacteristic
173C2×C42×C53C2311yescharacteristic
174#108×C53—22no—
175C4⋊C8×C53—21no—
176C4⋊C8×C53—21no—
177#104×C53—22no—
178#103×C53C2×C411yescharacteristic, complemented
179#103×C53C2×C411yescharacteristic, complemented
180#102×C53C2×C411yescharacteristic, complemented
181#102×C53C2×C411yescharacteristic, complemented
182C23×D53—21no—
183C23×D53#4111yescharacteristic
184#41×C53—21no—
185#41×C53—21no—
186#41×C53C2×D412yes—
187#41×C53C2×Q812yes—
188C2×Q8×C53C22×C411yescharacteristic
189C2×D4×C53—21no—
190C2×D4×C53C22×C411yescharacteristic
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53C2411yescharacteristic
194C2×C22⋊D53—21no—
195C2×C22⋊D53—21no—
196C2×C22⋊D53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53#4111yescharacteristic
200#11719949—22no—
201#11719949C4⋊C414yes—
202Q8×D53—22no—
203Q8×D53C4⋊C414yes—
204#11719947—24no—
205#11719947—24no—
206#11719947—22no—
207#11719947C4⋊C414yes—
208D4×D53—24no—
209D4×D53—24no—
210D4×D53—22no—
211D4×D53C4⋊C414yes—
212#11719945—21no—
213#11719945—21no—
214#11719945—24no—
215#11719945—24no—
216#11719945C2×D412yes—
217#11719945C2×Q812yes—
218C2×D212—21no—
219C2×D212C22×C411yescharacteristic
220C2×C4×D53—21no—
221C2×C4×D53—21no—
222C2×C4×D53—21no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—21no—
227C2×C4×D53—21no—
228C2×C4×D53—42no—
229C2×C4×D53—42no—
230C2×C4×D53C22×C411yescharacteristic
231C2×C4×D53C22×C411yescharacteristic
232C2×C4×D53C2×D412yes—
233C2×C4×D53C2×D412yes—
234C2×C4×D53C2×D411yescharacteristic
235C2×C4×D53C2×D411yescharacteristic
236C2×C4×D53C2×Q812yes—
237C2×C4×D53#4112yes—
238C2×Dic106—21no—
239C2×Dic106C22×C411yescharacteristic
240M16×C53—24no—
241M16×C53—21no—
242M16×C53—21no—
243M16×C53—21no—
244M16×C53C2×D412yes—
245C2×C8×C53—24no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—21no—
250C2×C8×C53—21no—
251C2×C8×C53—21no—
252C2×C8×C53C22×C411yescharacteristic
253C2×C8×C53C22×C411yescharacteristic
254C2×C8×C53C2×D411yescharacteristic
255C2×C8×C53C2×D411yescharacteristic
256C4⋊C4×C53C22×C411yescharacteristic
257C4⋊C4×C53C22×C411yescharacteristic
258C22⋊C4×C53—21no—
259C42×C53—21no—
260C42×C53—21no—
261C42×C53—21no—
262C22⋊Dic53—21no—
263#11719921—21no—
264#11719921—21no—
265C4⋊Dic53C22×C411yescharacteristic
266C4⋊Dic53C22×C411yescharacteristic
267#11719919—21no—
268#11719919—21no—
269C4×Dic53—21no—
270C4×Dic53—21no—
271C4×Dic53—21no—
272C4×Dic53—21no—
273C4×Dic53—21no—
274C4×Dic53—42no—
275#11719917—24no—
276#11719917—21no—
277#11719917—21no—
278#11719917—21no—
279#11719917C2×D412yes—
280C2×#88322—24no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—21no—
285C2×#88322—21no—
286C2×#88322—21no—
287C2×#88322C22×C411yescharacteristic
288C2×#88322C22×C411yescharacteristic
289C2×#88322C2×D411yescharacteristic
290C2×#88322C2×D411yescharacteristic
291#11719912—24no—
292#11719912—24no—
293#11719912—24no—
294#11719912—42no—
295C8×D53—24no—
296C8×D53—24no—
297C8×D53—22no—
298C8×D53—22no—
299C8×D53—22no—
300C8×D53—22no—
301C8×D53—22no—
302C8×D53—24no—
303C8×D53—22no—
304C8×D53—22no—
305C8×D53—22no—
306C8×D53—42no—
307C23×C53—21no—
308C23×C53C2×#4111yescharacteristic
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—21no—
312C22×D53—24no—
313C22×D53—42no—
314C22×D53—42no—
315C22×D53C4×D411yescharacteristic
316C22×D53C4×D411yescharacteristic
317C22×D53C22⋊Q812yes—
318C22×D53#12312yes—
319Q8×C53—21no—
320Q8×C53C2×C4⋊C412yes—
321D4×C53—22no—
322D4×C53—22no—
323D4×C53—21no—
324D4×C53C2×C4⋊C412yes—
325C2×C4×C53—21no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—41no—
332C2×C4×C53—41no—
333C2×C4×C53C23×C411yescharacteristic
334C2×C4×C53C22×D411yescharacteristic
335C2×C4×C53C22×D411yescharacteristic
336C2×C4×C53C22×D411yescharacteristic
337C2×C4×C53C22×Q811yescharacteristic
338C2×C4×C53C2×#4111yescharacteristic
339C22⋊D53—22no—
340C22⋊D53—22no—
341C22⋊D53—24no—
342C22⋊D53—24no—
343C2×Dic53—21no—
344C2×Dic53—24no—
345C2×Dic53—22no—
346C2×Dic53—21no—
347C2×Dic53—21no—
348C2×Dic53—41no—
349C2×Dic53—41no—
350C2×Dic53C4×D411yescharacteristic
351C2×Dic53C4×D411yescharacteristic
352C2×Dic53C22⋊Q812yes—
353C2×Dic53#12312yes—
354D212—24no—
355D212—21no—
356D212C2×C4⋊C412yes—
357C4×D53—24no—
358C4×D53—22no—
359C4×D53—22no—
360C4×D53—24no—
361C4×D53—48no—
362C4×D53—42no—
363C4×D53—42no—
364C4×D53C2×C4⋊C412yes—
365C4×D53C2×C4⋊C412yes—
366C4×D53C4×D412yes—
367C4×D53C4×D412yes—
368C4×D53#12012yes—
369C4×D53#12012yes—
370C4×D53C22⋊Q812yes—
371C4×D53C22⋊Q812yes—
372Dic106—21no—
373Dic106—24no—
374Dic106C2×C4⋊C412yes—
375C8×C53—21no—
376C8×C53—21no—
377C8×C53—21no—
378C8×C53—22no—
379C8×C53—21no—
380C8×C53—41no—
381#88322—21no—
382#88322—21no—
383#88322—21no—
384#88322—22no—
385#88322—21no—
386#88322—41no—
387C2×#1866—531nomaximal, Sylow
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—22no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53C2×C4×D411yescharacteristic
394C22×C53C2×C22⋊Q811yescharacteristic
395C22×C53C2×#12311yescharacteristic
396C2×D53—21no—
397C2×D53—21no—
398C2×D53—24no—
399C2×D53—24no—
400C2×D53—22no—
401C2×D53—41no—
402C2×D53—41no—
403C2×D53—48no—
404C2×D53#38512yes—
405C2×D53#38512yes—
406C2×D53#44312yes—
407C2×D53#44412yes—
408C4×C53—22no—
409C4×C53—42no—
410C4×C53—41no—
411C4×C53—41no—
412C4×C53C22×C4⋊C411yescharacteristic
413C4×C53C2×C4×D411yescharacteristic
414C4×C53C2×#12011yescharacteristic
415C4×C53C2×C22⋊Q811yescharacteristic
416Dic53—22no—
417Dic53—42no—
418Dic53—41no—
419Dic53—41no—
420Dic53#38512yes—
421Dic53#38512yes—
422C22×#131—531no—
423C22×#108—531no—
424C2×#424—531no—
425C22×#104—531no—
426C2×#416—531no—
427#1866—531no—
428#1866—531no—
429#1866—531no—
430#1866—531no—
431#1866—531no—
432#1866—531no—
433#1866—531no—
434#1866D5311yescharacteristic, direct product factor
435C2×#339—531no—
436C2×#336—531no—
437C2×C53—21no—
438C2×C53—21no—
439C2×C53—42no—
440C2×C53C2×#38511yescharacteristic
441C2×C53C2×#44311yescharacteristic
442C2×C53C2×#44411yescharacteristic
443D53—22no—
444D53—42no—
445D53#186614yesdirect product factor
446C22×#41—531no—
447C2×#131—531no—
448C2×#131—531no—
449C2×#131—531no—
450C2×#131—1061no—
451C2×#131—1061no—
452C2×#131—1064no—
453C2×#131—1064no—
454C2×#131C2×D5311yescharacteristic
455C22×M16—531no—
456C22×M16—531no—
457C22×M16—1061no—
458C23×C8—531no—
459C23×C8—531no—
460C23×C8—1061no—
461C2×#117—531no—
462C22×C42—531no—
463C2×#108—531no—
464C2×#108—531no—
465C2×#108—531no—
466C2×#108—1064no—
467C2×#108C2×D5311yescharacteristic, complemented
468#424—531no—
469#424—531no—
470#424—531no—
471#424—1061no—
472#424—1061no—
473#424C2×D5311yescharacteristic, complemented
474C2×C4⋊C8—1061no—
475C2×C4⋊C8—1061no—
476C2×#104—531no—
477C2×#104—531no—
478C2×#104—531no—
479C2×#104—1064no—
480C2×#104C2×D5311yescharacteristic
481#416—531no—
482#416—531no—
483#416—531no—
484#416—531no—
485#416—531no—
486#416—531no—
487#416—531no—
488#416C2×D5311yescharacteristic
489C2×#103—531no—
490C2×#103—531no—
491C2×#102—531no—
492C2×#102—531no—
493#339—531no—
494#339—531no—
495#339—531no—
496#339C2×D5311yescharacteristic, complemented
497#336—531no—
498#336—531no—
499#336—531no—
500#336C2×D5311yescharacteristic, complemented
501C53C2×#186611yescharacteristic, complemented, Sylow
502C2×#41—534no—
503C2×#41—534no—
504C2×#41—531no—
505C2×#41—531no—
506C2×#41—531no—
507C2×#41—1061no—
508C2×#41—1061no—
509C2×#41—1062no—
510C2×#41—1062no—
511C2×#41C22×D5311yescharacteristic
512C22×Q8—531no—
513C22×D4—531no—
514C22×D4—1061no—
515C23×C4—531no—
516C23×C4—1061no—
517C23×C4—1061no—
518#131—22no—
519#131—22no—
520#131—1062no—
521#131—1062no—
522#131—1068no—
523#131—1062no—
524#131—1068no—
525#131—1062no—
526#131—1062no—
527#131—1062no—
528C2×M16—21no—
529C2×M16—531no—
530C2×M16—534no—
531C2×M16—531no—
532C2×M16—1061no—
533C2×M16—1061no—
534C2×M16—1061no—
535C2×M16—1061no—
536C2×M16—1062no—
537C2×M16—1068no—
538C2×M16—1061no—
539C2×M16—1062no—
540C2×M16—1062no—
541C2×M16C22×D5311yescharacteristic
542C2×M16C22×D5311yescharacteristic
543C22×C8—21no—
544C22×C8—531no—
545C22×C8—531no—
546C22×C8—531no—
547C22×C8—531no—
548C22×C8—531no—
549C22×C8—531no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—531no—
553C22×C8—531no—
554C22×C8—1061no—
555C22×C8—1062no—
556C22×C8—1062no—
557C22×C8—1062no—
558C22×C8—1062no—
559C22×C8—1061no—
560C22×C8—1068no—
561C22×C8—1061no—
562C22×C8—1061no—
563C22×C8—1061no—
564C22×C8C22×D5311yescharacteristic
565C22×C8C22×D5311yescharacteristic
566#117—531no—
567#117—531no—
568#117—531no—
569#117—1061no—
570#117—1061no—
571#117C22×D5311yescharacteristic
572C2×C4⋊C4—531no—
573C2×C4⋊C4—531no—
574C2×C22⋊C4—1061no—
575C2×C42—531no—
576C2×C42—1061no—
577C2×C42—1062no—
578C2×C42—1062no—
579C2×C42—1061no—
580C2×C42C22×D5311yescharacteristic
581#108—22no—
582#108—1062no—
583#108—1062no—
584#108—1062no—
585C4⋊C8—21no—
586C4⋊C8—21no—
587C4⋊C8—1061no—
588C4⋊C8—1061no—
589C4⋊C8—1061no—
590C4⋊C8—1061no—
591C4⋊C8—1061no—
592C4⋊C8—1061no—
593#104—22no—
594#104—1062no—
595#104—1062no—
596#104—1062no—
597#103—531no—
598#103—531no—
599#103—531no—
600#103—531no—
601#103—531no—
602#103—531no—
603#103C4×D5311yescharacteristic, complemented
604#103C4×D5311yescharacteristic, complemented
605#102—531no—
606#102—531no—
607#102—531no—
608#102—531no—
609#102—531no—
610#102—531no—
611#102C4×D5311yescharacteristic, complemented
612#102C4×D5311yescharacteristic, complemented
613C24—531no—
614C24—1061no—
615#41—21no—
616#41—21no—
617#41—534no—
618#41—534no—
619#41—532no—
620#41—532no—
621#41—1064no—
622#41—1064no—
623#41—1064no—
624#41—1064no—
625#41—1062no—
626#41—1062no—
627#41—1061no—
628#41—1061no—
629#41D4×D5312yes—
630#41Q8×D5312yes—
631C2×Q8—534no—
632C2×Q8—531no—
633C2×Q8—1061no—
634C2×Q8—1062no—
635C2×Q8C2×C4×D5311yescharacteristic
636C2×D4—21no—
637C2×D4—534no—
638C2×D4—531no—
639C2×D4—1061no—
640C2×D4—1062no—
641C2×D4—1061no—
642C2×D4—1064no—
643C2×D4—1064no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4C2×C4×D5311yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—531no—
650C22×C4—531no—
651C22×C4—531no—
652C22×C4—532no—
653C22×C4—532no—
654C22×C4—531no—
655C22×C4—531no—
656C22×C4—532no—
657C22×C4—532no—
658C22×C4—1064no—
659C22×C4—1061no—
660C22×C4—1064no—
661C22×C4—1061no—
662C22×C4—1061no—
663C22×C4—1061no—
664C22×C4—1064no—
665C22×C4—1061no—
666C22×C4—1061no—
667C22×C4—1061no—
668C22×C4—2122no—
669C22×C4—2122no—
670C22×C4C23×D5311yescharacteristic
671M16—24no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—532no—
676M16—1064no—
677M16—1064no—
678M16—1064no—
679M16—1064no—
680M16—1061no—
681M16—1061no—
682M16—1061no—
683M16—2122no—
684M16D4×D5312yes—
685C2×C8—24no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—531no—
693C2×C8—531no—
694C2×C8—531no—
695C2×C8—531no—
696C2×C8—1062no—
697C2×C8—1062no—
698C2×C8—1062no—
699C2×C8—1062no—
700C2×C8—1062no—
701C2×C8—1062no—
702C2×C8—1062no—
703C2×C8—1062no—
704C2×C8—1064no—
705C2×C8—1064no—
706C2×C8—1064no—
707C2×C8—1064no—
708C2×C8—1061no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—1061no—
712C2×C8—1061no—
713C2×C8—1061no—
714C2×C8—2122no—
715C2×C8C2×C4×D5311yescharacteristic
716C2×C8C2×C4×D5311yescharacteristic
717C2×C8D4×D5311yescharacteristic
718C2×C8D4×D5311yescharacteristic
719C4⋊C4—531no—
720C4⋊C4—531no—
721C4⋊C4—1061no—
722C4⋊C4—1061no—
723C4⋊C4C2×C4×D5311yescharacteristic
724C4⋊C4C2×C4×D5311yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—1061no—
727C22⋊C4—1061no—
728C22⋊C4—1061no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—1061no—
733C42—1061no—
734C42—1061no—
735C42—1061no—
736C42—1061no—
737C42—2122no—
738C23—21no—
739C23—531no—
740C23—531no—
741C23—532no—
742C23—532no—
743C23—1062no—
744C23—1062no—
745C23—1064no—
746C23—1061no—
747C23—2122no—
748C23—2122no—
749C23#41×D5311yescharacteristic
750Q8—21no—
751Q8—532no—
752Q8—1064no—
753Q8—1061no—
754Q8C4⋊C4×D5312yes—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—532no—
759D4—1064no—
760D4—1064no—
761D4—1064no—
762D4—1062no—
763D4—1062no—
764D4—1061no—
765D4C4⋊C4×D5312yes—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—531no—
775C2×C4—531no—
776C2×C4—532no—
777C2×C4—532no—
778C2×C4—532no—
779C2×C4—532no—
780C2×C4—532no—
781C2×C4—532no—
782C2×C4—532no—
783C2×C4—532no—
784C2×C4—532no—
785C2×C4—532no—
786C2×C4—1064no—
787C2×C4—1064no—
788C2×C4—1064no—
789C2×C4—1061no—
790C2×C4—1062no—
791C2×C4—1062no—
792C2×C4—1062no—
793C2×C4—1061no—
794C2×C4—1061no—
795C2×C4—2122no—
796C2×C4—2122no—
797C2×C4—2128no—
798C2×C4—2121no—
799C2×C4—2121no—
800C2×C4C22×C4×D5311yescharacteristic
801C2×C4C2×D4×D5311yescharacteristic
802C2×C4C2×D4×D5311yescharacteristic
803C2×C4C2×D4×D5311yescharacteristic
804C2×C4C2×Q8×D5311yescharacteristic
805C2×C4#41×D5311yescharacteristic
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—41no—
812C8—1061no—
813C8—1061no—
814C8—1061no—
815C8—1061no—
816C8—1062no—
817C8—2121no—
818C22—21no—
819C22—21no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—532no—
824C22—532no—
825C22—532no—
826C22—532no—
827C22—1064no—
828C22—1064no—
829C22—1061no—
830C22—1061no—
831C22—1062no—
832C22—2128no—
833C22—2121no—
834C22—2121no—
835C22C4×D4×D5311yescharacteristic
836C22C22⋊Q8×D5311yescharacteristic
837C22#123×D5311yescharacteristic
838C4—22no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—532no—
843C4—532no—
844C4—1062no—
845C4—2122no—
846C4—2121no—
847C4—2121no—
848C4C2×C4⋊C4×D5311yescharacteristic
849C4C4×D4×D5311yescharacteristic
850C4#120×D5311yescharacteristic
851C4C22⋊Q8×D5311yescharacteristic
852C2—21no—
853C2—21no—
854C2—42no—
855C2—534no—
856C2—1062no—
857C2—2122no—
858C2#385×D5311yescharacteristic
859C2#443×D5311yescharacteristic
860C2#444×D5311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1866C2
socleC22×C53C2×C4×D4
prime radicalC2×#41×D53C22
cosocleC22×C4×C53C24
hypercenter#1866D53
hypocenterC53C2×#1866
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#108×D53C2semidirect
3. #424×D53C2semidirect
6. #20274993C2semidirect
7. #20274992C2semidirect
8. #20274991C2semidirect
9. #20274990C2semidirect
10. #20274989C2semidirect
11. #20274988C2semidirect
12. #20274987C2semidirect
13. #339×D53C2semidirect
14. #336×D53C2semidirect
15. C53×#1866C2semidirect
32. C2×#13133153C22semidirect
33. C2×#13133152C22semidirect
34. C2×#13133152C22semidirect
36. #16810651C22semidirect
37. #16810650C22semidirect
38. #16810649C22semidirect
49. #16810618C4semidirect
50. #16810618C4semidirect
52. #16810616C4semidirect
53. #16810616C4semidirect
54. #103×D53C4semidirect
55. #103×D53C4semidirect
56. #102×D53C4semidirect
57. #102×D53C4semidirect
58. #16810384C22semidirect
59. #16810383C22semidirect
60. #16810382C22semidirect
61. #16810378C22semidirect
62. #16810377C22semidirect
63. #16810377C22semidirect
65. C2×#108×C53C22semidirect
66. C53×#424C22semidirect
69. C53×#339C22semidirect
70. C53×#336C22semidirect
151. #13133142C2×C4semidirect
152. #13133142C2×C4semidirect
153. #13133141C2×C4semidirect
154. #13133141C2×C4semidirect
155. #13133140C2×C4semidirect
156. #13133140C2×C4semidirect
157. #13133139C2×C4semidirect
158. #13133139C2×C4semidirect
159. #13133138C2×C4semidirect
160. #13133138C2×C4semidirect
161. #13133137C2×C4semidirect
162. #13133137C2×C4semidirect
178. #103×C53C2×C4semidirect
179. #103×C53C2×C4semidirect
180. #102×C53C2×C4semidirect
181. #102×C53C2×C4semidirect
434. #1866D53direct (N × H)
445. D53#1866direct (N × H)
467. C2×#108C2×D53semidirect
473. #424C2×D53semidirect
496. #339C2×D53semidirect
500. #336C2×D53semidirect
501. C53C2×#1866semidirect
603. #103C4×D53semidirect
604. #103C4×D53semidirect
611. #102C4×D53semidirect
612. #102C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#131×D532
C2×#108×D532
#424×D532
C2×#104×D532
#416×D532
#202749932
#202749922
#202749912
#202749902
#202749892
#202749882
#202749872
#339×D532
#336×D532
C53×#18662
C2×#186653