Finite Group Databasebeta

← D53×#1919 #27386232

Subgroups — D53×#1919 #27386232

Order 13568.

1086 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D53C211yesmaximal, characteristic
2#389×D53C211yesmaximal, characteristic
3C4×C4⋊C4×D53C211yesmaximal, characteristic
4#20275296C211yesmaximal, characteristic, complemented
5#20275295C211yesmaximal, characteristic, complemented
6#20275294C211yesmaximal, characteristic, complemented
7#20275293C211yesmaximal, characteristic, complemented
8#20275292C211yesmaximal, characteristic, complemented
9#20275291C211yesmaximal, characteristic, complemented
10#20275290C211yesmaximal, characteristic, complemented
11#340×D53C211yesmaximal, characteristic
12#340×D53C211yesmaximal, characteristic
13#340×D53C211yesmaximal, characteristic
14#336×D53C211yesmaximal, characteristic
15C53×#1919C211yesmaximal, characteristic, complemented
16C22×C8×D53C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18C2×C4⋊C4×D53—21no—
19C2×C4⋊C4×D53C2211yescharacteristic
20C2×C4⋊C4×D53C2211yescharacteristic
21C2×C4⋊C4×D53C2211yescharacteristic
22C2×C4⋊C4×D53C2211yescharacteristic
23C2×C42×D53—21no—
24C2×C42×D53C2211yescharacteristic
25C2×#13133149C2211yescharacteristic
26C2×#13133148C2211yescharacteristic
27C2×#13133148C2211yescharacteristic
28#106×D53C418yescomplemented
29#16810522C2211yescharacteristic
30#16810521C2211yescharacteristic
31#16810520—21no—
32#16810519C2211yescharacteristic
33#16810518—21no—
34C4⋊C4×Dic53C2211yescharacteristic
35C4⋊C4×Dic53C2211yescharacteristic
36C4×#11719919—21no—
37C4×C4⋊Dic53C2211yescharacteristic
38#16810474—21no—
39#95×D53—21no—
40#95×D53—21no—
41#16810386C2211yescharacteristic
42#16810386C2211yescharacteristic
43#16810386C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810378C2211yescharacteristic
51#16810377C2211yescharacteristic
52#16810377C2211yescharacteristic
53C2×#106×C53C2211yescharacteristic
54C53×#389C2211yescharacteristic
55C4×C4⋊C4×C53C2211yescharacteristic
56C53×#340C2211yescharacteristic
57C53×#340C2211yescharacteristic
58C53×#340C2211yescharacteristic
59C53×#336C2211yescharacteristic
60C22×C4×D53—21no—
61C22×C4×D53—21no—
62C22×C4×D53—21no—
63C22×C4×D53—21no—
64C22×C4×D53D411yescharacteristic
65C22×C4×D53D411yescharacteristic
66C22×C4×D53C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C2×C8×D53—22no—
70C2×C8×D53—22no—
71C2×C8×D53—22no—
72C2×C8×D53—22no—
73C2×C8×D53—22no—
74C2×C8×D53C2×C414yes—
75C2×C4⋊Dic53—21no—
76C2×C4⋊Dic53C2311yescharacteristic
77C2×C4⋊Dic53C2311yescharacteristic
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×#11719919—21no—
81C2×#11719919—21no—
82C2×#11719919—21no—
83C2×#11719919—21no—
84C2×#11719919—21no—
85C2×#11719919—21no—
86C4⋊C4×D53—22no—
87C4⋊C4×D53—22no—
88C4⋊C4×D53—22no—
89C4⋊C4×D53—22no—
90C4⋊C4×D53—22no—
91C4⋊C4×D53—44no—
92C4⋊C4×D53C2×C414yes—
93C4⋊C4×D53C2×C414yes—
94C4⋊C4×D53Q814yes—
95C2×C4×Dic53—21no—
96C2×C4×Dic53—21no—
97C2×C4×Dic53—21no—
98C2×C4×Dic53D411yescharacteristic
99C2×C4×Dic53D411yescharacteristic
100C2×C4×Dic53C2311yescharacteristic
101C42×D53—22no—
102C42×D53—22no—
103C42×D53—44no—
104#13133149C2×C414yescomplemented
105#13133148C2×C414yescomplemented
106#13133148C2×C414yescomplemented
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113C22×C8×C53C2311yescharacteristic
114C22×C8×C53C2311yescharacteristic
115C2×C4⋊C4×C53—21no—
116C2×C4⋊C4×C53C2311yescharacteristic
117C2×C4⋊C4×C53C2311yescharacteristic
118C2×C4⋊C4×C53C2311yescharacteristic
119C2×C4⋊C4×C53C2311yescharacteristic
120C2×C42×C53—21no—
121C2×C42×C53C2311yescharacteristic
122#106×C53C2×C414yescomplemented
123#95×C53—21no—
124#95×C53—21no—
125C23×D53C2×D411yescharacteristic
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53C2×D411yescharacteristic
131C22×C4×C53C2×D411yescharacteristic
132C22×C4×C53C2411yescharacteristic
133C22×Dic53—21no—
134C22×Dic53—21no—
135C22×Dic53—21no—
136C22×Dic53—21no—
137C22×Dic53C2×D411yescharacteristic
138C22×Dic53C2×D411yescharacteristic
139C22×Dic53C2×D411yescharacteristic
140C2×C4×D53—22no—
141C2×C4×D53—22no—
142C2×C4×D53—24no—
143C2×C4×D53—24no—
144C2×C4×D53—24no—
145C2×C4×D53—22no—
146C2×C4×D53—22no—
147C2×C4×D53—22no—
148C2×C4×D53—42no—
149C2×C4×D53—42no—
150C2×C4×D53—42no—
151C2×C4×D53—42no—
152C2×C4×D53—42no—
153C2×C4×D53—42no—
154C2×C4×D53—42no—
155C2×C4×D53—42no—
156C2×C4×D53—42no—
157C2×C4×D53SD1614yes—
158C2×C4×D53C22×C412yes—
159C2×C4×D53C2×Q812yes—
160C2×C4×D53#4112yes—
161C2×C4×D53#4112yes—
162C2×C4×D53#4112yes—
163C2×C4×D53#4112yes—
164C2×C8×C53—21no—
165C2×C8×C53—21no—
166C2×C8×C53—21no—
167C2×C8×C53—21no—
168C2×C8×C53—21no—
169C2×C8×C53C22×C412yes—
170C4⋊C4×C53—21no—
171C4⋊C4×C53—21no—
172C4⋊C4×C53—21no—
173C4⋊C4×C53—21no—
174C4⋊C4×C53—21no—
175C4⋊C4×C53—42no—
176C4⋊C4×C53C22×C412yes—
177C4⋊C4×C53C22×C412yes—
178C4⋊C4×C53C2×Q812yes—
179C42×C53—21no—
180C42×C53—21no—
181C42×C53—42no—
182C4⋊Dic53—21no—
183C4⋊Dic53—21no—
184C4⋊Dic53—21no—
185C4⋊Dic53—21no—
186C4⋊Dic53—21no—
187C4⋊Dic53—42no—
188C4⋊Dic53C22×C412yes—
189C4⋊Dic53C22×C412yes—
190C4⋊Dic53C2×Q812yes—
191#11719919—24no—
192#11719919—24no—
193#11719919—24no—
194#11719919—42no—
195#11719919—42no—
196#11719919—42no—
197C4×Dic53—21no—
198C4×Dic53—21no—
199C4×Dic53—22no—
200C4×Dic53—22no—
201C4×Dic53—42no—
202C4×Dic53—42no—
203C4×Dic53—42no—
204C2×#88322—21no—
205C2×#88322—21no—
206C2×#88322—21no—
207C2×#88322—21no—
208C2×#88322—21no—
209C2×#88322C22×C412yes—
210C8×D53—28no—
211C8×D53—44no—
212C23×C53C22×D411yescharacteristic
213C22×D53C4×D412yes—
214C22×D53C22⋊Q812yes—
215C22×D53#12312yes—
216C22×D53C2×SD1612yes—
217C22×D53#13512yes—
218C22×D53AGL(1,ℤ/8)12yes—
219C22×D53#13712yes—
220C2×C4×C53—21no—
221C2×C4×C53—21no—
222C2×C4×C53—22no—
223C2×C4×C53—22no—
224C2×C4×C53—22no—
225C2×C4×C53—21no—
226C2×C4×C53—21no—
227C2×C4×C53—21no—
228C2×C4×C53—41no—
229C2×C4×C53—41no—
230C2×C4×C53—41no—
231C2×C4×C53—41no—
232C2×C4×C53—41no—
233C2×C4×C53—41no—
234C2×C4×C53—41no—
235C2×C4×C53—41no—
236C2×C4×C53—41no—
237C2×C4×C53C2×SD1612yes—
238C2×C4×C53C23×C411yescharacteristic
239C2×C4×C53C22×Q811yescharacteristic
240C2×C4×C53C2×#4111yescharacteristic
241C2×C4×C53C2×#4111yescharacteristic
242C2×C4×C53C2×#4111yescharacteristic
243C2×C4×C53C2×#4111yescharacteristic
244C2×Dic53—21no—
245C2×Dic53—21no—
246C2×Dic53—22no—
247C2×Dic53—22no—
248C2×Dic53—22no—
249C2×Dic53—21no—
250C2×Dic53—21no—
251C2×Dic53—21no—
252C2×Dic53—41no—
253C2×Dic53—41no—
254C2×Dic53—41no—
255C2×Dic53—41no—
256C2×Dic53—41no—
257C2×Dic53—41no—
258C2×Dic53—41no—
259C2×Dic53—41no—
260C2×Dic53—41no—
261C2×Dic53C4×D412yes—
262C2×Dic53C22⋊Q812yes—
263C2×Dic53#12312yes—
264C2×Dic53C2×SD1612yes—
265C4×D53—28no—
266C4×D53—48no—
267C4×D53—48no—
268C4×D53—48no—
269C4×D53—44no—
270C4×D53—84no—
271C4×D53#11714yes—
272C4×D53C4×Q814yes—
273C4×D53#12514yes—
274C4×D53#12614yes—
275C8×C53—22no—
276C8×C53—41no—
277#88322—22no—
278#88322—41no—
279C2×#1919—531nomaximal, Sylow
280C22×C53C2×C4×D411yescharacteristic
281C22×C53C2×C22⋊Q811yescharacteristic
282C22×C53C2×#12311yescharacteristic
283C22×C53C22×SD1611yescharacteristic
284C22×C53C2×#13511yescharacteristic
285C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C53C2×#13711yescharacteristic
287C2×D53#38714yes—
288C2×D53C4×SD1614yes—
289C2×D53#44014yes—
290C2×D53#47514yes—
291C2×D53#47814yes—
292C2×D53#48114yes—
293C2×D53#48514yes—
294C4×C53—22no—
295C4×C53—42no—
296C4×C53—41no—
297C4×C53—42no—
298C4×C53—42no—
299C4×C53—81no—
300C4×C53C2×#11711yescharacteristic
301C4×C53C2×C4×Q811yescharacteristic
302C4×C53C2×#12511yescharacteristic
303C4×C53C2×#12611yescharacteristic
304Dic53—22no—
305Dic53—42no—
306Dic53—41no—
307Dic53—42no—
308Dic53—42no—
309Dic53—81no—
310Dic53#38714yes—
311C22×#106—531no—
312C2×#389—531no—
313C2×C4×C4⋊C4—531no—
314#1919—531no—
315#1919—531no—
316#1919—531no—
317#1919—531no—
318#1919—531no—
319#1919—531no—
320#1919—531no—
321#1919D5311yescharacteristic, direct product factor
322C2×#340—531no—
323C2×#340—531no—
324C2×#340—531no—
325C2×#336—531no—
326C2×C53C2×#38711yescharacteristic
327C2×C53C2×C4×SD1611yescharacteristic
328C2×C53C2×#44011yescharacteristic
329C2×C53C2×#47811yescharacteristic
330C2×C53C2×#47511yescharacteristic
331C2×C53C2×#48511yescharacteristic
332C2×C53C2×#48111yescharacteristic
333D53#191918yesdirect product factor
334C23×C8—531no—
335C23×C8—531no—
336C22×C4⋊C4—531no—
337C22×C4⋊C4—531no—
338C22×C4⋊C4—531no—
339C22×C4⋊C4—531no—
340C22×C4⋊C4—1061no—
341C22×C42—531no—
342C22×C42—1061no—
343C2×#106—531no—
344C2×#106—531no—
345C2×#106—531no—
346C2×#106—538no—
347C2×#106C2×D5311yescharacteristic
348#389—531no—
349#389—531no—
350#389—531no—
351#389—1061no—
352#389—1061no—
353#389C2×D5311yescharacteristic
354C4×C4⋊C4—531no—
355C4×C4⋊C4—531no—
356C4×C4⋊C4—531no—
357C4×C4⋊C4—1061no—
358C4×C4⋊C4—1061no—
359C4×C4⋊C4C2×D5311yescharacteristic
360C2×#95—1061no—
361C2×#95—1061no—
362#340—531no—
363#340—531no—
364#340—531no—
365#340—531no—
366#340—531no—
367#340—531no—
368#340—531no—
369#340—531no—
370#340—531no—
371#340C2×D5311yescharacteristic
372#340C2×D5311yescharacteristic
373#340C2×D5311yescharacteristic
374#336—531no—
375#336—531no—
376#336—531no—
377#336C2×D5311yescharacteristic
378C53C2×#191911yescharacteristic, complemented, Sylow
379C23×C4—531no—
380C23×C4—531no—
381C23×C4—531no—
382C23×C4—1061no—
383C23×C4—1061no—
384C23×C4—1061no—
385C23×C4—1061no—
386C22×C8—531no—
387C22×C8—534no—
388C22×C8—531no—
389C22×C8—1062no—
390C22×C8—1062no—
391C22×C8—1062no—
392C22×C8—1062no—
393C22×C8—1062no—
394C22×C8C22×D5311yescharacteristic
395C22×C8C22×D5311yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4—531no—
398C2×C4⋊C4—531no—
399C2×C4⋊C4—531no—
400C2×C4⋊C4—534no—
401C2×C4⋊C4—534no—
402C2×C4⋊C4—534no—
403C2×C4⋊C4—531no—
404C2×C4⋊C4—1062no—
405C2×C4⋊C4—1062no—
406C2×C4⋊C4—1062no—
407C2×C4⋊C4—1062no—
408C2×C4⋊C4—1062no—
409C2×C4⋊C4—1061no—
410C2×C4⋊C4—1061no—
411C2×C4⋊C4—1061no—
412C2×C4⋊C4—1061no—
413C2×C4⋊C4—1061no—
414C2×C4⋊C4—1061no—
415C2×C4⋊C4—1061no—
416C2×C4⋊C4—2124no—
417C2×C4⋊C4C22×D5311yescharacteristic
418C2×C4⋊C4C22×D5311yescharacteristic
419C2×C4⋊C4C22×D5311yescharacteristic
420C2×C4⋊C4C22×D5311yescharacteristic
421C2×C42—21no—
422C2×C42—531no—
423C2×C42—531no—
424C2×C42—531no—
425C2×C42—1062no—
426C2×C42—1062no—
427C2×C42—1061no—
428C2×C42—1061no—
429C2×C42—1061no—
430C2×C42—2124no—
431C2×C42C22×D5311yescharacteristic
432#106—534no—
433#106—534no—
434#106—534no—
435#106C4×D5314yescomplemented
436#95—21no—
437#95—21no—
438#95—1061no—
439#95—1061no—
440#95—1061no—
441#95—1061no—
442#95—1061no—
443#95—1061no—
444C24—531no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—531no—
450C22×C4—532no—
451C22×C4—532no—
452C22×C4—532no—
453C22×C4—532no—
454C22×C4—532no—
455C22×C4—532no—
456C22×C4—531no—
457C22×C4—534no—
458C22×C4—531no—
459C22×C4—1062no—
460C22×C4—1062no—
461C22×C4—1062no—
462C22×C4—1064no—
463C22×C4—1064no—
464C22×C4—1064no—
465C22×C4—1062no—
466C22×C4—1062no—
467C22×C4—1061no—
468C22×C4—1061no—
469C22×C4—1061no—
470C22×C4—1061no—
471C22×C4—2122no—
472C22×C4—2122no—
473C22×C4—2122no—
474C22×C4—2122no—
475C22×C4—2122no—
476C22×C4—2122no—
477C22×C4—2122no—
478C22×C4—2122no—
479C22×C4—2122no—
480C22×C4D4×D5311yescharacteristic
481C22×C4D4×D5311yescharacteristic
482C22×C4C23×D5311yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—532no—
489C2×C8—1068no—
490C2×C8—1061no—
491C2×C8—1061no—
492C2×C8—1061no—
493C2×C8—1061no—
494C2×C8—1061no—
495C2×C8—2124no—
496C2×C8C2×C4×D5312yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—532no—
504C4⋊C4—532no—
505C4⋊C4—532no—
506C4⋊C4—1064no—
507C4⋊C4—1064no—
508C4⋊C4—1064no—
509C4⋊C4—1061no—
510C4⋊C4—1061no—
511C4⋊C4—1061no—
512C4⋊C4—1061no—
513C4⋊C4—1061no—
514C4⋊C4—2122no—
515C4⋊C4—2122no—
516C4⋊C4—2122no—
517C4⋊C4—2122no—
518C4⋊C4C2×C4×D5312yes—
519C4⋊C4C2×C4×D5312yes—
520C4⋊C4Q8×D5312yes—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—1062no—
525C42—1062no—
526C42—1061no—
527C42—1061no—
528C42—2122no—
529C42—2122no—
530C42—2122no—
531C23—532no—
532C23—532no—
533C23—532no—
534C23—532no—
535C23—532no—
536C23—532no—
537C23—532no—
538C23C2×D4×D5311yescharacteristic
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—532no—
557C2×C4—532no—
558C2×C4—532no—
559C2×C4—534no—
560C2×C4—534no—
561C2×C4—534no—
562C2×C4—534no—
563C2×C4—532no—
564C2×C4—1068no—
565C2×C4—1061no—
566C2×C4—1061no—
567C2×C4—1062no—
568C2×C4—1062no—
569C2×C4—1062no—
570C2×C4—1061no—
571C2×C4—1061no—
572C2×C4—1061no—
573C2×C4—4244no—
574C2×C4—2124no—
575C2×C4—2128no—
576C2×C4—2128no—
577C2×C4—2128no—
578C2×C4—2121no—
579C2×C4—2121no—
580C2×C4—2121no—
581C2×C4—2121no—
582C2×C4—2121no—
583C2×C4—2121no—
584C2×C4—2121no—
585C2×C4—2121no—
586C2×C4—2121no—
587C2×C4SD16×D5312yes—
588C2×C4C22×C4×D5311yescharacteristic
589C2×C4C2×Q8×D5311yescharacteristic
590C2×C4#41×D5311yescharacteristic
591C2×C4#41×D5311yescharacteristic
592C2×C4#41×D5311yescharacteristic
593C2×C4#41×D5311yescharacteristic
594C8—22no—
595C8—41no—
596C8—1062no—
597C8—2121no—
598C22—534no—
599C22—534no—
600C22—534no—
601C22—534no—
602C22—534no—
603C22—534no—
604C22—534no—
605C22C4×D4×D5311yescharacteristic
606C22C22⋊Q8×D5311yescharacteristic
607C22#123×D5311yescharacteristic
608C22C2×SD16×D5311yescharacteristic
609C22#135×D5311yescharacteristic
610C22AGL(1,ℤ/8)×D5311yescharacteristic
611C22#137×D5311yescharacteristic
612C4—22no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4—41no—
617C4—81no—
618C4—534no—
619C4—1062no—
620C4—4241no—
621C4—2122no—
622C4—2122no—
623C4—2122no—
624C4—2121no—
625C4#117×D5311yescharacteristic
626C4C4×Q8×D5311yescharacteristic
627C4#125×D5311yescharacteristic
628C4#126×D5311yescharacteristic
629C2—538no—
630C2#387×D5311yescharacteristic
631C2C4×SD16×D5311yescharacteristic
632C2#440×D5311yescharacteristic
633C2#478×D5311yescharacteristic
634C2#475×D5311yescharacteristic
635C2#485×D5311yescharacteristic
636C2#481×D5311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1919C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
cosocleC22×C4×C53C24
hypercenter#1919D53
hypocenterC53C2×#1919
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
4. #20275296C2semidirect
5. #20275295C2semidirect
6. #20275294C2semidirect
7. #20275293C2semidirect
8. #20275292C2semidirect
9. #20275291C2semidirect
10. #20275290C2semidirect
15. C53×#1919C2semidirect
28. #106×D53C4semidirect
104. #13133149C2×C4semidirect
105. #13133148C2×C4semidirect
106. #13133148C2×C4semidirect
122. #106×C53C2×C4semidirect
321. #1919D53direct (N × H)
333. D53#1919direct (N × H)
378. C53C2×#1919semidirect
435. #106C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D532
#389×D532
C4×C4⋊C4×D532
#202752962
#202752952
#202752942
#202752932
#202752922
#202752912
#202752902
#340×D532
#336×D532
C53×#19192
C2×#191953