Finite Group Databasebeta

← D53×#1872 #27385282

Subgroups — D53×#1872 #27385282

Order 13568.

2270 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D53C211yesmaximal, characteristic
2C22×C4⋊C4×D53C211yesmaximal, characteristic
3C2×#103×D53C212yesmaximal, complemented
4C2×C22⋊C8×D53C211yesmaximal, characteristic
5#20275023C211yesmaximal, characteristic, complemented
6#20275022C211yesmaximal, characteristic, complemented
7#20275021C212yesmaximal, complemented
8#20275020C211yesmaximal, characteristic, complemented
9#20275019C212yesmaximal, complemented
10#340×D53C212yesmaximal, complemented
11C53×#1872C211yesmaximal, characteristic, complemented
12C22×Q8×D53C2211yescharacteristic
13C23×C4×D53—21no—
14C23×C4×D53C2211yescharacteristic
15C22×C8×D53C2212yes—
16C2×#13133197C2211yescharacteristic
17C2×#13133196C2211yescharacteristic
18C2×#13133195—21no—
19C2×#13133194—21no—
20C2×#13133193C2211yescharacteristic
21C22⋊Q8×D53—24no—
22C22⋊Q8×D53C418yescomplemented
23C22×C4⋊Dic53C2211yescharacteristic
24C22×#11719919—21no—
25C2×C4⋊C4×D53—21no—
26C2×C4⋊C4×D53—21no—
27C2×C4⋊C4×D53—21no—
28C2×C4⋊C4×D53—28no—
29C2×C4⋊C4×D53C2212yes—
30C2×C4⋊C4×D53C2211yescharacteristic
31C2×C4⋊C4×D53C2212yes—
32C2×C22⋊C4×D53—21no—
33C2×#13133142C2212yescomplemented
34C2×#13133141C2212yescomplemented
35C2×#13133140C2212yescomplemented
36#103×D53—28no—
37C2×C22⋊#88322C2211yescharacteristic
38C2×#13133129C2212yes—
39C22⋊C8×D53—24no—
40#16810386C2212yescomplemented
41#16810385C2212yescomplemented
42#16810385C2212yescomplemented
43C2×C22⋊Q8×C53C2211yescharacteristic
44C22×C4⋊C4×C53C2211yescharacteristic
45C2×#103×C53C2212yescomplemented
46C2×C22⋊C8×C53C2211yescharacteristic
47C53×#340C2212yescomplemented
48C24×D53D411yescharacteristic
49C22×Dic106—21no—
50C22×Dic106C2311yescharacteristic
51C2×Q8×D53—22no—
52C2×Q8×D53—24no—
53C2×Q8×D53—24no—
54C2×Q8×D53C2×C414yescomplemented
55C23×Dic53—21no—
56C23×Dic53D411yescharacteristic
57C22×C4×D53—24no—
58C22×C4×D53—24no—
59C22×C4×D53—28no—
60C22×C4×D53—21no—
61C22×C4×D53—21no—
62C22×C4×D53—22no—
63C22×C4×D53—22no—
64C22×C4×D53—44no—
65C22×C4×D53—44no—
66C22×C4×D53C2×C414yes—
67C22×C4×D53D411yescharacteristic
68C22×C4×D53D411yescharacteristic
69C22×C4×D53D414yes—
70C22×C4×D53C2311yescharacteristic
71C22×C4×D53C2311yescharacteristic
72C22×#88322C2312yes—
73C2×C8×D53—24no—
74C2×C8×D53—24no—
75C2×C8×D53—24no—
76#13133197—22no—
77#13133197C2×C414yescomplemented
78#13133196—22no—
79#13133196C2×C414yescomplemented
80#13133195—28no—
81#13133194—28no—
82#13133193—22no—
83#13133193C2×C414yescomplemented
84C2×C4⋊Dic53—24no—
85C2×C4⋊Dic53—21no—
86C2×C4⋊Dic53—21no—
87C2×C4⋊Dic53C2311yescharacteristic
88C2×C4⋊Dic53C2312yes—
89C2×#11719919—28no—
90C2×#11719919—21no—
91C2×#11719919—22no—
92C2×#11719919—22no—
93C2×#11719919—21no—
94C2×#11719919—21no—
95C4⋊C4×D53—28no—
96C4⋊C4×D53—28no—
97C4⋊C4×D53—24no—
98C4⋊C4×D53—24no—
99C4⋊C4×D53—28no—
100C4⋊C4×D53—24no—
101C4⋊C4×D53—22no—
102C4⋊C4×D53C2×C414yescomplemented
103C4⋊C4×D53D418yes—
104C2×C22⋊Dic53—21no—
105C2×#11719921—21no—
106C2×#11719921—21no—
107C22⋊C4×D53—28no—
108#13133142—24no—
109#13133141—24no—
110#13133140—24no—
111C22⋊#88322—22no—
112#13133129—24no—
113C22×Q8×C53C2311yescharacteristic
114C23×C4×C53—21no—
115C23×C4×C53C2311yescharacteristic
116C22×C8×C53C2312yes—
117C22⋊Q8×C53—22no—
118C22⋊Q8×C53C2×C414yescomplemented
119C2×C4⋊C4×C53—24no—
120C2×C4⋊C4×C53—21no—
121C2×C4⋊C4×C53—21no—
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C4⋊C4×C53C2312yes—
124C2×C22⋊C4×C53—21no—
125#103×C53—24no—
126C22⋊C8×C53—22no—
127C24×C53C2×D411yescharacteristic
128C23×D53—22no—
129C23×D53—22no—
130C23×D53—22no—
131C23×D53—22no—
132C23×D53C22⋊C414yes—
133C23×D53SD1614yes—
134C23×D53Q1614yes—
135C23×D53C2×D411yescharacteristic
136C23×D53C2×D411yescharacteristic
137C2×Q8×C53—21no—
138C2×Q8×C53—22no—
139C2×Q8×C53—22no—
140C2×Q8×C53C22×C412yescomplemented
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—24no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—22no—
147C22×C4×C53—42no—
148C22×C4×C53—42no—
149C22×C4×C53C22×C412yes—
150C22×C4×C53C2×D411yescharacteristic
151C22×C4×C53C2×D412yes—
152C22×C4×C53C2411yescharacteristic
153C22×Dic53—22no—
154C22×Dic53—22no—
155C22×Dic53—24no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—22no—
159C22×Dic53—42no—
160C22×Dic53—42no—
161C22×Dic53C22⋊C414yes—
162C22×Dic53C2×D411yescharacteristic
163C22×Dic53C2×D411yescharacteristic
164Q8×D53—216no—
165Q8×D53—48no—
166C2×C4×D53—22no—
167C2×C4×D53—22no—
168C2×C4×D53—22no—
169C2×C4×D53—22no—
170C2×C4×D53—22no—
171C2×C4×D53—22no—
172C2×C4×D53—216no—
173C2×C4×D53—216no—
174C2×C4×D53—28no—
175C2×C4×D53—24no—
176C2×C4×D53—24no—
177C2×C4×D53—28no—
178C2×C4×D53—44no—
179C2×C4×D53—432no—
180C2×C4×D53—42no—
181C2×C4×D53—42no—
182C2×C4×D53—44no—
183C2×C4×D53—44no—
184C2×C4×D53—42no—
185C2×C4×D53—44no—
186C2×C4×D53—42no—
187C2×C4×D53C22⋊C414yes—
188C2×C4×D53C22⋊C414yes—
189C2×C4×D53C22×C412yes—
190C2×C4×D53C22×C412yes—
191C2×C4×D53C2×D412yes—
192C2×C4×D53C2×D414yes—
193C2×C4×D53C2×D412yes—
194C2×C4×D53#4114yes—
195C2×Dic106—22no—
196C2×Dic106—22no—
197C2×Dic106—21no—
198C2×Dic106—24no—
199C2×Dic106—42no—
200C2×Dic106—42no—
201C2×Dic106C22×C412yescomplemented
202C2×C8×C53—22no—
203C2×C8×C53—22no—
204C2×C8×C53—22no—
205C4⋊C4×C53—24no—
206C4⋊C4×C53—24no—
207C4⋊C4×C53—22no—
208C4⋊C4×C53—21no—
209C4⋊C4×C53C22×C412yescomplemented
210C4⋊C4×C53C2×D414yes—
211C22⋊C4×C53—24no—
212C22⋊Dic53—24no—
213#11719921—24no—
214#11719921—24no—
215C4⋊Dic53—24no—
216C4⋊Dic53—22no—
217C4⋊Dic53—21no—
218C4⋊Dic53—24no—
219C4⋊Dic53C22×C412yescomplemented
220C4⋊Dic53C2×D414yes—
221#11719919—28no—
222#11719919—24no—
223#11719919—24no—
224#11719919—24no—
225#11719919—28no—
226C2×#88322—22no—
227C2×#88322—22no—
228C2×#88322—22no—
229C8×D53—48no—
230C23×C53—21no—
231C23×C53—21no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53C2×C22⋊C412yes—
235C23×C53C2×SD1612yes—
236C23×C53C2×Q1612yes—
237C23×C53C22×D411yescharacteristic
238C22×D53—21no—
239C22×D53—21no—
240C22×D53—21no—
241C22×D53—21no—
242C22×D53—28no—
243C22×D53—28no—
244C22×D53—28no—
245C22×D53—28no—
246C22×D53—28no—
247C22×D53—28no—
248C22×D53#103116yescomplemented
249C22×D53C2×C22⋊C412yes—
250C22×D53C2×C22⋊C412yes—
251C22×D53#12012yes—
252C22×D53#12312yes—
253C22×D53C2×SD1612yes—
254C22×D53C2×SD1612yes—
255C22×D53C2×Q1612yes—
256C22×D53C2×Q1612yes—
257C22×D53AGL(1,ℤ/8)12yes—
258C22×D53#13712yes—
259Q8×C53—24no—
260Q8×C53—42no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—24no—
264C2×C4×C53—24no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—24no—
268C2×C4×C53—48no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—42no—
272C2×C4×C53—42no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53C2×C22⋊C412yes—
276C2×C4×C53C23×C411yescharacteristic
277C2×C4×C53C22×D412yes—
278C2×C4×C53C22×D411yescharacteristic
279C2×C4×C53C2×#4112yes—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—28no—
283C2×Dic53—22no—
284C2×Dic53—22no—
285C2×Dic53—24no—
286C2×Dic53—48no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—42no—
290C2×Dic53—42no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53C2×C22⋊C412yes—
294C2×Dic53C2×C22⋊C412yes—
295C2×Dic53#12012yes—
296C2×Dic53#12312yes—
297C4×D53—28no—
298C4×D53—24no—
299C4×D53—24no—
300C4×D53—28no—
301C4×D53—416no—
302C4×D53—48no—
303C4×D53—48no—
304C4×D53—416no—
305C4×D53C4×D418yes—
306C4×D53#12118yes—
307Dic106—24no—
308Dic106—42no—
309Dic106—48no—
310C8×C53—42no—
311#88322—42no—
312C2×#1872—531nomaximal, Sylow
313C22×C53—22no—
314C22×C53—22no—
315C22×C53—22no—
316C22×C53—22no—
317C22×C53—22no—
318C22×C53—22no—
319C22×C53C2×#10314yescomplemented
320C22×C53C22×C22⋊C411yescharacteristic
321C22×C53C2×#12011yescharacteristic
322C22×C53C2×#12311yescharacteristic
323C22×C53C22×SD1611yescharacteristic
324C22×C53C22×Q1611yescharacteristic
325C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C53C2×#13711yescharacteristic
327C2×D53—22no—
328C2×D53—22no—
329C2×D53—22no—
330C2×D53—22no—
331C2×D53—22no—
332C2×D53—22no—
333C2×D53—232no—
334C2×D53#38614yes—
335C2×D53C2×#10314yes—
336C2×D53C2×#10314yescomplemented
337C2×D53#41714yes—
338C2×D53#45014yes—
339C2×D53#45114yes—
340C2×D53#48314yes—
341C2×D53#48414yes—
342C4×C53—22no—
343C4×C53—42no—
344C4×C53—44no—
345C4×C53—42no—
346C4×C53C2×C4×D412yes—
347C4×C53C2×#12112yes—
348Dic53—22no—
349Dic53—42no—
350Dic53—44no—
351Dic53—42no—
352Dic53#38614yes—
353C22×C22⋊Q8—531no—
354C23×C4⋊C4—531no—
355C22×#103—532no—
356C22×C22⋊C8—531no—
357#1872—532no—
358#1872—531no—
359#1872—532no—
360#1872—531no—
361#1872—531no—
362#1872D5311yescharacteristic, direct product factor
363C2×#340—532no—
364C2×C53—24no—
365C2×C53C2×#38611yescharacteristic
366C2×C53C22×#10311yescharacteristic
367C2×C53C2×#41711yescharacteristic
368C2×C53C2×#45011yescharacteristic
369C2×C53C2×#45111yescharacteristic
370C2×C53C2×#48311yescharacteristic
371C2×C53C2×#48411yescharacteristic
372D53—24no—
373D53#187218yesdirect product factor
374C23×Q8—531no—
375C24×C4—531no—
376C24×C4—1061no—
377C23×C8—532no—
378C2×C22⋊Q8—531no—
379C2×C22⋊Q8—531no—
380C2×C22⋊Q8—538no—
381C2×C22⋊Q8—531no—
382C2×C22⋊Q8—1061no—
383C2×C22⋊Q8—1061no—
384C2×C22⋊Q8—1064no—
385C2×C22⋊Q8C2×D5311yescharacteristic
386C22×C4⋊C4—532no—
387C22×C4⋊C4—531no—
388C22×C4⋊C4—531no—
389C22×C4⋊C4—532no—
390C22×C4⋊C4—1068no—
391C22×C4⋊C4—1061no—
392C22×C4⋊C4—1061no—
393C22×C4⋊C4—1061no—
394C22×C4⋊C4—1061no—
395C22×C4⋊C4C2×D5311yescharacteristic
396C22×C22⋊C4—1061no—
397C2×#103—532no—
398C2×#103—532no—
399C2×#103—532no—
400C2×#103—1068no—
401C2×#103C2×D5312yescomplemented
402C2×C22⋊C8—531no—
403C2×C22⋊C8—532no—
404C2×C22⋊C8—1064no—
405C2×C22⋊C8C2×D5311yescharacteristic
406#340—532no—
407#340—532no—
408#340—532no—
409#340C2×D5312yescomplemented
410C53C2×#187211yescharacteristic, complemented, Sylow
411C25—531no—
412C22×Q8—534no—
413C22×Q8—531no—
414C22×Q8—1061no—
415C22×Q8—1062no—
416C22×Q8—1064no—
417C22×Q8—1064no—
418C22×Q8C22×D5311yescharacteristic
419C23×C4—21no—
420C23×C4—531no—
421C23×C4—531no—
422C23×C4—534no—
423C23×C4—531no—
424C23×C4—531no—
425C23×C4—534no—
426C23×C4—531no—
427C23×C4—1064no—
428C23×C4—1064no—
429C23×C4—1061no—
430C23×C4—1061no—
431C23×C4—1062no—
432C23×C4—1062no—
433C23×C4—1068no—
434C23×C4—1061no—
435C23×C4—2124no—
436C23×C4—2124no—
437C23×C4C22×D5311yescharacteristic
438C22×C8—532no—
439C22×C8—1064no—
440C22×C8—1064no—
441C22×C8—1064no—
442C22×C8C22×D5312yes—
443C22⋊Q8—22no—
444C22⋊Q8—534no—
445C22⋊Q8—534no—
446C22⋊Q8—534no—
447C22⋊Q8—1068no—
448C22⋊Q8—1068no—
449C22⋊Q8—1062no—
450C22⋊Q8—1062no—
451C22⋊Q8—1062no—
452C22⋊Q8C4×D5314yescomplemented
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—532no—
457C2×C4⋊C4—531no—
458C2×C4⋊C4—534no—
459C2×C4⋊C4—538no—
460C2×C4⋊C4—1064no—
461C2×C4⋊C4—1064no—
462C2×C4⋊C4—1062no—
463C2×C4⋊C4—1068no—
464C2×C4⋊C4—1068no—
465C2×C4⋊C4—1068no—
466C2×C4⋊C4—1064no—
467C2×C4⋊C4—1062no—
468C2×C4⋊C4—1062no—
469C2×C4⋊C4—1061no—
470C2×C4⋊C4—1061no—
471C2×C4⋊C4—1061no—
472C2×C4⋊C4—1068no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1064no—
476C2×C4⋊C4C22×D5311yescharacteristic
477C2×C4⋊C4C22×D5312yes—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1068no—
480C2×C22⋊C4—1061no—
481C2×C22⋊C4—1061no—
482C2×C22⋊C4—1061no—
483#103—24no—
484#103—1064no—
485#103—1064no—
486#103—1064no—
487C22⋊C8—22no—
488C22⋊C8—1064no—
489C22⋊C8—1062no—
490C24—531no—
491C24—534no—
492C24—534no—
493C24—534no—
494C24—531no—
495C24—1062no—
496C24—1062no—
497C24—1062no—
498C24—1062no—
499C24D4×D5311yescharacteristic
500C2×Q8—21no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—532no—
504C2×Q8—1064no—
505C2×Q8—10616no—
506C2×Q8—1061no—
507C2×Q8—1062no—
508C2×Q8—1062no—
509C2×Q8—2122no—
510C2×Q8—2122no—
511C2×Q8—2128no—
512C2×Q8C2×C4×D5312yescomplemented
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—531no—
522C22×C4—532no—
523C22×C4—534no—
524C22×C4—532no—
525C22×C4—534no—
526C22×C4—534no—
527C22×C4—531no—
528C22×C4—534no—
529C22×C4—534no—
530C22×C4—532no—
531C22×C4—532no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—10616no—
535C22×C4—10616no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1064no—
539C22×C4—1064no—
540C22×C4—1068no—
541C22×C4—1068no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—1064no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1062no—
550C22×C4—2122no—
551C22×C4—2122no—
552C22×C4—2124no—
553C22×C4—2124no—
554C22×C4—2124no—
555C22×C4—2122no—
556C22×C4—2122no—
557C22×C4—21232no—
558C22×C4—2124no—
559C22×C4—2122no—
560C22×C4—2122no—
561C22×C4C2×C4×D5312yes—
562C22×C4D4×D5311yescharacteristic
563C22×C4D4×D5312yes—
564C22×C4C23×D5311yescharacteristic
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—1062no—
569C2×C8—1062no—
570C2×C8—1062no—
571C2×C8—2128no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—532no—
577C4⋊C4—534no—
578C4⋊C4—1068no—
579C4⋊C4—1064no—
580C4⋊C4—1064no—
581C4⋊C4—1064no—
582C4⋊C4—1068no—
583C4⋊C4—1064no—
584C4⋊C4—1064no—
585C4⋊C4—1062no—
586C4⋊C4—1061no—
587C4⋊C4C2×C4×D5312yescomplemented
588C4⋊C4D4×D5314yes—
589C22⋊C4—24no—
590C22⋊C4—1064no—
591C22⋊C4—1064no—
592C22⋊C4—1064no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—532no—
598C23—532no—
599C23—532no—
600C23—532no—
601C23—532no—
602C23—532no—
603C23—532no—
604C23—532no—
605C23—5316no—
606C23—532no—
607C23—532no—
608C23—1068no—
609C23—1068no—
610C23—1068no—
611C23—1068no—
612C23—1068no—
613C23—1068no—
614C23—1061no—
615C23—1061no—
616C23—1061no—
617C23—1061no—
618C23C22⋊C4×D5312yes—
619C23SD16×D5312yes—
620C23Q16×D5312yes—
621C23C2×D4×D5311yescharacteristic
622Q8—24no—
623Q8—42no—
624Q8—1064no—
625Q8—2128no—
626Q8—2122no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—532no—
642C2×C4—532no—
643C2×C4—532no—
644C2×C4—538no—
645C2×C4—538no—
646C2×C4—532no—
647C2×C4—1068no—
648C2×C4—1068no—
649C2×C4—1068no—
650C2×C4—1061no—
651C2×C4—1061no—
652C2×C4—1064no—
653C2×C4—1064no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1064no—
657C2×C4—2128no—
658C2×C4—21216no—
659C2×C4—2128no—
660C2×C4—21216no—
661C2×C4—2128no—
662C2×C4—2121no—
663C2×C4—2121no—
664C2×C4—2122no—
665C2×C4—2121no—
666C2×C4—2122no—
667C2×C4—2121no—
668C2×C4C22⋊C4×D5312yes—
669C2×C4C22×C4×D5311yescharacteristic
670C2×C4C2×D4×D5312yes—
671C2×C4C2×D4×D5311yescharacteristic
672C2×C4#41×D5312yes—
673C8—42no—
674C8—2122no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—534no—
682C22—534no—
683C22—534no—
684C22—534no—
685C22—534no—
686C22—534no—
687C22—534no—
688C22—534no—
689C22—10632no—
690C22—1062no—
691C22—1062no—
692C22—1062no—
693C22—1062no—
694C22—1062no—
695C22—1062no—
696C22#103×D5314yescomplemented
697C22C2×C22⋊C4×D5311yescharacteristic
698C22#120×D5311yescharacteristic
699C22#123×D5311yescharacteristic
700C22C2×SD16×D5311yescharacteristic
701C22C2×Q16×D5311yescharacteristic
702C22AGL(1,ℤ/8)×D5311yescharacteristic
703C22#137×D5311yescharacteristic
704C4—22no—
705C4—42no—
706C4—42no—
707C4—44no—
708C4—534no—
709C4—1062no—
710C4—2122no—
711C4—2122no—
712C4—2124no—
713C4C4×D4×D5312yes—
714C4#121×D5312yes—
715C2—24no—
716C2—538no—
717C2—1064no—
718C2#386×D5311yescharacteristic
719C2C2×#103×D5311yescharacteristic
720C2#417×D5311yescharacteristic
721C2#450×D5311yescharacteristic
722C2#451×D5311yescharacteristic
723C2#483×D5311yescharacteristic
724C2#484×D5311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1872C2
socleC23×C53C22×D4
prime radicalC24×D53D4
cosocleC22×C4×C53C24
hypercenter#1872D53
hypocenterC53C2×#1872
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#103×D53C2semidirect
5. #20275023C2semidirect
6. #20275022C2semidirect
7. #20275021C2semidirect
8. #20275020C2semidirect
9. #20275019C2semidirect
10. #340×D53C2semidirect
11. C53×#1872C2semidirect
22. C22⋊Q8×D53C4semidirect
33. C2×#13133142C22semidirect
34. C2×#13133141C22semidirect
35. C2×#13133140C22semidirect
40. #16810386C22semidirect
41. #16810385C22semidirect
42. #16810385C22semidirect
45. C2×#103×C53C22semidirect
47. C53×#340C22semidirect
54. C2×Q8×D53C2×C4semidirect
77. #13133197C2×C4semidirect
79. #13133196C2×C4semidirect
83. #13133193C2×C4semidirect
102. C4⋊C4×D53C2×C4semidirect
118. C22⋊Q8×C53C2×C4semidirect
140. C2×Q8×C53C22×C4semidirect
201. C2×Dic106C22×C4semidirect
209. C4⋊C4×C53C22×C4semidirect
219. C4⋊Dic53C22×C4semidirect
248. C22×D53#103semidirect
319. C22×C53C2×#103semidirect
336. C2×D53C2×#103semidirect
362. #1872D53direct (N × H)
373. D53#1872direct (N × H)
401. C2×#103C2×D53semidirect
409. #340C2×D53semidirect
410. C53C2×#1872semidirect
452. C22⋊Q8C4×D53semidirect
512. C2×Q8C2×C4×D53semidirect
587. C4⋊C4C2×C4×D53semidirect
696. C22#103×D53semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D532
C22×C4⋊C4×D532
C2×#103×D532
C2×C22⋊C8×D532
#202750232
#202750222
#202750212
#202750202
#202750192
#340×D532
C53×#18722
C2×#187253