Finite Group Databasebeta

← #27305994

Subgroups — #27305994

Order 13568.

2950 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133177C211yesmaximal, characteristic
2C22×C4⋊C4×D53C211yesmaximal, characteristic, complemented
3C2×#16810499C212yesmaximal
4C2×#16810482C211yesmaximal, characteristic, complemented
5C2×#16810481C212yesmaximal, complemented
6#20272969C211yesmaximal, characteristic, complemented
7#20272965C211yesmaximal, characteristic, complemented
8#20272960C211yesmaximal, characteristic, complemented
9#20272943C212yesmaximal, complemented
10#20272936C212yesmaximal, complemented
11C53×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C23×C4×D53C2212yes—
15C23×C4×D53C2211yescharacteristic
16C2×#13133177—24no—
17C2×#13133177—24no—
18C2×#13133177C418yescomplemented
19C22×C4⋊Dic53C2211yescharacteristic
20C22×#11719919C2212yes—
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2212yes—
23C2×C4⋊C4×D53—24no—
24C2×C4⋊C4×D53—28no—
25C22×C22⋊Dic53C2212yes—
26C22×#11719921C2212yes—
27C22×#11719921C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29#16810499—28no—
30#16810482—24no—
31#16810481—28no—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2212yes—
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2212yes—
40C22×C22⋊C4×C53C2211yescharacteristic
41C2×#95×C53C2211yescharacteristic
42C2×#95×C53C2212yes—
43C24×D53C2311yescharacteristic
44C22×C22⋊D53—22no—
45C22×C22⋊D53—22no—
46C22×C22⋊D53—22no—
47C22×C22⋊D53—22no—
48C22×C22⋊D53C2×C414yes—
49C22×C22⋊D53D414yes—
50C22×C22⋊D53Q814yes—
51C23×Dic53—22no—
52C23×Dic53—22no—
53C23×Dic53—24no—
54C23×Dic53—24no—
55C23×Dic53C2×C414yescomplemented
56C23×Dic53C2312yes—
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2312yes—
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C22×C4×D53—24no—
62C22×C4×D53—24no—
63C22×C4×D53—24no—
64C22×C4×D53—24no—
65C22×C4×D53—24no—
66C22×C4×D53—24no—
67C22×C4×D53—24no—
68C22×C4×D53—42no—
69C22×C4×D53—42no—
70C22×C4×D53C2×C414yes—
71C22×C4×D53D414yes—
72C22×C4×D53D414yes—
73#13133177—232no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—24no—
76C2×#11719919—22no—
77C2×#11719919—22no—
78C2×#11719919—24no—
79C2×#11719919—24no—
80C2×#11719919—24no—
81C2×#11719919—24no—
82C2×#11719919—24no—
83C2×#11719919C2×C414yescomplemented
84C2×#11719919D418yescomplemented
85C4⋊C4×D53—232no—
86C2×C22⋊Dic53—24no—
87C2×C22⋊Dic53—24no—
88C2×C22⋊Dic53—42no—
89C2×#11719921—22no—
90C2×#11719921—22no—
91C2×#11719921—24no—
92C2×#11719921—24no—
93C2×#11719921—24no—
94C2×#11719921C2×C414yes—
95C2×C4×Dic53—22no—
96C2×C4×Dic53—22no—
97C2×C4×Dic53C2×C414yescomplemented
98#13133124—24no—
99#13133124—22no—
100#13133124—24no—
101#13133124—24no—
102#13133124—24no—
103#13133124—42no—
104C25×C53C2311yescharacteristic
105C23×C4×C53C2312yes—
106C23×C4×C53C2311yescharacteristic
107C23×C4×C53C2312yes—
108C23×C4×C53C2311yescharacteristic
109C2×C4⋊C4×C53—24no—
110C2×C4⋊C4×C53—22no—
111C2×C22⋊C4×C53—24no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—22no—
114C2×C22⋊C4×C53—24no—
115C2×C22⋊C4×C53—42no—
116C2×C22⋊C4×C53C2×C414yescomplemented
117#95×C53—22no—
118#95×C53—42no—
119C24×C53—22no—
120C24×C53—21no—
121C24×C53—21no—
122C24×C53—22no—
123C24×C53—21no—
124C24×C53—21no—
125C24×C53—22no—
126C24×C53—22no—
127C24×C53C22×C412yes—
128C24×C53C2×D412yes—
129C24×C53C2×Q812yes—
130C24×C53C2411yescharacteristic
131C23×D53—22no—
132C23×D53—22no—
133C23×D53—22no—
134C23×D53—22no—
135C23×D53C22×C412yes—
136C23×D53C2×D412yes—
137C23×D53C2×D412yes—
138C23×D53C2×D412yes—
139C23×D53C2×Q812yes—
140C23×D53#4112yes—
141C23×D53#4112yes—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53C22×C412yes—
162C22×C4×C53C22×C412yes—
163C22×C4×C53C2×D414yes—
164C22×C4×C53C2×D412yes—
165C22×C4×C53C2×D412yes—
166C2×C22⋊D53—28no—
167C2×C22⋊D53—28no—
168C2×C22⋊D53—28no—
169C2×C22⋊D53—28no—
170C2×C22⋊D53—28no—
171C2×C22⋊D53—28no—
172C2×C22⋊D53C4⋊C4116yescomplemented
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—28no—
188C22×Dic53—216no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—44no—
197C22×Dic53—48no—
198C22×Dic53—44no—
199C22×Dic53C22×C412yes—
200C22×Dic53C22×C412yes—
201C22×Dic53C22×C412yes—
202C22×Dic53C2×D414yes—
203C22×Dic53C2×D412yes—
204C22×Dic53C2×D412yes—
205C22×Dic53C2×D412yes—
206C22×Dic53C2×D414yes—
207C22×Dic53C2×Q812yes—
208C22×Dic53#4114yes—
209C2×C4×D53—216no—
210C2×C4×D53—28no—
211C2×C4×D53—216no—
212C2×C4×D53—28no—
213C2×C4×D53—216no—
214C2×C4×D53—48no—
215C2×C4×D53—48no—
216C2×C4×D53—48no—
217C2×C4×D53—48no—
218C2×C4×D53—48no—
219C2×C4×D53—48no—
220C2×C4×D53C22⋊C4116yescomplemented
221C4⋊C4×C53—28no—
222C22⋊C4×C53—28no—
223C22⋊C4×C53—48no—
224C22⋊Dic53—48no—
225#11719921—28no—
226#11719921—48no—
227C4⋊Dic53—28no—
228#11719919—28no—
229#11719919—216no—
230#11719919—48no—
231C4×Dic53—28no—
232C23×C53—22no—
233C23×C53—22no—
234C23×C53—24no—
235C23×C53—24no—
236C23×C53—22no—
237C23×C53—22no—
238C23×C53—22no—
239C23×C53—22no—
240C23×C53—24no—
241C23×C53—24no—
242C23×C53—24no—
243C23×C53—24no—
244C23×C53—41no—
245C23×C53—42no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—42no—
250C23×C53—42no—
251C23×C53—42no—
252C23×C53—42no—
253C23×C53—42no—
254C23×C53C2×C4⋊C414yescomplemented
255C23×C53C23×C411yescharacteristic
256C23×C53C22×D411yescharacteristic
257C23×C53C22×D411yescharacteristic
258C23×C53C22×D411yescharacteristic
259C23×C53C22×D412yes—
260C23×C53C22×Q811yescharacteristic
261C23×C53C2×#4111yescharacteristic
262C23×C53C2×#4111yescharacteristic
263C23×C53C2×#4112yes—
264C23×C53H(5,𝔽2)12yes—
265C23×C532−1+412yes—
266C22×D53—24no—
267C22×D53—24no—
268C22×D53—22no—
269C22×D53—24no—
270C22×D53—22no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—24no—
274C22×D53—24no—
275C22×D53—24no—
276C22×D53—24no—
277C22×D53—24no—
278C22×D53—24no—
279C22×D53—24no—
280C22×D53—24no—
281C22×D53—24no—
282C22×D53C2×C22⋊C414yes—
283C22×D53C2×C4⋊C414yes—
284C22×D53#11714yes—
285C22×D53#12114yes—
286C22×D53#12114yes—
287C22×D53C22⋊Q814yes—
288C22×D53C22⋊Q814yes—
289C2×C4×C53—24no—
290C2×C4×C53—22no—
291C2×C4×C53—24no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—24no—
295C2×C4×C53—24no—
296C2×C4×C53—24no—
297C2×C4×C53—24no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53C2×C22⋊C414yes—
313C22⋊D53—232no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—24no—
322C2×Dic53—24no—
323C2×Dic53—24no—
324C2×Dic53—24no—
325C2×Dic53—41no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—41no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—416no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53C2×C22⋊C414yes—
341C2×Dic53C2×C4⋊C414yescomplemented
342C2×Dic53C4×D418yes—
343C2×Dic53#12014yes—
344C2×Dic53#12118yes—
345C2×Dic53#12314yes—
346C4×D53—232no—
347C4×D53—432no—
348#13872—531nomaximal, Sylow
349C22×C53—28no—
350C22×C53—24no—
351C22×C53—42no—
352C22×C53—44no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—44no—
356C22×C53—44no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53C22×C22⋊C411yescharacteristic
361C22×C53C22×C4⋊C411yescharacteristic
362C22×C53C2×#11711yescharacteristic
363C22×C53C2×C4×D412yes—
364C22×C53#52012yes—
365C22×C53C2×#12011yescharacteristic
366C22×C53C2×#12111yescharacteristic
367C22×C53C2×#12111yescharacteristic
368C22×C53C2×#12112yes—
369C22×C53C2×C22⋊Q811yescharacteristic
370C22×C53C2×C22⋊Q811yescharacteristic
371C22×C53C2×#12311yescharacteristic
372C22×C53#53511yescharacteristic
373C22×C53#53611yescharacteristic
374C22×C53#53712yes—
375C22×C53D4212yes—
376C22×C53#54612yes—
377C22×C53#54712yes—
378C22×C53#54812yes—
379C22×C53D4×Q812yes—
380C22×C53#55212yes—
381C22×C53#55312yes—
382C22×C53#55412yes—
383C2×D53—24no—
384C2×D53—28no—
385C2×D53—28no—
386C2×D53—24no—
387C2×D53—24no—
388C2×D53—28no—
389C2×D53—28no—
390C2×D53—24no—
391C2×D53—24no—
392C2×D53—24no—
393C2×D53#38018yescomplemented
394C4×C53—24no—
395C4×C53—42no—
396C4×C53—44no—
397C4×C53—82no—
398Dic53—24no—
399Dic53—44no—
400Dic53—42no—
401Dic53—82no—
402Dic53#38618yescomplemented
403C22×C4×D4—531no—
404C23×C4⋊C4—531no—
405C2×#386—532no—
406C2×#380—531no—
407C2×#380—532no—
408#1441—531no—
409#1441—531no—
410#1439—531no—
411#1439D5311yescharacteristic, complemented
412C4⋊#95—532no—
413C22⋊#95—532no—
414C2×C53—44no—
415C2×C53C2×#38011yescharacteristic
416C2×C53C2×#38611yescharacteristic
417C2×C53#231111yescharacteristic
418C2×C53D4×C4⋊C412yes—
419C2×C53#235212yes—
420C2×C53#240811yescharacteristic
421C2×C53#240911yescharacteristic
422C2×C53#241612yes—
423C2×C53#241712yes—
424C2×C53#248611yescharacteristic
425C2×C53#248711yescharacteristic
426D53—28no—
427C23×D4—531no—
428C24×C4—531no—
429C24×C4—531no—
430C24×C4—532no—
431C2×C4×D4—538no—
432C2×C4×D4—1064no—
433C2×C4×D4—1064no—
434C22×C4⋊C4—532no—
435C22×C4⋊C4—531no—
436C22×C4⋊C4—532no—
437C22×C4⋊C4—531no—
438C22×C4⋊C4—1068no—
439C22×C4⋊C4—1064no—
440C22×C4⋊C4C2×D5311yescharacteristic
441C22×C22⋊C4—531no—
442C22×C22⋊C4—532no—
443C22×C22⋊C4—532no—
444C22×C22⋊C4C2×D5312yes—
445C22×C22⋊C4C2×D5311yescharacteristic
446C22×C42—531no—
447#386—1068no—
448#380—1064no—
449#380—1068no—
450C2×#95—532no—
451C2×#95—532no—
452C2×#95—532no—
453C2×#95—532no—
454C2×#95—531no—
455C2×#95—532no—
456C2×#95C2×D5311yescharacteristic
457C2×#95C2×D5312yes—
458C53#1387211yescharacteristic, complemented, Sylow
459C25—531no—
460C25C22×D5311yescharacteristic
461C22×D4—534no—
462C22×D4—534no—
463C22×D4—534no—
464C22×D4—1062no—
465C22×D4—1062no—
466C22×D4—1062no—
467C22×D4—1062no—
468C23×C4—531no—
469C23×C4—531no—
470C23×C4—534no—
471C23×C4—534no—
472C23×C4—534no—
473C23×C4—534no—
474C23×C4—532no—
475C23×C4—531no—
476C23×C4—532no—
477C23×C4—1064no—
478C23×C4—1064no—
479C23×C4—1064no—
480C23×C4—1064no—
481C23×C4—1064no—
482C23×C4—1064no—
483C23×C4—1062no—
484C23×C4—1062no—
485C23×C4—1064no—
486C23×C4—1064no—
487C23×C4—1064no—
488C23×C4—2122no—
489C23×C4—2122no—
490C23×C4C22×D5312yes—
491C23×C4C22×D5311yescharacteristic
492C23×C4C22×D5312yes—
493C23×C4C22×D5311yescharacteristic
494C4×D4—10632no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—534no—
498C2×C4⋊C4—538no—
499C2×C4⋊C4—10632no—
500C2×C4⋊C4—1064no—
501C2×C4⋊C4—1064no—
502C2×C4⋊C4—1064no—
503C2×C4⋊C4—1062no—
504C2×C4⋊C4—1062no—
505C2×C4⋊C4—1062no—
506C2×C4⋊C4—1064no—
507C2×C4⋊C4—1064no—
508C2×C4⋊C4—1064no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—534no—
515C2×C22⋊C4—1062no—
516C2×C22⋊C4—1062no—
517C2×C22⋊C4—1064no—
518C2×C22⋊C4—1064no—
519C2×C22⋊C4—1064no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—1064no—
522C2×C22⋊C4—2122no—
523C2×C22⋊C4C4×D5314yescomplemented
524C2×C42—534no—
525C2×C42—1062no—
526C2×C42—1062no—
527#95—22no—
528#95—42no—
529#95—1064no—
530#95—1064no—
531#95—1064no—
532#95—1064no—
533#95—1062no—
534#95—2122no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—21no—
540C24—21no—
541C24—22no—
542C24—22no—
543C24—532no—
544C24—532no—
545C24—532no—
546C24—532no—
547C24—532no—
548C24—532no—
549C24—532no—
550C24—1062no—
551C24—1062no—
552C24—1062no—
553C24—1062no—
554C24C2×C4×D5312yes—
555C24D4×D5312yes—
556C24Q8×D5312yes—
557C24C23×D5311yescharacteristic
558C2×D4—5316no—
559C2×D4—1068no—
560C2×D4—1068no—
561C2×D4—1068no—
562C2×D4—1068no—
563C2×D4—1068no—
564C2×D4—1068no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—532no—
585C22×C4—532no—
586C22×C4—532no—
587C22×C4—534no—
588C22×C4—534no—
589C22×C4—532no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—5316no—
593C22×C4—532no—
594C22×C4—534no—
595C22×C4—1068no—
596C22×C4—10616no—
597C22×C4—10616no—
598C22×C4—1068no—
599C22×C4—10616no—
600C22×C4—1068no—
601C22×C4—10616no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—2128no—
624C22×C4—2128no—
625C22×C4—2128no—
626C22×C4—2128no—
627C22×C4—2128no—
628C22×C4—2128no—
629C22×C4—2124no—
630C22×C4—2128no—
631C22×C4—2124no—
632C22×C4C2×C4×D5312yes—
633C22×C4C2×C4×D5312yes—
634C22×C4D4×D5314yes—
635C22×C4D4×D5312yes—
636C22×C4D4×D5312yes—
637C4⋊C4—28no—
638C4⋊C4—10616no—
639C4⋊C4—1068no—
640C4⋊C4—1068no—
641C4⋊C4—2128no—
642C22⋊C4—28no—
643C22⋊C4—48no—
644C22⋊C4—1068no—
645C22⋊C4—2128no—
646C22⋊C4—2128no—
647C42—1068no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—534no—
671C23—534no—
672C23—534no—
673C23—534no—
674C23—534no—
675C23—534no—
676C23—534no—
677C23—1064no—
678C23—1064no—
679C23—1064no—
680C23—1064no—
681C23—1064no—
682C23—1064no—
683C23—1064no—
684C23—1064no—
685C23—1062no—
686C23—1064no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—1064no—
691C23—1064no—
692C23—1064no—
693C23C4⋊C4×D5314yescomplemented
694C23C22×C4×D5311yescharacteristic
695C23C2×D4×D5311yescharacteristic
696C23C2×D4×D5312yes—
697C23C2×D4×D5311yescharacteristic
698C23C2×D4×D5311yescharacteristic
699C23C2×Q8×D5311yescharacteristic
700C23#41×D5312yes—
701C23#41×D5311yescharacteristic
702C23#41×D5311yescharacteristic
703C23#1313326212yes—
704C23#1313326412yes—
705D4—10632no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—534no—
730C2×C4—538no—
731C2×C4—534no—
732C2×C4—538no—
733C2×C4—534no—
734C2×C4—534no—
735C2×C4—10632no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1064no—
744C2×C4—1064no—
745C2×C4—1064no—
746C2×C4—1064no—
747C2×C4—21232no—
748C2×C4—21216no—
749C2×C4—2122no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4—2122no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2122no—
756C2×C4—2121no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4—2121no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4C22⋊C4×D5314yes—
764C22—24no—
765C22—28no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—44no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—42no—
774C22—42no—
775C22—538no—
776C22—1064no—
777C22—1064no—
778C22—1064no—
779C22—1068no—
780C22—1068no—
781C22—1064no—
782C22—1068no—
783C22—1068no—
784C22—1064no—
785C22—1064no—
786C22C2×C22⋊C4×D5311yescharacteristic
787C22C2×C4⋊C4×D5311yescharacteristic
788C22#117×D5311yescharacteristic
789C22C4×D4×D5312yes—
790C22#1681110212yes—
791C22#120×D5311yescharacteristic
792C22#121×D5311yescharacteristic
793C22#121×D5311yescharacteristic
794C22#121×D5312yes—
795C22C22⋊Q8×D5311yescharacteristic
796C22C22⋊Q8×D5311yescharacteristic
797C22#123×D5311yescharacteristic
798C22#1681118611yescharacteristic
799C22#1681119311yescharacteristic
800C22#1681120212yes—
801C22#1681125512yes—
802C22#1681126212yes—
803C22#1681127112yes—
804C22#1681128112yes—
805C22#1681128612yes—
806C22#1681130912yes—
807C22#1681131812yes—
808C22#1681132712yes—
809C4—24no—
810C4—44no—
811C4—42no—
812C4—82no—
813C4—538no—
814C4—1064no—
815C4—4242no—
816C4—2124no—
817C4—2122no—
818C2—44no—
819C2—1068no—
820C2#380×D5311yescharacteristic
821C2#386×D5311yescharacteristic
822C2#2027730511yescharacteristic
823C2#2027761312yes—
824C2#2027764312yes—
825C2#2027806411yescharacteristic
826C2#2027807311yescharacteristic
827C2#2027814812yes—
828C2#2027815912yes—
829C2#2027901611yescharacteristic
830C2#2027902511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1439C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1439D53
hypocenterC53#13872
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D53C2semidirect
4. C2×#16810482C2semidirect
5. C2×#16810481C2semidirect
6. #20272969C2semidirect
7. #20272965C2semidirect
8. #20272960C2semidirect
9. #20272943C2semidirect
10. #20272936C2semidirect
11. C53×#1439C2semidirect
18. C2×#13133177C4semidirect
55. C23×Dic53C2×C4semidirect
83. C2×#11719919C2×C4semidirect
84. C2×#11719919D4semidirect
97. C2×C4×Dic53C2×C4semidirect
116. C2×C22⋊C4×C53C2×C4semidirect
172. C2×C22⋊D53C4⋊C4semidirect
220. C2×C4×D53C22⋊C4semidirect
254. C23×C53C2×C4⋊C4semidirect
341. C2×Dic53C2×C4⋊C4semidirect
393. C2×D53#380semidirect
402. Dic53#386semidirect
411. #1439D53semidirect
458. C53#13872semidirect
523. C2×C22⋊C4C4×D53semidirect
693. C23C4⋊C4×D53semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C22×C4⋊C4×D532
C2×#168104992
C2×#168104822
C2×#168104812
#202729692
#202729652
#202729602
#202729432
#202729362
C53×#14392
#1387253