Finite Group Databasebeta

← #27307534

Subgroups — #27307534

Order 13568.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810526C211yesmaximal, characteristic
2C2×#16810526C211yesmaximal, characteristic
3C2×#16810517C212yesmaximal, complemented
4C2×C4×#11719919C211yesmaximal, characteristic, complemented
5C2×C4×C4⋊Dic53C211yesmaximal, characteristic, complemented
6#20272962C212yesmaximal, complemented
7#20272958C212yesmaximal, complemented
8#20272952C212yesmaximal, complemented
9#20272944C211yesmaximal, characteristic, complemented
10#20272944C211yesmaximal, characteristic, complemented
11C2×C53×#390C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×#11719919C2211yescharacteristic
15C22×#11719919C2211yescharacteristic
16C22×C22⋊Dic53C2212yes—
17C22×C22⋊Dic53C2212yes—
18C22×C22⋊Dic53C2212yes—
19C22×C22⋊Dic53C2212yes—
20C22×C4×Dic53C2211yescharacteristic
21C22×C4×Dic53C2212yes—
22C22×C4×Dic53C2211yescharacteristic
23#16810526—24no—
24#16810526C418yescomplemented
25#16810517—28no—
26C4×#11719919—24no—
27C4×C4⋊Dic53—24no—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C23×D4×C53C2211yescharacteristic
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2212yes—
38C22×C22⋊C4×C53C2212yes—
39C22×C42×C53C2211yescharacteristic
40C53×#390—24no—
41C23×Dic53C2312yes—
42C23×Dic53C2311yescharacteristic
43C23×Dic53C2311yescharacteristic
44C23×Dic53C2312yes—
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2311yescharacteristic
47C2×C4⋊Dic53—22no—
48C2×C4⋊Dic53—22no—
49C2×C4⋊Dic53—22no—
50C2×C4⋊Dic53—22no—
51C2×C4⋊Dic53C2×C414yes—
52C2×C4⋊Dic53D414yes—
53C2×#11719919—22no—
54C2×#11719919—22no—
55C2×#11719919—22no—
56C2×#11719919—22no—
57C2×#11719919—22no—
58C2×#11719919D414yescomplemented
59C2×C22⋊Dic53—24no—
60C2×C22⋊Dic53—24no—
61C2×C22⋊Dic53—24no—
62C2×C22⋊Dic53—24no—
63C2×C22⋊Dic53—24no—
64C2×C22⋊Dic53—24no—
65C2×C22⋊Dic53—42no—
66C2×C22⋊Dic53—42no—
67C2×C22⋊Dic53—42no—
68C2×C22⋊Dic53—42no—
69C2×C22⋊Dic53C2×C418yes—
70C2×C22⋊Dic53C2×C418yes—
71C2×C4×Dic53—22no—
72C2×C4×Dic53—24no—
73C2×C4×Dic53—22no—
74C2×C4×Dic53—22no—
75C2×C4×Dic53—22no—
76C2×C4×Dic53—22no—
77C2×C4×Dic53—24no—
78C2×C4×Dic53—42no—
79C2×C4×Dic53C2×C414yes—
80#13133124—22no—
81#13133124—22no—
82#13133124—24no—
83#13133124—24no—
84#13133124—24no—
85#13133124—42no—
86#13133124—42no—
87C25×C53C2312yes—
88C22×D4×C53—22no—
89C22×D4×C53—22no—
90C22×D4×C53—22no—
91C22×D4×C53—22no—
92C22×D4×C53—22no—
93C22×D4×C53—22no—
94C22×D4×C53C2×C414yes—
95C23×C4×C53C2312yes—
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2311yescharacteristic
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—22no—
102C2×C22⋊C4×C53—24no—
103C2×C22⋊C4×C53—24no—
104C2×C22⋊C4×C53—24no—
105C2×C22⋊C4×C53—24no—
106C2×C22⋊C4×C53—42no—
107C2×C22⋊C4×C53—42no—
108C2×C42×C53—22no—
109C2×C42×C53—22no—
110C2×C42×C53D414yes—
111C24×C53—22no—
112C24×C53—22no—
113C24×C53—22no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53—22no—
122C24×C53—22no—
123C24×C53—22no—
124C24×C53—22no—
125C24×C53C22×C414yes—
126C24×C53C2411yescharacteristic
127C2×D4×C53—28no—
128C2×D4×C53—28no—
129C2×D4×C53—28no—
130C2×D4×C53—44no—
131C2×D4×C53—44no—
132C2×D4×C53—44no—
133C2×D4×C53—44no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53C22×C412yes—
152C22×C4×C53C2×D412yes—
153C22×C4×C53C2×D412yes—
154C22×C4×C53C2×D412yes—
155C22×C4×C53C2×D412yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53#4112yes—
158C22×C4×C53#4112yes—
159C22×C4×C53#4112yes—
160C22×C4×C53#4112yes—
161C22×C4×C53#4112yes—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—22no—
172C22×Dic53—21no—
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—21no—
185C22×Dic53—21no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53C22×C412yes—
197C22×Dic53C22×C414yes—
198C22×Dic53C22×C412yes—
199C22×Dic53C2×D412yes—
200C22×Dic53C2×D414yes—
201C22×Dic53C2×D412yes—
202C22×Dic53#4112yes—
203C22×Dic53#4112yes—
204C4⋊C4×C53—44no—
205C22⋊C4×C53—48no—
206C22⋊C4×C53—48no—
207C42×C53—28no—
208C22⋊Dic53—216no—
209C22⋊Dic53—48no—
210C22⋊Dic53—48no—
211C22⋊Dic53—48no—
212C4⋊Dic53—28no—
213C4⋊Dic53—28no—
214#11719919—28no—
215#11719919—28no—
216C4×Dic53—28no—
217C4×Dic53—48no—
218C4×Dic53—44no—
219C23×C53—24no—
220C23×C53—24no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—24no—
224C23×C53—24no—
225C23×C53—24no—
226C23×C53—42no—
227C23×C53—42no—
228C23×C53—42no—
229C23×C53—42no—
230C23×C53—42no—
231C23×C53—42no—
232C23×C53—42no—
233C23×C53—42no—
234C23×C53—42no—
235C23×C53—42no—
236C23×C53—42no—
237C23×C53—42no—
238C23×C53—42no—
239C23×C53—42no—
240C23×C53—42no—
241C23×C53—42no—
242C23×C53—42no—
243C23×C53—42no—
244C23×C53—42no—
245C23×C53—42no—
246C23×C53—42no—
247C23×C53—42no—
248C23×C53—42no—
249C23×C53—42no—
250C23×C53—42no—
251C23×C53—42no—
252C23×C53—42no—
253C23×C53—42no—
254C23×C53C23×C411yescharacteristic
255C23×C53C22×D411yescharacteristic
256C23×C53C22×D411yescharacteristic
257C23×C53C22×D411yescharacteristic
258C23×C53C2×#4111yescharacteristic
259C23×C53C2×#4111yescharacteristic
260C23×C53C2×#4111yescharacteristic
261C23×C53C2×#4111yescharacteristic
262C23×C53C2×#4111yescharacteristic
263C23×C53C2×#4111yescharacteristic
264C23×C53C2×#4111yescharacteristic
265C23×C53H(5,𝔽2)11yescharacteristic
266C23×C53H(5,𝔽2)11yescharacteristic
267C23×C53H(5,𝔽2)11yescharacteristic
268C23×C532−1+411yescharacteristic
269D4×C53—416no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53#11714yes—
291C2×C4×C53C4×D414yes—
292C2×C4×C53C4×D414yes—
293C2×C4×C53#12114yes—
294C2×C4×C53#12114yes—
295C2×C4×C53#12314yes—
296C2×C4×C53#12414yes—
297C2×C4×C53#12614yes—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—24no—
306C2×Dic53—24no—
307C2×Dic53—24no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—24no—
312C2×Dic53—22no—
313C2×Dic53—24no—
314C2×Dic53—22no—
315C2×Dic53—24no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—42no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—42no—
328C2×Dic53—41no—
329C2×Dic53—42no—
330C2×Dic53—41no—
331C2×Dic53—42no—
332C2×Dic53—41no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53C4×D414yes—
340#14022—531nomaximal, Sylow
341C22×C53—44no—
342C22×C53—44no—
343C22×C53—44no—
344C22×C53—44no—
345C22×C53—44no—
346C22×C53—44no—
347C22×C53—44no—
348C22×C53—82no—
349C22×C53—82no—
350C22×C53—82no—
351C22×C53—82no—
352C22×C53—82no—
353C22×C53—82no—
354C22×C53—82no—
355C22×C53—82no—
356C22×C53C2×#11711yescharacteristic
357C22×C53C2×C4×D411yescharacteristic
358C22×C53C2×C4×D411yescharacteristic
359C22×C53C2×C4×D411yescharacteristic
360C22×C53C4×#4111yescharacteristic
361C22×C53#51811yescharacteristic
362C22×C53#52011yescharacteristic
363C22×C53C2×#12111yescharacteristic
364C22×C53C2×#12111yescharacteristic
365C22×C53C2×#12311yescharacteristic
366C22×C53#52511yescharacteristic
367C22×C53C2×#12411yescharacteristic
368C22×C53C2×#12611yescharacteristic
369C22×C53#52911yescharacteristic
370C22×C53#53211yescharacteristic
371C22×C53#53511yescharacteristic
372C22×C53#53711yescharacteristic
373C22×C53#54011yescharacteristic
374C22×C53#54211yescharacteristic
375C22×C53D4211yescharacteristic
376C22×C53#54611yescharacteristic
377C22×C53#54711yescharacteristic
378C22×C53#54811yescharacteristic
379C22×C53#55011yescharacteristic
380C22×C53#55011yescharacteristic
381C22×C53#55011yescharacteristic
382C22×C53#55311yescharacteristic
383C22×C53#55311yescharacteristic
384C22×C53#55511yescharacteristic
385C22×C53#55611yescharacteristic
386C22×C53#55611yescharacteristic
387C22×C53#55911yescharacteristic
388C22×C53#55911yescharacteristic
389C22×C53#55911yescharacteristic
390C22×C53#55911yescharacteristic
391C4×C53—24no—
392C4×C53—42no—
393C4×C53—82no—
394C4×C53#38818yescomplemented
395Dic53—24no—
396Dic53—42no—
397Dic53—44no—
398Dic53—42no—
399Dic53—42no—
400Dic53—44no—
401C2×#390—531no—
402C2×#390—531no—
403C2×#390D5311yescharacteristic
404C2×#388—532no—
405C2×C4×C4⋊C4—531no—
406C2×C4×C4⋊C4—531no—
407#1440—532no—
408#1439—532no—
409#1437—532no—
410C4⋊#95—531no—
411C4⋊#95—531no—
412C2×C53—84no—
413C2×C53C2×#38811yescharacteristic
414C2×C53C4×#12111yescharacteristic
415C2×C53#232411yescharacteristic
416C2×C53#235411yescharacteristic
417C2×C53#235711yescharacteristic
418C2×C53#236611yescharacteristic
419C2×C53#236711yescharacteristic
420C2×C53#241411yescharacteristic
421C2×C53#241611yescharacteristic
422C2×C53#244511yescharacteristic
423C2×C53#244811yescharacteristic
424C2×C53#251211yescharacteristic
425C2×C53#251311yescharacteristic
426C2×C53#254811yescharacteristic
427C2×C53#259211yescharacteristic
428C23×D4C2×D5311yescharacteristic
429C22×C4⋊C4—531no—
430C22×C4⋊C4—531no—
431C22×C4⋊C4—531no—
432C22×C4⋊C4—531no—
433C22×C4⋊C4C2×D5311yescharacteristic
434C22×C22⋊C4—532no—
435C22×C22⋊C4—532no—
436C22×C22⋊C4—532no—
437C22×C22⋊C4—532no—
438C22×C22⋊C4C2×D5312yes—
439C22×C22⋊C4C2×D5312yes—
440C22×C42—531no—
441C22×C42—531no—
442C22×C42—532no—
443C22×C42C2×D5311yescharacteristic
444#390—24no—
445#390—538no—
446#390—1064no—
447#388—1068no—
448C4×C4⋊C4—1064no—
449C4×C4⋊C4—1064no—
450C2×#95—532no—
451C2×#95—532no—
452C2×#95—531no—
453C2×#95—532no—
454C2×#95—531no—
455C2×#95—532no—
456C2×#95—532no—
457C53#1402211yescharacteristic, complemented, Sylow
458C25C22×D5312yes—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C4×D5314yes—
466C23×C4—531no—
467C23×C4—532no—
468C23×C4—531no—
469C23×C4—532no—
470C23×C4—531no—
471C23×C4—531no—
472C23×C4C22×D5312yes—
473C23×C4C22×D5311yescharacteristic
474C23×C4C22×D5311yescharacteristic
475C23×C4C22×D5311yescharacteristic
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—534no—
480C2×C4⋊C4—534no—
481C2×C4⋊C4—534no—
482C2×C4⋊C4—1062no—
483C2×C4⋊C4—1062no—
484C2×C4⋊C4—1062no—
485C2×C4⋊C4—1062no—
486C2×C4⋊C4—1062no—
487C2×C4⋊C4—1062no—
488C2×C4⋊C4—1062no—
489C2×C4⋊C4—1062no—
490C2×C4⋊C4—1062no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—538no—
498C2×C22⋊C4—538no—
499C2×C22⋊C4—1064no—
500C2×C22⋊C4—1064no—
501C2×C22⋊C4—1064no—
502C2×C22⋊C4—1064no—
503C2×C22⋊C4—1064no—
504C2×C22⋊C4—1064no—
505C2×C22⋊C4—2122no—
506C2×C22⋊C4—2122no—
507C2×C22⋊C4—2122no—
508C2×C22⋊C4—2122no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—534no—
512C2×C42—1062no—
513C2×C42—1062no—
514C2×C42—1064no—
515C2×C42—1064no—
516C2×C42—1062no—
517C2×C42—1062no—
518C2×C42—1062no—
519C2×C42—2122no—
520C2×C42C22⋊D5314yes—
521#95—1064no—
522#95—1064no—
523#95—1064no—
524#95—1062no—
525#95—1062no—
526#95—2122no—
527#95—2122no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24C2×C4×D5314yes—
543C24C23×D5311yescharacteristic
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—532no—
569C22×C4—532no—
570C22×C4—532no—
571C22×C4—532no—
572C22×C4—534no—
573C22×C4—532no—
574C22×C4—534no—
575C22×C4—532no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1062no—
594C22×C4—1061no—
595C22×C4—1062no—
596C22×C4—1061no—
597C22×C4—1062no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4C2×C4×D5312yes—
611C22×C4#1171994512yes—
612C22×C4D4×D5312yes—
613C22×C4D4×D5312yes—
614C22×C4#1171994712yes—
615C22×C4#1171994712yes—
616C22×C4#1171994712yes—
617C22×C4#1171994712yes—
618C22×C4C2×C22⋊D5312yes—
619C22×C4C2×C22⋊D5312yes—
620C22×C4C2×C22⋊D5312yes—
621C4⋊C4—44no—
622C4⋊C4—1068no—
623C4⋊C4—1068no—
624C4⋊C4—1068no—
625C4⋊C4—1068no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—10616no—
629C22⋊C4—2128no—
630C22⋊C4—2128no—
631C22⋊C4—2128no—
632C42—28no—
633C42—1068no—
634C42—2128no—
635C42—2124no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23C22×C4×D5311yescharacteristic
672C23C2×D4×D5311yescharacteristic
673C23C2×D4×D5311yescharacteristic
674C23C22×C22⋊D5311yescharacteristic
675C23#41×D5311yescharacteristic
676C23#41×D5311yescharacteristic
677C23C2×#1171994711yescharacteristic
678C23C2×#1171994711yescharacteristic
679C23C2×#1171994711yescharacteristic
680C23C2×#1171994711yescharacteristic
681C23C2×#1171994511yescharacteristic
682C23#1313326211yescharacteristic
683C23#1313326211yescharacteristic
684C23#1313326311yescharacteristic
685C23#1313326411yescharacteristic
686D4—416no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—534no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1064no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1064no—
719C2×C4—1064no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1064no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1064no—
726C2×C4—1062no—
727C2×C4—1064no—
728C2×C4—1062no—
729C2×C4—2121no—
730C2×C4—2122no—
731C2×C4—2121no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2121no—
735C2×C4—2121no—
736C2×C4—2122no—
737C2×C4—2122no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2122no—
741C2×C4—2121no—
742C2×C4—2121no—
743C2×C4—2121no—
744C2×C4—2121no—
745C2×C4—2121no—
746C2×C4—2122no—
747C2×C4—2121no—
748C2×C4—2122no—
749C2×C4#1313317314yes—
750C2×C4#1313317714yes—
751C2×C4C4×C22⋊D5314yes—
752C2×C4#1313318814yes—
753C2×C4#1313318914yes—
754C2×C4#1313319914yes—
755C2×C4#1313320414yes—
756C2×C4#1313321014yes—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22C2×#1313317311yescharacteristic
773C22C4×D4×D5311yescharacteristic
774C22C2×#1313317711yescharacteristic
775C22C2×C4×C22⋊D5311yescharacteristic
776C22C4×#1171994711yescharacteristic
777C22#1681109511yescharacteristic
778C22#1681110211yescharacteristic
779C22C2×#1313318811yescharacteristic
780C22C2×#1313318911yescharacteristic
781C22C2×#1313319911yescharacteristic
782C22#1681113011yescharacteristic
783C22C2×#1313320411yescharacteristic
784C22C2×#1313321011yescharacteristic
785C22#1681115511yescharacteristic
786C22#1681117011yescharacteristic
787C22#1681119011yescharacteristic
788C22#1681120111yescharacteristic
789C22#1681122411yescharacteristic
790C22#1681123811yescharacteristic
791C22#1681125711yescharacteristic
792C22#1681127011yescharacteristic
793C22#1681127311yescharacteristic
794C22#1681127911yescharacteristic
795C22#1681129111yescharacteristic
796C22#1681129311yescharacteristic
797C22#1681129311yescharacteristic
798C22#1681132011yescharacteristic
799C22#1681132511yescharacteristic
800C22#1681133711yescharacteristic
801C22#1681134211yescharacteristic
802C22#1681134211yescharacteristic
803C22#1681135511yescharacteristic
804C22#1681135511yescharacteristic
805C22#1681135911yescharacteristic
806C22#1681135911yescharacteristic
807C4—24no—
808C4—42no—
809C4—82no—
810C4—1064no—
811C4—2124no—
812C4—2122no—
813C4—2122no—
814C4—2122no—
815C4—2124no—
816C4#1681051718yescomplemented
817C2—84no—
818C2C2×#1681051711yescharacteristic
819C2C4×#1313318811yescharacteristic
820C2#2027740211yescharacteristic
821C2#2027766311yescharacteristic
822C2#2027768711yescharacteristic
823C2#2027777611yescharacteristic
824C2#2027778511yescharacteristic
825C2#2027813411yescharacteristic
826C2#2027815611yescharacteristic
827C2#2027848111yescharacteristic
828C2#2027851411yescharacteristic
829C2#2027930211yescharacteristic
830C2#2027931311yescharacteristic
831C2#2027971811yescharacteristic
832C2#2028020411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#390C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#390D53
hypocenterC53#14022
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#16810517C2semidirect
4. C2×C4×#11719919C2semidirect
5. C2×C4×C4⋊Dic53C2semidirect
6. #20272962C2semidirect
7. #20272958C2semidirect
8. #20272952C2semidirect
9. #20272944C2semidirect
10. #20272944C2semidirect
24. #16810526C4semidirect
58. C2×#11719919D4semidirect
394. C4×C53#388semidirect
457. C53#14022semidirect
816. C4#16810517semidirect

Maximal subgroups

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

subgroupindex
C2×#168105262
C2×#168105172
C2×C4×#117199192
C2×C4×C4⋊Dic532
#202729622
#202729582
#202729522
#202729442
C2×C53×#3902
#1402253