Finite Group Databasebeta

← #27307213

Subgroups — #27307213

Order 13568.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133198C211yesmaximal, characteristic
2C2×#16810503C211yesmaximal, characteristic
3C2×#16810496C211yesmaximal, characteristic, complemented
4C2×#16810484C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
6C22×#13133124C211yesmaximal, characteristic, complemented
7#20272981C212yesmaximal, complemented
8#20272958C212yesmaximal, complemented
9#20272952C212yesmaximal, complemented
10#20272943C212yesmaximal, complemented
11C2×C53×#386C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C2×#13133198—24no—
15C2×#13133198—24no—
16C2×#13133198C418yescomplemented
17C22×#11719919C2212yes—
18C22×#11719919C2212yes—
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C22⋊Dic53C2212yes—
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C4×Dic53C2212yes—
25#16810503—24no—
26#16810496—24no—
27#16810484—24no—
28C22⋊C4×Dic53—24no—
29C2×#13133124—24no—
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2211yescharacteristic
38C23×D4×C53C2211yescharacteristic
39C24×C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2212yes—
41C22×C22⋊C4×C53C2211yescharacteristic
42C53×#386—24no—
43C2×#95×C53C2212yes—
44C23×Dic53—22no—
45C23×Dic53—22no—
46C23×Dic53—22no—
47C23×Dic53—22no—
48C23×Dic53—22no—
49C23×Dic53—22no—
50C23×Dic53—22no—
51C23×Dic53—22no—
52C23×Dic53—24no—
53C23×Dic53—42no—
54C23×Dic53C2×C414yes—
55C23×Dic53D414yes—
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2312yes—
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2312yes—
61C23×Dic53C2311yescharacteristic
62#13133198—232no—
63C2×#11719919—24no—
64C2×#11719919—24no—
65C2×#11719919—24no—
66C2×#11719919—24no—
67C2×#11719919—42no—
68C2×#11719919C2×C418yescomplemented
69C2×C22⋊Dic53—22no—
70C2×C22⋊Dic53—22no—
71C2×C22⋊Dic53—22no—
72C2×C22⋊Dic53—24no—
73C2×C22⋊Dic53—24no—
74C2×C22⋊Dic53—22no—
75C2×C22⋊Dic53—22no—
76C2×C22⋊Dic53—24no—
77C2×C22⋊Dic53—42no—
78C2×C22⋊Dic53C2×C414yes—
79C2×C22⋊Dic53C2×C418yescomplemented
80C2×C22⋊Dic53D414yes—
81C2×C22⋊Dic53D414yes—
82C2×C4×Dic53—24no—
83C2×C4×Dic53—24no—
84C2×C4×Dic53—42no—
85#13133124—24no—
86#13133124—24no—
87#13133124—24no—
88#13133124—22no—
89#13133124—22no—
90#13133124—24no—
91#13133124—24no—
92#13133124—24no—
93C25×C53C2311yescharacteristic
94C25×C53C2311yescharacteristic
95C22×D4×C53—22no—
96C22×D4×C53—22no—
97C22×D4×C53—22no—
98C22×D4×C53—22no—
99C22×D4×C53—22no—
100C22×D4×C53—22no—
101C22×D4×C53C2×C414yes—
102C23×C4×C53—22no—
103C23×C4×C53—24no—
104C23×C4×C53—22no—
105C23×C4×C53—22no—
106C23×C4×C53—42no—
107C23×C4×C53C2311yescharacteristic
108C23×C4×C53C2312yes—
109C23×C4×C53C2312yes—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—24no—
113C2×C22⋊C4×C53—24no—
114C2×C22⋊C4×C53—42no—
115C2×C22⋊C4×C53D414yes—
116#95×C53—24no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53—21no—
122C24×C53—21no—
123C24×C53—21no—
124C24×C53—21no—
125C24×C53—22no—
126C24×C53—21no—
127C24×C53—21no—
128C24×C53—22no—
129C24×C53—22no—
130C24×C53—22no—
131C24×C53C22×C412yes—
132C24×C53C22×C412yes—
133C24×C53C2×D412yes—
134C24×C53C2×D412yes—
135C24×C53C2×D412yes—
136C24×C53C2×D412yes—
137C24×C53#4112yes—
138C24×C53#4112yes—
139C24×C53C2411yescharacteristic
140C2×D4×C53—28no—
141C2×D4×C53—28no—
142C2×D4×C53—28no—
143C2×D4×C53—44no—
144C2×D4×C53—44no—
145C2×D4×C53—44no—
146C2×D4×C53—44no—
147C22×C4×C53—28no—
148C22×C4×C53—21no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—48no—
167C22×C4×C53—48no—
168C22×C4×C53—44no—
169C22×C4×C53—44no—
170C22×C4×C53C22×C412yes—
171C22×C4×C53C2×D414yes—
172C22×C4×C53#4114yes—
173C22×Dic53—21no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—21no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—28no—
181C22×Dic53—28no—
182C22×Dic53—28no—
183C22×Dic53—28no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—21no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—21no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—28no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—44no—
206C22×Dic53—48no—
207C22×Dic53—48no—
208C22×Dic53—44no—
209C22×Dic53—44no—
210C22×Dic53—44no—
211C22×Dic53—44no—
212C22×Dic53C22×C414yes—
213C22×Dic53C22×C414yes—
214C22×Dic53C2×D412yes—
215C22×Dic53C2×D414yes—
216C22×Dic53C2×D414yes—
217C22×Dic53C2×D412yes—
218C22×Dic53#4114yes—
219C22⋊C4×C53—28no—
220C22⋊C4×C53—48no—
221C22⋊Dic53—216no—
222C22⋊Dic53—44no—
223C22⋊Dic53—44no—
224C22⋊Dic53—44no—
225C22⋊Dic53C22⋊C4116yescomplemented
226#11719919—216no—
227#11719919—48no—
228C4×Dic53—48no—
229C23×C53—24no—
230C23×C53—24no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—24no—
234C23×C53—22no—
235C23×C53—22no—
236C23×C53—24no—
237C23×C53—24no—
238C23×C53—24no—
239C23×C53—24no—
240C23×C53—24no—
241C23×C53—24no—
242C23×C53—24no—
243C23×C53—24no—
244C23×C53—24no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—24no—
249C23×C53—24no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—42no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—42no—
260C23×C53—42no—
261C23×C53—42no—
262C23×C53—42no—
263C23×C53—42no—
264C23×C53—42no—
265C23×C53—42no—
266C23×C53—42no—
267C23×C53—42no—
268C23×C53C2×C22⋊C414yes—
269C23×C53C4×D414yes—
270C23×C53C4×D414yes—
271C23×C53#12114yes—
272C23×C53#12114yes—
273C23×C53#12414yes—
274C23×C53#12714yes—
275C23×C53C23×C411yescharacteristic
276C23×C53C22×D411yescharacteristic
277C23×C53C22×D411yescharacteristic
278C23×C53C22×D411yescharacteristic
279C23×C53C22×D411yescharacteristic
280C23×C53C2×#4112yes—
281C23×C53C2×#4111yescharacteristic
282C23×C53C2×#4112yes—
283C23×C53C2×#4111yescharacteristic
284C23×C53H(5,𝔽2)12yes—
285C23×C532−1+412yes—
286D4×C53—416no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
292C2×C4×C53—24no—
293C2×C4×C53—24no—
294C2×C4×C53—24no—
295C2×C4×C53—24no—
296C2×C4×C53—416no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—41no—
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×Dic53—24no—
310C2×Dic53—24no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—24no—
314C2×Dic53—24no—
315C2×Dic53—24no—
316C2×Dic53—24no—
317C2×Dic53—24no—
318C2×Dic53—24no—
319C2×Dic53—24no—
320C2×Dic53—24no—
321C2×Dic53—24no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—416no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—416no—
333C2×Dic53—41no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53C2×C22⋊C418yes—
344C2×Dic53#12314yescomplemented
345#13996—531nomaximal, Sylow
346C22×C53—24no—
347C22×C53—28no—
348C22×C53—28no—
349C22×C53—24no—
350C22×C53—24no—
351C22×C53—28no—
352C22×C53—28no—
353C22×C53—24no—
354C22×C53—24no—
355C22×C53—24no—
356C22×C53—42no—
357C22×C53—44no—
358C22×C53—44no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—81no—
362C22×C53—81no—
363C22×C53—82no—
364C22×C53—82no—
365C22×C53—81no—
366C22×C53—81no—
367C22×C53#39018yes—
368C22×C53C22×C22⋊C411yescharacteristic
369C22×C53C2×C4×D411yescharacteristic
370C22×C53C2×C4×D411yescharacteristic
371C22×C53C4×#4112yes—
372C22×C53#52012yes—
373C22×C53C2×#12111yescharacteristic
374C22×C53C2×#12111yescharacteristic
375C22×C53C2×#12311yescharacteristic
376C22×C53#52511yescharacteristic
377C22×C53C2×#12411yescharacteristic
378C22×C53#52912yes—
379C22×C53C2×#12711yescharacteristic
380C22×C53#53411yescharacteristic
381C22×C53#53611yescharacteristic
382C22×C53#53912yes—
383C22×C53#54612yes—
384C22×C53#54612yes—
385C22×C53#54612yes—
386C22×C53#54712yes—
387C22×C53#54712yes—
388C22×C53#54712yes—
389C22×C53#55112yes—
390C22×C53#55212yes—
391C4×C53—44no—
392C4×C53—44no—
393C4×C53—42no—
394Dic53—28no—
395Dic53—24no—
396Dic53—42no—
397Dic53—44no—
398Dic53—81no—
399Dic53—81no—
400C22×#123—531no—
401C2×#386—531no—
402C2×#386D5311yescharacteristic
403C2×#385—531no—
404C2×#381—531no—
405C2×C4×C22⋊C4—531no—
406C22×#95—531no—
407#1445—532no—
408#1439—532no—
409#1437—532no—
410C4⋊#95—532no—
411C2×C53—28no—
412C2×C53—82no—
413C2×C53C2×#39011yescharacteristic
414C2×C53C4×#12311yescharacteristic
415C2×C53#232211yescharacteristic
416C2×C53#233912yes—
417C2×C53#235912yes—
418C2×C53#241211yescharacteristic
419C2×C53#241311yescharacteristic
420C2×C53#242512yes—
421C2×C53#248812yes—
422C2×C53#250111yescharacteristic
423C2×C53#253911yescharacteristic
424C23×D4C2×D5311yescharacteristic
425C24×C4—531no—
426C24×C4—531no—
427C24×C4C2×D5311yescharacteristic
428C2×#123—538no—
429C2×#123—1064no—
430C2×#123—1064no—
431C22×C4⋊C4—532no—
432C22×C4⋊C4—532no—
433C22×C22⋊C4—531no—
434C22×C22⋊C4—532no—
435C22×C22⋊C4—531no—
436C22×C22⋊C4—531no—
437C22×C22⋊C4—531no—
438C22×C22⋊C4C2×D5312yes—
439C22×C22⋊C4C2×D5311yescharacteristic
440C22×C42—532no—
441#386—24no—
442#386—1064no—
443#385—1064no—
444#381—1064no—
445C4×C22⋊C4—1064no—
446C2×#95—531no—
447C2×#95—532no—
448C2×#95—532no—
449C2×#95—532no—
450C2×#95—532no—
451C2×#95—532no—
452C2×#95—532no—
453C2×#95—531no—
454C2×#95—1064no—
455C2×#95C2×D5312yes—
456C53#1399611yescharacteristic, complemented, Sylow
457C25C22×D5311yescharacteristic
458C25C22×D5311yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C4×D5314yes—
466C23×C4—22no—
467C23×C4—24no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—42no—
471C23×C4—532no—
472C23×C4—531no—
473C23×C4—534no—
474C23×C4—532no—
475C23×C4—531no—
476C23×C4—534no—
477C23×C4—531no—
478C23×C4—531no—
479C23×C4—1064no—
480C23×C4—1062no—
481C23×C4—1062no—
482C23×C4—1062no—
483C23×C4—1062no—
484C23×C4—1062no—
485C23×C4—1062no—
486C23×C4—1062no—
487C23×C4—1062no—
488C23×C4—2122no—
489C23×C4C22×D5311yescharacteristic
490C23×C4C22×D5312yes—
491C23×C4C22×D5312yes—
492#123—10632no—
493C2×C4⋊C4—538no—
494C2×C4⋊C4—1064no—
495C2×C4⋊C4—1064no—
496C2×C4⋊C4—1064no—
497C2×C4⋊C4—1064no—
498C2×C4⋊C4—2122no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—534no—
505C2×C22⋊C4—534no—
506C2×C22⋊C4—534no—
507C2×C22⋊C4—538no—
508C2×C22⋊C4—1064no—
509C2×C22⋊C4—1064no—
510C2×C22⋊C4—1064no—
511C2×C22⋊C4—1062no—
512C2×C22⋊C4—1062no—
513C2×C22⋊C4—1062no—
514C2×C22⋊C4—1062no—
515C2×C22⋊C4—1062no—
516C2×C22⋊C4—2122no—
517C2×C22⋊C4C22⋊D5314yes—
518C2×C42—1064no—
519C2×C42—1064no—
520C2×C42—2122no—
521#95—24no—
522#95—1064no—
523#95—1064no—
524#95—1064no—
525#95—1064no—
526#95—1062no—
527#95—1062no—
528#95—1064no—
529#95—1064no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C2×C4×D5312yes—
545C24C2×C4×D5312yes—
546C24#1171994512yes—
547C24D4×D5312yes—
548C24D4×D5312yes—
549C24D4×D5312yes—
550C24#1171994712yes—
551C24C2×C22⋊D5312yes—
552C24C23×D5311yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—28no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—534no—
584C22×C4—532no—
585C22×C4—534no—
586C22×C4—534no—
587C22×C4—534no—
588C22×C4—534no—
589C22×C4—532no—
590C22×C4—1068no—
591C22×C4—1061no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1061no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1068no—
599C22×C4—1068no—
600C22×C4—1068no—
601C22×C4—1068no—
602C22×C4—1062no—
603C22×C4—1061no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1061no—
611C22×C4—1062no—
612C22×C4—1061no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—2124no—
623C22×C4—2128no—
624C22×C4—2128no—
625C22×C4—2124no—
626C22×C4—2124no—
627C22×C4—2124no—
628C22×C4—2124no—
629C22×C4C2×C4×D5312yes—
630C22×C4#1171994714yes—
631C22×C4C2×C22⋊D5314yes—
632C4⋊C4—10616no—
633C4⋊C4—2128no—
634C22⋊C4—28no—
635C22⋊C4—48no—
636C22⋊C4—5316no—
637C22⋊C4—10616no—
638C22⋊C4—2124no—
639C22⋊C4—2124no—
640C22⋊C4—2124no—
641C42—2128no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C22⋊C4×D5314yes—
682C23#1313317714yes—
683C23C4×C22⋊D5314yes—
684C23#1313318914yes—
685C23#1313319014yes—
686C23#1313320314yes—
687C23#1313321314yes—
688C23C22×C4×D5311yescharacteristic
689C23C2×D4×D5311yescharacteristic
690C23C2×D4×D5311yescharacteristic
691C23C2×D4×D5311yescharacteristic
692C23C22×C22⋊D5311yescharacteristic
693C23#41×D5312yes—
694C23C2×#1171994712yes—
695C23C2×#1171994711yescharacteristic
696C23C2×#1171994511yescharacteristic
697C23#1313326212yes—
698C23#1313326412yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—416no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—538no—
723C2×C4—534no—
724C2×C4—1064no—
725C2×C4—1064no—
726C2×C4—1064no—
727C2×C4—1064no—
728C2×C4—1064no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1064no—
732C2×C4—1064no—
733C2×C4—1064no—
734C2×C4—1064no—
735C2×C4—1064no—
736C2×C4—1064no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—21216no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2121no—
745C2×C4—2121no—
746C2×C4—2121no—
747C2×C4—2121no—
748C2×C4—2121no—
749C2×C4—2121no—
750C2×C4—2122no—
751C2×C4—21216no—
752C2×C4—2122no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2122no—
756C2×C4—2122no—
757C2×C4—2122no—
758C22—28no—
759C22—28no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—28no—
766C22—24no—
767C22—28no—
768C22—44no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—42no—
773C22—82no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—82no—
779C22#1681052318yes—
780C22C2×C22⋊C4×D5311yescharacteristic
781C22C2×#1313317711yescharacteristic
782C22C2×C4×C22⋊D5311yescharacteristic
783C22C4×#1171994712yes—
784C22#1681110212yes—
785C22C2×#1313318911yescharacteristic
786C22C2×#1313319011yescharacteristic
787C22#123×D5311yescharacteristic
788C22#1681112911yescharacteristic
789C22C2×#1313320311yescharacteristic
790C22#1681115412yes—
791C22C2×#1313321311yescharacteristic
792C22#1681118311yescharacteristic
793C22#1681119511yescharacteristic
794C22#1681121812yes—
795C22#1681126012yes—
796C22#1681126212yes—
797C22#1681126712yes—
798C22#1681127112yes—
799C22#1681127212yes—
800C22#1681127312yes—
801C22#1681130212yes—
802C22#1681131312yes—
803C4—44no—
804C4—44no—
805C4—42no—
806C4—1068no—
807C4—1064no—
808C4—4241no—
809C4—4241no—
810C4—2122no—
811C4—2124no—
812C2—28no—
813C2—82no—
814C2C2×#1681052311yescharacteristic
815C2#2027724011yescharacteristic
816C2#2027738911yescharacteristic
817C2#2027754112yes—
818C2#2027770112yes—
819C2#2027811411yescharacteristic
820C2#2027812511yescharacteristic
821C2#2027827212yes—
822C2#2027903912yes—
823C2#2027918411yescharacteristic
824C2#2027964311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#386C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#386D53
hypocenterC53#13996
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#16810496C2semidirect
4. C2×#16810484C2semidirect
5. C2×C22⋊C4×Dic53C2semidirect
6. C22×#13133124C2semidirect
7. #20272981C2semidirect
8. #20272958C2semidirect
9. #20272952C2semidirect
10. #20272943C2semidirect
16. C2×#13133198C4semidirect
68. C2×#11719919C2×C4semidirect
79. C2×C22⋊Dic53C2×C4semidirect
225. C22⋊Dic53C22⋊C4semidirect
344. C2×Dic53#123semidirect
456. C53#13996semidirect

Maximal subgroups

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

subgroupindex
C22×#131331982
C2×#168105032
C2×#168104962
C2×#168104842
C2×C22⋊C4×Dic532
C22×#131331242
#202729812
#202729582
#202729522
#202729432
C2×C53×#3862
#1399653