Finite Group Databasebeta

← #27307217

Subgroups — #27307217

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
1C2×#16810503C211yesmaximal, characteristic
2C2×#16810503C211yesmaximal, characteristic
3C2×#16810498C211yesmaximal, characteristic, complemented
4C2×#16810486C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
6C22×#13133124C211yesmaximal, characteristic, complemented
7#20272983C212yesmaximal, complemented
8#20272960C212yesmaximal, complemented
9#20272952C212yesmaximal, complemented
10#20272944C212yesmaximal, complemented
11C22×#123×C53C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2212yes—
15C22×C22⋊Dic53C2211yescharacteristic
16C22×C22⋊Dic53C2211yescharacteristic
17C22×C22⋊Dic53C2212yes—
18C22×C22⋊Dic53C2211yescharacteristic
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C4×Dic53C2212yes—
21#16810503—24no—
22#16810503—24no—
23#16810498—24no—
24#16810486—24no—
25C22⋊C4×Dic53—24no—
26C2×#13133124—24no—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2211yescharacteristic
36C23×D4×C53C2211yescharacteristic
37C24×C4×C53C2211yescharacteristic
38C2×#123×C53—24no—
39C2×#123×C53—24no—
40C2×#123×C53C418yescomplemented
41C22×C4⋊C4×C53C2212yes—
42C22×C22⋊C4×C53C2212yes—
43C22×C22⋊C4×C53C2211yescharacteristic
44C23×Dic53—22no—
45C23×Dic53—22no—
46C23×Dic53—22no—
47C23×Dic53—24no—
48C23×Dic53—24no—
49C23×Dic53—22no—
50C23×Dic53—22no—
51C23×Dic53—42no—
52C23×Dic53—42no—
53C23×Dic53D414yes—
54C23×Dic53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2312yes—
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2312yes—
59C23×Dic53C2311yescharacteristic
60C2×C4⋊Dic53—24no—
61C2×C4⋊Dic53—24no—
62C2×C4⋊Dic53—42no—
63C2×C22⋊Dic53—22no—
64C2×C22⋊Dic53—22no—
65C2×C22⋊Dic53—22no—
66C2×C22⋊Dic53—22no—
67C2×C22⋊Dic53—22no—
68C2×C22⋊Dic53—24no—
69C2×C22⋊Dic53—22no—
70C2×C22⋊Dic53—22no—
71C2×C22⋊Dic53—24no—
72C2×C22⋊Dic53—24no—
73C2×C22⋊Dic53—42no—
74C2×C22⋊Dic53—42no—
75C2×C22⋊Dic53D414yes—
76C2×C4×Dic53—24no—
77C2×C4×Dic53—24no—
78C2×C4×Dic53—42no—
79#13133124—24no—
80#13133124—24no—
81#13133124—24no—
82#13133124—22no—
83#13133124—22no—
84#13133124—24no—
85#13133124—24no—
86#13133124—24no—
87#13133124—24no—
88C25×C53C2311yescharacteristic
89C25×C53C2311yescharacteristic
90C22×D4×C53—22no—
91C22×D4×C53—22no—
92C22×D4×C53—22no—
93C22×D4×C53—22no—
94C22×D4×C53—22no—
95C22×D4×C53—22no—
96C22×D4×C53C2×C414yes—
97C23×C4×C53—22no—
98C23×C4×C53—22no—
99C23×C4×C53—22no—
100C23×C4×C53—22no—
101C23×C4×C53—22no—
102C23×C4×C53—22no—
103C23×C4×C53C2×C414yes—
104C23×C4×C53C2312yes—
105C23×C4×C53C2311yescharacteristic
106C23×C4×C53C2312yes—
107#123×C53—232no—
108C2×C4⋊C4×C53—24no—
109C2×C4⋊C4×C53—24no—
110C2×C4⋊C4×C53C2×C418yescomplemented
111C2×C22⋊C4×C53—24no—
112C2×C22⋊C4×C53—24no—
113C2×C22⋊C4×C53C2×C414yes—
114C2×C22⋊C4×C53C2×C418yescomplemented
115C2×C22⋊C4×C53D414yes—
116C2×C22⋊C4×C53D414yes—
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—21no—
126C24×C53—21no—
127C24×C53—22no—
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—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—28no—
152C22×C4×C53—28no—
153C22×C4×C53—28no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—44no—
167C22×C4×C53—44no—
168C22×C4×C53—44no—
169C22×C4×C53—44no—
170C22×C4×C53C22×C414yes—
171C22×C4×C53C22×C412yes—
172C22×C4×C53C22×C414yes—
173C22×C4×C53C2×D414yes—
174C22×C4×C53C2×D414yes—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—22no—
178C22×Dic53—28no—
179C22×Dic53—28no—
180C22×Dic53—21no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—21no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—28no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—44no—
208C22×Dic53—48no—
209C22×Dic53—48no—
210C22×Dic53—48no—
211C22×Dic53—48no—
212C22×Dic53—44no—
213C22×Dic53—44no—
214C22×Dic53C2×D414yes—
215C22×Dic53C2×D412yes—
216C22×Dic53C2×D412yes—
217C22×Dic53#4114yes—
218C22×Dic53#4114yes—
219C4⋊C4×C53—216no—
220C22⋊C4×C53—216no—
221C22⋊C4×C53C22⋊C4116yescomplemented
222C22⋊Dic53—28no—
223C22⋊Dic53—48no—
224C22⋊Dic53—44no—
225C22⋊Dic53—44no—
226C22⋊Dic53—44no—
227C4⋊Dic53—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×#4112yes—
282C23×C53C2×#4111yescharacteristic
283C23×C53C2×#4111yescharacteristic
284C23×C53H(5,𝔽2)12yes—
285C23×C532−1+412yes—
286D4×C53—416no—
287C2×C4×C53—24no—
288C2×C4×C53—24no—
289C2×C4×C53—24no—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
292C2×C4×C53—24no—
293C2×C4×C53—24no—
294C2×C4×C53—22no—
295C2×C4×C53—24no—
296C2×C4×C53—24no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—42no—
304C2×C4×C53—41no—
305C2×C4×C53—42no—
306C2×C4×C53—41no—
307C2×C4×C53—416no—
308C2×C4×C53C2×C22⋊C418yes—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—24no—
312C2×Dic53—24no—
313C2×Dic53—22no—
314C2×Dic53—24no—
315C2×Dic53—22no—
316C2×Dic53—24no—
317C2×Dic53—22no—
318C2×Dic53—24no—
319C2×Dic53—24no—
320C2×Dic53—24no—
321C2×Dic53—24no—
322C2×Dic53—416no—
323C2×Dic53—416no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
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—28no—
392C4×C53—44no—
393C4×C53—42no—
394Dic53—24no—
395Dic53—42no—
396Dic53—44no—
397Dic53—44no—
398Dic53—81no—
399Dic53—81no—
400C22×#123D5311yescharacteristic
401C2×#386—531no—
402C2×#386—531no—
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—24no—
429C2×#123—24no—
430C2×#123Dic5318yescomplemented
431C22×C4⋊C4—532no—
432C22×C4⋊C4C2×D5312yes—
433C22×C22⋊C4—531no—
434C22×C22⋊C4—531no—
435C22×C22⋊C4—531no—
436C22×C22⋊C4—532no—
437C22×C22⋊C4—531no—
438C22×C22⋊C4C2×D5312yes—
439C22×C22⋊C4C2×D5311yescharacteristic
440C22×C42—532no—
441#386—1064no—
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—532no—
454C2×#95—531no—
455C2×#95—1064no—
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×D4C2×Dic5314yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—531no—
473C23×C4—532no—
474C23×C4—532no—
475C23×C4—531no—
476C23×C4—534no—
477C23×C4—531no—
478C23×C4—531no—
479C23×C4—1064no—
480C23×C4—1064no—
481C23×C4—1062no—
482C23×C4—1062no—
483C23×C4—1062no—
484C23×C4—1062no—
485C23×C4—1062no—
486C23×C4—2122no—
487C23×C4—2122no—
488C23×C4C2×Dic5314yes—
489C23×C4C22×D5312yes—
490C23×C4C22×D5311yescharacteristic
491C23×C4C22×D5312yes—
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—1064no—
496C2×C4⋊C4—1064no—
497C2×C4⋊C4—2122no—
498C2×C4⋊C4C2×Dic5318yescomplemented
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—534no—
502C2×C22⋊C4—1062no—
503C2×C22⋊C4—1062no—
504C2×C22⋊C4—1064no—
505C2×C22⋊C4—1064no—
506C2×C22⋊C4—1062no—
507C2×C22⋊C4—1064no—
508C2×C22⋊C4—1062no—
509C2×C22⋊C4—1062no—
510C2×C22⋊C4—1062no—
511C2×C22⋊C4—1062no—
512C2×C22⋊C4—2122no—
513C2×C22⋊C4—2122no—
514C2×C22⋊C4C2×Dic5314yes—
515C2×C22⋊C4C2×Dic5318yescomplemented
516C2×C22⋊C4C22⋊D5314yes—
517C2×C22⋊C4C22⋊D5314yes—
518C2×C42—1064no—
519C2×C42—1064no—
520C2×C42—2122no—
521#95—1064no—
522#95—1064no—
523#95—1064no—
524#95—1064no—
525#95—1062no—
526#95—1064no—
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—
544C24D4×D5312yes—
545C24D4×D5312yes—
546C24#1171994712yes—
547C24#1171994712yes—
548C24C22×Dic5312yes—
549C24C22×Dic5312yes—
550C24C2×C22⋊D5312yes—
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—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—532no—
584C22×C4—534no—
585C22×C4—534no—
586C22×C4—532no—
587C22×C4—534no—
588C22×C4—1068no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1062no—
592C22×C4—1068no—
593C22×C4—1068no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1061no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1061no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—2124no—
621C22×C4—2128no—
622C22×C4—2128no—
623C22×C4—2128no—
624C22×C4—2128no—
625C22×C4—2124no—
626C22×C4—2124no—
627C22×C4C22×Dic5314yes—
628C22×C4C22×Dic5312yes—
629C22×C4C22×Dic5314yes—
630C22×C4C2×C22⋊D5314yes—
631C22×C4C2×C22⋊D5314yes—
632C4⋊C4—216no—
633C4⋊C4—2128no—
634C22⋊C4—216no—
635C22⋊C4—1068no—
636C22⋊C4—2124no—
637C22⋊C4—2128no—
638C22⋊C4—2124no—
639C22⋊C4—2124no—
640C22⋊C4C22⋊Dic53116yescomplemented
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—
681C23C2×C22⋊Dic5314yes—
682C23D4×Dic5314yes—
683C23D4×Dic5314yes—
684C23#1313318814yes—
685C23#1313318814yes—
686C23#1313320414yes—
687C23#1313321314yes—
688C23C23×Dic5311yescharacteristic
689C23C2×D4×D5311yescharacteristic
690C23C2×D4×D5311yescharacteristic
691C23C22×C22⋊D5311yescharacteristic
692C23C22×C22⋊D5311yescharacteristic
693C23#41×D5312yes—
694C23#41×D5312yes—
695C23C2×#1171994711yescharacteristic
696C23C2×#1171994711yescharacteristic
697C23#1313326312yes—
698C23#1313326412yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—416no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—534no—
722C2×C4—1064no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1064no—
726C2×C4—1064no—
727C2×C4—1064no—
728C2×C4—1064no—
729C2×C4—1064no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1064no—
733C2×C4—1062no—
734C2×C4—1064no—
735C2×C4—21216no—
736C2×C4—2122no—
737C2×C4—2122no—
738C2×C4—2122no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4—2121no—
742C2×C4—2121no—
743C2×C4—2121no—
744C2×C4—2121no—
745C2×C4—2122no—
746C2×C4—21216no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4—2122no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4—2122no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2122no—
756C2×C4—2122no—
757C2×C4C2×C22⋊Dic5318yes—
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#1681052618yes—
780C22C22×C22⋊Dic5311yescharacteristic
781C22C2×D4×Dic5311yescharacteristic
782C22C2×D4×Dic5311yescharacteristic
783C22#41×Dic5312yes—
784C22#1681110612yes—
785C22C2×#1313318811yescharacteristic
786C22C2×#1313318811yescharacteristic
787C22#123×D5311yescharacteristic
788C22#1681113111yescharacteristic
789C22C2×#1313320411yescharacteristic
790C22#1681115012yes—
791C22C2×#1313321311yescharacteristic
792C22#1681118411yescharacteristic
793C22#1681119511yescharacteristic
794C22#1681121712yes—
795C22#1681126112yes—
796C22#1681126112yes—
797C22#1681126512yes—
798C22#1681127112yes—
799C22#1681127212yes—
800C22#1681127212yes—
801C22#1681129612yes—
802C22#1681131012yes—
803C4—28no—
804C4—44no—
805C4—42no—
806C4—1064no—
807C4—4241no—
808C4—4241no—
809C4—2122no—
810C4—2124no—
811C4—2124no—
812C2—28no—
813C2—82no—
814C2C2×#1681052611yescharacteristic
815C2#123×Dic5311yescharacteristic
816C2#2027738711yescharacteristic
817C2#2027754512yes—
818C2#2027771112yes—
819C2#2027810711yescharacteristic
820C2#2027811811yescharacteristic
821C2#2027826212yes—
822C2#2027904512yes—
823C2#2027918411yescharacteristic
824C2#2027964511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×#123×C53C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC22×#123D53
hypocenterC53#13996
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
3. C2×#16810498C2semidirect
4. C2×#16810486C2semidirect
5. C2×C22⋊C4×Dic53C2semidirect
6. C22×#13133124C2semidirect
7. #20272983C2semidirect
8. #20272960C2semidirect
9. #20272952C2semidirect
10. #20272944C2semidirect
40. C2×#123×C53C4semidirect
110. C2×C4⋊C4×C53C2×C4semidirect
114. C2×C22⋊C4×C53C2×C4semidirect
221. C22⋊C4×C53C22⋊C4semidirect
344. C2×Dic53#123semidirect
430. C2×#123Dic53semidirect
456. C53#13996semidirect
498. C2×C4⋊C4C2×Dic53semidirect
515. C2×C22⋊C4C2×Dic53semidirect
640. C22⋊C4C22⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105032
C2×#168104982
C2×#168104862
C2×C22⋊C4×Dic532
C22×#131331242
#202729832
#202729602
#202729522
#202729442
C22×#123×C532
#1399653