Finite Group Databasebeta

← #27305388

Subgroups — #27305388

Order 13568.

2686 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D212C211yesmaximal, characteristic
2C2×#16810501C212yesmaximal
3C2×#16810470C211yesmaximal, characteristic, complemented
4C2×#95×D53C211yesmaximal, characteristic, complemented
5#20272951C212yesmaximal, complemented
6#20272949C212yesmaximal, complemented
7#20272942C211yesmaximal, characteristic, complemented
8#20272936C212yesmaximal, complemented
9#20272936C211yesmaximal, characteristic, complemented
10#20272936C211yesmaximal, characteristic, complemented
11C53×#1434C211yesmaximal, characteristic, complemented
12C23×D212C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C23×C4×D53C2212yes—
15C23×C4×D53C2211yescharacteristic
16C2×C4×D212—24no—
17C2×C4×D212—24no—
18C2×C4×D212C418yescomplemented
19C22×C4⋊Dic53C2211yescharacteristic
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2212yes—
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2212yes—
24C22×#11719921C2212yes—
25C22×C4×Dic53C2212yes—
26#16810501C4116yescomplemented
27#16810470—24no—
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35#95×D53—24no—
36C22×C42×C53C2211yescharacteristic
37C2×#95×C53C2211yescharacteristic
38C2×#95×C53C2211yescharacteristic
39C2×#95×C53C2212yes—
40C2×#95×C53C2212yes—
41C24×D53C2311yescharacteristic
42C24×D53C2311yescharacteristic
43C22×D212—22no—
44C22×D212—22no—
45C22×D212—24no—
46C22×D212C2×C418yes—
47C22×D212C2×C414yes—
48C23×Dic53C2312yes—
49C23×Dic53C2311yescharacteristic
50C23×Dic53C2312yes—
51C23×Dic53C2311yescharacteristic
52C22×C4×D53—24no—
53C22×C4×D53—24no—
54C22×C4×D53—22no—
55C22×C4×D53—22no—
56C22×C4×D53—42no—
57C22×C4×D53—42no—
58C22×C4×D53—42no—
59C22×C4×D53—42no—
60C22×C4×D53—42no—
61C22×C4×D53—42no—
62C22×C4×D53—42no—
63C22×C4×D53—42no—
64C22×C4×D53C2×C414yes—
65C22×C4×D53C2×C418yescomplemented
66C22×C4×D53C2×C414yescomplemented
67C22×C4×D53D414yes—
68C22×C4×D53D414yes—
69C4×D212—232no—
70C2×C4⋊Dic53—22no—
71C2×C4⋊Dic53—22no—
72C2×C4⋊Dic53C2×C414yescomplemented
73C2×#11719921—22no—
74C2×#11719921—22no—
75C2×#11719921—24no—
76C2×#11719921—24no—
77C2×#11719921—22no—
78C2×#11719921—22no—
79C2×#11719921—42no—
80C2×#11719921—42no—
81C2×#11719921—42no—
82C2×#11719921—42no—
83C2×#11719921C2×C414yes—
84C2×#11719921C2×C418yescomplemented
85C2×#11719921C2×C414yescomplemented
86C2×#11719921C2×C418yescomplemented
87C2×#11719921C2×C418yescomplemented
88C2×C4×Dic53—24no—
89C2×C4×Dic53—42no—
90C2×C4×Dic53—42no—
91#13133124—22no—
92#13133124—22no—
93#13133124—24no—
94#13133124—42no—
95#13133124—42no—
96#13133124—42no—
97#13133124C2×C418yescomplemented
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2312yes—
100C23×C4×C53C2312yes—
101C23×C4×C53C2311yescharacteristic
102C23×C4×C53C2311yescharacteristic
103C2×C42×C53—22no—
104C2×C42×C53—22no—
105C2×C42×C53C2×C414yescomplemented
106#95×C53—22no—
107#95×C53—22no—
108#95×C53—42no—
109#95×C53C2×C418yescomplemented
110C24×C53C2411yescharacteristic
111C23×D53—22no—
112C23×D53—22no—
113C23×D53—21no—
114C23×D53—21no—
115C23×D53—21no—
116C23×D53—21no—
117C23×D53—21no—
118C23×D53—21no—
119C23×D53—22no—
120C23×D53—21no—
121C23×D53—21no—
122C23×D53—22no—
123C23×D53—22no—
124C23×D53—21no—
125C23×D53—21no—
126C23×D53C22×C414yes—
127C23×D53C22×C412yes—
128C23×D53C22×C412yes—
129C23×D53C22×C414yes—
130C23×D53C2×D412yes—
131C23×D53C2×D412yes—
132C23×D53#4114yes—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—21no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—21no—
148C22×C4×C53—22no—
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—22no—
156C22×C4×C53C22×C414yes—
157C22×C4×C53C22×C414yes—
158C22×C4×C53C22×C412yes—
159C22×C4×C53C22×C414yes—
160C22×C4×C53C22×C412yes—
161C22×C4×C53C22×C412yes—
162C22×C4×C53C2×D412yes—
163C22×C4×C53C2×D412yes—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53C22×C414yes—
183C22×Dic53C22×C414yes—
184C22×Dic53C22×C412yes—
185C22×Dic53C22×C412yes—
186C22×Dic53C2×D412yes—
187C22×Dic53C2×D412yes—
188C2×D212—28no—
189C2×D212—28no—
190C2×D212—216no—
191C2×D212—216no—
192C2×D212C42116yescomplemented
193C2×C4×D53—216no—
194C2×C4×D53—28no—
195C2×C4×D53—44no—
196C2×C4×D53—44no—
197C2×C4×D53—44no—
198C2×C4×D53—44no—
199C2×C4×D53—48no—
200C2×C4×D53—48no—
201C2×C4×D53—48no—
202C2×C4×D53—48no—
203C2×C4×D53—48no—
204C2×C4×D53—48no—
205C2×C4×D53—48no—
206C2×C4×D53—48no—
207C2×C4×D53—48no—
208C2×C4×D53—48no—
209C2×C4×D53C22⋊C4116yescomplemented
210C42×C53—28no—
211#11719921—28no—
212#11719921—216no—
213#11719921—28no—
214#11719921—48no—
215#11719921—48no—
216C4⋊Dic53—28no—
217C4×Dic53—48no—
218C23×C53C23×C411yescharacteristic
219C23×C53C23×C412yes—
220C23×C53C22×D411yescharacteristic
221C23×C53C22×D411yescharacteristic
222C23×C53C2×#4112yes—
223C23×C53H(5,𝔽2)11yescharacteristic
224C23×C53H(5,𝔽2)12yes—
225C23×C53H(5,𝔽2)12yes—
226C23×C53H(5,𝔽2)11yescharacteristic
227C23×C532−1+411yescharacteristic
228C23×C532−1+411yescharacteristic
229C22×D53—24no—
230C22×D53—22no—
231C22×D53—22no—
232C22×D53—24no—
233C22×D53—22no—
234C22×D53—24no—
235C22×D53—22no—
236C22×D53—24no—
237C22×D53—24no—
238C22×D53—24no—
239C22×D53—22no—
240C22×D53—22no—
241C22×D53—22no—
242C22×D53—22no—
243C22×D53—24no—
244C22×D53—24no—
245C22×D53—24no—
246C22×D53—24no—
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—24no—
250C22×D53—24no—
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—24no—
254C22×D53—24no—
255C22×D53—22no—
256C22×D53—24no—
257C22×D53—22no—
258C22×D53—24no—
259C22×D53—42no—
260C22×D53—42no—
261C22×D53—41no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—42no—
266C22×D53—42no—
267C22×D53—42no—
268C22×D53—42no—
269C22×D53C2×C4214yes—
270C22×D53C2×C4214yes—
271C22×D53C2×C22⋊C414yes—
272C22×D53#11714yes—
273C22×D53C4×D418yes—
274C22×D53C4×D418yes—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—24no—
278C2×C4×C53—24no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—24no—
282C2×C4×C53—24no—
283C2×C4×C53—22no—
284C2×C4×C53—24no—
285C2×C4×C53—24no—
286C2×C4×C53—24no—
287C2×C4×C53—24no—
288C2×C4×C53—24no—
289C2×C4×C53—22no—
290C2×C4×C53—24no—
291C2×C4×C53—22no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—42no—
299C2×C4×C53—41no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53C2×C4214yes—
305C2×C4×C53C2×C22⋊C414yes—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—24no—
309C2×Dic53—24no—
310C2×Dic53—22no—
311C2×Dic53—24no—
312C2×Dic53—24no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—24no—
316C2×Dic53—24no—
317C2×Dic53—24no—
318C2×Dic53—24no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53C2×C22⋊C414yes—
330D212—232no—
331C4×D53—416no—
332C4×D53—416no—
333C4×D53—432no—
334#13784—531nomaximal, Sylow
335C22×C53C22×C4211yescharacteristic
336C22×C53C22×C22⋊C411yescharacteristic
337C22×C53C2×#11711yescharacteristic
338C22×C53C2×C4×D412yes—
339C22×C53C2×C4×D412yes—
340C22×C53#51812yes—
341C22×C53#51811yescharacteristic
342C22×C53#51811yescharacteristic
343C22×C53#51812yes—
344C22×C53#52011yescharacteristic
345C22×C53#52012yes—
346C22×C53#52011yescharacteristic
347C22×C53#52012yes—
348C22×C53#53412yes—
349C22×C53#53412yes—
350C22×C53#53511yescharacteristic
351C22×C53#53611yescharacteristic
352C22×C53#53711yescharacteristic
353C22×C53#53711yescharacteristic
354C22×C53#53812yes—
355C22×C53#53812yes—
356C22×C53#53912yes—
357C22×C53#53912yes—
358C2×D53—24no—
359C2×D53—24no—
360C2×D53—24no—
361C2×D53—24no—
362C2×D53—28no—
363C2×D53—28no—
364C2×D53—28no—
365C2×D53—28no—
366C2×D53—24no—
367C2×D53—24no—
368C2×D53—24no—
369C2×D53—24no—
370C2×D53—24no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—44no—
376C2×D53—44no—
377C2×D53—44no—
378C2×D53—44no—
379C2×D53C4×C22⋊C418yes—
380C4×C53—24no—
381C4×C53—24no—
382C4×C53—42no—
383C4×C53—44no—
384C4×C53—44no—
385Dic53—24no—
386Dic53—42no—
387Dic53—44no—
388Dic53—44no—
389C22×C4×D4—531no—
390C2×#386—532no—
391C2×C4×C22⋊C4—531no—
392C22×#95—531no—
393#1437—532no—
394#1436—532no—
395#1434—531no—
396#1434D5311yescharacteristic, complemented
397C22⋊#95—532no—
398C22⋊#95—531no—
399C22⋊#95—531no—
400C2×C53C2×C4×C22⋊C411yescharacteristic
401C2×C53#227511yescharacteristic
402C2×C53#227511yescharacteristic
403C2×C53#230811yescharacteristic
404C2×C53#231111yescharacteristic
405C2×C53#231811yescharacteristic
406C2×C53#231811yescharacteristic
407C2×C53#232112yes—
408C2×C53#232212yes—
409C2×C53#232512yes—
410C2×C53#232512yes—
411D53—28no—
412D53—44no—
413C23×D4—531no—
414C24×C4—531no—
415C24×C4—531no—
416C24×C4—532no—
417C2×C4×D4—538no—
418C2×C4×D4—1064no—
419C2×C4×D4—1064no—
420C22×C4⋊C4—531no—
421C22×C22⋊C4—531no—
422C22×C22⋊C4—531no—
423C22×C22⋊C4—532no—
424C22×C22⋊C4—532no—
425C22×C22⋊C4—532no—
426C22×C42—532no—
427C22×C42C2×D5311yescharacteristic
428#386—5316no—
429C4×C22⋊C4—1064no—
430C2×#95—532no—
431C2×#95—531no—
432C2×#95—531no—
433C2×#95—532no—
434C2×#95—532no—
435C2×#95—532no—
436C2×#95—532no—
437C2×#95—1064no—
438C2×#95C2×D5311yescharacteristic
439C2×#95C2×D5311yescharacteristic
440C2×#95C2×D5312yes—
441C2×#95C2×D5312yes—
442C53#1378411yescharacteristic, complemented, Sylow
443C25—531no—
444C25—531no—
445C22×D4—534no—
446C22×D4—538no—
447C22×D4—1062no—
448C22×D4—1062no—
449C22×D4—1064no—
450C23×C4—531no—
451C23×C4—534no—
452C23×C4—534no—
453C23×C4—534no—
454C23×C4—532no—
455C23×C4—531no—
456C23×C4—532no—
457C23×C4—534no—
458C23×C4—538no—
459C23×C4—1064no—
460C23×C4—1064no—
461C23×C4—1062no—
462C23×C4—1062no—
463C23×C4—2122no—
464C23×C4—2122no—
465C23×C4—2122no—
466C23×C4—2122no—
467C23×C4—2122no—
468C23×C4—2122no—
469C23×C4—2122no—
470C23×C4—2122no—
471C23×C4C22×D5311yescharacteristic
472C23×C4C22×D5312yes—
473C23×C4C22×D5312yes—
474C23×C4C22×D5311yescharacteristic
475C23×C4C22×D5311yescharacteristic
476C4×D4—10632no—
477C2×C4⋊C4—534no—
478C2×C4⋊C4—1062no—
479C2×C4⋊C4—1062no—
480C2×C22⋊C4—534no—
481C2×C22⋊C4—534no—
482C2×C22⋊C4—538no—
483C2×C22⋊C4—538no—
484C2×C22⋊C4—538no—
485C2×C22⋊C4—1062no—
486C2×C22⋊C4—1062no—
487C2×C22⋊C4—1062no—
488C2×C22⋊C4—1062no—
489C2×C22⋊C4—1064no—
490C2×C22⋊C4—1064no—
491C2×C22⋊C4—2122no—
492C2×C22⋊C4—2122no—
493C2×C22⋊C4—2122no—
494C2×C22⋊C4—2122no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—1064no—
498C2×C42—2122no—
499C2×C42—2122no—
500C2×C42C4×D5314yescomplemented
501#95—22no—
502#95—22no—
503#95—42no—
504#95—538no—
505#95—1064no—
506#95—1062no—
507#95—1062no—
508#95—2122no—
509#95—2122no—
510#95—2122no—
511#95C4×D5318yescomplemented
512C24—532no—
513C24—534no—
514C24—532no—
515C24—532no—
516C24—534no—
517C24—534no—
518C24—532no—
519C24—1061no—
520C24—1062no—
521C24—1062no—
522C24—1061no—
523C24—1061no—
524C24—1061no—
525C24—1061no—
526C24—1061no—
527C24—1062no—
528C24—1061no—
529C24—1061no—
530C24—1062no—
531C24—1062no—
532C24—1061no—
533C24—1061no—
534C24C23×D5311yescharacteristic
535C2×D4—5316no—
536C2×D4—1068no—
537C2×D4—1068no—
538C2×D4—10616no—
539C2×D4—10616no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—532no—
564C22×C4—532no—
565C22×C4—532no—
566C22×C4—5316no—
567C22×C4—534no—
568C22×C4—534no—
569C22×C4—532no—
570C22×C4—10616no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1068no—
590C22×C4—2124no—
591C22×C4—2124no—
592C22×C4—2124no—
593C22×C4—2124no—
594C22×C4—2128no—
595C22×C4—2128no—
596C22×C4—2128no—
597C22×C4—2128no—
598C22×C4—2128no—
599C22×C4—2128no—
600C22×C4—2128no—
601C22×C4—2128no—
602C22×C4—2128no—
603C22×C4—2128no—
604C22×C4C2×C4×D5314yes—
605C22×C4C2×C4×D5314yes—
606C22×C4C2×C4×D5312yes—
607C22×C4C2×C4×D5314yes—
608C22×C4C2×C4×D5312yes—
609C22×C4C2×C4×D5312yes—
610C22×C4D4×D5312yes—
611C22×C4D4×D5312yes—
612C4⋊C4—1068no—
613C22⋊C4—1068no—
614C22⋊C4—1068no—
615C22⋊C4—10616no—
616C22⋊C4—2128no—
617C22⋊C4—2128no—
618C42—28no—
619C42—2128no—
620C23—534no—
621C23—534no—
622C23—534no—
623C23—538no—
624C23—538no—
625C23—534no—
626C23—1064no—
627C23—1062no—
628C23—1062no—
629C23—1064no—
630C23—1062no—
631C23—1064no—
632C23—1062no—
633C23—1064no—
634C23—1064no—
635C23—1064no—
636C23—1062no—
637C23—1062no—
638C23—1062no—
639C23—1062no—
640C23—1064no—
641C23—1064no—
642C23—1064no—
643C23—1064no—
644C23—1062no—
645C23—1062no—
646C23—1064no—
647C23—1064no—
648C23—1064no—
649C23—1064no—
650C23—1062no—
651C23—1062no—
652C23—1062no—
653C23—1064no—
654C23—1062no—
655C23—1064no—
656C23—2122no—
657C23—2122no—
658C23—2121no—
659C23—2121no—
660C23—2121no—
661C23—2121no—
662C23—2122no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23C22×C4×D5311yescharacteristic
667C23C22×C4×D5312yes—
668C23C2×D4×D5311yescharacteristic
669C23C2×D4×D5311yescharacteristic
670C23#41×D5312yes—
671C23#1313326211yescharacteristic
672C23#1313326312yes—
673C23#1313326312yes—
674C23#1313326311yescharacteristic
675C23#1313326411yescharacteristic
676C23#1313326511yescharacteristic
677D4—10632no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—534no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1064no—
711C2×C4—1064no—
712C2×C4—1062no—
713C2×C4—1064no—
714C2×C4—1064no—
715C2×C4—1064no—
716C2×C4—1064no—
717C2×C4—1062no—
718C2×C4—1062no—
719C2×C4—1064no—
720C2×C4—1064no—
721C2×C4—21216no—
722C2×C4—21216no—
723C2×C4—21232no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4—2122no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4C42×D5314yes—
735C2×C4C22⋊C4×D5314yes—
736C22—538no—
737C22—1064no—
738C22—1064no—
739C22—1064no—
740C22—1064no—
741C22—1064no—
742C22—1064no—
743C22—1068no—
744C22—1068no—
745C22—1068no—
746C22—1068no—
747C22—1064no—
748C22—1064no—
749C22—1064no—
750C22—2122no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22—2124no—
755C22—2124no—
756C22—2124no—
757C22—2124no—
758C22C2×C42×D5311yescharacteristic
759C22C2×C22⋊C4×D5311yescharacteristic
760C22#117×D5311yescharacteristic
761C22C4×D4×D5312yes—
762C22C4×D4×D5312yes—
763C22#1681109512yes—
764C22#1681109711yescharacteristic
765C22#1681109711yescharacteristic
766C22#1681109712yes—
767C22#1681110311yescharacteristic
768C22#1681110312yes—
769C22#1681110411yescharacteristic
770C22#1681110512yes—
771C22#1681118412yes—
772C22#1681118412yes—
773C22#1681118911yescharacteristic
774C22#1681119611yescharacteristic
775C22#1681120211yescharacteristic
776C22#1681120311yescharacteristic
777C22#1681120712yes—
778C22#1681121212yes—
779C22#1681121412yes—
780C22#1681122112yes—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—44no—
785C4—44no—
786C4—1064no—
787C4—2122no—
788C4—2124no—
789C4—2124no—
790C2—1068no—
791C2—2124no—
792C2C4×C22⋊C4×D5311yescharacteristic
793C2#2027707511yescharacteristic
794C2#2027707711yescharacteristic
795C2#2027729211yescharacteristic
796C2#2027730411yescharacteristic
797C2#2027734611yescharacteristic
798C2#2027735111yescharacteristic
799C2#2027737712yes—
800C2#2027738812yes—
801C2#2027741412yes—
802C2#2027741912yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC53×#1434C2
socle, cosocleC24×C53C24
prime radicalC23×D212C22
hypercenter#1434D53
hypocenterC53#13784
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#16810470C2semidirect
4. C2×#95×D53C2semidirect
5. #20272951C2semidirect
6. #20272949C2semidirect
7. #20272942C2semidirect
8. #20272936C2semidirect
9. #20272936C2semidirect
10. #20272936C2semidirect
11. C53×#1434C2semidirect
18. C2×C4×D212C4semidirect
26. #16810501C4semidirect
65. C22×C4×D53C2×C4semidirect
66. C22×C4×D53C2×C4semidirect
72. C2×C4⋊Dic53C2×C4semidirect
84. C2×#11719921C2×C4semidirect
85. C2×#11719921C2×C4semidirect
86. C2×#11719921C2×C4semidirect
87. C2×#11719921C2×C4semidirect
97. #13133124C2×C4semidirect
105. C2×C42×C53C2×C4semidirect
109. #95×C53C2×C4semidirect
192. C2×D212C42semidirect
209. C2×C4×D53C22⋊C4semidirect
396. #1434D53semidirect
442. C53#13784semidirect
500. C2×C42C4×D53semidirect
511. #95C4×D53semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2122
C2×#168105012
C2×#168104702
C2×#95×D532
#202729512
#202729492
#202729422
#202729362
C53×#14342
#1378453