Finite Group Databasebeta

← #27306278

Subgroups — #27306278

Order 13568.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D212C211yesmaximal, characteristic
2C2×#16810501C212yesmaximal
3C2×#16810497C212yesmaximal, complemented
4C2×#16810482C211yesmaximal, characteristic, complemented
5C2×#95×D53C211yesmaximal, characteristic, complemented
6#20272967C212yesmaximal, complemented
7#20272961C212yesmaximal, complemented
8#20272945C211yesmaximal, characteristic, complemented
9#20272936C211yesmaximal, characteristic, complemented
10#20272936C211yesmaximal, characteristic, complemented
11C53×#1434C211yesmaximal, characteristic, complemented
12C23×D212C2211yescharacteristic
13C23×C4×D53C2212yes—
14C23×C4×D53C2211yescharacteristic
15C23×C4×D53C2211yescharacteristic
16C2×C4×D212—28no—
17C2×C4×D212C418yescomplemented
18C22×C4⋊Dic53C2212yes—
19C22×C4⋊Dic53C2211yescharacteristic
20C22×#11719919C2212yes—
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×#11719921C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26#16810501—28no—
27#16810497—28no—
28#16810482—24no—
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35#95×D53—24no—
36C22×C42×C53C2211yescharacteristic
37C2×#95×C53C2211yescharacteristic
38C2×#95×C53C2212yes—
39C2×#95×C53C2212yes—
40C2×#95×C53C2211yescharacteristic
41C24×D53C2311yescharacteristic
42C24×D53C2311yescharacteristic
43C22×D212—24no—
44C22×D212—24no—
45C22×D212C2×C414yes—
46C22×D212D414yes—
47C22×D212Q814yes—
48C23×Dic53C2312yes—
49C23×Dic53C2311yescharacteristic
50C23×Dic53C2312yes—
51C23×Dic53C2311yescharacteristic
52C22×C4×D53—24no—
53C22×C4×D53—24no—
54C22×C4×D53—24no—
55C22×C4×D53—22no—
56C22×C4×D53—22no—
57C22×C4×D53—22no—
58C22×C4×D53—22no—
59C22×C4×D53—24no—
60C22×C4×D53—24no—
61C22×C4×D53—24no—
62C22×C4×D53—24no—
63C22×C4×D53—42no—
64C22×C4×D53—42no—
65C22×C4×D53—42no—
66C22×C4×D53—42no—
67C22×C4×D53C2×C414yes—
68C22×C4×D53C2×C414yescomplemented
69C4×D212—232no—
70C2×C4⋊Dic53—24no—
71C2×C4⋊Dic53—24no—
72C2×C4⋊Dic53—24no—
73C2×C4⋊Dic53—42no—
74C2×C4⋊Dic53C2×C414yescomplemented
75C2×#11719919—24no—
76C2×#11719919—24no—
77C2×#11719919—42no—
78C2×#11719921—24no—
79C2×#11719921—24no—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921—24no—
83C2×#11719921—24no—
84C2×#11719921—24no—
85C2×#11719921—24no—
86C2×#11719921—42no—
87C2×#11719921—42no—
88C2×#11719921C2×C414yes—
89C2×#11719921C2×C414yescomplemented
90C2×#11719921D418yes—
91#13133124—24no—
92#13133124—24no—
93#13133124—22no—
94#13133124—22no—
95#13133124—24no—
96#13133124—42no—
97C23×C4×C53C2312yes—
98C23×C4×C53C2312yes—
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2311yescharacteristic
101C23×C4×C53C2311yescharacteristic
102C2×C42×C53—24no—
103C2×C42×C53C2×C414yescomplemented
104#95×C53—24no—
105#95×C53—24no—
106#95×C53—22no—
107#95×C53D414yescomplemented
108C24×C53C2411yescharacteristic
109C23×D53—21no—
110C23×D53—21no—
111C23×D53—22no—
112C23×D53—22no—
113C23×D53—21no—
114C23×D53—21no—
115C23×D53—21no—
116C23×D53—22no—
117C23×D53—22no—
118C23×D53—21no—
119C23×D53—22no—
120C23×D53—21no—
121C23×D53—22no—
122C23×D53—21no—
123C23×D53C22×C412yes—
124C23×D53C22×C412yes—
125C23×D53C2×D412yes—
126C23×D53C2×D414yes—
127C23×D53C2×D412yes—
128C23×D53C2×Q812yes—
129C23×D53C2×Q812yes—
130C23×D53#4114yes—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—21no—
136C22×C4×C53—22no—
137C22×C4×C53—21no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
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×C53C22×C412yes—
153C22×C4×C53C22×C412yes—
154C22×C4×C53C2×D414yes—
155C22×C4×C53C2×D414yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2×Q812yes—
159C22×C4×C53#4112yes—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—22no—
163C22×Dic53—21no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—21no—
169C22×Dic53—22no—
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×Dic53C22×C412yes—
181C22×Dic53C22×C412yes—
182C22×Dic53C2×D414yes—
183C22×Dic53#4114yes—
184C2×D212—28no—
185C2×D212—28no—
186C2×D212—216no—
187C2×D212—216no—
188C2×D212C4⋊C4116yescomplemented
189C2×C4×D53—216no—
190C2×C4×D53—28no—
191C2×C4×D53—28no—
192C2×C4×D53—28no—
193C2×C4×D53—28no—
194C2×C4×D53—44no—
195C2×C4×D53—44no—
196C2×C4×D53—48no—
197C2×C4×D53—48no—
198C2×C4×D53—48no—
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—
206C42×C53—28no—
207#11719921—28no—
208#11719921—48no—
209#11719921—48no—
210#11719921—48no—
211#11719921C22⋊C4116yescomplemented
212C4⋊Dic53—28no—
213C4⋊Dic53—48no—
214#11719919—48no—
215C23×C53C23×C411yescharacteristic
216C23×C53C22×D412yes—
217C23×C53C22×D411yescharacteristic
218C23×C53C22×D411yescharacteristic
219C23×C53C22×Q811yescharacteristic
220C23×C53C2×#4112yes—
221C23×C53C2×#4112yes—
222C23×C53C2×#4111yescharacteristic
223C23×C53H(5,𝔽2)12yes—
224C23×C53H(5,𝔽2)11yescharacteristic
225C23×C532−1+411yescharacteristic
226C22×D53—22no—
227C22×D53—22no—
228C22×D53—22no—
229C22×D53—22no—
230C22×D53—24no—
231C22×D53—24no—
232C22×D53—24no—
233C22×D53—24no—
234C22×D53—24no—
235C22×D53—22no—
236C22×D53—24no—
237C22×D53—24no—
238C22×D53—24no—
239C22×D53—24no—
240C22×D53—22no—
241C22×D53—22no—
242C22×D53—24no—
243C22×D53—22no—
244C22×D53—22no—
245C22×D53—22no—
246C22×D53—22no—
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—22no—
250C22×D53—24no—
251C22×D53—24no—
252C22×D53—22no—
253C22×D53—24no—
254C22×D53—22no—
255C22×D53—22no—
256C22×D53—24no—
257C22×D53—22no—
258C22×D53—42no—
259C22×D53—42no—
260C22×D53—42no—
261C22×D53—42no—
262C22×D53—42no—
263C22×D53—42no—
264C22×D53—42no—
265C22×D53—42no—
266C22×D53C2×C22⋊C414yes—
267C22×D53C2×C4⋊C414yes—
268C22×D53C2×C4⋊C414yes—
269C22×D53#11714yes—
270C22×D53#12118yes—
271C22×D53C22⋊Q818yes—
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—24no—
279C2×C4×C53—24no—
280C2×C4×C53—24no—
281C2×C4×C53—24no—
282C2×C4×C53—24no—
283C2×C4×C53—24no—
284C2×C4×C53—24no—
285C2×C4×C53—24no—
286C2×C4×C53—24no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53C2×C22⋊C414yes—
299C2×C4×C53C2×C4⋊C414yes—
300C2×C4×C53C4×D414yes—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—24no—
304C2×Dic53—24no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—24no—
309C2×Dic53—24no—
310C2×Dic53—24no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53C2×C22⋊C414yes—
325D212—232no—
326C4×D53—416no—
327C4×D53—416no—
328C4×D53—432no—
329#13899—531nomaximal, Sylow
330C22×C53C22×C22⋊C411yescharacteristic
331C22×C53C22×C4⋊C411yescharacteristic
332C22×C53C2×#11711yescharacteristic
333C22×C53C2×C4×D411yescharacteristic
334C22×C53C4×#4111yescharacteristic
335C22×C53#51811yescharacteristic
336C22×C53#52011yescharacteristic
337C22×C53C2×#12112yes—
338C22×C53C2×C22⋊Q812yes—
339C22×C53#52512yes—
340C22×C53#52912yes—
341C22×C53#53812yes—
342C22×C53#53912yes—
343C22×C53D4212yes—
344C22×C53D4211yescharacteristic
345C22×C53#54612yes—
346C22×C53#54612yes—
347C22×C53#54612yes—
348C22×C53#54712yes—
349C22×C53#54711yescharacteristic
350C22×C53D4×Q811yescharacteristic
351C22×C53#55412yes—
352C22×C53#55411yescharacteristic
353C2×D53—24no—
354C2×D53—24no—
355C2×D53—24no—
356C2×D53—24no—
357C2×D53—24no—
358C2×D53—28no—
359C2×D53—28no—
360C2×D53—28no—
361C2×D53—28no—
362C2×D53—24no—
363C2×D53—24no—
364C2×D53—24no—
365C2×D53—24no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—44no—
370C2×D53—44no—
371C2×D53—44no—
372C2×D53—44no—
373C2×D53—42no—
374C2×D53#38018yescomplemented
375C4×C53—24no—
376C4×C53—24no—
377C4×C53—24no—
378C4×C53—44no—
379C4×C53—82no—
380Dic53—24no—
381Dic53—42no—
382Dic53—44no—
383Dic53—82no—
384C22×C4×D4—531no—
385C2×#386—532no—
386C2×#385—532no—
387C2×#380—531no—
388C22×#95—531no—
389#1441—532no—
390#1439—532no—
391C4⋊#95—531no—
392#1434D5311yescharacteristic, complemented
393C22⋊#95—531no—
394C22⋊#95—531no—
395C2×C53C2×#38011yescharacteristic
396C2×C53#229011yescharacteristic
397C2×C53#231811yescharacteristic
398C2×C53D4×C22⋊C411yescharacteristic
399C2×C53#233911yescharacteristic
400C2×C53D4×C4⋊C411yescharacteristic
401C2×C53#234911yescharacteristic
402C2×C53#242412yes—
403C2×C53#242512yes—
404C2×C53#244912yes—
405C2×C53#245012yes—
406D53—28no—
407D53—44no—
408C23×D4—531no—
409C24×C4—531no—
410C24×C4—531no—
411C24×C4—532no—
412C2×C4×D4—538no—
413C2×C4×D4—1068no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4—532no—
416C22×C4⋊C4—532no—
417C22×C22⋊C4—531no—
418C22×C22⋊C4—531no—
419C22×C22⋊C4—532no—
420C22×C22⋊C4—532no—
421C22×C22⋊C4—532no—
422C22×C42C2×D5311yescharacteristic
423#386—1068no—
424#385—1068no—
425#380—1064no—
426C2×#95—531no—
427C2×#95—531no—
428C2×#95—532no—
429C2×#95—532no—
430C2×#95—532no—
431C2×#95—532no—
432C2×#95—1064no—
433C2×#95C2×D5311yescharacteristic
434C2×#95C2×D5312yes—
435C2×#95C2×D5312yes—
436C2×#95C2×D5311yescharacteristic
437C53#1389911yescharacteristic, complemented, Sylow
438C25—531no—
439C25—531no—
440C22×D4—534no—
441C22×D4—534no—
442C22×D4—534no—
443C22×D4—1064no—
444C22×D4—1064no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4—532no—
448C23×C4—534no—
449C23×C4—534no—
450C23×C4—532no—
451C23×C4—1064no—
452C23×C4—1064no—
453C23×C4—1064no—
454C23×C4—1064no—
455C23×C4—1064no—
456C23×C4—1064no—
457C23×C4—1064no—
458C23×C4—1062no—
459C23×C4—1062no—
460C23×C4—1062no—
461C23×C4—1062no—
462C23×C4—2122no—
463C23×C4—2122no—
464C23×C4—2122no—
465C23×C4—2122no—
466C23×C4C22×D5312yes—
467C23×C4C22×D5312yes—
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470C23×C4C22×D5311yescharacteristic
471C4×D4—10632no—
472C2×C4⋊C4—534no—
473C2×C4⋊C4—1064no—
474C2×C4⋊C4—1064no—
475C2×C4⋊C4—1064no—
476C2×C4⋊C4—1064no—
477C2×C4⋊C4—1064no—
478C2×C4⋊C4—2122no—
479C2×C4⋊C4—2122no—
480C2×C22⋊C4—534no—
481C2×C22⋊C4—538no—
482C2×C22⋊C4—534no—
483C2×C22⋊C4—1064no—
484C2×C22⋊C4—1064no—
485C2×C22⋊C4—1064no—
486C2×C22⋊C4—1064no—
487C2×C22⋊C4—1064no—
488C2×C22⋊C4—1064no—
489C2×C22⋊C4—1064no—
490C2×C22⋊C4—1064no—
491C2×C22⋊C4—2122no—
492C2×C22⋊C4—2122no—
493C2×C42—24no—
494C2×C42C4×D5314yescomplemented
495#95—22no—
496#95—24no—
497#95—24no—
498#95—1064no—
499#95—1064no—
500#95—1062no—
501#95—1062no—
502#95—1064no—
503#95—2122no—
504#95D21214yescomplemented
505C24—532no—
506C24—534no—
507C24—532no—
508C24—532no—
509C24—534no—
510C24—532no—
511C24—532no—
512C24—532no—
513C24—1061no—
514C24—1062no—
515C24—1061no—
516C24—1061no—
517C24—1062no—
518C24—1061no—
519C24—1062no—
520C24—1061no—
521C24—1062no—
522C24—1062no—
523C24—1061no—
524C24—1061no—
525C24—1062no—
526C24—1061no—
527C24C23×D5311yescharacteristic
528C2×D4—5316no—
529C2×D4—1068no—
530C2×D4—1068no—
531C2×D4—10616no—
532C2×D4—10616no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—532no—
554C22×C4—534no—
555C22×C4—532no—
556C22×C4—534no—
557C22×C4—1068no—
558C22×C4—1068no—
559C22×C4—10616no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1061no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1061no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1068no—
574C22×C4—1068no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—2124no—
583C22×C4—2124no—
584C22×C4—2128no—
585C22×C4—2128no—
586C22×C4—2128no—
587C22×C4—2128no—
588C22×C4—2128no—
589C22×C4—2128no—
590C22×C4—2128no—
591C22×C4—2128no—
592C22×C4—2128no—
593C22×C4—2128no—
594C22×C4C2×C4×D5312yes—
595C22×C4C2×C4×D5312yes—
596C22×C4C2×C4×D5312yes—
597C22×C4C2×D21214yes—
598C22×C4C2×D21212yes—
599C22×C4#1171994512yes—
600C22×C4D4×D5314yes—
601C22×C4D4×D5312yes—
602C22×C4Q8×D5312yes—
603C4⋊C4—1068no—
604C4⋊C4—2128no—
605C4⋊C4—2128no—
606C22⋊C4—5316no—
607C22⋊C4—1068no—
608C22⋊C4—2128no—
609C22⋊C4—2128no—
610C22⋊C4—2128no—
611C42—28no—
612C23—534no—
613C23—534no—
614C23—534no—
615C23—538no—
616C23—538no—
617C23—534no—
618C23—1064no—
619C23—1064no—
620C23—1064no—
621C23—1064no—
622C23—1062no—
623C23—1062no—
624C23—1064no—
625C23—1062no—
626C23—1062no—
627C23—1062no—
628C23—1062no—
629C23—1062no—
630C23—1064no—
631C23—1064no—
632C23—1064no—
633C23—1064no—
634C23—1064no—
635C23—1062no—
636C23—1064no—
637C23—1062no—
638C23—1062no—
639C23—1062no—
640C23—1064no—
641C23—1062no—
642C23—1062no—
643C23—1062no—
644C23—1062no—
645C23—1062no—
646C23—1062no—
647C23—1064no—
648C23—1064no—
649C23—1062no—
650C23—2122no—
651C23—2122no—
652C23—2122no—
653C23—2122no—
654C23—2122no—
655C23—2122no—
656C23—2122no—
657C23—2122no—
658C23C22×C4×D5311yescharacteristic
659C23C2×D4×D5312yes—
660C23C2×D4×D5311yescharacteristic
661C23C22×D21211yescharacteristic
662C23C2×Q8×D5311yescharacteristic
663C23#41×D5312yes—
664C23#41×D5312yes—
665C23C2×#1171994511yescharacteristic
666C23#1313326311yescharacteristic
667C23#1313326312yes—
668C23#1313326411yescharacteristic
669D4—10632no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—534no—
697C2×C4—1064no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1064no—
701C2×C4—1064no—
702C2×C4—1064no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1064no—
707C2×C4—21216no—
708C2×C4—21216no—
709C2×C4—21232no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4—2122no—
713C2×C4—2122no—
714C2×C4—2122no—
715C2×C4—2122no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4C22⋊C4×D5314yes—
724C2×C4C4⋊C4×D5314yes—
725C2×C4C4×D21214yes—
726C22—538no—
727C22—1068no—
728C22—1068no—
729C22—1064no—
730C22—1064no—
731C22—1064no—
732C22—1064no—
733C22—1064no—
734C22—1064no—
735C22—1068no—
736C22—1068no—
737C22—1064no—
738C22—1064no—
739C22—1064no—
740C22—2124no—
741C22—2124no—
742C22—2122no—
743C22—2122no—
744C22—2122no—
745C22—2122no—
746C22—2124no—
747C22—2124no—
748C22C2×C22⋊C4×D5311yescharacteristic
749C22C2×C4⋊C4×D5311yescharacteristic
750C22#117×D5311yescharacteristic
751C22C2×C4×D21211yescharacteristic
752C22#1681109111yescharacteristic
753C22#1681109711yescharacteristic
754C22#1681110311yescharacteristic
755C22#121×D5312yes—
756C22C22⋊Q8×D5312yes—
757C22#1681113512yes—
758C22#1681115112yes—
759C22#1681121212yes—
760C22#1681121412yes—
761C22D4×D21212yes—
762C22D4×D21211yescharacteristic
763C22#1681126512yes—
764C22#1681126612yes—
765C22#1681126912yes—
766C22#1681127112yes—
767C22#1681127811yescharacteristic
768C22Q8×D21211yescharacteristic
769C22#1681132912yes—
770C22#1681133311yescharacteristic
771C4—24no—
772C4—24no—
773C4—24no—
774C4—44no—
775C4—82no—
776C4—1064no—
777C4—4242no—
778C4—2122no—
779C4—2124no—
780C2—1068no—
781C2—2124no—
782C2#380×D5311yescharacteristic
783C2#2027715911yescharacteristic
784C2#2027734611yescharacteristic
785C2C22⋊C4×D21211yescharacteristic
786C2#2027753911yescharacteristic
787C2C4⋊C4×D21211yescharacteristic
788C2#2027762311yescharacteristic
789C2#2027825612yes—
790C2#2027827112yes—
791C2#2027852912yes—
792C2#2027853812yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1434C2
socle, cosocleC24×C53C24
prime radicalC23×D212C22
hypercenter#1434D53
hypocenterC53#13899
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#16810497C2semidirect
4. C2×#16810482C2semidirect
5. C2×#95×D53C2semidirect
6. #20272967C2semidirect
7. #20272961C2semidirect
8. #20272945C2semidirect
9. #20272936C2semidirect
10. #20272936C2semidirect
11. C53×#1434C2semidirect
17. C2×C4×D212C4semidirect
68. C22×C4×D53C2×C4semidirect
74. C2×C4⋊Dic53C2×C4semidirect
89. C2×#11719921C2×C4semidirect
103. C2×C42×C53C2×C4semidirect
107. #95×C53D4semidirect
188. C2×D212C4⋊C4semidirect
211. #11719921C22⋊C4semidirect
374. C2×D53#380semidirect
392. #1434D53semidirect
437. C53#13899semidirect
494. C2×C42C4×D53semidirect
504. #95D212semidirect

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×#168104972
C2×#168104822
C2×#95×D532
#202729672
#202729612
#202729452
#202729362
C53×#14342
#1389953