Finite Group Databasebeta

← #27315548

Subgroups — #27315548

Order 13568.

2558 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×#13133196C211yesmaximal, characteristic, complemented
2C2×#16810543C211yesmaximal, characteristic, complemented
3C2×#16810535C211yesmaximal, characteristic, complemented
4C2×#16810496C212yesmaximal, complemented
5#20272968C211yesmaximal, characteristic, complemented
6#20272960C211yesmaximal, characteristic, complemented
7#20272958C212yesmaximal, complemented
8#20272956C212yesmaximal
9#20272948C212yesmaximal, complemented
10#20272938C211yesmaximal, characteristic, complemented
11C22×C4×D4×C53C211yesmaximal, characteristic
12C23×Dic106C2211yescharacteristic
13C2×#13133196—28no—
14C2×#13133196—24no—
15C22×C4⋊Dic53C2211yescharacteristic
16C22×#11719919C2212yes—
17C22×#11719919C2212yes—
18C22×C22⋊Dic53C2212yes—
19C22×C22⋊Dic53C2212yes—
20C22×C22⋊Dic53C2212yes—
21C22×C22⋊Dic53C2212yes—
22#16810543—24no—
23#16810535—24no—
24#16810496—28no—
25C2×#13133124C2212yes—
26C2×#13133124C2211yescharacteristic
27C2×#13133124C2211yescharacteristic
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C23×D4×C53C2211yescharacteristic
34C24×C4×C53C2211yescharacteristic
35C24×C4×C53C2211yescharacteristic
36C2×C4×D4×C53—24no—
37C2×C4×D4×C53—24no—
38C2×C4×D4×C53—24no—
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C22×C22⋊C4×C53C2211yescharacteristic
42C22×C42×C53C2211yescharacteristic
43C22×Dic106—22no—
44C22×Dic106—24no—
45C22×Dic106—22no—
46C22×Dic106—22no—
47C22×Dic106—42no—
48C23×Dic53C2312yes—
49C23×Dic53C2312yes—
50C23×Dic53C2312yes—
51C23×Dic53C2312yes—
52#13133196—232no—
53C2×C4⋊Dic53—22no—
54C2×C4⋊Dic53—24no—
55C2×#11719919—24no—
56C2×#11719919—24no—
57C2×#11719919—24no—
58C2×#11719919—24no—
59C2×#11719919—42no—
60C2×#11719919D418yescomplemented
61C2×C22⋊Dic53—24no—
62C2×C22⋊Dic53—24no—
63C2×C22⋊Dic53—24no—
64C2×C22⋊Dic53—24no—
65C2×C22⋊Dic53—24no—
66C2×C22⋊Dic53—24no—
67C2×C22⋊Dic53—24no—
68C2×C22⋊Dic53—24no—
69C2×C22⋊Dic53—24no—
70C2×C22⋊Dic53—24no—
71C2×C22⋊Dic53—42no—
72C2×C22⋊Dic53—42no—
73#13133124—24no—
74#13133124—24no—
75#13133124—22no—
76#13133124—22no—
77#13133124—24no—
78#13133124—24no—
79#13133124—24no—
80#13133124—24no—
81C25×C53C2311yescharacteristic
82C25×C53C2311yescharacteristic
83C22×D4×C53—22no—
84C22×D4×C53—22no—
85C22×D4×C53—22no—
86C22×D4×C53—22no—
87C22×D4×C53—22no—
88C22×D4×C53—22no—
89C22×D4×C53Q814yescomplemented
90C23×C4×C53—22no—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53—22no—
95C23×C4×C53—24no—
96C23×C4×C53—24no—
97C23×C4×C53—42no—
98C23×C4×C53—42no—
99C23×C4×C53D414yes—
100C23×C4×C53C2311yescharacteristic
101C23×C4×C53C2311yescharacteristic
102C23×C4×C53C2311yescharacteristic
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2311yescharacteristic
105C4×D4×C53—232no—
106C2×C4⋊C4×C53—22no—
107C2×C4⋊C4×C53—22no—
108C2×C4⋊C4×C53D414yes—
109C2×C22⋊C4×C53—22no—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—22no—
114C2×C22⋊C4×C53D414yes—
115C2×C42×C53—22no—
116C2×C42×C53—22no—
117C2×C42×C53—22no—
118C24×C53—21no—
119C24×C53—21no—
120C24×C53—21no—
121C24×C53—21no—
122C24×C53—22no—
123C24×C53—22no—
124C24×C53—21no—
125C24×C53—21no—
126C24×C53—21no—
127C24×C53—21no—
128C24×C53—22no—
129C24×C53—22no—
130C24×C53—22no—
131C24×C53—22no—
132C24×C53—22no—
133C24×C53—22no—
134C24×C53C2×D412yes—
135C24×C53C2×D412yes—
136C24×C53C2×Q812yes—
137C24×C53C2×Q812yes—
138C24×C53#4112yes—
139C24×C53#4112yes—
140C24×C53C2411yescharacteristic
141C2×D4×C53—28no—
142C2×D4×C53—28no—
143C2×D4×C53—28no—
144C2×D4×C53—28no—
145C2×D4×C53—28no—
146C2×D4×C53—28no—
147C2×D4×C53—28no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—22no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—28no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—28no—
167C22×C4×C53—28no—
168C22×C4×C53—44no—
169C22×C4×C53—48no—
170C22×C4×C53—48no—
171C22×C4×C53—48no—
172C22×C4×C53—48no—
173C22×C4×C53—44no—
174C22×C4×C53—44no—
175C22×C4×C53C2×D412yes—
176C22×C4×C53C2×D412yes—
177C22×C4×C53C2×D414yes—
178C22×C4×C53C2×D412yes—
179C22×C4×C53C2×D412yes—
180C22×C4×C53C2×D412yes—
181C22×C4×C53C2×D412yes—
182C22×C4×C53C2×D412yes—
183C22×C4×C53C2×Q812yes—
184C22×C4×C53#4112yes—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53C2×D414yes—
211C22×Dic53C2×D414yes—
212C22×Dic53#4114yes—
213C2×Dic106—28no—
214C2×Dic106—48no—
215C2×Dic106—48no—
216C2×Dic106—44no—
217C2×Dic106—44no—
218C4⋊C4×C53—28no—
219C22⋊C4×C53—28no—
220C22⋊C4×C53—28no—
221C42×C53—28no—
222C22⋊Dic53—216no—
223C22⋊Dic53—216no—
224C22⋊Dic53—48no—
225C22⋊Dic53—48no—
226C4⋊Dic53—28no—
227#11719919—216no—
228#11719919—48no—
229C23×C53—22no—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—22no—
234C23×C53—22no—
235C23×C53—22no—
236C23×C53—22no—
237C23×C53—22no—
238C23×C53—22no—
239C23×C53—22no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—24no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—24no—
247C23×C53—24no—
248C23×C53—24no—
249C23×C53—24no—
250C23×C53—24no—
251C23×C53—24no—
252C23×C53—24no—
253C23×C53—24no—
254C23×C53—24no—
255C23×C53—41no—
256C23×C53—42no—
257C23×C53—41no—
258C23×C53—42no—
259C23×C53—42no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—42no—
263C23×C53—42no—
264C23×C53—42no—
265C23×C53—42no—
266C23×C53—42no—
267C23×C53—42no—
268C23×C53—42no—
269C23×C53—42no—
270C23×C53—42no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53C22⋊Q814yes—
274C23×C53C22⋊Q814yescomplemented
275C23×C53C22×D412yes—
276C23×C53C22×D411yescharacteristic
277C23×C53C22×D411yescharacteristic
278C23×C53C22×D411yescharacteristic
279C23×C53C22×Q811yescharacteristic
280C23×C53C2×#4112yes—
281C23×C53C2×#4111yescharacteristic
282C23×C53C2×#4111yescharacteristic
283C23×C53C2×#4111yescharacteristic
284C23×C53H(5,𝔽2)12yes—
285C23×C532−1+412yes—
286D4×C53—232no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—24no—
298C2×C4×C53—24no—
299C2×C4×C53—24no—
300C2×C4×C53—24no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—24no—
304C2×C4×C53—24no—
305C2×C4×C53—416no—
306C2×C4×C53—416no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53#12014yes—
314C2×C4×C53#12014yes—
315C2×C4×C53C22⋊Q814yescomplemented
316C2×Dic53—24no—
317C2×Dic53—24no—
318C2×Dic53—24no—
319C2×Dic53—24no—
320C2×Dic53—24no—
321C2×Dic53—24no—
322C2×Dic53—24no—
323C2×Dic53—24no—
324C2×Dic53—24no—
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—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344Dic106—416no—
345#14723—531nomaximal, Sylow
346C22×C53—24no—
347C22×C53—24no—
348C22×C53—24no—
349C22×C53—24no—
350C22×C53—28no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—44no—
362C22×C53—44no—
363C22×C53—44no—
364C22×C53—44no—
365C22×C53—44no—
366C22×C53—44no—
367C22×C53—44no—
368C22×C53C2×#12011yescharacteristic
369C22×C53C2×#12011yescharacteristic
370C22×C53C2×C22⋊Q811yescharacteristic
371C22×C53C2×C22⋊Q811yescharacteristic
372C22×C53C2×C22⋊Q811yescharacteristic
373C22×C53#52512yes—
374C22×C53#52511yescharacteristic
375C22×C53#52511yescharacteristic
376C22×C53#52511yescharacteristic
377C22×C53#53211yescharacteristic
378C22×C53#53212yes—
379C22×C53#53411yescharacteristic
380C22×C53#53611yescharacteristic
381C22×C53#53912yes—
382C22×C53#54212yes—
383C22×C53D4212yes—
384C22×C53D4212yes—
385C22×C53#54712yes—
386C22×C53#54812yes—
387C22×C53#54812yes—
388C22×C53D4×Q812yes—
389C22×C53#55112yes—
390C22×C53#55412yes—
391C4×C53—24no—
392C4×C53—24no—
393C4×C53—24no—
394C4×C53—42no—
395C4×C53—42no—
396Dic53—44no—
397Dic53—44no—
398Dic53—44no—
399Dic53—82no—
400C22×C22⋊Q8—531no—
401C22×C4×D4D5311yescharacteristic
402C2×#395—531no—
403C2×#393—531no—
404C2×#385—532no—
405#1441—531no—
406#1439—532no—
407#1439—531no—
408#1438—532no—
409#1436—532no—
410C22⋊#95—531no—
411C2×C53—44no—
412C2×C53—44no—
413C2×C53#238811yescharacteristic
414C2×C53#240311yescharacteristic
415C2×C53#240911yescharacteristic
416C2×C53#243211yescharacteristic
417C2×C53#244912yes—
418C2×C53#245212yes—
419C2×C53#246112yes—
420C2×C53#246312yes—
421C2×C53#256411yescharacteristic
422C2×C53#263811yescharacteristic
423C2×C53#284811yescharacteristic
424C23×Q8—531no—
425C23×D4C2×D5311yescharacteristic
426C24×C4C2×D5311yescharacteristic
427C24×C4C2×D5311yescharacteristic
428C2×C22⋊Q8—1068no—
429C2×C22⋊Q8—1064no—
430C2×C4×D4—24no—
431C2×C4×D4—24no—
432C2×C4×D4—24no—
433C22×C4⋊C4—532no—
434C22×C4⋊C4—531no—
435C22×C4⋊C4—532no—
436C22×C4⋊C4C2×D5311yescharacteristic
437C22×C22⋊C4—532no—
438C22×C22⋊C4—532no—
439C22×C22⋊C4—532no—
440C22×C22⋊C4—532no—
441C22×C22⋊C4C2×D5311yescharacteristic
442C22×C22⋊C4C2×D5311yescharacteristic
443C22×C42C2×D5311yescharacteristic
444#395—1064no—
445#393—1064no—
446#385—1068no—
447C2×#95—531no—
448C2×#95—532no—
449C2×#95—531no—
450C2×#95—532no—
451C2×#95—532no—
452C2×#95—532no—
453C2×#95—532no—
454C2×#95—532no—
455C53#1472311yescharacteristic, complemented, Sylow
456C25C22×D5311yescharacteristic
457C25C22×D5311yescharacteristic
458C22×Q8—1064no—
459C22×Q8—1062no—
460C22×Q8—1062no—
461C22×Q8—1062no—
462C22×Q8—2122no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4Dic10614yescomplemented
470C23×C4—22no—
471C23×C4—24no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—24no—
477C23×C4—42no—
478C23×C4—42no—
479C23×C4—532no—
480C23×C4—532no—
481C23×C4—532no—
482C23×C4—532no—
483C23×C4C22⋊D5314yes—
484C23×C4C22×D5311yescharacteristic
485C23×C4C22×D5311yescharacteristic
486C23×C4C22×D5311yescharacteristic
487C23×C4C22×D5311yescharacteristic
488C23×C4C22×D5311yescharacteristic
489C22⋊Q8—10632no—
490C4×D4—232no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—538no—
494C2×C4⋊C4—1064no—
495C2×C4⋊C4—1064no—
496C2×C4⋊C4—1064no—
497C2×C4⋊C4—1062no—
498C2×C4⋊C4—1064no—
499C2×C4⋊C4—1064no—
500C2×C4⋊C4—2122no—
501C2×C4⋊C4C22⋊D5314yes—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—1064no—
508C2×C22⋊C4—1064no—
509C2×C22⋊C4—1064no—
510C2×C22⋊C4—1064no—
511C2×C22⋊C4—1064no—
512C2×C22⋊C4—1064no—
513C2×C22⋊C4—1064no—
514C2×C22⋊C4—1064no—
515C2×C22⋊C4—1064no—
516C2×C22⋊C4—1064no—
517C2×C22⋊C4—2122no—
518C2×C22⋊C4—2122no—
519C2×C22⋊C4C22⋊D5314yes—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523#95—1064no—
524#95—1064no—
525#95—1064no—
526#95—1064no—
527#95—1064no—
528#95—1062no—
529#95—1062no—
530#95—1064no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—22no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24C2×Dic10612yes—
548C24C2×Dic10612yes—
549C24#1171994512yes—
550C24#1171994512yes—
551C24C2×C22⋊D5312yes—
552C24C2×C22⋊D5312yes—
553C24C23×D5311yescharacteristic
554C2×Q8—1068no—
555C2×Q8—2128no—
556C2×Q8—2128no—
557C2×Q8—2124no—
558C2×Q8—2124no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—28no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—44no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—534no—
594C22×C4—534no—
595C22×C4—534no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4C2×Dic10612yes—
622C22×C4#1171994512yes—
623C22×C4D4×D5314yes—
624C22×C4C2×C22⋊D5312yes—
625C22×C4C2×C22⋊D5312yes—
626C22×C4C2×C22⋊D5312yes—
627C22×C4C2×C22⋊D5312yes—
628C22×C4C2×C22⋊D5312yes—
629C22×C4C2×C22⋊D5312yes—
630C22×C4C2×C22⋊D5312yes—
631C4⋊C4—28no—
632C4⋊C4—1068no—
633C4⋊C4—10616no—
634C4⋊C4—2128no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—10616no—
638C22⋊C4—10616no—
639C22⋊C4—2128no—
640C22⋊C4—2128no—
641C42—28no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—42no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23#1313319614yes—
687C23#1313319614yescomplemented
688C23C2×D4×D5312yes—
689C23C22×C22⋊D5311yescharacteristic
690C23C22×C22⋊D5311yescharacteristic
691C23C22×C22⋊D5311yescharacteristic
692C23C22×Dic10611yescharacteristic
693C23#41×D5312yes—
694C23C2×#1171994511yescharacteristic
695C23C2×#1171994511yescharacteristic
696C23C2×#1171994511yescharacteristic
697C23#1313326212yes—
698C23#1313326412yes—
699Q8—21216no—
700D4—232no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—1064no—
728C2×C4—1064no—
729C2×C4—1064no—
730C2×C4—1064no—
731C2×C4—1064no—
732C2×C4—1064no—
733C2×C4—1064no—
734C2×C4—1064no—
735C2×C4—1064no—
736C2×C4—2122no—
737C2×C4—2122no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2122no—
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#1313318514yes—
756C2×C4#1313318614yes—
757C2×C4#1313319614yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—28no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—44no—
774C22—44no—
775C22—42no—
776C22—42no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22C2×#1313318511yescharacteristic
781C22C2×#1313318611yescharacteristic
782C22C2×#1313319611yescharacteristic
783C22C2×#1313319611yescharacteristic
784C22C2×#1313319611yescharacteristic
785C22#1681113212yes—
786C22#1681113411yescharacteristic
787C22#1681113411yescharacteristic
788C22#1681113411yescharacteristic
789C22#1681116911yescharacteristic
790C22#1681117012yes—
791C22#1681118211yescharacteristic
792C22#1681119411yescharacteristic
793C22#1681121512yes—
794C22#1681123812yes—
795C22D4×C22⋊D5312yes—
796C22D4×C22⋊D5312yes—
797C22#1681127212yes—
798C22#1681128012yes—
799C22#1681128212yes—
800C22D4×Dic10612yes—
801C22#1681130212yes—
802C22#1681133212yes—
803C4—24no—
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—4242no—
809C4—2124no—
810C4—2124no—
811C4—2124no—
812C2—44no—
813C2—44no—
814C2#2027793011yescharacteristic
815C2#2027802511yescharacteristic
816C2#2027808011yescharacteristic
817C2#2027833911yescharacteristic
818C2#2027851812yes—
819C2#2027855912yes—
820C2#2027867612yes—
821C2#2027870612yes—
822C2#2027989111yescharacteristic
823C2#2028063211yescharacteristic
824C2#2028300211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, cosocleC24×C53C24
FittingC22×C4×D4×C53C2
prime radicalC23×D4×C53C22
hypercenterC22×C4×D4D53
hypocenterC53#14723
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#13133196C2semidirect
2. C2×#16810543C2semidirect
3. C2×#16810535C2semidirect
4. C2×#16810496C2semidirect
5. #20272968C2semidirect
6. #20272960C2semidirect
7. #20272958C2semidirect
9. #20272948C2semidirect
10. #20272938C2semidirect
60. C2×#11719919D4semidirect
89. C22×D4×C53Q8semidirect
274. C23×C53C22⋊Q8semidirect
315. C2×C4×C53C22⋊Q8semidirect
455. C53#14723semidirect
469. C22×D4Dic106semidirect
687. C23#13133196semidirect
757. C2×C4#13133196semidirect

Maximal subgroups

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

subgroupindex
C22×#131331962
C2×#168105432
C2×#168105352
C2×#168104962
#202729682
#202729602
#202729582
#202729562
#202729482
#202729382
C22×C4×D4×C532
#1472353