Finite Group Databasebeta

← #764624

Subgroups — #764624

Order 512.

4398 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2405C211yesmaximal, characteristic
2C22×#394C211yesmaximal, characteristic
3C2×#2315C211yesmaximal, characteristic, complemented
4C2×#2312C211yesmaximal, characteristic, complemented
5#15612C214yesmaximal, complemented
6#15473C214yesmaximal, complemented
7#15411C214yesmaximal, complemented
8#15303C214yesmaximal, complemented
9#14728C212yesmaximal, complemented
10#14726C212yesmaximal, complemented
11#14127C211yesmaximal, characteristic, complemented
12#14044C212yesmaximal, complemented
13#13971C212yesmaximal, complemented
14#13869C211yesmaximal, characteristic, complemented
15#13867C211yesmaximal, characteristic
16C24×D4C2211yescharacteristic
17C22×#123C2212yes—
18C23×C4⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25#2405—28no—
26C2×#398C2214yescomplemented
27C2×#396C2214yescomplemented
28C2×#394—28no—
29C2×#394C2214yes—
30C2×#394C2214yes—
31C2×#394C2214yes—
32#2315—28no—
33#2312—28no—
34C2×#388C2214yescomplemented
35C2×#388C2214yescomplemented
36C2×#388C2214yescomplemented
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yescomplemented
45C2×#385C2212yescomplemented
46C2×#385C2212yescomplemented
47C2×#381C2212yescomplemented
48C2×#380C2212yes—
49C2×#380C2212yescomplemented
50C2×#380C2212yescomplemented
51C2×#379C2211yescharacteristic
52C2×#379C2212yes—
53C2×#379C2212yes—
54C2×#379C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56C22×#95C2211yescharacteristic
57#1444C2214yescomplemented
58#1442C2214yescomplemented
59#1442C2214yescomplemented
60#1441C2214yescomplemented
61#1441C2214yescomplemented
62#1440C2214yescomplemented
63#1440C2214yescomplemented
64#1439C2214yescomplemented
65#1439C2214yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1439C2214yescomplemented
69#1438C2214yes—
70#1437C2214yescomplemented
71#1436C2214yescomplemented
72C4⋊#95C2214yescomplemented
73C22⋊#95C2212yes—
74C22⋊#95C2212yes—
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C22⋊#95C2212yescomplemented
78C22⋊#95C2212yescomplemented
79C26C2311yescharacteristic
80C26C2311yescharacteristic
81C23×D4—24no—
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—44no—
85C23×D4—44no—
86C23×D4C2312yes—
87C23×D4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C2×#123—28no—
98C2×#123—44no—
99C2×#123—44no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—44no—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—28no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—44no—
121C22×C22⋊C4—44no—
122C22×C22⋊C4—44no—
123C22×C22⋊C4D418yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C42C2314yes—
145#398—48no—
146#396—48no—
147#394—216no—
148#394—216no—
149#394—216no—
150#388—216no—
151#388—216no—
152#388—48no—
153#386—28no—
154#386—44no—
155#386—44no—
156#385—28no—
157#385—28no—
158#385—28no—
159#385—28no—
160#385—28no—
161#385—28no—
162#385—44no—
163#381—44no—
164#380—28no—
165#380—28no—
166#380—28no—
167#379—24no—
168#379—28no—
169#379—28no—
170#379D418yes—
171C4×C22⋊C4—28no—
172C2×#95—24no—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C25—24no—
191C25—24no—
192C25—22no—
193C25—24no—
194C25—22no—
195C25—22no—
196C25—24no—
197C25—24no—
198C25—42no—
199C25—42no—
200C25—42no—
201C25—42no—
202C25—42no—
203C25—42no—
204C25—42no—
205C25C2×D414yes—
206C25C2×D414yes—
207C25#4114yes—
208C25C2412yes—
209C25C2411yescharacteristic
210C25C2411yescharacteristic
211C25C2411yescharacteristic
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—42no—
223C22×D4—42no—
224C22×D4—42no—
225C22×D4—42no—
226C22×D4—416no—
227C22×D4—432no—
228C22×D4—432no—
229C22×D4—416no—
230C22×D4—416no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—24no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4C2×D414yes—
271C23×C4C2×D414yes—
272C23×C4C2414yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2414yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283#123—432no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—416no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C22⋊C4—232no—
306C2×C22⋊C4—232no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—416no—
354C2×C22⋊C4—416no—
355C2×C22⋊C4—416no—
356C2×C22⋊C4—416no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4C2×D418yes—
366C2×C22⋊C4C2×D418yes—
367C2×C22⋊C4C2×D418yes—
368C2×C22⋊C4C2×D418yes—
369C2×C22⋊C4C2×D418yes—
370C2×C22⋊C4#4118yes—
371C2×C42—28no—
372C2×C42—44no—
373C2×C42—44no—
374#95—28no—
375#95—28no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—28no—
408C24—28no—
409C24—216no—
410C24—216no—
411C24—28no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—24no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—24no—
422C24—44no—
423C24—44no—
424C24—44no—
425C24—48no—
426C24—48no—
427C24—44no—
428C24—48no—
429C24—48no—
430C24—48no—
431C24—48no—
432C24—416no—
433C24—416no—
434C24—44no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—48no—
441C24—48no—
442C24—84no—
443C24—84no—
444C24—88no—
445C24—88no—
446C24—88no—
447C24—88no—
448C24—88no—
449C24—88no—
450C24#121116yes—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C22×D412yes—
454C24C22×D412yes—
455C24C22×D412yes—
456C24C22×D412yes—
457C24C2×#4112yes—
458C24C2×#4112yes—
459C24C2×#4112yes—
460C24C2×#4114yes—
461C24H(5,𝔽2)14yes—
462C242−1+414yes—
463C24C2511yescharacteristic
464C2×D4—216no—
465C2×D4—216no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—4128no—
477C2×D4—48no—
478C2×D4—48no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—416no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—88no—
558C22×C4—88no—
559C22×C4—84no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—84no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—82no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4—82no—
571C22×C4—84no—
572C22×C4—84no—
573C22×C4—88no—
574C22×C4C22×D414yes—
575C22×C4C22×D418yes—
576C22×C4C22×D414yes—
577C22×C4C2×#4114yes—
578C22×C4C2×#4114yes—
579C22×C4H(5,𝔽2)14yes—
580C22×C4H(5,𝔽2)14yes—
581C4⋊C4—416no—
582C4⋊C4—416no—
583C4⋊C4—88no—
584C4⋊C4—84no—
585C4⋊C4—84no—
586C4⋊C4—84no—
587C4⋊C4—84no—
588C4⋊C4—88no—
589C22⋊C4—216no—
590C22⋊C4—216no—
591C22⋊C4—216no—
592C22⋊C4—216no—
593C22⋊C4—216no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—416no—
597C22⋊C4—416no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—416no—
601C22⋊C4—416no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—88no—
606C22⋊C4—88no—
607C22⋊C4—84no—
608C22⋊C4—84no—
609C42—88no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—24no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—232no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—28no—
651C23—28no—
652C23—416no—
653C23—416no—
654C23—416no—
655C23—416no—
656C23—416no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—44no—
669C23—44no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—832no—
684C23—88no—
685C23—832no—
686C23—88no—
687C23—88no—
688C23—88no—
689C23—832no—
690C23—832no—
691C23—88no—
692C23—88no—
693C23—88no—
694C23—88no—
695C23C2×#12114yes—
696C23C2×#12114yes—
697C23C2×#12114yes—
698C23#52514yes—
699C23#53614yes—
700C23#54718yes—
701C23#55218yes—
702C23C23×D411yescharacteristic
703C23C23×D411yescharacteristic
704C23C22×#4111yescharacteristic
705C23C22×#4112yes—
706C23C2×H(5,𝔽2)12yes—
707C23C2×H(5,𝔽2)12yes—
708C23C2×H(5,𝔽2)12yes—
709C23C2×2−1+412yes—
710C23#58512yes—
711D4—432no—
712D4—432no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—28no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—88no—
777C2×C4—88no—
778C2×C4—88no—
779C2×C4—88no—
780C2×C4—88no—
781C2×C4—88no—
782C2×C4—88no—
783C22—216no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—216no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—48no—
798C22—48no—
799C22—42no—
800C22—42no—
801C22—48no—
802C22—48no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—48no—
810C22—44no—
811C22—44no—
812C22—48no—
813C22—44no—
814C22—832no—
815C22—832no—
816C22—84no—
817C22—82no—
818C22—84no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22#241318yes—
823C22C22×#12111yescharacteristic
824C22C2×#52511yescharacteristic
825C22C2×#53611yescharacteristic
826C22C2×#54712yes—
827C22C2×#55212yes—
828C22#348412yes—
829C22#348411yescharacteristic
830C22#348411yescharacteristic
831C22#348411yescharacteristic
832C22#348511yescharacteristic
833C22#349012yes—
834C22#349612yes—
835C22#350512yes—
836C22#351414yes—
837C22#351914yes—
838C22#353514yes—
839C22#353614yes—
840C4—48no—
841C4—44no—
842C4—44no—
843C4—44no—
844C4—44no—
845C4—44no—
846C4—44no—
847C4—84no—
848C4—82no—
849C4—82no—
850C4—82no—
851C2—28no—
852C2—44no—
853C2—44no—
854C2—84no—
855C2C2×#241311yescharacteristic
856C2#3534811yescharacteristic
857C2#3535511yescharacteristic
858C2#3535811yescharacteristic
859C2#3545111yescharacteristic
860C2#3671811yescharacteristic
861C2#3672011yescharacteristic
862C2#4302014yes—
863C2#4304914yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2315C2semidirect
4. C2×#2312C2semidirect
5. #15612C2semidirect
6. #15473C2semidirect
7. #15411C2semidirect
8. #15303C2semidirect
9. #14728C2semidirect
10. #14726C2semidirect
11. #14127C2semidirect
12. #14044C2semidirect
13. #13971C2semidirect
14. #13869C2semidirect
26. C2×#398C22semidirect
27. C2×#396C22semidirect
34. C2×#388C22semidirect
35. C2×#388C22semidirect
36. C2×#388C22semidirect
44. C2×#385C22semidirect
45. C2×#385C22semidirect
46. C2×#385C22semidirect
47. C2×#381C22semidirect
49. C2×#380C22semidirect
50. C2×#380C22semidirect
57. #1444C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1440C22semidirect
63. #1440C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
70. #1437C22semidirect
71. #1436C22semidirect
72. C4⋊#95C22semidirect
77. C22⋊#95C22semidirect
78. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24052
C22×#3942
C2×#23152
C2×#23122
#156122
#154732
#154112
#153032
#147282
#147262
#141272
#140442
#139712
#138692
#138672