Finite Group Databasebeta

← #357778

Subgroups — #357778

Order 512.

2858 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2911C211yesmaximal, characteristic, complemented
2C22×#421C211yesmaximal, characteristic
3C2×#2896C211yesmaximal, characteristic
4C2×#2311C211yesmaximal, characteristic
5C22×#343C211yesmaximal, characteristic, complemented
6C2×#1733C211yesmaximal, characteristic, complemented
7#13795C211yesmaximal, characteristic, complemented
8#11113C218yesmaximal, complemented
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16#2911—24no—
17#2911—24no—
18C2×#428—22no—
19C2×#428C2214yescomplemented
20C2×#427—22no—
21C2×#421—24no—
22C2×#421—24no—
23C2×#421C418yescomplemented
24C22×#104C2214yes—
25#2896—24no—
26#2896—24no—
27C2×#417C2214yes—
28C2×#419—21no—
29C2×#418—21no—
30C2×#416—22no—
31#2311—22no—
32#2311—22no—
33#2311—22no—
34#2311C2214yes—
35C2×#391—21no—
36C2×#390—21no—
37C2×#386—22no—
38C2×#380—22no—
39C2×#343—24no—
40C2×#343C2214yescomplemented
41#1733—24no—
42C2×#339C2214yescomplemented
43C4⋊#95—22no—
44C4⋊#95C2214yescomplemented
45C22⋊#95—22no—
46C22×#41—21no—
47C22×#41—21no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41C2×C414yes—
59C22×#41D412yes—
60C22×#41Q814yes—
61C22×#41C2312yes—
62C23×Q8D411yescharacteristic
63C23×D4—21no—
64C23×D4D411yescharacteristic
65C24×C4—21no—
66C24×C4D412yes—
67C24×C4C2311yescharacteristic
68C22×M16—21no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—21no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16C2×C414yes—
79C22×M16D414yes—
80C22×M16D414yes—
81C22×M16D414yes—
82C22×M16C2312yes—
83C22×M16C2312yes—
84C23×C8—21no—
85C23×C8—21no—
86C2×#117—21no—
87C2×#117—21no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—21no—
95C2×#117—21no—
96C2×#117—22no—
97C2×#117—21no—
98C2×#117—21no—
99C2×#117—22no—
100C2×#117—22no—
101C2×#117—22no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117C2×C414yes—
105C2×#117D412yes—
106C2×#117D414yes—
107C2×#117C2312yes—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—22no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4—22no—
115C22×C4⋊C4—22no—
116C22×C4⋊C4—22no—
117C22×C4⋊C4D412yes—
118C22×C4⋊C4D412yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—24no—
125C22×C42—21no—
126C22×C42—21no—
127C22×C42C2312yes—
128#428—216no—
129#428—28no—
130#428—28no—
131#427—216no—
132C2×#107—24no—
133C2×#106—24no—
134#421—232no—
135C2×#104—28no—
136C2×#104—28no—
137C2×#104C2×C4116yescomplemented
138#419—28no—
139#418—28no—
140#417—28no—
141#417—28no—
142#416—216no—
143C2×#103—24no—
144C2×#102—24no—
145#391—24no—
146#391—24no—
147#390—24no—
148#390—24no—
149#386—28no—
150#386—28no—
151#380—28no—
152#380—28no—
153C2×#95—24no—
154C2×#95—28no—
155#343—28no—
156#339—28no—
157C25—21no—
158C25C2×D411yescharacteristic
159C2×#41—24no—
160C2×#41—24no—
161C2×#41—24no—
162C2×#41—24no—
163C2×#41—24no—
164C2×#41—22no—
165C2×#41—22no—
166C2×#41—28no—
167C2×#41—28no—
168C2×#41—28no—
169C2×#41—28no—
170C2×#41—24no—
171C2×#41—24no—
172C2×#41—24no—
173C2×#41—28no—
174C2×#41—28no—
175C2×#41—28no—
176C2×#41—28no—
177C2×#41—24no—
178C2×#41—22no—
179C2×#41—22no—
180C2×#41—22no—
181C2×#41—22no—
182C2×#41—22no—
183C2×#41—22no—
184C2×#41—22no—
185C2×#41—22no—
186C2×#41—42no—
187C2×#41—42no—
188C2×#41—42no—
189C2×#41—44no—
190C2×#41—42no—
191C2×#41—42no—
192C2×#41—44no—
193C2×#41—44no—
194C2×#41—44no—
195C2×#41—42no—
196C2×#41—42no—
197C2×#41—44no—
198C2×#41—44no—
199C2×#41—44no—
200C2×#41—44no—
201C2×#41—42no—
202C2×#41C4⋊C418yes—
203C2×#41C22×C414yes—
204C2×#41C2×Q814yes—
205C22×Q8—21no—
206C22×Q8—22no—
207C22×Q8—22no—
208C22×Q8—22no—
209C22×Q8—22no—
210C22×Q8—22no—
211C22×Q8C4⋊C414yes—
212C22×Q8C2×D412yes—
213C22×D4—24no—
214C22×D4—22no—
215C22×D4—24no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—21no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—42no—
224C22×D4—42no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4C4⋊C414yes—
228C22×D4C2×D412yes—
229C23×C4—21no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—24no—
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—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—84no—
246C23×C4C22×C412yes—
247C23×C4C2×D414yes—
248C23×C4C2×D412yes—
249C23×C4C2×D412yes—
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D412yes—
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D412yes—
257C23×C4C2×Q812yes—
258C23×C4#4112yes—
259C23×C4#4112yes—
260C23×C4#4112yes—
261C23×C4#4112yes—
262C23×C4#4112yes—
263C23×C4#4112yes—
264C23×C4C2411yescharacteristic
265C2×M16—24no—
266C2×M16—28no—
267C2×M16—24no—
268C2×M16—24no—
269C2×M16—28no—
270C2×M16—28no—
271C2×M16—22no—
272C2×M16—22no—
273C2×M16—22no—
274C2×M16—24no—
275C2×M16—22no—
276C2×M16—28no—
277C2×M16—28no—
278C2×M16—22no—
279C2×M16—22no—
280C2×M16—22no—
281C2×M16—22no—
282C2×M16—42no—
283C2×M16—44no—
284C2×M16—42no—
285C2×M16—44no—
286C2×M16C22⋊C4116yescomplemented
287C2×M16C22×C414yes—
288C2×M16C2×D414yes—
289C2×M16C2×D414yes—
290C2×M16C2×D414yes—
291C22×C8—24no—
292C22×C8—24no—
293C22×C8—24no—
294C22×C8—22no—
295C22×C8—24no—
296C22×C8—22no—
297C22×C8—42no—
298C22×C8—42no—
299#117—28no—
300#117—28no—
301#117—24no—
302#117—24no—
303#117—24no—
304#117—24no—
305#117—24no—
306#117—24no—
307#117—22no—
308#117—22no—
309#117—22no—
310#117—22no—
311#117—42no—
312#117—44no—
313#117—42no—
314#117—42no—
315#117—42no—
316#117—42no—
317#117—42no—
318#117—42no—
319#117—44no—
320#117—42no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4C2×D414yes—
351C2×C4⋊C4C2×D414yes—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—216no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—88no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—42no—
374C2×C42—41no—
375C2×C42—41no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42C22×C414yes—
379#107—216no—
380#106—216no—
381#104—232no—
382#103—216no—
383#102—216no—
384#95—216no—
385#95—88no—
386C24—22no—
387C24—24no—
388C24—42no—
389C24—42no—
390C24—44no—
391C24—44no—
392C24—42no—
393C24—42no—
394C24C4×D412yes—
395C24#12011yescharacteristic
396C24#12011yescharacteristic
397C24#12112yes—
398C24#12112yes—
399C24C22⋊Q812yes—
400C24#12312yes—
401C24#12712yes—
402C24C22×D411yescharacteristic
403#41—24no—
404#41—24no—
405#41—24no—
406#41—24no—
407#41—24no—
408#41—24no—
409#41—24no—
410#41—24no—
411#41—216no—
412#41—216no—
413#41—42no—
414#41—42no—
415#41—42no—
416#41—42no—
417#41—42no—
418#41—42no—
419#41—42no—
420#41—42no—
421#41—48no—
422#41—48no—
423#41—48no—
424#41—48no—
425#41—48no—
426#41—48no—
427#41—48no—
428#41—48no—
429#41—48no—
430#41—48no—
431C2×Q8—22no—
432C2×Q8—24no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8C2×C4⋊C414yes—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—28no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—24no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—42no—
466C2×D4—44no—
467C2×D4—42no—
468C2×D4—44no—
469C2×D4C2×C4⋊C414yes—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—28no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—48no—
488C22×C4—48no—
489C22×C4—44no—
490C22×C4—48no—
491C22×C4—44no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—48no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—84no—
509C22×C4—88no—
510C22×C4—88no—
511C22×C4C2×C22⋊C414yes—
512C22×C4C2×C4⋊C412yes—
513C22×C4C2×C4⋊C412yes—
514C22×C4#11714yes—
515C22×C4C4×D414yes—
516C22×C4C4×D414yes—
517C22×C4C4×D412yes—
518C22×C4C4×D412yes—
519C22×C4C4×D412yes—
520C22×C4#12012yes—
521C22×C4#12012yes—
522C22×C4#12012yes—
523C22×C4#12012yes—
524C22×C4#12011yescharacteristic
525C22×C4#12011yescharacteristic
526C22×C4#12112yes—
527C22×C4#12112yes—
528C22×C4#12112yes—
529C22×C4#12112yes—
530C22×C4#12114yes—
531C22×C4#12112yes—
532C22×C4#12112yes—
533C22×C4#12112yes—
534C22×C4#12112yes—
535C22×C4#12114yes—
536C22×C4#12112yes—
537C22×C4#12112yes—
538C22×C4C22⋊Q814yes—
539C22×C4C22⋊Q814yes—
540C22×C4C22⋊Q814yes—
541C22×C4C22⋊Q814yes—
542C22×C4C22⋊Q812yes—
543C22×C4C22⋊Q812yes—
544C22×C4C22⋊Q812yes—
545C22×C4#12312yes—
546C22×C4#12312yes—
547C22×C4#12312yes—
548C22×C4#12312yes—
549C22×C4#12314yes—
550C22×C4#12314yes—
551C22×C4#12312yes—
552C22×C4#12412yes—
553C22×C4#12412yes—
554C22×C4#12414yes—
555C22×C4#12414yes—
556C22×C4#12614yes—
557C22×C4#12614yes—
558C22×C4#12712yes—
559C22×C4C23×C411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×Q811yescharacteristic
567C22×C4C2×#4111yescharacteristic
568C22×C4C2×#4111yescharacteristic
569C22×C4C2×#4111yescharacteristic
570C22×C4C2×#4111yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4C2×#4111yescharacteristic
573M16—24no—
574M16—24no—
575M16—24no—
576M16—216no—
577M16—24no—
578M16—24no—
579M16—42no—
580M16—42no—
581M16—48no—
582M16C2×C22⋊C418yescomplemented
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—24no—
586C2×C8—216no—
587C2×C8—24no—
588C2×C8—42no—
589C2×C8—42no—
590C2×C8—48no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—48no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—48no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—816no—
612C42—24no—
613C42—24no—
614C42—42no—
615C42—42no—
616C42—42no—
617C42—42no—
618C42—44no—
619C42—44no—
620C42—44no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—42no—
629C23—42no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—44no—
634C23—42no—
635C23—44no—
636C23—416no—
637C23—42no—
638C23—42no—
639C23—48no—
640C23—44no—
641C23—44no—
642C23—88no—
643C23—84no—
644C23—84no—
645C23#38512yes—
646C23#38512yes—
647C23#38814yes—
648C23#39014yes—
649C23#39212yes—
650C23#39212yes—
651C23#39412yes—
652C23#39412yes—
653C23#39614yes—
654C23#39914yes—
655C23C2×C4×D411yescharacteristic
656C23C2×#12011yescharacteristic
657C23C2×#12111yescharacteristic
658C23C2×#12111yescharacteristic
659C23C2×C22⋊Q811yescharacteristic
660C23C2×#12311yescharacteristic
661C23C2×#12711yescharacteristic
662Q8—24no—
663Q8—24no—
664Q8—42no—
665Q8—42no—
666Q8—48no—
667D4—24no—
668D4—24no—
669D4—44no—
670D4—44no—
671D4—416no—
672D4—44no—
673D4—44no—
674D4—42no—
675D4—42no—
676D4—48no—
677C2×C4—24no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—48no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—416no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—48no—
687C2×C4—48no—
688C2×C4—48no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—48no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—84no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4—84no—
700C2×C4—88no—
701C2×C4—88no—
702C2×C4—88no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—84no—
706C2×C4#38014yes—
707C2×C4#38014yes—
708C2×C4#38512yes—
709C2×C4#38512yes—
710C2×C4#38514yes—
711C2×C4#38514yes—
712C2×C4#38614yes—
713C2×C4#38614yes—
714C2×C4#38814yes—
715C2×C4#38814yes—
716C2×C4#38814yes—
717C2×C4#39014yes—
718C2×C4#39212yes—
719C2×C4#39212yes—
720C2×C4#39314yes—
721C2×C4#39314yes—
722C2×C4#39414yes—
723C2×C4#39414yes—
724C2×C4#39412yes—
725C2×C4#39412yes—
726C2×C4#39614yes—
727C2×C4#39614yes—
728C2×C4#39614yes—
729C2×C4#39714yes—
730C2×C4#39714yes—
731C2×C4#39914yes—
732C2×C4C22×C22⋊C411yescharacteristic
733C2×C4C22×C4⋊C411yescharacteristic
734C2×C4C2×#11711yescharacteristic
735C2×C4C2×C4×D411yescharacteristic
736C2×C4C2×C4×D411yescharacteristic
737C2×C4C2×C4×D411yescharacteristic
738C2×C4C2×#12011yescharacteristic
739C2×C4C2×#12011yescharacteristic
740C2×C4C2×#12111yescharacteristic
741C2×C4C2×#12111yescharacteristic
742C2×C4C2×#12111yescharacteristic
743C2×C4C2×#12111yescharacteristic
744C2×C4C2×#12111yescharacteristic
745C2×C4C2×#12111yescharacteristic
746C2×C4C2×C22⋊Q811yescharacteristic
747C2×C4C2×C22⋊Q811yescharacteristic
748C2×C4C2×C22⋊Q811yescharacteristic
749C2×C4C2×C22⋊Q811yescharacteristic
750C2×C4C2×C22⋊Q811yescharacteristic
751C2×C4C2×#12311yescharacteristic
752C2×C4C2×#12311yescharacteristic
753C2×C4C2×#12311yescharacteristic
754C2×C4C2×#12311yescharacteristic
755C2×C4C2×#12411yescharacteristic
756C2×C4C2×#12411yescharacteristic
757C2×C4C2×#12411yescharacteristic
758C2×C4C2×#12611yescharacteristic
759C2×C4C2×#12611yescharacteristic
760C8—28no—
761C8—44no—
762C22—22no—
763C22—22no—
764C22—24no—
765C22—24no—
766C22—22no—
767C22—24no—
768C22—22no—
769C22—24no—
770C22—21no—
771C22—21no—
772C22—22no—
773C22—22no—
774C22—21no—
775C22—22no—
776C22—21no—
777C22—22no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—48no—
784C22—816no—
785C22—84no—
786C22—82no—
787C22—82no—
788C22#143914yes—
789C22#143914yes—
790C22C2×#38511yescharacteristic
791C22C2×#38811yescharacteristic
792C22C2×#39011yescharacteristic
793C22C2×#39211yescharacteristic
794C22C2×#39411yescharacteristic
795C22C2×#39611yescharacteristic
796C22C2×#39911yescharacteristic
797C22#301912yes—
798C22#302012yes—
799C4—44no—
800C4—84no—
801C4—84no—
802C4—84no—
803C4—84no—
804C4#143914yes—
805C4#143914yes—
806C4C2×#38011yescharacteristic
807C4C2×#38511yescharacteristic
808C4C2×#38611yescharacteristic
809C4C2×#38811yescharacteristic
810C4C2×#39311yescharacteristic
811C4C2×#39411yescharacteristic
812C4C2×#39611yescharacteristic
813C4C2×#39711yescharacteristic
814C2—21no—
815C2—24no—
816C2—21no—
817C2—21no—
818C2—24no—
819C2—21no—
820C2—84no—
821C2C2×#143911yescharacteristic
822C2#2086412yes—
823C2#2340912yes—
824C2#2349311yescharacteristic
825C2#2349411yescharacteristic
subgroupG/H
center, socleC23C2×#120
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2911C2semidirect
5. C22×#343C2semidirect
6. C2×#1733C2semidirect
7. #13795C2semidirect
8. #11113C2semidirect
19. C2×#428C22semidirect
23. C2×#421C4semidirect
40. C2×#343C22semidirect
42. C2×#339C22semidirect
44. C4⋊#95C22semidirect
137. C2×#104C2×C4semidirect
286. C2×M16C22⋊C4semidirect
582. M16C2×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29112
C22×#4212
C2×#28962
C2×#23112
C22×#3432
C2×#17332
#137952
#111132