Finite Group Databasebeta

← #414586

Subgroups — #414586

Order 512.

1984 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×SD16C211yesmaximal, characteristic
2C2×#2582C211yesmaximal, characteristic, complemented
3C2×#2538C211yesmaximal, characteristic
4C2×#1984C211yesmaximal, characteristic, complemented
5C2×#1803C211yesmaximal, characteristic, complemented
6C2×#1802C211yesmaximal, characteristic
7#11327C212yesmaximal, complemented
8#11067C212yesmaximal, complemented
9#11066C212yesmaximal
10#11023C212yesmaximal
11#10841C211yesmaximal, characteristic, complemented
12C23×SD16C2211yescharacteristic
13C22×C22⋊Q8—21no—
14C22×C4×Q8C2211yescharacteristic
15C22×C4×Q8C2211yescharacteristic
16C22×C4×D4C2211yescharacteristic
17C2×C4×SD16—24no—
18C2×C4×SD16—24no—
19C2×C4×SD16—24no—
20C22×#106C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2212yes—
24C22×#102C2211yescharacteristic
25C22×#102C2212yes—
26C22×C4×C8C2211yescharacteristic
27#2582—24no—
28#2582—24no—
29#2538—24no—
30#2538—24no—
31C2×#398—22no—
32C2×#396—22no—
33C2×#391—21no—
34C2×#391C2212yes—
35C2×#390C2212yes—
36C2×#389—21no—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#384C2211yescharacteristic
40C2×#384C2211yescharacteristic
41C2×#380—21no—
42#1984—24no—
43#1803—24no—
44#1802—24no—
45C2×#340C2212yes—
46C2×#340C2212yes—
47C2×#340C2212yes—
48C2×#340C2212yes—
49C2×#336C2212yes—
50C2×#336C2212yes—
51C23×Q8D411yescharacteristic
52C23×Q8C2311yescharacteristic
53C23×D4C2311yescharacteristic
54C24×C4—21no—
55C22×SD16—22no—
56C22×SD16—22no—
57C22×SD16—22no—
58C22×SD16—22no—
59C22×SD16—22no—
60C22×SD16—22no—
61C22×SD16Q814yescomplemented
62C23×C8C2312yes—
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C2×C22⋊Q8—28no—
66C2×C22⋊Q8—44no—
67C2×C22⋊Q8—44no—
68C2×C4×Q8—22no—
69C2×C4×Q8—22no—
70C2×C4×Q8—22no—
71C2×C4×Q8—22no—
72C2×C4×Q8—22no—
73C2×C4×Q8—22no—
74C2×C4×Q8—22no—
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8D414yes—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4D414yes—
86C22×C4⋊C4—22no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4D412yes—
94C22×C4⋊C4D411yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2312yes—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—22no—
101C22×C22⋊C4—22no—
102C22×C42—21no—
103C22×C42C2312yes—
104C22×C42C2311yescharacteristic
105C4×SD16—232no—
106C2×#106—22no—
107C2×#106—22no—
108C2×#106—22no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112C2×#103—22no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—24no—
116C2×#103—24no—
117C2×#103—42no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—24no—
122C2×#102—24no—
123C2×#102—42no—
124C2×C4×C8—22no—
125C2×C4×C8—22no—
126C2×C4×C8D414yes—
127#398—216no—
128#396—216no—
129#391—28no—
130#391—24no—
131#391—24no—
132#390—24no—
133#390—24no—
134#389—28no—
135#389—24no—
136#389—24no—
137#389—24no—
138#389—24no—
139#384—22no—
140#384—22no—
141#384D414yes—
142#384D414yes—
143#380—28no—
144C2×#95—22no—
145C2×#95—22no—
146C2×#95—22no—
147C2×#95—22no—
148#340—24no—
149#340—24no—
150#340—24no—
151#340—42no—
152#336—24no—
153#336—24no—
154C25—21no—
155C22×Q8—22no—
156C22×Q8—22no—
157C22×Q8—22no—
158C22×Q8—22no—
159C22×Q8—22no—
160C22×Q8—22no—
161C22×Q8—21no—
162C22×Q8—21no—
163C22×Q8—21no—
164C22×Q8—21no—
165C22×Q8—21no—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172C22×Q8SD1614yescomplemented
173C22×Q8C2×D412yes—
174C22×Q8C2×Q812yes—
175C22×Q8#4112yes—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4C2×D412yes—
188C22×D4C2×Q812yes—
189C22×D4#4112yes—
190C23×C4—21no—
191C23×C4—22no—
192C23×C4—21no—
193C23×C4—22no—
194C23×C4—21no—
195C23×C4—24no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4C2×D412yes—
203C23×C4C2×D412yes—
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2411yescharacteristic
207C2×SD16—28no—
208C2×SD16—28no—
209C2×SD16—28no—
210C2×SD16—28no—
211C2×SD16—28no—
212C2×SD16—28no—
213C2×SD16—28no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—22no—
228C22×C8—22no—
229C22×C8—22no—
230C22×C8—22no—
231C22×C8C2×D412yes—
232C22×C8C2×D412yes—
233C22×C8C2×Q812yes—
234C22×C8#4112yes—
235C22⋊Q8—432no—
236C4×Q8—28no—
237C4×Q8—28no—
238C4×Q8—44no—
239C4×Q8—44no—
240C4×Q8—44no—
241C4×Q8—44no—
242C4×Q8—44no—
243C4×Q8—44no—
244C4×D4—28no—
245C4×D4—28no—
246C4×D4—44no—
247C4×D4—44no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—28no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—81no—
290C2×C4⋊C4—81no—
291C2×C4⋊C4—81no—
292C2×C4⋊C4—81no—
293C2×C4⋊C4—82no—
294C2×C4⋊C4—82no—
295C2×C4⋊C4C2×D412yes—
296C2×C4⋊C4C2×D412yes—
297C2×C4⋊C4C2×D414yes—
298C2×C4⋊C4C2×D414yes—
299C2×C22⋊C4—28no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—44no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—44no—
306C2×C22⋊C4—82no—
307C2×C22⋊C4—82no—
308C2×C42—24no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—42no—
316C2×C42—42no—
317C2×C42C2×D412yes—
318C2×C42C2×D412yes—
319C2×C42C2×D412yes—
320C2×C42C2×D412yes—
321C2×C42C2×D412yes—
322C2×C42#4112yes—
323#106—28no—
324C4⋊C8—44no—
325#103—28no—
326#103—48no—
327#102—28no—
328#102—48no—
329C4×C8—28no—
330#95—28no—
331#95—28no—
332#95—28no—
333#95—28no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24—41no—
338C24—41no—
339C24—41no—
340C24—41no—
341C24—41no—
342C24—41no—
343C24—41no—
344C24—41no—
345C24—41no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24C22×D411yescharacteristic
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—28no—
354C2×Q8—28no—
355C2×Q8—28no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8—41no—
373C2×Q8—41no—
374C2×Q8—41no—
375C2×Q8—41no—
376C2×Q8—41no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8—44no—
381C2×Q8—44no—
382C2×Q8—44no—
383C2×Q8—44no—
384C2×Q8C22⋊Q814yescomplemented
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4C22⋊Q814yes—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—41no—
451C22×C4—42no—
452C22×C4—41no—
453C22×C4—42no—
454C22×C4—41no—
455C22×C4—42no—
456C22×C4—41no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—41no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—48no—
466C22×C4—48no—
467C22×C4—48no—
468C22×C4—84no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4—84no—
472C22×C4#12012yes—
473C22×C4#12012yes—
474C22×C4#12012yes—
475C22×C4#12012yes—
476C22×C4#12112yes—
477C22×C4#12112yes—
478C22×C4C2×SD1614yes—
479C22×C4C2×SD1612yes—
480C22×C4#13512yes—
481C22×C4AGL(1,ℤ/8)12yes—
482C22×C4#13712yes—
483C22×C4C22×D411yescharacteristic
484C22×C4C22×D411yescharacteristic
485C22×C4C22×D411yescharacteristic
486C22×C4C22×D411yescharacteristic
487C22×C4C22×D411yescharacteristic
488C22×C4C22×Q811yescharacteristic
489C22×C4C2×#4111yescharacteristic
490C22×C4C2×#4111yescharacteristic
491C22×C4C2×#4111yescharacteristic
492C22×C4C2×#4111yescharacteristic
493C22×C4H(5,𝔽2)11yescharacteristic
494C22×C42−1+411yescharacteristic
495C22×C42−1+411yescharacteristic
496C22×C42−1+411yescharacteristic
497SD16—232no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—42no—
512C2×C8—42no—
513C2×C8—42no—
514C2×C8—42no—
515C2×C8—42no—
516C2×C8—42no—
517C2×C8—42no—
518C2×C8C22⋊Q814yescomplemented
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—416no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—48no—
537C4⋊C4—44no—
538C4⋊C4—48no—
539C4⋊C4—48no—
540C4⋊C4—48no—
541C4⋊C4—84no—
542C4⋊C4—84no—
543C4⋊C4—88no—
544C22⋊C4—416no—
545C22⋊C4—48no—
546C22⋊C4—88no—
547C42—42no—
548C42—42no—
549C42—42no—
550C42—42no—
551C42—48no—
552C42#12014yes—
553C42#12114yes—
554C42#12114yes—
555C42#12714yes—
556C23—24no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—81no—
576C23—81no—
577C23—81no—
578C23—81no—
579C23—81no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—81no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23—81no—
590C23—81no—
591C23C2×#12011yescharacteristic
592C23C2×#12011yescharacteristic
593C23C2×#12111yescharacteristic
594C23#54811yescharacteristic
595C23#54811yescharacteristic
596C23D4×Q811yescharacteristic
597C23#55011yescharacteristic
598C23C22×SD1611yescharacteristic
599C23C2×#13511yescharacteristic
600C23C2×AGL(1,ℤ/8)11yescharacteristic
601C23C2×#13711yescharacteristic
602C23#57611yescharacteristic
603C23#57711yescharacteristic
604C23#57711yescharacteristic
605C23#57811yescharacteristic
606Q8—24no—
607Q8—24no—
608Q8—42no—
609Q8—42no—
610Q8—42no—
611Q8—42no—
612Q8—416no—
613Q8—42no—
614Q8—42no—
615D4—24no—
616D4—24no—
617D4—42no—
618D4—42no—
619D4—42no—
620D4—42no—
621D4—42no—
622D4—42no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—42no—
650C2×C4—44no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—44no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—44no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—82no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4—82no—
666C2×C4—82no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4—82no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—816no—
679C2×C4#39214yes—
680C2×C4#39214yes—
681C2×C4#44814yes—
682C2×C4#44914yes—
683C2×C4#45014yes—
684C2×C4#45214yes—
685C2×C4#46514yes—
686C2×C4#46814yes—
687C2×C4C2×#12011yescharacteristic
688C2×C4C2×#12111yescharacteristic
689C2×C4C2×#12111yescharacteristic
690C2×C4C2×C22⋊Q811yescharacteristic
691C2×C4C2×C22⋊Q811yescharacteristic
692C2×C4C2×C22⋊Q811yescharacteristic
693C2×C4#52511yescharacteristic
694C2×C4#52511yescharacteristic
695C2×C4#52511yescharacteristic
696C2×C4C2×#12711yescharacteristic
697C2×C4#53611yescharacteristic
698C2×C4#53611yescharacteristic
699C2×C4#53611yescharacteristic
700C2×C4#53711yescharacteristic
701C2×C4#53711yescharacteristic
702C2×C4#53711yescharacteristic
703C2×C4#54611yescharacteristic
704C2×C4#54611yescharacteristic
705C2×C4#54711yescharacteristic
706C2×C4#54711yescharacteristic
707C2×C4#54811yescharacteristic
708C2×C4#54811yescharacteristic
709C2×C4D4×Q811yescharacteristic
710C2×C4D4×Q811yescharacteristic
711C2×C4#55211yescharacteristic
712C2×C4#55211yescharacteristic
713C2×C4#55411yescharacteristic
714C2×C4#55611yescharacteristic
715C8—24no—
716C8—42no—
717C8—82no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—82no—
722C22—82no—
723C22—82no—
724C22—82no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22C2×#39211yescharacteristic
734C22#240711yescharacteristic
735C22#240711yescharacteristic
736C22#240911yescharacteristic
737C22#240911yescharacteristic
738C22#253611yescharacteristic
739C22#253811yescharacteristic
740C22C2×#45011yescharacteristic
741C22C2×#44811yescharacteristic
742C22C2×#44911yescharacteristic
743C22C2×#45211yescharacteristic
744C22#301211yescharacteristic
745C22#301211yescharacteristic
746C22#301311yescharacteristic
747C22#301311yescharacteristic
748C22C2×#46511yescharacteristic
749C22C2×#46811yescharacteristic
750C22#306011yescharacteristic
751C22#306111yescharacteristic
752C22#335911yescharacteristic
753C22#336111yescharacteristic
754C22#336211yescharacteristic
755C22#336411yescharacteristic
756C22#336811yescharacteristic
757C22#336911yescharacteristic
758C22#337211yescharacteristic
759C22#337311yescharacteristic
760C22Q8×SD1611yescharacteristic
761C22#338111yescharacteristic
762C22#338511yescharacteristic
763C22#338611yescharacteristic
764C22#339211yescharacteristic
765C22#339411yescharacteristic
766C22#339811yescharacteristic
767C22#339911yescharacteristic
768C4—24no—
769C4—44no—
770C4—44no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—84no—
775C4—84no—
776C4#200018yes—
777C4#241511yescharacteristic
778C4#241511yescharacteristic
779C4#241711yescharacteristic
780C4#241711yescharacteristic
781C4#254011yescharacteristic
782C4#254211yescharacteristic
783C4#261611yescharacteristic
784C4#284811yescharacteristic
785C2—84no—
786C2#1517711yescharacteristic
787C2C2×#200011yescharacteristic
788C2#2339011yescharacteristic
789C2#2418611yescharacteristic
790C2#2418711yescharacteristic
791C2#2418811yescharacteristic
792C2#2418911yescharacteristic
793C2#2432811yescharacteristic
794C2#2432911yescharacteristic
795C2#2433011yescharacteristic
796C2#2433111yescharacteristic
797C2#2818611yescharacteristic
798C2#2819511yescharacteristic
799C2#2826411yescharacteristic
800C2#2827211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2582C2semidirect
4. C2×#1984C2semidirect
5. C2×#1803C2semidirect
7. #11327C2semidirect
8. #11067C2semidirect
11. #10841C2semidirect
61. C22×SD16Q8semidirect
172. C22×Q8SD16semidirect
384. C2×Q8C22⋊Q8semidirect
518. C2×C8C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C4×SD162
C2×#25822
C2×#25382
C2×#19842
C2×#18032
C2×#18022
#113272
#110672
#110662
#110232
#108412