Finite Group Databasebeta

← #6470343

Subgroups — #6470343

Order 512.

3840 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3187C211yesmaximal, characteristic, complemented
2C23×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×#2848C211yesmaximal, characteristic, complemented
4C2×#2847C211yesmaximal, characteristic
5#32929C214yesmaximal, complemented
6#29734C214yesmaximal, complemented
7#24553C214yesmaximal, complemented
8#24551C214yesmaximal, complemented
9#24381C214yesmaximal, complemented
10#24379C214yesmaximal, complemented
11#21938C211yesmaximal, characteristic, complemented
12#21759C211yesmaximal, characteristic, complemented
13#21758C211yesmaximal, characteristic, complemented
14C25×C4C2211yescharacteristic
15C24×C8C2212yescomplemented
16C22×C22⋊Q8C2211yescharacteristic
17C22×C22⋊Q8C2212yescomplemented
18C22×#121C2211yescharacteristic
19C22×#121C2212yes—
20C22×#120—21no—
21#3187—28no—
22C2×#481C2212yescomplemented
23C2×#483C2212yescomplemented
24C2×#465C2214yescomplemented
25C2×#465C2218yescomplemented
26C2×#448C2212yescomplemented
27C2×#450C2212yescomplemented
28C22×C22⋊C8—28no—
29C22×C22⋊C8C2214yes—
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2212yescomplemented
33C22×C22⋊C8C2214yescomplemented
34#2848—21no—
35#2848—21no—
36#2848—22no—
37#2848C2214yes—
38#2848C2212yescomplemented
39#2848C2212yescomplemented
40#2847—21no—
41#2847—21no—
42#2847—22no—
43#2847C2212yes—
44#2847C2214yes—
45#2847C2212yes—
46C2×#386—22no—
47C2×#386—21no—
48C2×#385—21no—
49C2×#385—22no—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2212yescomplemented
54C2×#379—21no—
55#2077C2218yescomplemented
56#2035C2218yescomplemented
57#2034C2218yescomplemented
58#2000C2218yescomplemented
59#1893C2214yescomplemented
60#1893C2218yescomplemented
61#1892C2214yescomplemented
62#1892C2218yescomplemented
63#1874C2214yescomplemented
64#1872C2214yescomplemented
65#1853C2214yescomplemented
66#1853C2214yescomplemented
67#1824C2212yescomplemented
68#1823C2212yescomplemented
69#1807C2214yescomplemented
70#1807C2218yescomplemented
71#1787C2212yescomplemented
72#1786C2212yescomplemented
73C26D411yescharacteristic
74C23×Q8C2311yescharacteristic
75C23×D4—22no—
76C23×D4—21no—
77C23×D4C2311yescharacteristic
78C24×C4—24no—
79C24×C4—24no—
80C24×C4—48no—
81C24×C4D411yescharacteristic
82C24×C4D411yescharacteristic
83C24×C4D412yes—
84C24×C4D412yes—
85C24×C4D411yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2312yes—
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C22×SD16C2314yescomplemented
92C23×C8—28no—
93C23×C8—48no—
94C23×C8C2318yes—
95C23×C8C2312yes—
96C23×C8C2312yes—
97C2×C22⋊Q8—21no—
98C2×C22⋊Q8—21no—
99C2×C22⋊Q8—22no—
100C2×C22⋊Q8—22no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—48no—
104C2×C22⋊Q8C2312yes—
105C2×C22⋊Q8C2314yes—
106C2×C22⋊Q8C2312yes—
107C2×C22⋊Q8C2314yes—
108C2×#121—22no—
109C2×#121—22no—
110C2×#121—21no—
111C2×#121—21no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—48no—
115C2×#121C2312yes—
116C2×#121C2312yes—
117C2×#121C2314yes—
118C2×#121C2314yes—
119C2×#120—22no—
120C2×#120—24no—
121C2×#120—22no—
122C2×#120—48no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—22no—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C22⋊C4—22no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—22no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—22no—
135C22×C22⋊C4—22no—
136C22×C22⋊C4—21no—
137#483—28no—
138#481—28no—
139#465—216no—
140#465—416no—
141#450—28no—
142#448—28no—
143C2×#106C2314yescomplemented
144C2×#106C2318yescomplemented
145C2×#103C2314yescomplemented
146C2×#103C2318yescomplemented
147C2×#102C2314yescomplemented
148C2×#102C2318yescomplemented
149C2×C22⋊C8—24no—
150C2×C22⋊C8—28no—
151C2×C22⋊C8—216no—
152C2×C22⋊C8—216no—
153C2×C22⋊C8D418yescomplemented
154C2×C22⋊C8C2318yes—
155C2×C22⋊C8C2312yes—
156C2×C22⋊C8C2312yes—
157C2×C22⋊C8C2312yes—
158C2×C22⋊C8C2312yes—
159#386—24no—
160#386—22no—
161#386—24no—
162#386—24no—
163#386—24no—
164#386—22no—
165#386—24no—
166#385—24no—
167#385—24no—
168#385—24no—
169#385—24no—
170#385—22no—
171#385—22no—
172#385—24no—
173#380—22no—
174#380—22no—
175#380—21no—
176#380—21no—
177#380—21no—
178#380—21no—
179#380—22no—
180#380—22no—
181#380C2312yes—
182#380C2314yes—
183#380C2314yes—
184#380C2312yes—
185#380C2314yes—
186#380C2314yes—
187#380C2312yes—
188#380C2312yes—
189#379—24no—
190#379—22no—
191#379—22no—
192C2×#95—21no—
193C2×#95—22no—
194C2×#95—21no—
195C2×#95—22no—
196#340C2318yescomplemented
197#340C2318yescomplemented
198#340C2318yescomplemented
199C25—24no—
200C25—24no—
201C25—21no—
202C25—44no—
203C25—44no—
204C25SD1618yescomplemented
205C25C2×D411yescharacteristic
206C25C2×D412yes—
207C25C2×D412yes—
208C25C2×D411yescharacteristic
209C25C2×D411yescharacteristic
210C22×Q8—21no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—44no—
214C22×Q8C2412yes—
215C22×D4—24no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—24no—
219C22×D4—22no—
220C22×D4—21no—
221C22×D4—22no—
222C22×D4—44no—
223C22×D4—48no—
224C22×D4—48no—
225C22×D4—44no—
226C22×D4—48no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4C2412yes—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—28no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—28no—
236C23×C4—28no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—28no—
245C23×C4—28no—
246C23×C4—21no—
247C23×C4—22no—
248C23×C4—21no—
249C23×C4—22no—
250C23×C4—21no—
251C23×C4—44no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4—44no—
256C23×C4—44no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—432no—
263C23×C4—432no—
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D412yes—
266C23×C4C2×D412yes—
267C23×C4C2×D412yes—
268C23×C4C2×D412yes—
269C23×C4C2×D412yes—
270C23×C4C2×D412yes—
271C23×C4C2×D412yes—
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D412yes—
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D414yes—
278C23×C4#4114yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C2×SD16—28no—
285C2×SD16—48no—
286C22×C8—24no—
287C22×C8—216no—
288C22×C8—216no—
289C22×C8—44no—
290C22×C8—48no—
291C22×C8—44no—
292C22×C8—432no—
293C22×C8C2×D418yescomplemented
294C22×C8C2414yes—
295C22×C8C2414yes—
296C22⋊Q8—24no—
297C22⋊Q8—24no—
298C22⋊Q8—24no—
299C22⋊Q8—24no—
300C22⋊Q8—216no—
301C22⋊Q8—48no—
302C22⋊Q8—48no—
303C22⋊Q8—48no—
304C22⋊Q8—44no—
305C22⋊Q8—44no—
306#121—24no—
307#121—24no—
308#121—24no—
309#121—24no—
310#121—216no—
311#121—48no—
312#121—48no—
313#121—48no—
314#121—44no—
315#121—44no—
316#120—48no—
317#120—416no—
318#120—48no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—48no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4C2412yes—
336C2×C4⋊C4C2414yes—
337C2×C4⋊C4C2412yes—
338C2×C4⋊C4C2414yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—48no—
356C2×C22⋊C4—48no—
357C2×C22⋊C4—48no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—48no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363#106—28no—
364#106—48no—
365#103—28no—
366#103—48no—
367#102—28no—
368#102—48no—
369C22⋊C8—24no—
370C22⋊C8—24no—
371C22⋊C8—216no—
372C22⋊C8C2×D418yes—
373C22⋊C8C2×D418yescomplemented
374#95—24no—
375#95—22no—
376#95—22no—
377#95—24no—
378#95—24no—
379#95—22no—
380#95—22no—
381#95—24no—
382C24—22no—
383C24—24no—
384C24—22no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—22no—
389C24—24no—
390C24—24no—
391C24—24no—
392C24—24no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—232no—
397C24—22no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—432no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—416no—
408C24—416no—
409C24—432no—
410C24—44no—
411C24—44no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24#12114yes—
416C24C2×SD1614yes—
417C24C2×SD1618yes—
418C24C2×SD1618yes—
419C24C2×SD1614yes—
420C24C2×SD1614yes—
421C24#13514yes—
422C24C22×D412yes—
423C24C22×D411yescharacteristic
424C24C22×D411yescharacteristic
425C24C22×D411yescharacteristic
426C24C22×D412yes—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—28no—
430C2×Q8—44no—
431C2×Q8—42no—
432C2×Q8—84no—
433C2×Q8—84no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—28no—
437C2×D4—44no—
438C2×D4—48no—
439C2×D4—48no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—48no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—48no—
450C2×D4—42no—
451C2×D4—84no—
452C2×D4—84no—
453C2×D4—832no—
454C2×D4—816no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—416no—
506C22×C4—416no—
507C22×C4—416no—
508C22×C4—416no—
509C22×C4—416no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—416no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—416no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—44no—
526C22×C4—42no—
527C22×C4—44no—
528C22×C4—42no—
529C22×C4#12114yes—
530C22×C4#12114yes—
531C22×C4#12114yes—
532C22×C4C22×D412yes—
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4H(5,𝔽2)18yes—
544C22×C4C2511yescharacteristic
545SD16—88no—
546C2×C8—28no—
547C2×C8—24no—
548C2×C8—28no—
549C2×C8—48no—
550C2×C8—432no—
551C2×C8—48no—
552C2×C8C22×D418yes—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—48no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—44no—
571C22⋊C4—44no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C22⋊C4—44no—
579C22⋊C4—48no—
580C22⋊C4—44no—
581C22⋊C4—44no—
582C22⋊C4—48no—
583C23—28no—
584C23—28no—
585C23—216no—
586C23—22no—
587C23—216no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—28no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—216no—
600C23—216no—
601C23—22no—
602C23—22no—
603C23—216no—
604C23—216no—
605C23—28no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—44no—
610C23—44no—
611C23—48no—
612C23—48no—
613C23—48no—
614C23—48no—
615C23—48no—
616C23—48no—
617C23—48no—
618C23—48no—
619C23—48no—
620C23—48no—
621C23—48no—
622C23—48no—
623C23—48no—
624C23—44no—
625C23—4128no—
626C23—44no—
627C23—48no—
628C23—42no—
629C23—44no—
630C23—42no—
631C23—42no—
632C23—44no—
633C23—88no—
634C23—84no—
635C23—84no—
636C23—88no—
637C23—84no—
638C23#465116yescomplemented
639C23C2×#12112yes—
640C23C2×#12112yes—
641C23C2×#12112yes—
642C23#53414yes—
643C23C22×SD1614yes—
644C23C22×SD1614yes—
645C23C22×SD1612yes—
646C23C22×SD1612yes—
647C23C22×SD1612yes—
648C23C2×#13512yes—
649C23C2×#13512yes—
650C23C2×#13512yes—
651C23#57514yes—
652C23C23×D411yescharacteristic
653Q8—44no—
654Q8—44no—
655Q8—84no—
656D4—44no—
657D4—44no—
658D4—84no—
659D4—816no—
660D4—816no—
661D4—88no—
662D4—88no—
663C2×C4—216no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—28no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—48no—
685C2×C4—48no—
686C2×C4—48no—
687C2×C4—48no—
688C2×C4—48no—
689C2×C4—48no—
690C2×C4—48no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—84no—
708C2×C4—88no—
709C2×C4—88no—
710C2×C4—84no—
711C2×C4—84no—
712C2×C4C2×#12112yes—
713C2×C4C2×#12112yes—
714C2×C4C2×#12112yes—
715C2×C4#53414yes—
716C2×C4C23×D411yescharacteristic
717C2×C4C22×#4111yescharacteristic
718C2×C4C2×H(5,𝔽2)14yes—
719C8—28no—
720C8—44no—
721C22—232no—
722C22—24no—
723C22—22no—
724C22—22no—
725C22—24no—
726C22—22no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—22no—
737C22—24no—
738C22—22no—
739C22—22no—
740C22—24no—
741C22—24no—
742C22—24no—
743C22—416no—
744C22—432no—
745C22—432no—
746C22—416no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—82no—
752C22—82no—
753C22—84no—
754C22—84no—
755C22—82no—
756C22—168no—
757C22C2×#46514yes—
758C22C2×#46514yes—
759C22C2×#46514yes—
760C22#318718yescomplemented
761C22C22×#12111yescharacteristic
762C22C2×#53412yes—
763C22C23×SD1611yescharacteristic
764C22C22×#13511yescharacteristic
765C22C2×#57512yes—
766C4—22no—
767C4—24no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—82no—
772C4—82no—
773C4—84no—
774C4—84no—
775C4—82no—
776C4#348412yes—
777C4#349012yes—
778C2—28no—
779C2—24no—
780C2—24no—
781C2—24no—
782C2—44no—
783C2—162no—
784C2#3498111yescharacteristic
785C2C22×#46511yescharacteristic
786C2#6044411yescharacteristic
787C2C2×#318712yes—
788C2#6073412yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3187C2semidirect
2. C23×C22⋊C8C2semidirect
3. C2×#2848C2semidirect
5. #32929C2semidirect
6. #29734C2semidirect
7. #24553C2semidirect
8. #24551C2semidirect
9. #24381C2semidirect
10. #24379C2semidirect
11. #21938C2semidirect
12. #21759C2semidirect
13. #21758C2semidirect
15. C24×C8C22semidirect
17. C22×C22⋊Q8C22semidirect
22. C2×#481C22semidirect
23. C2×#483C22semidirect
24. C2×#465C22semidirect
25. C2×#465C22semidirect
26. C2×#448C22semidirect
27. C2×#450C22semidirect
32. C22×C22⋊C8C22semidirect
33. C22×C22⋊C8C22semidirect
38. #2848C22semidirect
39. #2848C22semidirect
53. C2×#380C22semidirect
55. #2077C22semidirect
56. #2035C22semidirect
57. #2034C22semidirect
58. #2000C22semidirect
59. #1893C22semidirect
60. #1893C22semidirect
61. #1892C22semidirect
62. #1892C22semidirect
63. #1874C22semidirect
64. #1872C22semidirect
65. #1853C22semidirect
66. #1853C22semidirect
67. #1824C22semidirect
68. #1823C22semidirect
69. #1807C22semidirect
70. #1807C22semidirect
71. #1787C22semidirect
72. #1786C22semidirect
91. C22×SD16C23semidirect
143. C2×#106C23semidirect
144. C2×#106C23semidirect
145. C2×#103C23semidirect
146. C2×#103C23semidirect
147. C2×#102C23semidirect
148. C2×#102C23semidirect
153. C2×C22⋊C8D4semidirect
196. #340C23semidirect
197. #340C23semidirect
198. #340C23semidirect
204. C25SD16semidirect
293. C22×C8C2×D4semidirect
373. C22⋊C8C2×D4semidirect
638. C23#465semidirect
760. C22#3187semidirect

Maximal subgroups

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

subgroupindex
C2×#31872
C23×C22⋊C82
C2×#28482
C2×#28472
#329292
#297342
#245532
#245512
#243812
#243792
#219382
#217592
#217582