Finite Group Databasebeta

← #6644484

Subgroups — #6644484

Order 512.

2428 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35000C211yesmaximal, characteristic, complemented
2C2×#2537C211yesmaximal, characteristic, complemented
3#33002C212yesmaximal, complemented
4#31994C214yesmaximal, complemented
5#31382C214yesmaximal, complemented
6#30557C214yesmaximal, complemented
7#30396C214yesmaximal, complemented
8#29906C212yesmaximal, complemented
9#27600C211yesmaximal, characteristic, complemented
10#24550C212yesmaximal, complemented
11#24378C212yesmaximal, complemented
12#24002C211yesmaximal, characteristic, complemented
13#24002C211yesmaximal, characteristic, complemented
14#23918C211yesmaximal, characteristic, complemented
15#21738C211yesmaximal, characteristic, complemented
16C2×#534—21no—
17C22×#121—21no—
18C22×#121C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×#121C2211yescharacteristic, complemented
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic, complemented
23C2×#480C2212yes—
24C2×#480C2212yescomplemented
25C2×#466C2214yescomplemented
26C2×#447C2212yes—
27C2×#447C2212yescomplemented
28C22×C22⋊C8C2212yescomplemented
29#2854C2212yes—
30#2847C2212yes—
31#2618—21no—
32#2617—21no—
33#2543—22no—
34#2537—22no—
35#2537—22no—
36#2537C2214yes—
37#2537C2214yescomplemented
38#2534—22no—
39#2486C2212yescomplemented
40#2416C2212yescomplemented
41#2416C2212yescomplemented
42#2408C2212yescomplemented
43C2×#394—21no—
44C2×#394—21no—
45#2308—21no—
46C2×#384C2211yescharacteristic, complemented
47C2×#380—21no—
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic, complemented
51#2099C2214yescomplemented
52#2093C2214yescomplemented
53#2083C2214yescomplemented
54#2075C2214yescomplemented
55#2075C2214yescomplemented
56#2071C2214yescomplemented
57#2033C2214yescomplemented
58#2033C2214yescomplemented
59#2033C2214yescomplemented
60#2033C2214yescomplemented
61#1999C2214yescomplemented
62#1999C2214yescomplemented
63#1893C2214yescomplemented
64#1893C2214yescomplemented
65#1879C2214yescomplemented
66#1879C2214yescomplemented
67#1874C2212yes—
68#1874C2212yes—
69#1874C2212yescomplemented
70#1874C2212yescomplemented
71#1869C2214yescomplemented
72#1869C2214yescomplemented
73#1862C2214yescomplemented
74#1862C2214yescomplemented
75#1852C2212yescomplemented
76#1852C2212yescomplemented
77#1852C2212yescomplemented
78#1852C2212yescomplemented
79#1823C2212yescomplemented
80#1823C2212yescomplemented
81#1817C2212yescomplemented
82#1808C2214yescomplemented
83#1786C2212yescomplemented
84#1786C2212yescomplemented
85#1779C2211yescharacteristic
86#1779C2211yescharacteristic
87C23×D4—21no—
88C23×D4—21no—
89C23×D4—21no—
90C23×D4D411yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2311yescharacteristic
93C24×C4—21no—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C22×D8C2314yes—
97C23×C8C2314yes—
98#534—48no—
99C2×#123—22no—
100C2×#123—22no—
101C2×#121—24no—
102C2×#121—24no—
103C2×#121—22no—
104C2×#121—22no—
105C2×#121—21no—
106C2×#121—21no—
107C2×#121—21no—
108C2×#121—21no—
109C2×#121—22no—
110C2×#121—44no—
111C2×#121—44no—
112C2×#121—44no—
113C2×#121—48no—
114C2×#121C2312yes—
115C2×#121C2312yes—
116C2×#121C2312yes—
117C2×#121C2314yes—
118C2×#121C2312yes—
119C2×#121C2312yes—
120C2×#121C2312yes—
121C2×#120—22no—
122C2×#120—22no—
123C2×C4×D4—22no—
124C2×C4×D4—44no—
125C2×C4×D4—44no—
126C2×C4×D4D412yes—
127C2×C4×D4D412yes—
128C2×C4×D4C2314yes—
129C2×C4×D4C2312yes—
130C2×C4×D4C2312yes—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4D411yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4D411yescharacteristic
148C22×C22⋊C4D411yescharacteristic
149C22×C42C2311yescharacteristic
150#480—44no—
151#480—44no—
152#466—48no—
153#447—44no—
154#447—44no—
155C2×#107C2314yes—
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×C22⋊C8—44no—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2314yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172#398—22no—
173#397—22no—
174#396—22no—
175#396—22no—
176#394—22no—
177#394—22no—
178#394—22no—
179#394—24no—
180#394—24no—
181#394—24no—
182#394—24no—
183#392—22no—
184#390C2312yes—
185#390C2312yes—
186#389C2312yes—
187#389C2312yes—
188#388—22no—
189#388—22no—
190#386—22no—
191#386—22no—
192#386—22no—
193#386—22no—
194#386—22no—
195#386—22no—
196#384—22no—
197#384C2314yes—
198#381—22no—
199#380—21no—
200#380—21no—
201#380—21no—
202#380—21no—
203#380—22no—
204#380—24no—
205#380—24no—
206#380C2312yes—
207#380C2314yes—
208#380C2312yes—
209#380C2312yes—
210#380C2312yes—
211#380C2312yes—
212#380C2312yes—
213#379—22no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217#340C2314yes—
218#340C2314yes—
219#340C2314yes—
220#340C2314yes—
221#340C2314yes—
222#340C2314yes—
223#336C2314yes—
224#336C2314yes—
225C25—21no—
226C25—21no—
227C25C2×D411yescharacteristic
228C25C2×D411yescharacteristic
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—24no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—82no—
254C22×D4—82no—
255C22×D4D818yescomplemented
256C22×D4C2×D412yes—
257C22×D4C2×D412yes—
258C22×D4C2412yes—
259C22×D4C2412yes—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—24no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C2×D8—28no—
288C2×D8—44no—
289C2×D8—44no—
290C22×C8—44no—
291C22×C8—44no—
292C22×C8—44no—
293C22×C8C2414yes—
294C22×C8C2414yes—
295#123—48no—
296#123—48no—
297#121—24no—
298#121—28no—
299#121—24no—
300#121—24no—
301#121—24no—
302#121—42no—
303#121—44no—
304#121—42no—
305#121—42no—
306#121—42no—
307#121—44no—
308#121—44no—
309#121—44no—
310#121—44no—
311#121—48no—
312#121—416no—
313#121—416no—
314#121—48no—
315#121—48no—
316#121—44no—
317#121—44no—
318#120—48no—
319#120—48no—
320C4×D4—44no—
321C4×D4—44no—
322C4×D4—44no—
323C4×D4—44no—
324C4×D4—42no—
325C4×D4—42no—
326C4×D4—42no—
327C4×D4—42no—
328C4×D4—48no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
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—44no—
347C2×C4⋊C4—82no—
348C2×C4⋊C4C2×D412yes—
349C2×C4⋊C4C2×D412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C2×D412yes—
385C2×C22⋊C4C2×D412yes—
386C2×C22⋊C4C2×D412yes—
387C2×C22⋊C4C2×D412yes—
388C2×C42—24no—
389C2×C42C2×D412yes—
390C2×C42C2412yes—
391#107—44no—
392#107—44no—
393#107—44no—
394#102—28no—
395#102—44no—
396#102—44no—
397#102—44no—
398#102—44no—
399#102—44no—
400C22⋊C8—24no—
401C22⋊C8—24no—
402C22⋊C8—44no—
403C22⋊C8—42no—
404C22⋊C8—42no—
405C22⋊C8—42no—
406C22⋊C8—42no—
407#95—24no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—22no—
422C24—22no—
423C24—41no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—81no—
441C24—81no—
442C24—81no—
443C24—81no—
444C24C2×D814yes—
445C24C2×D814yes—
446C24C22×D411yescharacteristic
447C24C22×D412yes—
448C24C22×D411yescharacteristic
449C24C22×D411yescharacteristic
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—416no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—416no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—44no—
467C2×D4—48no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—42no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4—88no—
484C2×D4—82no—
485C2×D4—84no—
486C2×D4—82no—
487C2×D4—82no—
488C2×D4—82no—
489C2×D4—82no—
490C2×D4—82no—
491C2×D4—816no—
492C2×D4—816no—
493C2×D4—816no—
494C2×D4C2×D818yes—
495C2×D4C2×D818yes—
496C2×D4H(5,𝔽2)14yes—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—42no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—42no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—48no—
552C22×C4—88no—
553C22×C4—88no—
554C22×C4—816no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4C2×D814yes—
560C22×C4C22×D412yes—
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D412yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D412yes—
566C22×C4H(5,𝔽2)14yes—
567C22×C4C2511yescharacteristic
568D8—88no—
569C2×C8—24no—
570C2×C8—24no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—88no—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—48no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—81no—
594C4⋊C4—81no—
595C4⋊C4—84no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—48no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—48no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C42—24no—
620C42—22no—
621C42—22no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—21no—
629C23—21no—
630C23—22no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—21no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—28no—
645C23—28no—
646C23—24no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—48no—
652C23—48no—
653C23—48no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23—82no—
673C23—82no—
674C23—82no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—162no—
683C23—162no—
684C23—162no—
685C23—162no—
686C23#53412yes—
687C23C22×D812yes—
688C23C22×D814yes—
689C23C22×D812yes—
690C23C22×D812yes—
691C23#57512yes—
692C23C23×D411yescharacteristic
693D4—28no—
694D4—48no—
695D4—48no—
696D4—48no—
697D4—44no—
698D4—44no—
699D4—44no—
700D4—84no—
701D4—88no—
702D4—816no—
703D4—88no—
704D4—88no—
705D4—88no—
706D4—164no—
707D4—164no—
708C2×C4—28no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—84no—
750C2×C4—82no—
751C2×C4—82no—
752C2×C4—816no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4—84no—
758C2×C4—84no—
759C2×C4—162no—
760C2×C4—162no—
761C2×C4#53412yes—
762C2×C4C22×D814yes—
763C2×C4C2×H(5,𝔽2)12yes—
764C2×C4C2×H(5,𝔽2)12yes—
765C2×C4#58512yes—
766C8—44no—
767C8—44no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—24no—
777C22—22no—
778C22—24no—
779C22—22no—
780C22—22no—
781C22—24no—
782C22—22no—
783C22—41no—
784C22—42no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—41no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—88no—
799C22—88no—
800C22—816no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—168no—
813C22#318614yes—
814C22C2×#53411yescharacteristic
815C22#348411yescharacteristic
816C22#348511yescharacteristic
817C22C23×D811yescharacteristic
818C22C2×#57511yescharacteristic
819C22#358511yescharacteristic
820C22#358611yescharacteristic
821C4—24no—
822C4—22no—
823C4—42no—
824C4—41no—
825C4—42no—
826C4—41no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4#353414yes—
834C2—24no—
835C2—42no—
836C2—44no—
837C2—42no—
838C2—84no—
839C2—162no—
840C2#3711711yescharacteristic
841C2C2×#318611yescharacteristic
842C2#6075511yescharacteristic
843C2#6155911yescharacteristic
844C2#6157511yescharacteristic
845C2#6169411yescharacteristic
846C2#6171011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35000C2semidirect
2. C2×#2537C2semidirect
3. #33002C2semidirect
4. #31994C2semidirect
5. #31382C2semidirect
6. #30557C2semidirect
7. #30396C2semidirect
8. #29906C2semidirect
9. #27600C2semidirect
10. #24550C2semidirect
11. #24378C2semidirect
12. #24002C2semidirect
13. #24002C2semidirect
14. #23918C2semidirect
15. #21738C2semidirect
20. C22×#121C22semidirect
22. C22×C4×D4C22semidirect
24. C2×#480C22semidirect
25. C2×#466C22semidirect
27. C2×#447C22semidirect
28. C22×C22⋊C8C22semidirect
37. #2537C22semidirect
39. #2486C22semidirect
40. #2416C22semidirect
41. #2416C22semidirect
42. #2408C22semidirect
46. C2×#384C22semidirect
50. C2×#380C22semidirect
51. #2099C22semidirect
52. #2093C22semidirect
53. #2083C22semidirect
54. #2075C22semidirect
55. #2075C22semidirect
56. #2071C22semidirect
57. #2033C22semidirect
58. #2033C22semidirect
59. #2033C22semidirect
60. #2033C22semidirect
61. #1999C22semidirect
62. #1999C22semidirect
63. #1893C22semidirect
64. #1893C22semidirect
65. #1879C22semidirect
66. #1879C22semidirect
69. #1874C22semidirect
70. #1874C22semidirect
71. #1869C22semidirect
72. #1869C22semidirect
73. #1862C22semidirect
74. #1862C22semidirect
75. #1852C22semidirect
76. #1852C22semidirect
77. #1852C22semidirect
78. #1852C22semidirect
79. #1823C22semidirect
80. #1823C22semidirect
81. #1817C22semidirect
82. #1808C22semidirect
83. #1786C22semidirect
84. #1786C22semidirect
255. C22×D4D8semidirect

Maximal subgroups

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

subgroupindex
#350002
C2×#25372
#330022
#319942
#313822
#305572
#303962
#299062
#276002
#245502
#243782
#240022
#239182
#217382