Finite Group Databasebeta

← #6475832

Subgroups — #6475832

Order 512.

3616 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
1#36624C211yesmaximal, characteristic, complemented
2C22×#390C211yesmaximal, characteristic, complemented
3#32979C212yesmaximal, complemented
4#32878C212yesmaximal, complemented
5#29952C212yesmaximal, complemented
6#29712C212yesmaximal, complemented
7#29109C212yesmaximal, complemented
8#28310C212yesmaximal, complemented
9#28117C214yesmaximal, complemented
10#27585C212yesmaximal, complemented
11#24506C214yesmaximal, complemented
12#23930C212yesmaximal, complemented
13#22046C214yesmaximal, complemented
14#20715C211yesmaximal, characteristic, complemented
15C24×D4C2211yescharacteristic
16C2×#532C2211yescharacteristic, complemented
17C2×#525—21no—
18C23×C4⋊C4C2211yescharacteristic
19C23×C22⋊C4—21no—
20C23×C22⋊C4—21no—
21C23×C42C2211yescharacteristic
22C2×#481C2214yescomplemented
23C2×#447C2214yes—
24C2×#447C2214yes—
25C2×#447C2214yes—
26C2×#432C2212yescomplemented
27#2857C2211yescharacteristic, complemented
28#2857C2211yescharacteristic, complemented
29#2856C2211yescharacteristic, complemented
30#2856C2211yescharacteristic, complemented
31#2854—21no—
32#2854C2212yescomplemented
33#2850—21no—
34#2850—21no—
35#2847—21no—
36#2847C2212yes—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121C2212yescomplemented
40C4×#121C2212yescomplemented
41#2297—21no—
42C2×#390—21no—
43C2×#390—21no—
44C2×#390—21no—
45C2×#390—21no—
46C2×#390—21no—
47C2×#390—21no—
48C2×#390C2212yes—
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#390C2212yes—
52C2×#390C2212yes—
53C2×#390C2212yes—
54#2285C2211yescharacteristic, complemented
55#2094C2214yescomplemented
56#2071C2214yescomplemented
57#2065C2218yescomplemented
58#2054C2218yescomplemented
59#2023C2214yescomplemented
60#2011C2214yescomplemented
61#1972C2218yescomplemented
62#1936C2218yescomplemented
63#1926C2218yescomplemented
64#1879C2218yescomplemented
65#1874C2214yescomplemented
66#1874C2214yescomplemented
67#1853C2214yescomplemented
68#1853C2214yescomplemented
69#1824C2214yescomplemented
70#1817C2212yescomplemented
71#1797C2212yescomplemented
72#1797C2212yescomplemented
73#1786C2214yes—
74#1786C2214yes—
75#1786C2214yes—
76#1779C2212yes—
77#1749C2212yescomplemented
78#1749C2212yescomplemented
79C26—21no—
80C22×#41—21no—
81C23×D4—28no—
82C23×D4—21no—
83C23×D4—21no—
84C23×D4—21no—
85C23×D4—44no—
86C23×D4—44no—
87C23×D4C2312yes—
88C23×D4C2312yes—
89C23×D4C2312yes—
90C24×C4—21no—
91C24×C4D411yescharacteristic
92C24×C4D411yescharacteristic
93C24×C4C2311yescharacteristic
94C22×D8C2318yes—
95#532—44no—
96C2×C4⋊Q8C2311yescharacteristic, complemented
97C2×#127C2311yescharacteristic, complemented
98C2×#124—21no—
99#525—48no—
100C2×#123—22no—
101C2×C22⋊Q8—21no—
102C2×C22⋊Q8—21no—
103C2×#121—21no—
104C2×#121—21no—
105C2×#121—21no—
106C2×#121—21no—
107C2×#121—21no—
108C2×#121C2312yes—
109C2×#121C2312yes—
110C2×#121C2312yes—
111C2×#120—22no—
112C2×C4×D4—22no—
113C2×C4×D4—22no—
114C2×C4×D4—21no—
115C2×C4×D4C2312yescomplemented
116C2×#117—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—44no—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4—22no—
125C22×C22⋊C4—22no—
126C22×C22⋊C4—22no—
127C22×C22⋊C4—22no—
128C22×C22⋊C4—22no—
129C22×C22⋊C4—22no—
130C22×C22⋊C4—22no—
131C22×C22⋊C4—22no—
132C22×C22⋊C4—22no—
133C22×C22⋊C4—22no—
134C22×C22⋊C4—22no—
135C22×C22⋊C4—22no—
136C22×C22⋊C4—48no—
137C22×C22⋊C4—48no—
138C22×C42—44no—
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#481—48no—
152#447—216no—
153#447—48no—
154#447—48no—
155#432—44no—
156C2×#106C2318yescomplemented
157C2×C4⋊C8C2314yescomplemented
158C2×#102C2318yes—
159C2×#102C2318yes—
160C2×#102C2318yes—
161C2×#102C2318yescomplemented
162C2×C22⋊C8C2314yes—
163C2×C22⋊C8C2314yes—
164C2×C22⋊C8C2314yes—
165C2×#97C2314yescomplemented
166#391—21no—
167#391—21no—
168#390—21no—
169#390—21no—
170#390—21no—
171#390—21no—
172#390—22no—
173#390—22no—
174#390—22no—
175#390—22no—
176#390—22no—
177#390—22no—
178#390—22no—
179#390—22no—
180#390—22no—
181#390—22no—
182#390—22no—
183#390—22no—
184#390C2314yes—
185#390C2314yes—
186#390C2314yes—
187#390C2314yes—
188#390C2312yescomplemented
189#390C2312yescomplemented
190#389—21no—
191#389—21no—
192#389C2312yescomplemented
193#389C2312yescomplemented
194#388—22no—
195#388—22no—
196#388—22no—
197#388—22no—
198#386—22no—
199#386—22no—
200#386—22no—
201#386—22no—
202#386—22no—
203#386—22no—
204#384C2311yescharacteristic, complemented
205#384C2311yescharacteristic, complemented
206#382—21no—
207#380—21no—
208#380—21no—
209#380—21no—
210#380C2312yes—
211#380C2312yes—
212#380C2312yes—
213C4×C4⋊C4—21no—
214C4×C4⋊C4C2312yescomplemented
215C4×C22⋊C4—22no—
216C4×C22⋊C4—22no—
217#340C2318yescomplemented
218#340C2318yescomplemented
219#336C2314yescomplemented
220#336C2314yescomplemented
221C25—28no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—44no—
226C25—44no—
227C25—44no—
228C25—44no—
229C25—44no—
230C25—44no—
231C25C2×D411yescharacteristic
232C2×#41—44no—
233C2×#41—44no—
234C2×#41—44no—
235C22×Q8—21no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—28no—
240C22×D4—28no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—21no—
248C22×D4—21no—
249C22×D4—24no—
250C22×D4—28no—
251C22×D4—28no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—464no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4#4118yescomplemented
264C22×D4C2412yes—
265C22×D4C2414yes—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×D8—216no—
301C2×D8—48no—
302C2×D8—48no—
303C22×C8C2418yes—
304C4⋊Q8—42no—
305#127—42no—
306#124—44no—
307#123—48no—
308C22⋊Q8—44no—
309C22⋊Q8—44no—
310#121—28no—
311#121—28no—
312#121—28no—
313#121—44no—
314#121—44no—
315#121—44no—
316#121—44no—
317#121—44no—
318#120—48no—
319C4×D4—44no—
320C4×D4—44no—
321C4×D4—48no—
322C4×D4—48no—
323#117—44no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4C2414yes—
341C2×C4⋊C4C2412yes—
342C2×C4⋊C4C2412yes—
343C2×C4⋊C4C2412yes—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—48no—
364C2×C22⋊C4—48no—
365C2×C22⋊C4—48no—
366C2×C22⋊C4—48no—
367C2×C22⋊C4—48no—
368C2×C22⋊C4—48no—
369C2×C22⋊C4—48no—
370C2×C22⋊C4—48no—
371C2×C22⋊C4—48no—
372C2×C22⋊C4—48no—
373C2×C22⋊C4—48no—
374C2×C22⋊C4—48no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—22no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2411yescharacteristic
401C2×C42C2411yescharacteristic
402C2×C42C2411yescharacteristic
403C2×C42C2411yescharacteristic
404#106—48no—
405C4⋊C8—44no—
406#102—216no—
407#102—48no—
408#102—48no—
409#102—48no—
410C22⋊C8—28no—
411C22⋊C8—28no—
412C22⋊C8—28no—
413#97—44no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—28no—
427C24—28no—
428C24—28no—
429C24—24no—
430C24—22no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—44no—
435C24—432no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—432no—
441C24—432no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24—44no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—44no—
452C24—816no—
453C24—816no—
454C24—816no—
455C24—816no—
456C24AGL(1,ℤ/8)14yes—
457C24C22×D411yescharacteristic
458C24C22×D411yescharacteristic
459C24C22×D411yescharacteristic
460#41—816no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—416no—
474C2×D4—432no—
475C2×D4—432no—
476C2×D4—432no—
477C2×D4—432no—
478C2×D4—432no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—416no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4C2×#4118yes—
502C22×C4—232no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—416no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—416no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—816no—
571C22×C4AGL(1,ℤ/8)14yes—
572C22×C4AGL(1,ℤ/8)14yes—
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C2×#4114yes—
585C22×C4H(5,𝔽2)14yes—
586C22×C4H(5,𝔽2)14yes—
587C22×C4C2511yescharacteristic
588D8—816no—
589C2×C8—28no—
590C2×C8—28no—
591C2×C8—28no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—28no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—44no—
605C4⋊C4—42no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—44no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—44no—
642C23—28no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—28no—
654C23—28no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—28no—
662C23—416no—
663C23—416no—
664C23—416no—
665C23—416no—
666C23—416no—
667C23—416no—
668C23—416no—
669C23—416no—
670C23—416no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—8128no—
685C23—88no—
686C23—88no—
687C23—88no—
688C23—88no—
689C23—88no—
690C23—88no—
691C23—88no—
692C23—88no—
693C23—88no—
694C23—88no—
695C23—88no—
696C23—88no—
697C23#52512yes—
698C23#53412yes—
699C23#53512yes—
700C23C2×AGL(1,ℤ/8)12yes—
701C23C2×AGL(1,ℤ/8)12yes—
702C23C2×AGL(1,ℤ/8)12yes—
703C23C2×AGL(1,ℤ/8)12yes—
704C23C2×AGL(1,ℤ/8)12yes—
705C23#57512yes—
706C23C23×D411yescharacteristic
707Q8—84no—
708D4—216no—
709D4—416no—
710D4—416no—
711D4—416no—
712D4—48no—
713D4—48no—
714D4—84no—
715D4—84no—
716D4—88no—
717D4—88no—
718D4—88no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—28no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—28no—
738C2×C4—28no—
739C2×C4—28no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—88no—
776C2×C4—88no—
777C2×C4—88no—
778C2×C4—88no—
779C2×C4#52512yes—
780C2×C4#53412yes—
781C2×C4#53512yes—
782C2×C4C2×AGL(1,ℤ/8)12yes—
783C2×C4C2×AGL(1,ℤ/8)12yes—
784C2×C4C2×AGL(1,ℤ/8)12yes—
785C2×C4C2×AGL(1,ℤ/8)12yes—
786C2×C4C22×#4112yes—
787C2×C4C2×H(5,𝔽2)12yes—
788C2×C4C2×H(5,𝔽2)12yes—
789C8—48no—
790C22—232no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—48no—
810C22—48no—
811C22—48no—
812C22—832no—
813C22—832no—
814C22—832no—
815C22—84no—
816C22—84no—
817C22—84no—
818C22—84no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22#310914yes—
827C22#319214yes—
828C22#321314yes—
829C22C2×#52511yescharacteristic
830C22C2×#53411yescharacteristic
831C22C2×#53511yescharacteristic
832C22C22×AGL(1,ℤ/8)11yescharacteristic
833C22C22×AGL(1,ℤ/8)11yescharacteristic
834C22C22×AGL(1,ℤ/8)11yescharacteristic
835C22C2×#57511yescharacteristic
836C4—22no—
837C4—22no—
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—22no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—84no—
851C4#349014yes—
852C2—24no—
853C2—24no—
854C2—24no—
855C2—88no—
856C2—162no—
857C2#3505011yescharacteristic
858C2C2×#310911yescharacteristic
859C2#6055811yescharacteristic
860C2C2×#319211yescharacteristic
861C2#6075011yescharacteristic
862C2C2×#321311yescharacteristic
863C2#6079811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36624C2semidirect
2. C22×#390C2semidirect
3. #32979C2semidirect
4. #32878C2semidirect
5. #29952C2semidirect
6. #29712C2semidirect
7. #29109C2semidirect
8. #28310C2semidirect
9. #28117C2semidirect
10. #27585C2semidirect
11. #24506C2semidirect
12. #23930C2semidirect
13. #22046C2semidirect
14. #20715C2semidirect
16. C2×#532C22semidirect
22. C2×#481C22semidirect
26. C2×#432C22semidirect
27. #2857C22semidirect
28. #2857C22semidirect
29. #2856C22semidirect
30. #2856C22semidirect
32. #2854C22semidirect
39. C4×#121C22semidirect
40. C4×#121C22semidirect
54. #2285C22semidirect
55. #2094C22semidirect
56. #2071C22semidirect
57. #2065C22semidirect
58. #2054C22semidirect
59. #2023C22semidirect
60. #2011C22semidirect
61. #1972C22semidirect
62. #1936C22semidirect
63. #1926C22semidirect
64. #1879C22semidirect
65. #1874C22semidirect
66. #1874C22semidirect
67. #1853C22semidirect
68. #1853C22semidirect
69. #1824C22semidirect
70. #1817C22semidirect
71. #1797C22semidirect
72. #1797C22semidirect
77. #1749C22semidirect
78. #1749C22semidirect
96. C2×C4⋊Q8C23semidirect
97. C2×#127C23semidirect
115. C2×C4×D4C23semidirect
156. C2×#106C23semidirect
157. C2×C4⋊C8C23semidirect
161. C2×#102C23semidirect
165. C2×#97C23semidirect
188. #390C23semidirect
189. #390C23semidirect
192. #389C23semidirect
193. #389C23semidirect
204. #384C23semidirect
205. #384C23semidirect
214. C4×C4⋊C4C23semidirect
217. #340C23semidirect
218. #340C23semidirect
219. #336C23semidirect
220. #336C23semidirect
263. C22×D4#41semidirect

Maximal subgroups

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

subgroupindex
#366242
C22×#3902
#329792
#328782
#299522
#297122
#291092
#283102
#281172
#275852
#245062
#239302
#220462
#207152