Finite Group Databasebeta

← #6494160

Subgroups — #6494160

Order 512.

2264 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3247C212yesmaximal, complemented
2#36631C211yesmaximal, characteristic, complemented
3C4×#532C211yesmaximal, characteristic, complemented
4#33199C212yesmaximal, complemented
5#33164C212yesmaximal, complemented
6#29832C214yesmaximal, complemented
7#28284C211yesmaximal, characteristic, complemented
8#28282C212yesmaximal, complemented
9#28280C211yesmaximal, characteristic, complemented
10#28253C212yesmaximal, complemented
11#28252C211yesmaximal, characteristic, complemented
12#28251C211yesmaximal, characteristic, complemented
13#24754C214yesmaximal, complemented
14#24751C212yesmaximal, complemented
15#24750C212yesmaximal, complemented
16#21887C212yesmaximal, complemented
17C2×#1842C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#529C2212yes—
20C2×C4×#41—21no—
21#3247—216no—
22C2×#477C2212yes—
23C2×#478C2214yes—
24C2×#476C2212yes—
25C2×#466C2214yes—
26C2×#465C2214yes—
27C2×#460C2212yes—
28C2×#463C2214yes—
29C2×#463C2214yes—
30C2×#461C2212yes—
31C2×#459C2212yes—
32C2×#459C2212yes—
33C22×C4⋊C8C2212yes—
34C22×C4⋊C8C2212yes—
35C22×C4⋊C8C2212yes—
36#2861C2212yes—
37#2860—21no—
38#2860—21no—
39#2859C2211yescharacteristic
40#2858C2211yescharacteristic
41#2857C2211yescharacteristic
42#2856C2211yescharacteristic
43#2854—21no—
44#2854—21no—
45#2850C2212yes—
46C4×C4⋊Q8C2211yescharacteristic
47C4×C4⋊Q8C2211yescharacteristic
48C4×C4⋊Q8C2211yescharacteristic
49C4×#127C2211yescharacteristic
50C4×#127C2211yescharacteristic
51C4×#127C2211yescharacteristic
52C4×#124—21no—
53C4×#124—21no—
54C4×#124C2212yes—
55C4×#121—21no—
56C4×#121—21no—
57C4×#121—21no—
58C4×#121—21no—
59C4×#121C2212yes—
60C4×#121C2212yes—
61#2297—21no—
62#2293—21no—
63#2293—21no—
64#2293—21no—
65#2293C2212yes—
66#2285C2211yescharacteristic
67C42×D4—21no—
68C42×D4C2212yes—
69C2×C43C2211yescharacteristic
70#2068C2214yes—
71#2067C2214yes—
72#2066C2214yes—
73#2065C2214yes—
74#2055C2214yes—
75#2055C2214yes—
76#2054C2214yes—
77#2054C2214yes—
78#1989C2214yes—
79#1983C2214yes—
80#1983C2214yes—
81#1982C2212yes—
82#1981C2212yes—
83#1949C2214yes—
84#1948C2212yes—
85#1947C2212yes—
86#1893C2214yes—
87#1892C2214yes—
88#1842C2211yescharacteristic
89#1842C2211yescharacteristic
90#1842C2212yes—
91#1842C2212yes—
92#1842C2212yes—
93#1804C2214yes—
94#1803C2212yes—
95#1803C2212yes—
96#1802C2212yes—
97#1802C2212yes—
98#1802C2212yes—
99#1802C2212yes—
100C22×#41—21no—
101C22×SD16C2314yes—
102C22×D8C2314yes—
103C23×C8C2314yes—
104#532—24no—
105#532D418yescomplemented
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109C2×#127C2311yescharacteristic
110#529—28no—
111#529—28no—
112C2×#126—22no—
113C2×#125C2312yes—
114C2×#124—21no—
115C2×#124C2312yes—
116C2×#124C2312yes—
117C2×#123—22no—
118C2×C22⋊Q8C2312yes—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121C2312yes—
123C2×#121C2312yes—
124C4×#41—48no—
125C2×C4×Q8—21no—
126C2×C4×Q8—21no—
127C2×C4×Q8C2312yes—
128C2×C4×D4—22no—
129C2×C4×D4—22no—
130C2×C4×D4—22no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4C2312yes—
139C2×C4×D4C2312yes—
140C2×C4×D4C2312yes—
141C2×C4×D4C2312yes—
142C2×#117—21no—
143C2×#117—22no—
144C2×#117—22no—
145C22×C42—22no—
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#478—216no—
154#477—28no—
155#476—28no—
156#466—216no—
157#465—216no—
158#463—216no—
159#463—48no—
160#461—44no—
161#460—28no—
162#459—28no—
163#459—44no—
164C2×#107C2314yes—
165C2×#106C2314yes—
166C2×C4⋊C8—28no—
167C2×C4⋊C8—44no—
168C2×C4⋊C8—44no—
169C2×C4⋊C8C2314yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2314yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2314yes—
177C2×C4⋊C8C2312yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186#391—21no—
187#391—21no—
188#391C2312yes—
189#391C2312yes—
190#390—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390C2312yes—
203#390C2312yes—
204#390C2312yes—
205#390C2312yes—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389C2312yes—
217#389C2312yes—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#382—21no—
239#382C2312yes—
240#380—21no—
241#380—21no—
242#380—21no—
243#380C2312yes—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4C2312yes—
250C4×C4⋊C4C2312yes—
251C4×C4⋊C4C2312yes—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256C4×C22⋊C4—22no—
257C4×C22⋊C4—22no—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C43D411yescharacteristic
261C43D411yescharacteristic
262C43D411yescharacteristic
263C43D411yescharacteristic
264C43C2311yescharacteristic
265C43C2311yescharacteristic
266C43C2311yescharacteristic
267C43C2311yescharacteristic
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272C2×#41—28no—
273C2×#41—44no—
274C2×#41—44no—
275C22×Q8—21no—
276C22×Q8C2412yes—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C2412yes—
284C22×D4C2412yes—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2411yescharacteristic
296C2×SD16—28no—
297C2×SD16—44no—
298C2×SD16—44no—
299C2×D8—28no—
300C2×D8—44no—
301C2×D8—44no—
302C22×C8—28no—
303C22×C8—44no—
304C22×C8—44no—
305C22×C8C2414yes—
306C22×C8C2414yes—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8C2×D414yes—
311#127—22no—
312#127—22no—
313#127—22no—
314#127C2×D414yes—
315#126—48no—
316#125—24no—
317#125—24no—
318#124—28no—
319#124—24no—
320#124—24no—
321#124—24no—
322#124—24no—
323#123—48no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326#121—28no—
327#121—24no—
328#121—24no—
329#121—24no—
330#121—44no—
331#121—44no—
332#121C2×D418yes—
333C4×Q8—24no—
334C4×Q8—24no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×D4—28no—
338C4×D4—24no—
339C4×D4—24no—
340C4×D4—24no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—24no—
345C4×D4—44no—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4—48no—
350C4×D4—48no—
351C4×D4—48no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4C2×D418yes—
355#117—48no—
356#117—44no—
357#117—48no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—42no—
411C2×C42—48no—
412C2×C42—42no—
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D414yes—
435C2×C42C2×D411yescharacteristic
436C2×C42#4114yes—
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443#107—28no—
444#106—28no—
445C4⋊C8—24no—
446C4⋊C8—24no—
447C4⋊C8—28no—
448C4⋊C8—24no—
449C4⋊C8—24no—
450C4⋊C8—28no—
451C4⋊C8—44no—
452C4⋊C8—42no—
453C4⋊C8—42no—
454#103—28no—
455#103—44no—
456#103—44no—
457#102—28no—
458#102—28no—
459#102—28no—
460#102—44no—
461#102—44no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474C24—22no—
475C24—22no—
476C24C22×D411yescharacteristic
477#41—432no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×D4—28no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4C22×D414yes—
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—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—28no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4#12114yes—
555C22×C4#12114yes—
556C22×C4AGL(1,ℤ/8)14yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D412yes—
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C2×#4112yes—
572C22×C4C2511yescharacteristic
573SD16—88no—
574D8—88no—
575C2×C8—24no—
576C2×C8—24no—
577C2×C8—24no—
578C2×C8—24no—
579C2×C8—24no—
580C2×C8—24no—
581C2×C8—88no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—44no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4C22×D414yes—
609C22⋊C4—28no—
610C22⋊C4—28no—
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—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42—44no—
656C42#12114yes—
657C42#12114yes—
658C42#13514yes—
659C42C22×D412yes—
660C42C22×D412yes—
661C42C2×#4112yes—
662C42C2×#4112yes—
663C42H(5,𝔽2)12yes—
664C42H(5,𝔽2)12yes—
665C422−1+412yes—
666C422−1+412yes—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—24no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C2×#12112yes—
686C23C2×AGL(1,ℤ/8)12yes—
687C23#57512yes—
688C23C23×D411yescharacteristic
689Q8—48no—
690Q8—42no—
691Q8—42no—
692Q8—42no—
693Q8—42no—
694D4—24no—
695D4—24no—
696D4—48no—
697D4—416no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—48no—
705D4—84no—
706D4—88no—
707D4—84no—
708C2×C4—28no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—28no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—28no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—28no—
734C2×C4—24no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—416no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—88no—
762C2×C4—88no—
763C2×C4—88no—
764C2×C4C2×#12112yes—
765C2×C4C2×#12112yes—
766C2×C4C2×#12112yes—
767C2×C4C2×#12112yes—
768C2×C4C2×#12112yes—
769C2×C4#53712yes—
770C2×C4#53712yes—
771C2×C4#53712yes—
772C2×C4#53712yes—
773C2×C4C2×#13512yes—
774C2×C4C2×#13512yes—
775C2×C4C2×#13512yes—
776C2×C4C2×AGL(1,ℤ/8)12yes—
777C2×C4C2×AGL(1,ℤ/8)12yes—
778C2×C4#57512yes—
779C2×C4C23×D411yescharacteristic
780C2×C4C22×#4111yescharacteristic
781C2×C4C2×H(5,𝔽2)11yescharacteristic
782C2×C4C2×H(5,𝔽2)11yescharacteristic
783C2×C4C2×2−1+411yescharacteristic
784C2×C4C2×2−1+411yescharacteristic
785C8—44no—
786C8—44no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22#303614yes—
808C22C22×#12111yescharacteristic
809C22C2×#53711yescharacteristic
810C22C2×#53711yescharacteristic
811C22C22×#13511yescharacteristic
812C22C22×AGL(1,ℤ/8)11yescharacteristic
813C22C2×#57511yescharacteristic
814C22C2×#57511yescharacteristic
815C4—22no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—41no—
825C4—41no—
826C4—44no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4#303514yes—
833C4#324714yescomplemented
834C4#349811yescharacteristic
835C4#349911yescharacteristic
836C4#351111yescharacteristic
837C4#351111yescharacteristic
838C2—24no—
839C2—84no—
840C2—162no—
841C2#3527311yescharacteristic
842C2C2×#303511yescharacteristic
843C2C2×#303611yescharacteristic
844C2C2×#324711yescharacteristic
845C2#6090011yescharacteristic
846C2#6091611yescharacteristic
847C2#6091711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3247C2semidirect
2. #36631C2semidirect
3. C4×#532C2semidirect
4. #33199C2semidirect
5. #33164C2semidirect
6. #29832C2semidirect
7. #28284C2semidirect
8. #28282C2semidirect
9. #28280C2semidirect
10. #28253C2semidirect
11. #28252C2semidirect
12. #28251C2semidirect
13. #24754C2semidirect
14. #24751C2semidirect
15. #24750C2semidirect
16. #21887C2semidirect
17. C2×#1842C2semidirect
105. #532D4semidirect
833. C4#3247semidirect

Maximal subgroups

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

subgroupindex
C2×#32472
#366312
C4×#5322
#331992
#331642
#298322
#282842
#282822
#282802
#282532
#282522
#282512
#247542
#247512
#247502
#218872
C2×#18422