Finite Group Databasebeta

← #6477085

Subgroups — #6477085

Order 512.

2236 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2851C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#33150C212yesmaximal, complemented
4#32959C212yesmaximal, complemented
5#30167C214yesmaximal, complemented
6#29298C212yesmaximal, complemented
7#29104C212yesmaximal, complemented
8#27651C212yesmaximal, complemented
9#27603C211yesmaximal, characteristic, complemented
10#27601C211yesmaximal, characteristic, complemented
11#24704C214yesmaximal, complemented
12#24305C212yesmaximal, complemented
13#24005C211yesmaximal, characteristic
14#24002C211yesmaximal, characteristic
15#22076C212yesmaximal, complemented
16#22075C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C22×#125C2211yescharacteristic, complemented
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#481C2212yes—
24C2×#480C2212yes—
25C2×#478C2214yescomplemented
26C2×#431C2212yescomplemented
27#2851—21no—
28#2851—21no—
29#2851—21no—
30#2851—21no—
31#2851C2212yes—
32#2851C2212yes—
33#2851C2212yescomplemented
34#2851C2212yescomplemented
35C4×#121—21no—
36C4×#121—21no—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121C2212yes—
40C4×#121C2212yes—
41C4×#121C2212yes—
42C4×#121C2212yes—
43C2×#390C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic, complemented
46C2×#389C2211yescharacteristic, complemented
47C2×#388—21no—
48C2×#387—21no—
49C2×#387—21no—
50C2×#386—21no—
51C2×#385—21no—
52C2×#385—21no—
53C2×#382C2211yescharacteristic, complemented
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2085C2214yescomplemented
60#2077C2214yescomplemented
61#2076C2214yescomplemented
62#2073C2214yescomplemented
63#2059C2214yescomplemented
64#2034C2214yes—
65#2033C2214yes—
66#2025C2214yescomplemented
67#1989C2214yescomplemented
68#1949C2214yescomplemented
69#1942C2214yescomplemented
70#1941C2214yescomplemented
71#1934C2214yescomplemented
72#1934C2214yescomplemented
73#1920C2214yescomplemented
74#1918C2214yescomplemented
75#1874C2212yes—
76#1874C2212yes—
77#1864C2214yescomplemented
78#1862C2214yescomplemented
79#1853C2212yes—
80#1853C2212yes—
81#1853C2212yescomplemented
82#1852C2212yes—
83#1852C2212yes—
84#1852C2212yescomplemented
85#1824C2212yes—
86#1824C2212yes—
87#1824C2212yescomplemented
88#1823C2212yescomplemented
89#1817C2212yescomplemented
90#1804C2214yescomplemented
91#1797C2212yes—
92#1797C2212yescomplemented
93#1786C2212yes—
94#1786C2212yes—
95#1779C2211yescharacteristic
96#1779C2211yescharacteristic
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C2×#125—21no—
106C2×#125—21no—
107C2×#125—44no—
108C2×#125C2312yes—
109C2×#125C2312yes—
110C2×#121—21no—
111C2×#121—21no—
112C2×#121—28no—
113C2×#121C2312yes—
114C2×#121C2312yes—
115C2×C4×D4—22no—
116C2×C4×D4—22no—
117C2×C4×D4—22no—
118C2×C4×D4—22no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4—44no—
122C2×C4×D4—48no—
123C2×C4×D4C2312yes—
124C2×C4×D4C2312yes—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C42—21no—
145C22×C42—44no—
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#481—28no—
159#480—28no—
160#478—48no—
161#431—44no—
162C2×#107C2314yes—
163C2×#107C2314yes—
164C2×#106C2314yes—
165C2×#106C2314yes—
166C2×C4⋊C8C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C4×C8C2314yes—
178#390—21no—
179#390—21no—
180#390C2312yes—
181#390C2312yes—
182#389—21no—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389C2312yes—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#388—22no—
195#388—22no—
196#388—22no—
197#388—22no—
198#387—22no—
199#387—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#387—22no—
205#387—22no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#382—21no—
219#382—21no—
220#382C2312yes—
221#382C2312yes—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380C2312yes—
229#380C2312yes—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4C2312yes—
237C4×C4⋊C4C2312yes—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C2×#95—21no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95—21no—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#336C2314yes—
260#336C2314yes—
261C25—21no—
262C25C2×D411yescharacteristic
263C22×D4—28no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—24no—
267C22×D4—21no—
268C22×D4—24no—
269C22×D4—42no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4C2412yes—
273C23×C4—24no—
274C23×C4—21no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C22×C8C2414yes—
313C22×C8C2414yes—
314#125—28no—
315#125—44no—
316#125—44no—
317#125—44no—
318#121—28no—
319#121—28no—
320#121—24no—
321#121—24no—
322#121—24no—
323#121#4118yes—
324C4×D4—28no—
325C4×D4—44no—
326C4×D4—44no—
327C4×D4—44no—
328C4×D4—48no—
329C4×D4—48no—
330C4×D4—48no—
331C4×D4—48no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C22⋊C4—28no—
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—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—44no—
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420#107—28no—
421#107—44no—
422#106—28no—
423#106—44no—
424C4⋊C8—28no—
425#102—28no—
426#102—28no—
427#102—44no—
428#102—44no—
429C22⋊C8—24no—
430C22⋊C8—24no—
431C22⋊C8—24no—
432C22⋊C8—24no—
433C22⋊C8—42no—
434C22⋊C8—42no—
435C4×C8—44no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—24no—
459C24—22no—
460C24—41no—
461C24—41no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24#13514yes—
469C24C22×D411yescharacteristic
470C24C22×D411yescharacteristic
471C24C22×D411yescharacteristic
472C2×D4—24no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—22no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—416no—
479C2×D4—42no—
480C2×D4—44no—
481C2×D4—432no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—42no—
486C2×D4C2×#4114yes—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
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—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—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—416no—
547C22×C4—416no—
548C22×C4—416no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—816no—
576C22×C4AGL(1,ℤ/8)14yes—
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C2×#4114yes—
589C22×C42−1+414yes—
590C22×C4C2511yescharacteristic
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—44no—
606C4⋊C4—42no—
607C4⋊C4—44no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4C2×#4114yes—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—44no—
652C42—44no—
653C42H(5,𝔽2)14yes—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—28no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—28no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—24no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—48no—
677C23—48no—
678C23—48no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23#52512yes—
690C23#53612yes—
691C23C2×#13512yes—
692C23C2×#13512yes—
693C23C2×#13512yes—
694C23C2×AGL(1,ℤ/8)12yes—
695C23#57512yes—
696C23C23×D411yescharacteristic
697D4—28no—
698D4—48no—
699D4—416no—
700D4—416no—
701D4—44no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—21no—
721C2×C4—24no—
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—21no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—48no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
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—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—88no—
769C2×C4—88no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4#52512yes—
777C2×C4#53412yes—
778C2×C4#53412yes—
779C2×C4#53612yes—
780C2×C4C2×AGL(1,ℤ/8)12yes—
781C2×C4C2×AGL(1,ℤ/8)12yes—
782C2×C4#57512yes—
783C2×C4C22×#4112yes—
784C2×C4C2×H(5,𝔽2)12yes—
785C2×C4C2×2−1+412yes—
786C8—44no—
787C8—44no—
788C22—22no—
789C22—22no—
790C22—22no—
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—416no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—816no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22#310514yes—
817C22#323214yes—
818C22C2×#52511yescharacteristic
819C22C2×#53411yescharacteristic
820C22C2×#53611yescharacteristic
821C22C22×#13511yescharacteristic
822C22C22×AGL(1,ℤ/8)11yescharacteristic
823C22C2×#57511yescharacteristic
824C22C2×#57511yescharacteristic
825C4—22no—
826C4—22no—
827C4—22no—
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—44no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4#352014yes—
844C2—24no—
845C2—24no—
846C2—42no—
847C2—84no—
848C2#3508411yescharacteristic
849C2C2×#310511yescharacteristic
850C2#6056311yescharacteristic
851C2#6073411yescharacteristic
852C2#6075011yescharacteristic
853C2C2×#323211yescharacteristic
854C2#6086411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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. C2×#2851C2semidirect
3. #33150C2semidirect
4. #32959C2semidirect
5. #30167C2semidirect
6. #29298C2semidirect
7. #29104C2semidirect
8. #27651C2semidirect
9. #27603C2semidirect
10. #27601C2semidirect
11. #24704C2semidirect
12. #24305C2semidirect
15. #22076C2semidirect
16. #22075C2semidirect
17. #20714C2semidirect
18. C22×#125C22semidirect
25. C2×#478C22semidirect
26. C2×#431C22semidirect
33. #2851C22semidirect
34. #2851C22semidirect
45. C2×#389C22semidirect
46. C2×#389C22semidirect
53. C2×#382C22semidirect
59. #2085C22semidirect
60. #2077C22semidirect
61. #2076C22semidirect
62. #2073C22semidirect
63. #2059C22semidirect
66. #2025C22semidirect
67. #1989C22semidirect
68. #1949C22semidirect
69. #1942C22semidirect
70. #1941C22semidirect
71. #1934C22semidirect
72. #1934C22semidirect
73. #1920C22semidirect
74. #1918C22semidirect
77. #1864C22semidirect
78. #1862C22semidirect
81. #1853C22semidirect
84. #1852C22semidirect
87. #1824C22semidirect
88. #1823C22semidirect
89. #1817C22semidirect
90. #1804C22semidirect
92. #1797C22semidirect
98. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28512
C2×C4×#1212
#331502
#329592
#301672
#292982
#291042
#276512
#276032
#276012
#247042
#243052
#240052
#240022
#220762
#220752
#207142