Finite Group Databasebeta

← #6482931

Subgroups — #6482931

Order 512.

1910 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic, complemented
3#33097C214yesmaximal, complemented
4#29896C214yesmaximal, complemented
5#27891C211yesmaximal, characteristic, complemented
6#27891C211yesmaximal, characteristic, complemented
7#27890C211yesmaximal, characteristic, complemented
8#27890C211yesmaximal, characteristic, complemented
9#27878C211yesmaximal, characteristic, complemented
10#27877C211yesmaximal, characteristic, complemented
11#27876C211yesmaximal, characteristic, complemented
12#27875C211yesmaximal, characteristic, complemented
13#27633C214yesmaximal, complemented
14#27632C214yesmaximal, complemented
15#21984C211yesmaximal, characteristic, complemented
16#21984C211yesmaximal, characteristic, complemented
17#21863C211yesmaximal, characteristic, complemented
18#21863C211yesmaximal, characteristic, complemented
19#20714C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×#525—21no—
22C23×C42C2211yescharacteristic
23C2×#431C2211yescharacteristic
24C2×#431C2211yescharacteristic
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic
27#2856C2211yescharacteristic
28#2856C2211yescharacteristic
29#2854—21no—
30#2854C2212yes—
31#2850—21no—
32#2850—21no—
33#2847—21no—
34#2847C2212yes—
35C4×#121—21no—
36C4×#121—21no—
37C4×#121C2212yes—
38C4×#121C2212yes—
39#2297—21no—
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45#2285C2211yescharacteristic
46#2285C2211yescharacteristic
47#2283—21no—
48#2283—21no—
49#2283—21no—
50#2283—21no—
51#2283C2212yes—
52#2283C2212yes—
53#2280—21no—
54#2280—21no—
55#2280C2212yes—
56C4×#117—21no—
57C4×#117—21no—
58C4×#117C2212yes—
59#2077C2214yes—
60#2077C2214yes—
61#2076C2214yes—
62#2075C2214yes—
63#2034C2214yes—
64#2034C2214yes—
65#2033C2214yes—
66#2033C2214yes—
67#1990C2211yescharacteristic, complemented
68#1990C2211yescharacteristic, complemented
69#1990C2211yescharacteristic, complemented
70#1990C2211yescharacteristic, complemented
71#1957C2211yescharacteristic, complemented
72#1957C2211yescharacteristic, complemented
73#1957C2211yescharacteristic, complemented
74#1957C2211yescharacteristic, complemented
75#1949C2214yescomplemented
76#1949C2214yescomplemented
77#1926C2214yescomplemented
78#1926C2214yescomplemented
79#1925C2214yescomplemented
80#1925C2214yescomplemented
81#1921C2214yescomplemented
82#1920C2214yescomplemented
83#1919C2214yescomplemented
84#1918C2214yescomplemented
85#1875C2214yes—
86#1875C2214yes—
87#1854C2214yes—
88#1854C2214yes—
89#1845C2211yescharacteristic, complemented
90#1845C2211yescharacteristic, complemented
91#1844C2211yescharacteristic, complemented
92#1844C2211yescharacteristic, complemented
93#1834C2211yescharacteristic, complemented
94#1834C2211yescharacteristic, complemented
95#1834C2211yescharacteristic, complemented
96#1834C2211yescharacteristic, complemented
97#1817C2212yes—
98#1804C2214yescomplemented
99#1804C2214yescomplemented
100#1797C2212yes—
101#1797C2212yes—
102#1779C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C22×#41—21no—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111#532—24no—
112#532—24no—
113C2×C4⋊Q8C2311yescharacteristic
114C2×#127C2311yescharacteristic
115C2×#124—21no—
116#525—48no—
117C2×#123—22no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#120—22no—
129C2×C4×D4—22no—
130C2×C4×D4—22no—
131C2×C4×D4—21no—
132C2×C4×D4C2312yes—
133C2×#117—21no—
134C2×#117—21no—
135C2×#117—21no—
136C2×#117—21no—
137C2×#117—21no—
138C2×#117C2312yes—
139C2×#117C2312yes—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#431—24no—
155#431—24no—
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×#106C2314yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×#102C2314yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2312yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C2×C4×C8C2311yescharacteristic
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176#391—21no—
177#391—21no—
178#390—21no—
179#390—21no—
180#390—21no—
181#390—21no—
182#390C2312yes—
183#390C2312yes—
184#389—21no—
185#389—21no—
186#389C2312yes—
187#389C2312yes—
188#388—22no—
189#388—22no—
190#388—22no—
191#388—22no—
192#386—22no—
193#386—22no—
194#386—22no—
195#386—22no—
196#386—22no—
197#386—22no—
198#384C2311yescharacteristic
199#384C2311yescharacteristic
200#384C2311yescharacteristic
201#384C2311yescharacteristic
202#384C2311yescharacteristic
203#384C2311yescharacteristic
204#383—22no—
205#383—22no—
206#382—21no—
207#382—21no—
208#382—21no—
209#382—21no—
210#382—21no—
211#382C2312yes—
212#382C2312yes—
213#381—22no—
214#381—22no—
215#381—22no—
216#380—21no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380C2312yes—
228#380C2312yes—
229#380C2312yes—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#379—22no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C4⋊C4C2312yes—
247C4×C4⋊C4C2312yes—
248C4×C4⋊C4C2312yes—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256C4×C22⋊C4—22no—
257#376—22no—
258#376—22no—
259#376—22no—
260C43—22no—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#336C2312yes—
270#336C2312yes—
271#336C2312yes—
272#336C2312yes—
273C25C2×D411yescharacteristic
274C2×#41—44no—
275C2×#41—44no—
276C2×#41—44no—
277C22×Q8—21no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C2412yes—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
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×C4C2×D411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319#127—22no—
320#127—22no—
321#124—44no—
322#123—48no—
323C22⋊Q8—44no—
324C22⋊Q8—44no—
325#121—24no—
326#121—24no—
327#121—44no—
328#121—44no—
329#121—44no—
330#121—44no—
331#121—44no—
332#121—44no—
333#121—44no—
334#120—48no—
335C4×D4—24no—
336C4×D4—24no—
337C4×D4—48no—
338C4×D4—48no—
339C4×D4—44no—
340#117—44no—
341#117—44no—
342#117—44no—
343#117—44no—
344#117—44no—
345#117—44no—
346#117—44no—
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—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
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—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
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×C42#4114yes—
422C2×C42#4114yes—
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427#107—44no—
428#107—44no—
429#106—44no—
430#106—44no—
431C4⋊C8—24no—
432C4⋊C8—24no—
433#102—44no—
434#102—44no—
435#102—44no—
436#102—44no—
437C22⋊C8—24no—
438C22⋊C8—24no—
439C22⋊C8—42no—
440C22⋊C8—42no—
441C22⋊C8—42no—
442C22⋊C8—42no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—41no—
470C24—41no—
471C24—41no—
472C24—41no—
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475C24C22×D411yescharacteristic
476#41—816no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
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—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
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—22no—
544C22×C4—22no—
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—41no—
557C22×C4—416no—
558C22×C4—416no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4#12314yes—
565C22×C4#12314yes—
566C22×C4#13514yes—
567C22×C4AGL(1,ℤ/8)14yes—
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4C2511yescharacteristic
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
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—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—44no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42#12314yes—
656C42#12314yes—
657C42C2×#4112yes—
658C42C2×#4112yes—
659C42C2×#4112yes—
660C42C2×#4112yes—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23C2×#12312yes—
694C23C2×#13512yes—
695C23C2×AGL(1,ℤ/8)12yes—
696C23C23×D411yescharacteristic
697Q8—84no—
698D4—44no—
699D4—44no—
700D4—88no—
701D4—88no—
702D4—88no—
703D4—84no—
704D4—84no—
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—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—21no—
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—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—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—88no—
770C2×C4C2×#12312yes—
771C2×C4C2×#12312yes—
772C2×C4C2×#12312yes—
773C2×C4C2×#12312yes—
774C2×C4C2×#12312yes—
775C2×C4C2×#13512yes—
776C2×C4C2×#13512yes—
777C2×C4C2×AGL(1,ℤ/8)12yes—
778C2×C4C2×AGL(1,ℤ/8)12yes—
779C2×C4#57512yes—
780C2×C4#57512yes—
781C2×C4C22×#4111yescharacteristic
782C2×C4C22×#4111yescharacteristic
783C2×C4#58512yes—
784C2×C4#58512yes—
785C8—42no—
786C8—42no—
787C8—42no—
788C8—42no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—416no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22C22×#12311yescharacteristic
819C22#344911yescharacteristic
820C22#344911yescharacteristic
821C22C22×#13511yescharacteristic
822C22C22×AGL(1,ℤ/8)11yescharacteristic
823C22C2×#57511yescharacteristic
824C22C2×#57511yescharacteristic
825C4—22no—
826C4—22no—
827C4—22no—
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4#309114yes—
842C4#309414yes—
843C4#349312yes—
844C4#349312yes—
845C2—42no—
846C2—42no—
847C2—42no—
848C2—162no—
849C2#3515711yescharacteristic
850C2C2×#309111yescharacteristic
851C2C2×#309411yescharacteristic
852C2#6094411yescharacteristic
853C2#6094611yescharacteristic
854C2#6096511yescharacteristic
855C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
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
2. #34012C2semidirect
3. #33097C2semidirect
4. #29896C2semidirect
5. #27891C2semidirect
6. #27891C2semidirect
7. #27890C2semidirect
8. #27890C2semidirect
9. #27878C2semidirect
10. #27877C2semidirect
11. #27876C2semidirect
12. #27875C2semidirect
13. #27633C2semidirect
14. #27632C2semidirect
15. #21984C2semidirect
16. #21984C2semidirect
17. #21863C2semidirect
18. #21863C2semidirect
19. #20714C2semidirect
67. #1990C22semidirect
68. #1990C22semidirect
69. #1990C22semidirect
70. #1990C22semidirect
71. #1957C22semidirect
72. #1957C22semidirect
73. #1957C22semidirect
74. #1957C22semidirect
75. #1949C22semidirect
76. #1949C22semidirect
77. #1926C22semidirect
78. #1926C22semidirect
79. #1925C22semidirect
80. #1925C22semidirect
81. #1921C22semidirect
82. #1920C22semidirect
83. #1919C22semidirect
84. #1918C22semidirect
89. #1845C22semidirect
90. #1845C22semidirect
91. #1844C22semidirect
92. #1844C22semidirect
93. #1834C22semidirect
94. #1834C22semidirect
95. #1834C22semidirect
96. #1834C22semidirect
98. #1804C22semidirect
99. #1804C22semidirect

Maximal subgroups

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

subgroupindex
#366242
#340122
#330972
#298962
#278912
#278902
#278782
#278772
#278762
#278752
#276332
#276322
#219842
#218632
#207142