Finite Group Databasebeta

← #6490095

Subgroups — #6490095

Order 512.

1328 conjugacy classes of subgroups.

The subgroup lattice has 765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37630C211yesmaximal, characteristic
2#34337C211yesmaximal, characteristic
3#33093C212yesmaximal
4#33077C212yesmaximal
5#30164C212yesmaximal
6#30104C212yesmaximal
7#27569C212yesmaximal
8#27316C212yesmaximal
9#27152C212yesmaximal
10#26883C212yesmaximal
11#26506C211yesmaximal, characteristic
12#26276C211yesmaximal, characteristic
13#26112C211yesmaximal, characteristic
14#25840C211yesmaximal, characteristic
15#25456C211yesmaximal, characteristic
16#24996C211yesmaximal, characteristic
17#24818C211yesmaximal, characteristic
18#24332C211yesmaximal, characteristic
19#22247C211yesmaximal, characteristic
20#22118C211yesmaximal, characteristic
21#22023C211yesmaximal, characteristic
22#21615C211yesmaximal, characteristic
23#21119C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C2×#500C2211yescharacteristic
26C2×#475C2211yescharacteristic
27C2×#475C2211yescharacteristic
28C2×C4×Q16C2211yescharacteristic
29#2839—22no—
30#2655—22no—
31#2647C2212yes—
32#2645—21no—
33#2645C2212yes—
34#2642—21no—
35#2582C2211yescharacteristic
36#2568C2211yescharacteristic
37#2552C2211yescharacteristic
38#2546C2211yescharacteristic
39#2511C2212yes—
40#2509C2212yes—
41#2453—21no—
42#2446—21no—
43#2370—22no—
44#2370C2212yes—
45#2365—21no—
46#2365C2211yescharacteristic
47Q8×C4⋊C4—21no—
48Q8×C4⋊C4C2211yescharacteristic
49Q8×C4⋊C4C2211yescharacteristic
50Q8×C4⋊C4C2212yes—
51#2330—22no—
52#2330C2212yes—
53C4×C4⋊Q8—21no—
54C4×C4⋊Q8C2211yescharacteristic
55C4×C4⋊Q8C2211yescharacteristic
56#2295—21no—
57#2295C2211yescharacteristic
58#2295C2211yescharacteristic
59#2276C2212yes—
60C42×Q8C2211yescharacteristic
61#2100C2212yes—
62#2100C2212yes—
63#2099C2212yes—
64#2099C2212yes—
65#2087C2212yes—
66#2086C2212yes—
67#2085C2212yes—
68#2085C2212yes—
69#2083C2212yes—
70#2072C2212yes—
71#2068C2212yes—
72#2066C2212yes—
73#2059C2212yes—
74#2059C2212yes—
75#2059C2212yes—
76#2026C2212yes—
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1988C2211yescharacteristic
80#1988C2211yescharacteristic
81#1984C2211yescharacteristic
82#1984C2211yescharacteristic
83#1949C2212yes—
84#1947C2211yescharacteristic
85#1947C2212yes—
86#1947C2211yescharacteristic
87#1944C2212yes—
88#1939C2211yescharacteristic
89#1939C2211yescharacteristic
90#1935C2212yes—
91#1928C2211yescharacteristic
92#1928C2212yes—
93#1928C2212yes—
94#1928C2212yes—
95#1928C2211yescharacteristic
96#1921C2211yescharacteristic
97#1921C2212yes—
98#1921C2211yescharacteristic
99#1920C2212yes—
100#1919C2212yes—
101#1918C2212yes—
102#1918C2212yes—
103#1918C2212yes—
104#1918C2212yes—
105#1918C2212yes—
106#1918C2212yes—
107#1918C2212yes—
108#1917C2212yes—
109#1917C2212yes—
110#1878C2212yes—
111#1878C2211yescharacteristic
112#1878C2212yes—
113#1878C2211yescharacteristic
114#1865C2212yes—
115#1863C2212yes—
116#1863C2211yescharacteristic
117#1863C2212yes—
118#1863C2212yes—
119#1863C2212yes—
120#1863C2211yescharacteristic
121#1840C2212yes—
122#1834C2211yescharacteristic
123#1832C2212yes—
124#1805C2212yes—
125#1803C2211yescharacteristic
126#1803C2212yes—
127#1803C2211yescharacteristic
128#1776C2212yes—
129C4×#107C2211yescharacteristic
130#1767C2211yescharacteristic
131#1763C2212yes—
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134#1744C2211yescharacteristic
135C22×Q16C2311yescharacteristic
136#557—24no—
137#557—24no—
138C2×C4⋊Q8—21no—
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8C2311yescharacteristic
141C2×C4⋊Q8C2311yescharacteristic
142C2×#125—22no—
143C2×#125—21no—
144C2×#125C2312yes—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2312yes—
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2312yes—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156C2×C4×Q8C2311yescharacteristic
157#500—24no—
158#475—24no—
159#475—24no—
160C4×Q16—24no—
161C2×#107C2311yescharacteristic
162C2×#107C2312yes—
163C2×#107C2312yes—
164C2×#107C2311yescharacteristic
165C2×#107C2312yes—
166C2×#107C2311yescharacteristic
167C2×#107C2312yes—
168C2×#106C2312yes—
169C2×#106C2312yes—
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×#103C2312yes—
175C2×#103C2312yes—
176C2×#103C2311yescharacteristic
177C2×#103C2312yes—
178C2×#103C2311yescharacteristic
179C2×#103C2311yescharacteristic
180C2×#103C2311yescharacteristic
181C2×#103C2311yescharacteristic
182C2×#103C2312yes—
183C2×#103C2311yescharacteristic
184C2×#97C2312yes—
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187#401—22no—
188#400—22no—
189#400—22no—
190#400—22no—
191#400—22no—
192#400—22no—
193#400—22no—
194#400—22no—
195#400—22no—
196#400—22no—
197#400—22no—
198#398—22no—
199#398—22no—
200#398—22no—
201#398—22no—
202#398—22no—
203#391—21no—
204#391—21no—
205#391—21no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—21no—
210#391D411yescharacteristic
211#391D411yescharacteristic
212#391C2312yes—
213#391C2312yes—
214#391C2311yescharacteristic
215#391C2311yescharacteristic
216#389—21no—
217#389—22no—
218#389—22no—
219#389—21no—
220#389—21no—
221#389—22no—
222#389—21no—
223#389—21no—
224#389—22no—
225#389—22no—
226#389—22no—
227#389—22no—
228#389—22no—
229#389D411yescharacteristic
230#389D411yescharacteristic
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#387—22no—
242#387—22no—
243#387—21no—
244#387—21no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387D412yes—
252#387D412yes—
253#384—21no—
254#384—22no—
255#384C2311yescharacteristic
256#384C2311yescharacteristic
257#384C2312yes—
258#384C2312yes—
259#382C2312yes—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—21no—
264C4×C4⋊C4—21no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—22no—
269C4×C4⋊C4—22no—
270C4×C4⋊C4—22no—
271C4×C4⋊C4—22no—
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2312yes—
282#376—21no—
283#376—22no—
284#376C2312yes—
285C43—21no—
286C43C2311yescharacteristic
287#340C2312yes—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2311yescharacteristic
292#340C2311yescharacteristic
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2311yescharacteristic
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2311yescharacteristic
304#340C2312yes—
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#336C2312yes—
308#336C2312yes—
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2311yescharacteristic
314#336C2312yes—
315#336C2311yescharacteristic
316#336C2311yescharacteristic
317#336C2311yescharacteristic
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8C2×D411yescharacteristic
321C22×Q8C2411yescharacteristic
322C22×Q8C2411yescharacteristic
323C2×Q16—22no—
324C2×Q16—22no—
325C2×Q16—22no—
326C22×C8C2411yescharacteristic
327C22×C8C2411yescharacteristic
328C22×C8C2411yescharacteristic
329C22×C8C2411yescharacteristic
330C22×C8C2412yes—
331C22×C8C2412yes—
332C4⋊Q8—28no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—82no—
337C4⋊Q8#4114yes—
338#125—216no—
339#125—24no—
340#125—24no—
341#125—82no—
342C4×Q8—28no—
343C4×Q8—24no—
344C4×Q8—22no—
345C4×Q8—24no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—24no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—41no—
355C4×Q8—42no—
356C4×Q8—82no—
357C4×Q8—82no—
358C4×Q8—82no—
359C4×Q8—82no—
360C4×Q8#4114yes—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D412yes—
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2×D412yes—
394C2×C4⋊C4C2×D412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2411yescharacteristic
397C2×C4⋊C4C2411yescharacteristic
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2411yescharacteristic
401C2×C4⋊C4C2411yescharacteristic
402C2×C4⋊C4C2411yescharacteristic
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2411yescharacteristic
405C2×C42—22no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—22no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—21no—
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2412yes—
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2412yes—
427C2×C42C2411yescharacteristic
428#107—22no—
429#107—24no—
430#107—24no—
431#107—22no—
432#107—24no—
433#107—42no—
434#107—41no—
435#106—24no—
436#106—24no—
437C4⋊C8—22no—
438C4⋊C8—22no—
439C4⋊C8—42no—
440C4⋊C8—42no—
441#103—22no—
442#103—24no—
443#103—22no—
444#103—24no—
445#103—22no—
446#103—22no—
447#103—24no—
448#103—22no—
449#103—42no—
450#103—41no—
451#97—42no—
452C4×C8—22no—
453C4×C8—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—22no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—22no—
467#95—22no—
468#95—21no—
469#95—22no—
470#95—21no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95C2×D412yes—
483#95C2×D412yes—
484#95C2×D412yes—
485#95C2×D412yes—
486#95C2×D412yes—
487#95C2×D412yes—
488#95C2×D412yes—
489C2×Q8—22no—
490C2×Q8—24no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8C2×#4112yes—
508C2×Q82−1+412yes—
509C2×Q82−1+412yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D412yes—
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D412yes—
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C2511yescharacteristic
533Q16—44no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—21no—
541C2×C8—22no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—22no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—21no—
551C2×C8—21no—
552C4⋊C4—24no—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—28no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—44no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—81no—
589C4⋊C4—81no—
590C4⋊C4—81no—
591C4⋊C4—82no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4C2×#4112yes—
604C4⋊C4C2×#4114yes—
605C4⋊C42−1+412yes—
606C42—24no—
607C42—28no—
608C42—24no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—22no—
617C42—21no—
618C42—22no—
619C42—41no—
620C42—41no—
621C42—42no—
622C42—44no—
623C42—42no—
624C42—42no—
625C42—42no—
626C42—42no—
627C42—81no—
628C42—82no—
629C42—82no—
630C42—82no—
631C42—82no—
632C42C2×#4112yes—
633C42C2×#4112yes—
634C23C23×D411yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—44no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—84no—
645Q8#54114yes—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4#52512yes—
709C2×C4#52512yes—
710C2×C4#57612yes—
711C2×C4#57812yes—
712C2×C4C22×#4111yescharacteristic
713C2×C4C22×#4111yescharacteristic
714C2×C4C2×2−1+411yescharacteristic
715C2×C4C2×2−1+411yescharacteristic
716C2×C4C2×2−1+411yescharacteristic
717C2×C4#58511yescharacteristic
718C8—41no—
719C8—41no—
720C8—42no—
721C8—41no—
722C8—42no—
723C8—41no—
724C22C2×#52511yescharacteristic
725C22#348611yescharacteristic
726C22#348911yescharacteristic
727C22C2×#57611yescharacteristic
728C22C2×#57811yescharacteristic
729C22#358611yescharacteristic
730C22#358611yescharacteristic
731C4—22no—
732C4—24no—
733C4—42no—
734C4—44no—
735C4—41no—
736C4—42no—
737C4—42no—
738C4—41no—
739C4—42no—
740C4—41no—
741C4—42no—
742C4—41no—
743C4—42no—
744C4—82no—
745C4—81no—
746C4—81no—
747C4—82no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—82no—
752C4#312414yes—
753C4C2×#54111yescharacteristic
754C4#346111yescharacteristic
755C4#351611yescharacteristic
756C4#352311yescharacteristic
757C2#3524411yescharacteristic
758C2C2×#312411yescharacteristic
759C2#6057711yescharacteristic
760C2#6185211yescharacteristic
761C2#6185711yescharacteristic
762C2#6218611yescharacteristic
763C2#6219211yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#376302
#343372
#330932
#330772
#301642
#301042
#275692
#273162
#271522
#268832
#265062
#262762
#261122
#258402
#254562
#249962
#248182
#243322
#222472
#221182
#220232
#216152
#211192