Finite Group Databasebeta

← #6486603

Subgroups — #6486603

Order 512.

1216 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37344C212yesmaximal
2#33273C211yesmaximal, characteristic
3#33267C211yesmaximal, characteristic
4#33261C211yesmaximal, characteristic
5#33258C211yesmaximal, characteristic
6#30388C212yesmaximal
7#30385C212yesmaximal
8#28827C211yesmaximal, characteristic
9#28679C211yesmaximal, characteristic
10#28535C211yesmaximal, characteristic
11#28265C211yesmaximal, characteristic
12#28054C212yesmaximal
13#28050C212yesmaximal
14#28015C211yesmaximal, characteristic
15#28015C211yesmaximal, characteristic
16#27994C211yesmaximal, characteristic
17#27992C211yesmaximal, characteristic
18#27741C212yesmaximal
19#25484C212yesmaximal
20#22124C212yesmaximal
21#21723C211yesmaximal, characteristic
22#21281C211yesmaximal, characteristic
23#20516C211yesmaximal, characteristic
24C2×#499C2211yescharacteristic
25C2×#479C2212yes—
26C2×#446C2211yescharacteristic
27C2×C8×Q8C2211yescharacteristic
28C2×C4×Q16C2211yescharacteristic
29#2863C2212yes—
30#2859C2212yes—
31#2802—22no—
32#2776—22no—
33#2769—22no—
34#2762—22no—
35#2755—22no—
36#2719—22no—
37#2719—22no—
38#2719—22no—
39#2647C2212yes—
40#2645C2212yes—
41#2584C2212yes—
42#2582C2212yes—
43#2565C2212yes—
44#2552C2212yes—
45#2511C2212yes—
46#2511C2212yes—
47#2508C2212yes—
48#2506C2212yes—
49#2330C2212yes—
50#2320C2212yes—
51#2295C2211yescharacteristic
52#2101C2212yes—
53#2099C2212yes—
54#2097C2212yes—
55#2096C2212yes—
56#2088C2212yes—
57#2088C2212yes—
58#2088C2212yes—
59#2086C2212yes—
60#2083C2212yes—
61#2083C2212yes—
62#2072C2212yes—
63#2072C2212yes—
64#2068C2212yes—
65#2068C2212yes—
66#2068C2212yes—
67#2068C2212yes—
68#1992C2212yes—
69#1989C2212yes—
70#1969C2211yescharacteristic
71#1969C2211yescharacteristic
72#1969C2211yescharacteristic
73#1969C2211yescharacteristic
74#1969C2211yescharacteristic
75#1969C2211yescharacteristic
76#1947C2212yes—
77#1944C2212yes—
78#1944C2212yes—
79#1943C2212yes—
80#1942C2211yescharacteristic
81#1942C2211yescharacteristic
82#1942C2211yescharacteristic
83#1942C2211yescharacteristic
84#1942C2211yescharacteristic
85#1942C2211yescharacteristic
86#1942C2211yescharacteristic
87#1942C2211yescharacteristic
88#1942C2211yescharacteristic
89#1942C2211yescharacteristic
90#1942C2212yes—
91#1942C2212yes—
92#1942C2211yescharacteristic
93#1942C2211yescharacteristic
94#1935C2212yes—
95#1935C2212yes—
96#1935C2212yes—
97#1935C2212yes—
98#1935C2212yes—
99#1933C2212yes—
100#1933C2212yes—
101#1933C2212yes—
102#1928C2212yes—
103#1928C2212yes—
104#1920C2212yes—
105#1918C2212yes—
106#1846C2211yescharacteristic
107#1845C2211yescharacteristic
108#1845C2211yescharacteristic
109#1845C2211yescharacteristic
110#1845C2211yescharacteristic
111#1836C2212yes—
112#1834C2212yes—
113#1803C2212yes—
114#1776C2212yes—
115C4×#107C2211yescharacteristic
116C4×#107C2211yescharacteristic
117C4×#107C2211yescharacteristic
118#1771C2211yescharacteristic
119#1771C2211yescharacteristic
120#1770C2211yescharacteristic
121C8×C4⋊C4C2211yescharacteristic
122C8×C4⋊C4C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124#1768C2211yescharacteristic
125#1768C2211yescharacteristic
126#1767C2211yescharacteristic
127#1763C2212yes—
128#1726C2211yescharacteristic
129#1726C2211yescharacteristic
130C42×C8C2211yescharacteristic
131C22×Q16C2311yescharacteristic
132C2×#125—22no—
133C2×#125—22no—
134C2×#125—22no—
135C2×#125C2312yes—
136C2×C4×Q8C2312yes—
137C2×C4×Q8C2311yescharacteristic
138#499—24no—
139#479—28no—
140#446—24no—
141C8×Q8—24no—
142C4×Q16—24no—
143C2×#107C2312yes—
144C2×#107C2311yescharacteristic
145C2×#107C2311yescharacteristic
146C2×#107C2311yescharacteristic
147C2×#107C2311yescharacteristic
148C2×#107C2311yescharacteristic
149C2×#107C2311yescharacteristic
150C2×#107C2311yescharacteristic
151C2×#107C2312yes—
152C2×#107C2312yes—
153C2×#107C2312yes—
154C2×#106C2312yes—
155C2×#106C2312yes—
156C2×C4⋊C8C2311yescharacteristic
157C2×C4⋊C8C2311yescharacteristic
158C2×C4⋊C8C2311yescharacteristic
159C2×C4⋊C8C2311yescharacteristic
160C2×C4⋊C8C2311yescharacteristic
161C2×C4⋊C8C2311yescharacteristic
162C2×#103C2312yes—
163C2×#103C2312yes—
164C2×#103C2312yes—
165C2×#103C2312yes—
166C2×#103C2312yes—
167C2×#103C2312yes—
168C2×#103C2312yes—
169C2×#97C2311yescharacteristic
170C2×#97C2311yescharacteristic
171C2×#97C2311yescharacteristic
172C2×#97C2311yescharacteristic
173C2×#97C2311yescharacteristic
174C2×#97C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185#401—22no—
186#400—22no—
187#400—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#398—22no—
198#398—22no—
199#398—22no—
200#398—22no—
201#398—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#398—22no—
206#398—22no—
207#398—22no—
208#395—22no—
209#391—22no—
210#391D411yescharacteristic
211#391D411yescharacteristic
212#391C2312yes—
213#391C2312yes—
214#391C2312yes—
215#391C2312yes—
216#391C2312yes—
217#391C2312yes—
218#389—22no—
219#389—22no—
220#389—22no—
221#389—22no—
222#389—22no—
223#389—22no—
224#389—22no—
225#389—22no—
226#389D411yescharacteristic
227#389D411yescharacteristic
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#387—22no—
241#387—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387D411yescharacteristic
256#387D411yescharacteristic
257#387D411yescharacteristic
258#387D411yescharacteristic
259#384C2312yes—
260#384C2312yes—
261#384C2312yes—
262#384C2312yes—
263#383—22no—
264#383—22no—
265#382—22no—
266#382—22no—
267#382—22no—
268#382C2312yes—
269C4×C4⋊C4C2312yes—
270C4×C4⋊C4C2312yes—
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2311yescharacteristic
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2311yescharacteristic
275#376C2311yescharacteristic
276#376C2311yescharacteristic
277C43C2311yescharacteristic
278#340C2312yes—
279#340C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#336C2311yescharacteristic
294#336C2311yescharacteristic
295#336C2311yescharacteristic
296#336C2311yescharacteristic
297#336C2311yescharacteristic
298#336C2311yescharacteristic
299C22×Q8C2×D411yescharacteristic
300C22×Q8C2412yes—
301C2×Q16—22no—
302C2×Q16—22no—
303C2×Q16—22no—
304C22×C8C2411yescharacteristic
305C22×C8C2411yescharacteristic
306C22×C8C2411yescharacteristic
307C22×C8C2411yescharacteristic
308C22×C8C2411yescharacteristic
309C22×C8C2411yescharacteristic
310C22×C8C2411yescharacteristic
311C22×C8C2411yescharacteristic
312#125—24no—
313#125—24no—
314#125—84no—
315#125—84no—
316#125—84no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8—24no—
320C4×Q8—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
345C2×C4⋊C4C2×D411yescharacteristic
346C2×C4⋊C4C2×D411yescharacteristic
347C2×C4⋊C4C2×D411yescharacteristic
348C2×C4⋊C4C2×D411yescharacteristic
349C2×C4⋊C4C2×D411yescharacteristic
350C2×C4⋊C4C2×D411yescharacteristic
351C2×C4⋊C4C2×D411yescharacteristic
352C2×C4⋊C4C2×D411yescharacteristic
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42C2×D411yescharacteristic
365C2×C42C2×D411yescharacteristic
366C2×C42C2×D411yescharacteristic
367C2×C42C2×D411yescharacteristic
368C2×C42C2411yescharacteristic
369C2×C42C2411yescharacteristic
370C2×C42C2411yescharacteristic
371C2×C42C2411yescharacteristic
372C2×C42C2411yescharacteristic
373C2×C42C2411yescharacteristic
374C2×C42C2411yescharacteristic
375#107—22no—
376#107—24no—
377#107—22no—
378#107—22no—
379#107—22no—
380#107—22no—
381#107—22no—
382#107—22no—
383#107—42no—
384#107—42no—
385#107—42no—
386#106—24no—
387#106—24no—
388C4⋊C8—22no—
389C4⋊C8—22no—
390C4⋊C8—22no—
391C4⋊C8—22no—
392C4⋊C8—22no—
393C4⋊C8#4114yes—
394#103—24no—
395#103—24no—
396#103—24no—
397#103—24no—
398#103—42no—
399#103—42no—
400#103—42no—
401#97—22no—
402#97—22no—
403#97—22no—
404#97—22no—
405#97—41no—
406#97—41no—
407C4×C8—22no—
408C4×C8—22no—
409C4×C8—22no—
410C4×C8—22no—
411C4×C8—22no—
412C4×C8—22no—
413C4×C8—22no—
414C4×C8—22no—
415C4×C8—41no—
416C4×C8#4114yes—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
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#95C2×D411yescharacteristic
447#95C2×D411yescharacteristic
448#95C2×D411yescharacteristic
449#95C2×D411yescharacteristic
450#95C2×D411yescharacteristic
451#95C2×D411yescharacteristic
452#95C2×D411yescharacteristic
453#95C2×D411yescharacteristic
454#95C2×D411yescharacteristic
455#95C2×D411yescharacteristic
456#95C2×D411yescharacteristic
457#95C2×D411yescharacteristic
458#95C2×D411yescharacteristic
459#95C2×D411yescharacteristic
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—41no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4C22×D411yescharacteristic
478C22×C4C22×D411yescharacteristic
479C22×C4C22×D411yescharacteristic
480C22×C4C22×D411yescharacteristic
481C22×C4C22×D411yescharacteristic
482C22×C4C22×D411yescharacteristic
483C22×C4C22×D411yescharacteristic
484C22×C4C22×D411yescharacteristic
485C22×C4C22×D411yescharacteristic
486C22×C4C22×D411yescharacteristic
487C22×C4C22×D411yescharacteristic
488C22×C4C22×D411yescharacteristic
489C22×C4C22×D411yescharacteristic
490C22×C4C22×D411yescharacteristic
491C22×C4C2511yescharacteristic
492Q16—44no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8C2×#4112yes—
511C2×C8C2×#4112yes—
512C2×C8C2×#4112yes—
513C2×C8C2×#4112yes—
514C2×C82−1+412yes—
515C2×C82−1+412yes—
516C2×C82−1+412yes—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—41no—
540C4⋊C4—44no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4—44no—
547C4⋊C4—44no—
548C4⋊C4—82no—
549C4⋊C4—82no—
550C4⋊C4—82no—
551C4⋊C4—82no—
552C4⋊C4—82no—
553C4⋊C4—82no—
554C4⋊C4—82no—
555C4⋊C4—82no—
556C4⋊C4—82no—
557C4⋊C4—82no—
558C4⋊C4—82no—
559C4⋊C4—82no—
560C4⋊C4—82no—
561C4⋊C4—82no—
562C4⋊C4—82no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—41no—
579C42—44no—
580C42—82no—
581C42—82no—
582C42—82no—
583C42C2×#4112yes—
584C42C2×#4112yes—
585C23C23×D411yescharacteristic
586Q8—44no—
587Q8—42no—
588Q8—42no—
589Q8—42no—
590Q8—42no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4#53212yes—
653C2×C4#53212yes—
654C2×C4#57612yes—
655C2×C4#57812yes—
656C2×C4#57812yes—
657C2×C4C22×#4111yescharacteristic
658C2×C4C22×#4111yescharacteristic
659C2×C4C2×2−1+411yescharacteristic
660C2×C4C2×2−1+411yescharacteristic
661C2×C4C2×2−1+411yescharacteristic
662C2×C4#58511yescharacteristic
663C8—22no—
664C8—22no—
665C8—22no—
666C8—22no—
667C8—41no—
668C8—41no—
669C8—41no—
670C8#54114yes—
671C22C2×#53211yescharacteristic
672C22#349711yescharacteristic
673C22#349911yescharacteristic
674C22C2×#57611yescharacteristic
675C22C2×#57811yescharacteristic
676C22C2×#57811yescharacteristic
677C22#358411yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—41no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—82no—
693C4—82no—
694C4—82no—
695C4—82no—
696C4—82no—
697C4—82no—
698C4—82no—
699C4—82no—
700C4C2×#54111yescharacteristic
701C4#346111yescharacteristic
702C4#351511yescharacteristic
703C4#352311yescharacteristic
704C2#3520911yescharacteristic
705C2#6070811yescharacteristic
706C2#6071811yescharacteristic
707C2#6237411yescharacteristic
708C2#6237911yescharacteristic
709C2#6248711yescharacteristic
710C2#6249311yescharacteristic
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
#373442
#332732
#332672
#332612
#332582
#303882
#303852
#288272
#286792
#285352
#282652
#280542
#280502
#280152
#279942
#279922
#277412
#254842
#221242
#217232
#212812
#205162