Finite Group Databasebeta

← #208011

Subgroups — #208011

Order 512.

824 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35135C211yesmaximal, characteristic
2#20480C211yesmaximal, characteristic, complemented
3#20465C211yesmaximal, characteristic, complemented
4#9894C211yesmaximal, characteristic, complemented
5#9891C211yesmaximal, characteristic, complemented
6#9688C211yesmaximal, characteristic, complemented
7#9687C211yesmaximal, characteristic, complemented
8#9126C211yesmaximal, characteristic, complemented
9#9124C211yesmaximal, characteristic
10#9122C211yesmaximal, characteristic, complemented
11#9120C211yesmaximal, characteristic
12#8227C211yesmaximal, characteristic, complemented
13#8226C211yesmaximal, characteristic, complemented
14C4×#330C211yesmaximal, characteristic, complemented
15C4×#329C211yesmaximal, characteristic, complemented
16C2×#433—21no—
17C2×#432C2211yescharacteristic
18C2×C4×M16C2211yescharacteristic
19#2861C2211yescharacteristic
20#2859C2211yescharacteristic
21#2851C2211yescharacteristic
22#2850C2211yescharacteristic
23#2654—21no—
24#2649—21no—
25#2530—21no—
26#2529—21no—
27#2512C411yescharacteristic
28#2511C411yescharacteristic
29#2490C411yescharacteristic
30#2489C411yescharacteristic
31#2479—21no—
32#2470—21no—
33#2454C411yescharacteristic
34#2453C411yescharacteristic
35#2423C411yescharacteristic
36#2422C411yescharacteristic
37#2335—21no—
38#2334—21no—
39C4×#125C2211yescharacteristic
40C4×#124C2211yescharacteristic
41C4×#117C2211yescharacteristic
42#1770—21no—
43C8×C4⋊C4—21no—
44#1768—21no—
45#1767C2211yescharacteristic
46#1767C2211yescharacteristic
47#1753—21no—
48#1753—21no—
49#1750—21no—
50#1749C2211yescharacteristic
51#1749C2211yescharacteristic
52#1746—21no—
53#1745C2211yescharacteristic
54#1745C2211yescharacteristic
55C4×#97C2211yescharacteristic
56C4×#97C2211yescharacteristic
57C4×#97C2211yescharacteristic
58C4×#97C2211yescharacteristic
59C2×#330C2211yescharacteristic
60C2×#330C2211yescharacteristic
61C2×#330C2211yescharacteristic
62C2×#330C2211yescharacteristic
63C2×#329C2211yescharacteristic
64C2×#329C2211yescharacteristic
65C2×#329C2211yescharacteristic
66C2×#329C2211yescharacteristic
67#1295C2211yescharacteristic
68#1295C2211yescharacteristic
69#1295C2211yescharacteristic
70#1295C2211yescharacteristic
71#1295C2211yescharacteristic
72#1295C2211yescharacteristic
73#1295C2211yescharacteristic
74#1295C2211yescharacteristic
75C22×M16—21no—
76C2×#126—21no—
77C2×#125C2×C411yescharacteristic
78C2×#125C2×C411yescharacteristic
79C2×#125C2311yescharacteristic
80C2×#124C2311yescharacteristic
81C2×#123—21no—
82C2×C22⋊Q8C2×C411yescharacteristic
83C2×#121C2×C411yescharacteristic
84C2×C4×Q8C2×C411yescharacteristic
85C2×C4×D4C2×C411yescharacteristic
86C2×#117D411yescharacteristic
87C2×#117D411yescharacteristic
88C22×C42C2311yescharacteristic
89#433—28no—
90#432—22no—
91#432—22no—
92C2×C4⋊C8—21no—
93C2×C4⋊C8—21no—
94C2×C4⋊C8—21no—
95C2×C22⋊C8—21no—
96C2×C22⋊C8—21no—
97C2×C22⋊C8—21no—
98C4×M16—22no—
99C4×M16—22no—
100C2×#97—21no—
101C2×#97—21no—
102C2×#97—21no—
103C2×#97—21no—
104C2×#97C2311yescharacteristic
105C2×#97C2311yescharacteristic
106C2×#97C2311yescharacteristic
107C2×#97C2311yescharacteristic
108C2×#97C2311yescharacteristic
109C2×#97C2311yescharacteristic
110C2×#97C2311yescharacteristic
111C2×#97C2311yescharacteristic
112C2×C4×C8—21no—
113C2×C4×C8—21no—
114C2×C4×C8—21no—
115C2×C4×C8—21no—
116C2×C4×C8—21no—
117#400—21no—
118#400—21no—
119#400—21no—
120#400—21no—
121#399—21no—
122#399—21no—
123#398—21no—
124#398—21no—
125#397—21no—
126#397—21no—
127#397—21no—
128#397—21no—
129#396—21no—
130#396—21no—
131#394—21no—
132#394—21no—
133#391C2×C411yescharacteristic
134#391C2×C411yescharacteristic
135#391C2×C411yescharacteristic
136#391C2×C411yescharacteristic
137#390—21no—
138#390C2×C411yescharacteristic
139#390C2×C411yescharacteristic
140#390C2×C411yescharacteristic
141#390C2×C411yescharacteristic
142#389—21no—
143#389—21no—
144#389—21no—
145#389—21no—
146#389—21no—
147#389C2×C411yescharacteristic
148#389C2×C411yescharacteristic
149#389C2×C411yescharacteristic
150#389C2×C411yescharacteristic
151#388—21no—
152#388—21no—
153#388—21no—
154#388—21no—
155#388—21no—
156#388—21no—
157#388—21no—
158#388—21no—
159#388—21no—
160#388—21no—
161#388—21no—
162#388—21no—
163#387—21no—
164#387—21no—
165#387—21no—
166#387—21no—
167#387—21no—
168#387—21no—
169#387—21no—
170#387—21no—
171#386—21no—
172#386—21no—
173#385—21no—
174#385—21no—
175#385—21no—
176#385—21no—
177#384C2×C411yescharacteristic
178#384C2×C411yescharacteristic
179#382—21no—
180#382C2311yescharacteristic
181#382C2311yescharacteristic
182#380—21no—
183#380C2×C411yescharacteristic
184#380C2×C411yescharacteristic
185C4×C4⋊C4—21no—
186C4×C4⋊C4—21no—
187C4×C4⋊C4C2×C411yescharacteristic
188C4×C4⋊C4C2×C411yescharacteristic
189C4×C4⋊C4C2×C411yescharacteristic
190C4×C4⋊C4C2×C411yescharacteristic
191C4×C4⋊C4D411yescharacteristic
192C4×C4⋊C4D411yescharacteristic
193C4×C22⋊C4—21no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4C2×C411yescharacteristic
196C4×C22⋊C4C2×C411yescharacteristic
197C4×C22⋊C4D411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199#376D411yescharacteristic
200#376D411yescharacteristic
201C43C2311yescharacteristic
202C43C2311yescharacteristic
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211#330—22no—
212#330—22no—
213#330—22no—
214#330—22no—
215#329—22no—
216#329—22no—
217#329—22no—
218#329—22no—
219C22×Q8C22×C411yescharacteristic
220C22×D4—21no—
221C22×D4C22×C411yescharacteristic
222C23×C4—21no—
223C23×C4C22×C411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C2×M16—24no—
227C2×M16—42no—
228C2×M16—42no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237#126—44no—
238#125—21no—
239#125—21no—
240#125—21no—
241#125—21no—
242#125—81no—
243#125—81no—
244#124—21no—
245#124—21no—
246#124—21no—
247#124—21no—
248#123—44no—
249C22⋊Q8—81no—
250#121—81no—
251C4×Q8—81no—
252C4×D4—81no—
253#117—24no—
254#117—42no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C22⋊C411yescharacteristic
272C2×C4⋊C4C22⋊C411yescharacteristic
273C2×C4⋊C4C22⋊C411yescharacteristic
274C2×C4⋊C4C22⋊C411yescharacteristic
275C2×C4⋊C4C22×C411yescharacteristic
276C2×C4⋊C4C22×C411yescharacteristic
277C2×C4⋊C4C22×C411yescharacteristic
278C2×C4⋊C4C22×C411yescharacteristic
279C2×C4⋊C4C22×C411yescharacteristic
280C2×C4⋊C4C22×C411yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4C22⋊C411yescharacteristic
297C2×C22⋊C4C22⋊C411yescharacteristic
298C2×C22⋊C4C22⋊C411yescharacteristic
299C2×C22⋊C4C22⋊C411yescharacteristic
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42C22×C411yescharacteristic
308C2×C42C22×C411yescharacteristic
309C2×C42C22×C411yescharacteristic
310C2×C42C22×C411yescharacteristic
311C2×C42C22×C411yescharacteristic
312C2×C42C2×D411yescharacteristic
313C2×C42C2×D411yescharacteristic
314C2×C42C2×D411yescharacteristic
315C2×C42C2×D411yescharacteristic
316C2×C42C2×D411yescharacteristic
317C2×C42C2×D411yescharacteristic
318C2×C42C2×D411yescharacteristic
319C2×C42C2×D411yescharacteristic
320C2×C42C2×D411yescharacteristic
321C2×C42C2×D411yescharacteristic
322C2×C42C2411yescharacteristic
323C4⋊C8—24no—
324C4⋊C8—24no—
325C4⋊C8—24no—
326C22⋊C8—24no—
327C22⋊C8—24no—
328C22⋊C8—24no—
329#97—24no—
330#97—21no—
331#97—21no—
332#97—21no—
333#97—21no—
334#97—21no—
335#97—21no—
336#97—21no—
337#97—21no—
338#97—21no—
339#97—21no—
340#97—21no—
341#97—21no—
342#97—42no—
343#97—42no—
344#97—42no—
345#97#4112yes—
346#97#4112yes—
347#97#4112yes—
348#97#4112yes—
349C4×C8—24no—
350C4×C8—24no—
351C4×C8—42no—
352C4×C8—42no—
353C4×C8—42no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95C22⋊C411yescharacteristic
375#95C22⋊C411yescharacteristic
376#95C22⋊C411yescharacteristic
377#95C22⋊C411yescharacteristic
378#95C22⋊C411yescharacteristic
379#95C22⋊C411yescharacteristic
380#95C22⋊C411yescharacteristic
381#95C22⋊C411yescharacteristic
382C24—21no—
383C24C2×C22⋊C411yescharacteristic
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C2×D4—81no—
394C2×D4—81no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—42no—
415C22×C4—81no—
416C22×C4—81no—
417C22×C4C2×C22⋊C411yescharacteristic
418C22×C4C2×C22⋊C411yescharacteristic
419C22×C4C2×C22⋊C411yescharacteristic
420C22×C4C2×C22⋊C411yescharacteristic
421C22×C4C2×C22⋊C411yescharacteristic
422C22×C4C2×C22⋊C411yescharacteristic
423C22×C4C2×C22⋊C411yescharacteristic
424C22×C4C2×C22⋊C411yescharacteristic
425C22×C4C2×C22⋊C411yescharacteristic
426C22×C4C2×C22⋊C411yescharacteristic
427C22×C4C2×C22⋊C411yescharacteristic
428C22×C4C23×C411yescharacteristic
429C22×C4C22×D411yescharacteristic
430C22×C4C22×D411yescharacteristic
431M16—48no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—41no—
443C2×C8—41no—
444C2×C8—41no—
445C2×C8—41no—
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—41no—
449C2×C8—41no—
450C2×C8—41no—
451C2×C8—41no—
452C2×C8—41no—
453C2×C8—41no—
454C2×C8—41no—
455C2×C8—41no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—42no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4#10414yes—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—41no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—81no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C22⋊C4—81no—
503C22⋊C4—81no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—22no—
514C42—22no—
515C42—22no—
516C42—41no—
517C42—41no—
518C42—41no—
519C42—41no—
520C42—41no—
521C42—41no—
522C42—41no—
523C42—41no—
524C42—41no—
525C42—42no—
526C42—81no—
527C42—81no—
528C42C2×#4111yescharacteristic
529C42C2×#4111yescharacteristic
530C42C2×#4111yescharacteristic
531C42C2×#4111yescharacteristic
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C22×C22⋊C411yescharacteristic
547Q8—81no—
548Q8—81no—
549D4—81no—
550D4—81no—
551D4—162no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—162no—
615C2×C4C2×#10412yes—
616C2×C4C2×#10412yes—
617C2×C4C2×#10412yes—
618C2×C4#42112yes—
619C2×C4C4×#4111yescharacteristic
620C2×C4C4×#4111yescharacteristic
621C2×C4#52511yescharacteristic
622C2×C4#52511yescharacteristic
623C2×C4#53211yescharacteristic
624C2×C4#53211yescharacteristic
625C8—24no—
626C8—42no—
627C8—42no—
628C8—42no—
629C8—42no—
630C8—42no—
631C8—42no—
632C8—42no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22#229711yescharacteristic
648C22#288811yescharacteristic
649C22#288911yescharacteristic
650C22C22×#10411yescharacteristic
651C22C2×#42111yescharacteristic
652C22#290111yescharacteristic
653C22#290111yescharacteristic
654C4—22no—
655C4—21no—
656C4—21no—
657C4—22no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—21no—
662C4—22no—
663C4—22no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—81no—
678C2—81no—
679C2—161no—
680C2#1765311yescharacteristic
681C2#1765511yescharacteristic
682C2#1767911yescharacteristic
683C2#1768211yescharacteristic
684C2#2138211yescharacteristic
685C2#2141911yescharacteristic
686C2#2142711yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC2×#121C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #20480C2semidirect
3. #20465C2semidirect
4. #9894C2semidirect
5. #9891C2semidirect
6. #9688C2semidirect
7. #9687C2semidirect
8. #9126C2semidirect
10. #9122C2semidirect
12. #8227C2semidirect
13. #8226C2semidirect
14. C4×#330C2semidirect
15. C4×#329C2semidirect

Maximal subgroups

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

subgroupindex
#351352
#204802
#204652
#98942
#98912
#96882
#96872
#91262
#91242
#91222
#91202
#82272
#82262
C4×#3302
C4×#3292