Finite Group Databasebeta

← #441874

Subgroups — #441874

Order 512.

1152 conjugacy classes of subgroups.

The subgroup lattice has 717 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2097C211yesmaximal, characteristic
2C2×#2072C211yesmaximal, characteristic
3C2×#2056C211yesmaximal, characteristic
4C2×#1969C211yesmaximal, characteristic
5C2×#1947C211yesmaximal, characteristic
6C2×#1927C211yesmaximal, characteristic
7#15240C211yesmaximal, characteristic
8#14003C211yesmaximal, characteristic
9#11325C211yesmaximal, characteristic
10#11124C211yesmaximal, characteristic
11#11052C211yesmaximal, characteristic
12#11052C211yesmaximal, characteristic
13#11024C211yesmaximal, characteristic
14#10876C211yesmaximal, characteristic
15#10842C211yesmaximal, characteristic
16C23×Q16C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×#382C2211yescharacteristic
36C2×#382C2211yescharacteristic
37C2×#382C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39#2097—24no—
40#2072—24no—
41#2056—24no—
42#1969—24no—
43#1947—24no—
44#1927—24no—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1445—22no—
56#1445—22no—
57#1443—22no—
58C4⋊#95C2211yescharacteristic
59#1434—22no—
60C4×#95C2211yescharacteristic
61C23×Q8C2311yescharacteristic
62C23×Q8C2311yescharacteristic
63C22×Q16—22no—
64C22×Q16—22no—
65C22×Q16—22no—
66C22×Q16—22no—
67C22×Q16—22no—
68C22×Q16—41no—
69C22×Q16—41no—
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C42—21no—
83C22×C42C2311yescharacteristic
84C22×C42C2311yescharacteristic
85C22×C42C2311yescharacteristic
86C2×#107—22no—
87C2×#107—22no—
88C2×#107—22no—
89C2×#107—22no—
90C2×#107—41no—
91C2×#107—41no—
92C2×#106—22no—
93C2×#106—22no—
94C2×#106—41no—
95C2×C4⋊C8—22no—
96C2×C4⋊C8—22no—
97C2×C4⋊C8D414yes—
98C2×#103—22no—
99C2×#103—22no—
100C2×#103—22no—
101C2×#103—22no—
102C2×#103—22no—
103C2×#103—22no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—22no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103—41no—
115C2×#103—41no—
116C2×C4×C8—22no—
117C2×C4×C8—22no—
118C2×C4×C8—41no—
119#391—22no—
120#391—22no—
121#391—22no—
122#391—22no—
123#391—22no—
124#391—22no—
125#391—22no—
126#391—22no—
127#391—41no—
128#391—41no—
129#391—41no—
130#391D414yes—
131#384—22no—
132#384—22no—
133#382—22no—
134#382—22no—
135#382—22no—
136#382—41no—
137#382—41no—
138#382—41no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4—22no—
141C2×#95—22no—
142C2×#95—21no—
143C2×#95—22no—
144C2×#95—22no—
145C2×#95—22no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—22no—
149C2×#95—22no—
150C2×#95—22no—
151C2×#95—22no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95D412yes—
155C2×#95D412yes—
156#340—22no—
157#340—22no—
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#336—22no—
163#336—22no—
164#336—41no—
165#336D414yes—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172C22×Q8—21no—
173C22×Q8—21no—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8C2×D412yes—
193C22×Q8#4112yes—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4C2×D412yes—
203C23×C4C2×D412yes—
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2411yescharacteristic
207C2×Q16—28no—
208C2×Q16—44no—
209C2×Q16—44no—
210C2×Q16—44no—
211C2×Q16—44no—
212C2×Q16—44no—
213C2×Q16—44no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8C2×D412yes—
237C22×C8C2×D412yes—
238C22×C8C2×D412yes—
239C22×C8C2×D412yes—
240C22×C8#4112yes—
241C22×C8#4112yes—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
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⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—44no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4C2×D412yes—
281C2×C4⋊C4#4112yes—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—42no—
297C2×C42—44no—
298C2×C42C2×D412yes—
299C2×C42C2×D412yes—
300C2×C42C2×D412yes—
301C2×C42#4112yes—
302#107—44no—
303#107—44no—
304#106—44no—
305C4⋊C8—28no—
306#103—28no—
307#103—44no—
308#103—44no—
309#103—44no—
310#103—44no—
311#103—44no—
312C4×C8—44no—
313#95—28no—
314#95—24no—
315#95—42no—
316#95—44no—
317#95—44no—
318#95—44no—
319#95—44no—
320#95—44no—
321#95—44no—
322#95—44no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—42no—
328C24C22×D411yescharacteristic
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8—41no—
366C2×Q8—41no—
367C2×Q8—41no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8—41no—
373C2×Q8—41no—
374C2×Q8—41no—
375C2×Q8—41no—
376C2×Q8—41no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4#12114yes—
450C22×C4#12712yes—
451C22×C4#12712yes—
452C22×C4#13514yes—
453C22×C4C22×D411yescharacteristic
454C22×C4C22×D411yescharacteristic
455C22×C4C22×D411yescharacteristic
456C22×C4C2×#4111yescharacteristic
457C22×C4C2×#4111yescharacteristic
458C22×C4C2×#4111yescharacteristic
459C22×C4C2×#4111yescharacteristic
460C22×C4C2×#4111yescharacteristic
461C22×C4H(5,𝔽2)11yescharacteristic
462C22×C4H(5,𝔽2)11yescharacteristic
463C22×C4H(5,𝔽2)11yescharacteristic
464C22×C42−1+411yescharacteristic
465C22×C42−1+411yescharacteristic
466C22×C42−1+411yescharacteristic
467Q16—416no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8#12314yes—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—84no—
521C4⋊C4—84no—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—41no—
531C42—41no—
532C42—41no—
533C42—41no—
534C42—84no—
535C23C2×#12111yescharacteristic
536C23C2×#12711yescharacteristic
537C23#53511yescharacteristic
538C23#54611yescharacteristic
539C23#54711yescharacteristic
540C23#54711yescharacteristic
541C23#54811yescharacteristic
542C23C2×#13512yes—
543C23#57512yes—
544C23#57812yes—
545C23#57812yes—
546Q8—42no—
547Q8—42no—
548Q8—42no—
549Q8—42no—
550Q8—42no—
551Q8—42no—
552Q8—42no—
553Q8—42no—
554Q8—81no—
555Q8—81no—
556Q8—81no—
557Q8—81no—
558Q8—81no—
559Q8—81no—
560Q8—81no—
561Q8—81no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—42no—
589C2×C4—44no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—82no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4—81no—
601C2×C4—82no—
602C2×C4—81no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—81no—
609C2×C4—82no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—81no—
618C2×C4—82no—
619C2×C4—82no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—82no—
623C2×C4—82no—
624C2×C4—81no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4—81no—
628C2×C4—82no—
629C2×C4#49514yes—
630C2×C4C2×#12311yescharacteristic
631C2×C4#52511yescharacteristic
632C2×C4#52511yescharacteristic
633C2×C4#52911yescharacteristic
634C2×C4#53611yescharacteristic
635C2×C4#53611yescharacteristic
636C2×C4#53711yescharacteristic
637C2×C4#53811yescharacteristic
638C2×C4#53911yescharacteristic
639C2×C4#53911yescharacteristic
640C2×C4#54211yescharacteristic
641C2×C4#54211yescharacteristic
642C2×C4D4211yescharacteristic
643C2×C4D4211yescharacteristic
644C2×C4#54611yescharacteristic
645C2×C4#54611yescharacteristic
646C2×C4#54711yescharacteristic
647C2×C4#54711yescharacteristic
648C2×C4#54711yescharacteristic
649C2×C4#54811yescharacteristic
650C2×C4#55011yescharacteristic
651C2×C4#55011yescharacteristic
652C2×C4#55111yescharacteristic
653C2×C4#55211yescharacteristic
654C2×C4#55611yescharacteristic
655C2×C4#55911yescharacteristic
656C2×C4#56211yescharacteristic
657C2×C4#56311yescharacteristic
658C8—24no—
659C8—42no—
660C8—42no—
661C8—42no—
662C22#241511yescharacteristic
663C22#242511yescharacteristic
664C22#250111yescharacteristic
665C22#254011yescharacteristic
666C22#254111yescharacteristic
667C22#271011yescharacteristic
668C22#272311yescharacteristic
669C22#303512yes—
670C22#304412yes—
671C22C2×#49511yescharacteristic
672C22#315311yescharacteristic
673C22#315611yescharacteristic
674C22#315611yescharacteristic
675C22#321212yes—
676C22#322312yes—
677C22#330212yes—
678C22#331312yes—
679C22#333612yes—
680C22#333612yes—
681C22#334912yes—
682C22#335212yes—
683C22#336412yes—
684C22#337712yes—
685C4—24no—
686C4—42no—
687C4—44no—
688C4—82no—
689C4—82no—
690C4—82no—
691C4—82no—
692C4—82no—
693C4—161no—
694C4—161no—
695C4—161no—
696C4—161no—
697C4#241811yescharacteristic
698C4#244811yescharacteristic
699C4#245511yescharacteristic
700C4#247911yescharacteristic
701C4#267211yescharacteristic
702C4#267411yescharacteristic
703C4#269411yescharacteristic
704C4#272711yescharacteristic
705C2#1569611yescharacteristic
706C2#2468712yes—
707C2#2521512yes—
708C2#2793111yescharacteristic
709C2#2794311yescharacteristic
710C2#2840311yescharacteristic
711C2#2842411yescharacteristic
712C2#2843911yescharacteristic
713C2#2845611yescharacteristic
714C2#3205512yes—
715C2#3243412yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#20972
C2×#20722
C2×#20562
C2×#19692
C2×#19472
C2×#19272
#152402
#140032
#113252
#111242
#110522
#110242
#108762
#108422