Finite Group Databasebeta

← #759898

Subgroups — #759898

Order 512.

2258 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2568C211yesmaximal, characteristic
2C2×C4×C4⋊Q8C211yesmaximal, characteristic
3#16576C214yesmaximal
4#15241C212yesmaximal
5#15232C212yesmaximal
6#15186C212yesmaximal
7#15186C212yesmaximal
8#14858C214yesmaximal
9#14155C211yesmaximal, characteristic
10#14021C212yesmaximal
11#13978C212yesmaximal
12#13931C212yesmaximal
13#13926C211yesmaximal, characteristic
14#13911C211yesmaximal, characteristic
15#13885C212yesmaximal
16C4×#391C211yesmaximal, characteristic
17C4×#389C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×C4×Q8C2212yes—
21#2568—28no—
22C2×#400C2214yes—
23C4×C4⋊Q8—28no—
24C2×#391C2212yes—
25C2×#391C2211yescharacteristic
26C2×#391C2212yes—
27C2×#391C2212yes—
28C2×#391C2212yes—
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#391C2211yescharacteristic
32C2×#391C2212yes—
33C2×#389C2211yescharacteristic
34C2×#389C2212yes—
35C2×#389C2211yescharacteristic
36C2×#389C2212yes—
37C2×#384C2211yescharacteristic
38C2×#382C2212yes—
39C2×#382C2212yes—
40C2×C4×C4⋊C4C2212yes—
41C2×C4×C4⋊C4C2212yes—
42C2×C4×C4⋊C4C2212yes—
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C43C2211yescharacteristic
47#1445C2214yes—
48#1445C2214yes—
49#1445C2214yes—
50#1445C2214yes—
51#1443C2214yes—
52#1443C2214yes—
53#1443C2214yes—
54#1443C2214yes—
55#1443C2214yes—
56#1443C2214yes—
57#1442C2214yes—
58#1442C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1441C2214yes—
62#1436C2212yes—
63#1436C2212yes—
64#1436C2214yes—
65#1436C2214yes—
66#1436C2212yes—
67#1436C2212yes—
68C4⋊#95C2211yescharacteristic
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80#1434C2214yes—
81#1434C2214yes—
82C4×#95C2212yes—
83C4×#95C2212yes—
84C4×#95C2212yes—
85C23×Q8C2312yes—
86C23×Q8C2311yescharacteristic
87C2×C4⋊Q8—24no—
88C2×C4⋊Q8—24no—
89C2×C4⋊Q8D418yes—
90C2×C4×Q8—28no—
91C2×C4×Q8—24no—
92C2×C4×Q8—28no—
93C2×C4×Q8—24no—
94C2×C4×Q8—24no—
95C2×C4×Q8—44no—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2312yes—
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C42C2312yes—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115C22×C42C2312yes—
116C22×C42C2312yes—
117C22×C42C2312yes—
118C22×C42C2311yescharacteristic
119C22×C42C2314yes—
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124#400—216no—
125#391—28no—
126#391—28no—
127#391—28no—
128#391—24no—
129#391—28no—
130#391—28no—
131#391—28no—
132#391—24no—
133#391—44no—
134#389—28no—
135#389—28no—
136#389—24no—
137#389—24no—
138#384—24no—
139#382—28no—
140#382—44no—
141C4×C4⋊C4—28no—
142C4×C4⋊C4—28no—
143C4×C4⋊C4—24no—
144C4×C4⋊C4—28no—
145C4×C4⋊C4—24no—
146C4×C4⋊C4—24no—
147C2×#95C2312yes—
148C2×#95C2314yes—
149C2×#95C2314yes—
150C2×#95C2314yes—
151C2×#95C2314yes—
152C2×#95C2312yes—
153C2×#95C2312yes—
154C2×#95C2312yes—
155C2×#95C2312yes—
156C2×#95C2312yes—
157C2×#95C2312yes—
158C2×#95C2312yes—
159C2×#95C2312yes—
160C2×#95C2312yes—
161C2×#95C2312yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C43—24no—
183C22×Q8—22no—
184C22×Q8—22no—
185C22×Q8—22no—
186C22×Q8—24no—
187C22×Q8—24no—
188C22×Q8—24no—
189C22×Q8—24no—
190C22×Q8—22no—
191C22×Q8—24no—
192C22×Q8—22no—
193C22×Q8—22no—
194C22×Q8—24no—
195C22×Q8C2×D418yes—
196C22×Q8#4114yes—
197C23×C4C2414yes—
198C23×C4C2412yes—
199C23×C4C2412yes—
200C23×C4C2412yes—
201C23×C4C2412yes—
202C23×C4C2412yes—
203C23×C4C2412yes—
204C23×C4C2414yes—
205C23×C4C2411yescharacteristic
206C23×C4C2412yes—
207C23×C4C2411yescharacteristic
208C23×C4C2412yes—
209C23×C4C2411yescharacteristic
210C23×C4C2411yescharacteristic
211C23×C4C2411yescharacteristic
212C23×C4C2411yescharacteristic
213C23×C4C2411yescharacteristic
214C4⋊Q8—232no—
215C4×Q8—432no—
216C4×Q8—416no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—28no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—28no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4—44no—
262C2×C4⋊C4C2×D418yes—
263C2×C4⋊C4C2×D418yes—
264C2×C4⋊C4#4114yes—
265C2×C42—22no—
266C2×C42—22no—
267C2×C42—22no—
268C2×C42—22no—
269C2×C42—22no—
270C2×C42—22no—
271C2×C42—22no—
272C2×C42—28no—
273C2×C42—24no—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42—24no—
278C2×C42—28no—
279C2×C42—24no—
280C2×C42—24no—
281C2×C42—24no—
282C2×C42—24no—
283C2×C42—24no—
284C2×C42—24no—
285C2×C42—22no—
286C2×C42—24no—
287C2×C42—22no—
288C2×C42—24no—
289C2×C42—24no—
290C2×C42—22no—
291C2×C42—22no—
292C2×C42—24no—
293C2×C42—44no—
294C2×C42—41no—
295C2×C42—41no—
296C2×C42C2×D414yes—
297C2×C42#4114yes—
298C2×C42#4114yes—
299C2×C42#4114yes—
300C2×C42#4114yes—
301#95—28no—
302#95—28no—
303#95—24no—
304#95—28no—
305#95—28no—
306#95—28no—
307#95—28no—
308#95—24no—
309#95—24no—
310#95—24no—
311#95—24no—
312#95—24no—
313#95—24no—
314#95—24no—
315#95—24no—
316#95—28no—
317#95—28no—
318#95—28no—
319#95—24no—
320#95—24no—
321#95—28no—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—42no—
326#95—42no—
327#95—42no—
328#95—44no—
329#95—44no—
330#95—44no—
331#95—44no—
332#95—44no—
333#95—44no—
334#95—44no—
335#95—44no—
336C24C2511yescharacteristic
337C2×Q8—216no—
338C2×Q8—28no—
339C2×Q8—216no—
340C2×Q8—216no—
341C2×Q8—28no—
342C2×Q8—28no—
343C2×Q8—44no—
344C2×Q8—48no—
345C2×Q8—44no—
346C2×Q8—48no—
347C2×Q8—44no—
348C2×Q8—44no—
349C2×Q8—48no—
350C2×Q8—48no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4C22×D418yes—
445C22×C4C22×D412yes—
446C22×C4C22×D412yes—
447C22×C4C22×D412yes—
448C22×C4C2×#4114yes—
449C22×C4C2×#4114yes—
450C22×C4C2×#4112yes—
451C22×C4C2×#4112yes—
452C22×C4C2×#4112yes—
453C22×C4C2×#4112yes—
454C22×C4C2×#4112yes—
455C22×C4C2×#4112yes—
456C22×C4C2×#4112yes—
457C22×C4C2×#4112yes—
458C22×C4C2×#4112yes—
459C22×C4C2×#4112yes—
460C22×C4C2×#4112yes—
461C22×C4C2×#4112yes—
462C22×C4C2×#4112yes—
463C22×C4C2×#4112yes—
464C22×C4H(5,𝔽2)12yes—
465C22×C42−1+412yes—
466C22×C42−1+412yes—
467C22×C42−1+412yes—
468C22×C42−1+412yes—
469C22×C42−1+412yes—
470C4⋊C4—216no—
471C4⋊C4—216no—
472C4⋊C4—28no—
473C4⋊C4—48no—
474C4⋊C4—416no—
475C4⋊C4—48no—
476C4⋊C4—48no—
477C4⋊C4—44no—
478C4⋊C4—44no—
479C4⋊C4—44no—
480C4⋊C4—48no—
481C4⋊C4—44no—
482C4⋊C4—48no—
483C4⋊C4—44no—
484C4⋊C4—48no—
485C4⋊C4—44no—
486C42—28no—
487C42—28no—
488C42—28no—
489C42—416no—
490C42—44no—
491C42—48no—
492C42—48no—
493C42—44no—
494C42—44no—
495C42—48no—
496C42—48no—
497C42#123116yes—
498C23C23×D411yescharacteristic
499C23C22×#4111yescharacteristic
500C23C22×#4111yescharacteristic
501C23C22×#4111yescharacteristic
502C23C22×#4111yescharacteristic
503C23C22×#4111yescharacteristic
504C23C22×#4111yescharacteristic
505C23C2×H(5,𝔽2)11yescharacteristic
506C23C2×2−1+411yescharacteristic
507C23C2×2−1+411yescharacteristic
508C23C2×2−1+411yescharacteristic
509C23C2×2−1+411yescharacteristic
510C23C2×2−1+411yescharacteristic
511C23#58511yescharacteristic
512C23#58511yescharacteristic
513Q8—416no—
514Q8—432no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—28no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—28no—
532C2×C4—28no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—44no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—44no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4C2×#12314yes—
619C2×C4C2×#12314yes—
620C2×C4C2×#12314yes—
621C2×C4#52914yes—
622C2×C4#52914yes—
623C2×C4#54114yes—
624C2×C4#54214yes—
625C2×C4#54614yes—
626C2×C4#54714yes—
627C2×C4#54814yes—
628C2×C4#54814yes—
629C2×C4#55214yes—
630C2×C4#55614yes—
631C2×C4#55614yes—
632C2×C4#55614yes—
633C2×C4#55914yes—
634C22C22×#12311yescharacteristic
635C22C2×#52911yescharacteristic
636C22C2×#52911yescharacteristic
637C22C2×#54111yescharacteristic
638C22C2×#54211yescharacteristic
639C22#346111yescharacteristic
640C22#346111yescharacteristic
641C22C2×#54611yescharacteristic
642C22C2×#54711yescharacteristic
643C22C2×#54811yescharacteristic
644C22C2×#54811yescharacteristic
645C22C2×#55211yescharacteristic
646C22C2×#55611yescharacteristic
647C22C2×#55611yescharacteristic
648C22C2×#55611yescharacteristic
649C22#347511yescharacteristic
650C22C2×#55911yescharacteristic
651C22#348011yescharacteristic
652C22#348211yescharacteristic
653C22#348611yescharacteristic
654C22#348711yescharacteristic
655C22#350711yescharacteristic
656C22#350711yescharacteristic
657C22#350711yescharacteristic
658C22#350711yescharacteristic
659C22#350911yescharacteristic
660C22#351111yescharacteristic
661C22#351711yescharacteristic
662C22#351811yescharacteristic
663C22#352311yescharacteristic
664C22#352311yescharacteristic
665C22#355211yescharacteristic
666C22#355411yescharacteristic
667C22#355511yescharacteristic
668C22#355611yescharacteristic
669C4—24no—
670C4—24no—
671C4—44no—
672C4—48no—
673C4—44no—
674C4—42no—
675C4—42no—
676C4—42no—
677C4—82no—
678C4—82no—
679C4—82no—
680C4—82no—
681C4—84no—
682C4—82no—
683C4—82no—
684C4#242118yes—
685C4#244718yes—
686C2C2×#244711yescharacteristic
687C2C2×#242111yescharacteristic
688C2#3494511yescharacteristic
689C2#3518211yescharacteristic
690C2#3518411yescharacteristic
691C2#3518711yescharacteristic
692C2#3763011yescharacteristic
693C2#5906511yescharacteristic
694C2#5907111yescharacteristic
695C2#5907811yescharacteristic
696C2#5913411yescharacteristic
697C2#5944311yescharacteristic
698C2#5945111yescharacteristic
699C2#5963911yescharacteristic
700C2#5987511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25682
C2×C4×C4⋊Q82
#165762
#152412
#152322
#151862
#148582
#141552
#140212
#139782
#139312
#139262
#139112
#138852
C4×#3912
C4×#3892