Finite Group Databasebeta

← #158607

Subgroups — #158607

Order 512.

2804 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C2×#1442C212yesmaximal
3C2×#1441C212yesmaximal
4C2×#1441C212yesmaximal
5C2×C4⋊#95C211yesmaximal, characteristic
6#7557C212yesmaximal
7#7556C214yesmaximal
8#7554C211yesmaximal, characteristic
9C23×C4⋊C4C2212yes—
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C2×#389—24no—
16C2×#389—28no—
17C22×#95C2212yes—
18C22×#95C2214yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2214yes—
23C22×#95C2214yes—
24C22×#95C2212yes—
25C22×#95C2214yes—
26C22×#95C2212yes—
27#1442—28no—
28#1441—28no—
29#1441—28no—
30C4⋊#95—24no—
31C24×C4C2312yes—
32C24×C4C2312yes—
33C24×C4C2314yes—
34C24×C4C2312yes—
35C24×C4C2312yes—
36C24×C4C2311yescharacteristic
37C24×C4C2311yescharacteristic
38C24×C4C2311yescharacteristic
39C22×C4⋊C4—24no—
40C22×C4⋊C4—22no—
41C22×C4⋊C4—24no—
42C22×C4⋊C4—22no—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4—24no—
46C22×C4⋊C4—24no—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—24no—
53C22×C4⋊C4—24no—
54C22×C4⋊C4—24no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—42no—
58C22×C4⋊C4—42no—
59C22×C4⋊C4—42no—
60C22×C4⋊C4—42no—
61C22×C4⋊C4D418yes—
62C22×C4⋊C4D414yes—
63C22×C4⋊C4D414yes—
64C22×C42—24no—
65C22×C42—24no—
66C22×C42—42no—
67C22×C42D414yes—
68#389—232no—
69C2×#95—24no—
70C2×#95—24no—
71C2×#95—24no—
72C2×#95—24no—
73C2×#95—24no—
74C2×#95—24no—
75C2×#95—24no—
76C2×#95—28no—
77C2×#95—28no—
78C2×#95—28no—
79C2×#95—28no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—28no—
83C2×#95—28no—
84C2×#95—24no—
85C2×#95—28no—
86C2×#95—24no—
87C2×#95—28no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—28no—
91C2×#95—44no—
92C2×#95—44no—
93C2×#95—42no—
94C2×#95—42no—
95C2×#95—44no—
96C2×#95—44no—
97C2×#95Q818yes—
98C25C2411yescharacteristic
99C23×C4—22no—
100C23×C4—22no—
101C23×C4—22no—
102C23×C4—22no—
103C23×C4—22no—
104C23×C4—22no—
105C23×C4—22no—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—22no—
109C23×C4—22no—
110C23×C4—22no—
111C23×C4—22no—
112C23×C4—22no—
113C23×C4—22no—
114C23×C4—22no—
115C23×C4—22no—
116C23×C4—22no—
117C23×C4—21no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—21no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—24no—
132C23×C4—24no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—24no—
136C23×C4—24no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—24no—
143C23×C4—24no—
144C23×C4—24no—
145C23×C4—24no—
146C23×C4—24no—
147C23×C4—24no—
148C23×C4—24no—
149C23×C4—22no—
150C23×C4—24no—
151C23×C4—22no—
152C23×C4—24no—
153C23×C4—24no—
154C23×C4—24no—
155C23×C4—24no—
156C23×C4—24no—
157C23×C4—24no—
158C23×C4—24no—
159C23×C4—22no—
160C23×C4—24no—
161C23×C4—24no—
162C23×C4—24no—
163C23×C4—24no—
164C23×C4—24no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—24no—
168C23×C4—24no—
169C23×C4—22no—
170C23×C4C2×D414yes—
171C23×C4C2×D414yes—
172C23×C4C2×D414yes—
173C23×C4C2×D414yes—
174C23×C4C2×D412yes—
175C23×C4C2×D414yes—
176C23×C4C2×D412yes—
177C23×C4C2×D412yes—
178C23×C4C2×D412yes—
179C23×C4C2×D412yes—
180C23×C4C2×Q818yes—
181C23×C4C2×Q814yes—
182C23×C4#4114yes—
183C23×C4#4114yes—
184C23×C4#4114yes—
185C23×C4#4112yes—
186C23×C4#4114yes—
187C23×C4#4112yes—
188C23×C4#4114yes—
189C2×C4⋊C4—28no—
190C2×C4⋊C4—216no—
191C2×C4⋊C4—28no—
192C2×C4⋊C4—216no—
193C2×C4⋊C4—28no—
194C2×C4⋊C4—28no—
195C2×C4⋊C4—28no—
196C2×C4⋊C4—216no—
197C2×C4⋊C4—28no—
198C2×C4⋊C4—216no—
199C2×C4⋊C4—216no—
200C2×C4⋊C4—48no—
201C2×C4⋊C4—416no—
202C2×C4⋊C4—416no—
203C2×C4⋊C4—44no—
204C2×C4⋊C4—44no—
205C2×C4⋊C4—44no—
206C2×C4⋊C4—44no—
207C2×C4⋊C4—48no—
208C2×C4⋊C4—44no—
209C2×C4⋊C4—48no—
210C2×C4⋊C4—48no—
211C2×C4⋊C4—44no—
212C2×C4⋊C4—48no—
213C2×C4⋊C4—48no—
214C2×C42—28no—
215C2×C42—28no—
216C2×C42—44no—
217C2×C42—416no—
218#95—216no—
219#95—216no—
220#95—416no—
221#95—416no—
222#95—48no—
223#95—416no—
224#95—416no—
225#95—48no—
226#95—48no—
227#95—48no—
228C24C22×D411yescharacteristic
229C24C22×D412yes—
230C24C22×D411yescharacteristic
231C24C22×D411yescharacteristic
232C24C22×Q812yes—
233C24C2×#4111yescharacteristic
234C24C2×#4112yes—
235C24C2×#4111yescharacteristic
236C24C2×#4112yes—
237C24C2×#4112yes—
238C24C2×#4112yes—
239C24C2×#4112yes—
240C24H(5,𝔽2)12yes—
241C24H(5,𝔽2)12yes—
242C24H(5,𝔽2)11yescharacteristic
243C242−1+411yescharacteristic
244C242−1+412yes—
245C242−1+412yes—
246C242−1+412yes—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—28no—
264C22×C4—28no—
265C22×C4—28no—
266C22×C4—28no—
267C22×C4—28no—
268C22×C4—28no—
269C22×C4—28no—
270C22×C4—28no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—28no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—28no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—28no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—28no—
306C22×C4—28no—
307C22×C4—28no—
308C22×C4—28no—
309C22×C4—24no—
310C22×C4—28no—
311C22×C4—28no—
312C22×C4—28no—
313C22×C4—28no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—28no—
317C22×C4—28no—
318C22×C4—24no—
319C22×C4—28no—
320C22×C4—28no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—44no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—44no—
343C22×C4—42no—
344C22×C4—44no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—44no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—44no—
362C22×C4—44no—
363C22×C4—44no—
364C22×C4—44no—
365C22×C4—44no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—44no—
374C22×C4—44no—
375C22×C4—44no—
376C22×C4—42no—
377C22×C4—44no—
378C22×C4—44no—
379C22×C4—44no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—44no—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4—44no—
386C22×C4—44no—
387C22×C4—44no—
388C22×C4—44no—
389C22×C4—44no—
390C22×C4—44no—
391C22×C4—44no—
392C22×C4—44no—
393C22×C4—44no—
394C22×C4—44no—
395C22×C4—44no—
396C22×C4—44no—
397C22×C4—42no—
398C22×C4—44no—
399C22×C4—44no—
400C22×C4—44no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4—42no—
404C22×C4—44no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—42no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—42no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4#12014yes—
426C22×C4#12118yes—
427C22×C4#12118yes—
428C22×C4#12114yes—
429C22×C4#12114yes—
430C22×C4C22⋊Q818yes—
431C22×C4#12318yes—
432C22×C4#12314yes—
433C22×C4#12414yes—
434C22×C4#12414yes—
435C22×C4#12518yes—
436C22×C4C4⋊Q814yes—
437C4⋊C4—232no—
438C4⋊C4—416no—
439C4⋊C4—416no—
440C4⋊C4—416no—
441C4⋊C4—432no—
442C42—416no—
443C23C2×#12011yescharacteristic
444C23C2×#12111yescharacteristic
445C23C2×#12112yes—
446C23C2×#12111yescharacteristic
447C23C2×#12112yes—
448C23C2×C22⋊Q812yes—
449C23C2×#12311yescharacteristic
450C23C2×#12312yes—
451C23#52511yescharacteristic
452C23#52511yescharacteristic
453C23#52512yes—
454C23C2×#12411yescharacteristic
455C23C2×#12411yescharacteristic
456C23C2×#12512yes—
457C23#52914yes—
458C23#52912yes—
459C23C2×C4⋊Q811yescharacteristic
460C23#53212yes—
461C23#53314yes—
462C23#53411yescharacteristic
463C23#53412yes—
464C23#53511yescharacteristic
465C23#53611yescharacteristic
466C23#53611yescharacteristic
467C23#53611yescharacteristic
468C23#53612yes—
469C23#53711yescharacteristic
470C23#53712yes—
471C23#53712yes—
472C23#53812yes—
473C23#53812yes—
474C23#53912yes—
475C23#53912yes—
476C23#54112yes—
477C23#54114yes—
478C23#54114yes—
479C23#54212yes—
480C23#54214yes—
481C23#54414yes—
482C23D4211yescharacteristic
483C23#54614yes—
484C23#54614yes—
485C23#54711yescharacteristic
486C23#54712yes—
487C23#54712yes—
488C23#54711yescharacteristic
489C23#54812yes—
490C23#54812yes—
491C23#54814yes—
492C23D4×Q814yes—
493C23D4×Q812yes—
494C23#55012yes—
495C23#55212yes—
496C23#55214yes—
497C23#55214yes—
498C23#55212yes—
499C23#55212yes—
500C23#55312yes—
501C23#55314yes—
502C23#55314yes—
503C23#55414yes—
504C23#55412yes—
505C23#55511yescharacteristic
506C23#55612yes—
507C23#55612yes—
508C23#55712yes—
509C23#55712yes—
510C23#55912yes—
511C23#56212yes—
512C23#56314yes—
513C23#56312yes—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—216no—
524C2×C4—24no—
525C2×C4—216no—
526C2×C4—216no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—216no—
530C2×C4—28no—
531C2×C4—24no—
532C2×C4—28no—
533C2×C4—24no—
534C2×C4—28no—
535C2×C4—24no—
536C2×C4—42no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—48no—
547C2×C4—48no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—48no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—48no—
562C2×C4—48no—
563C2×C4—48no—
564C2×C4—48no—
565C2×C4—48no—
566C2×C4—48no—
567C2×C4—48no—
568C2×C4—48no—
569C2×C4—48no—
570C2×C4—48no—
571C2×C4—48no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—48no—
575C2×C4—44no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—84no—
585C2×C4—84no—
586C2×C4—84no—
587C2×C4—84no—
588C2×C4—82no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—84no—
592C2×C4—84no—
593C2×C4—84no—
594C2×C4—82no—
595C2×C4—84no—
596C2×C4—84no—
597C2×C4—84no—
598C2×C4—84no—
599C2×C4—82no—
600C2×C4—82no—
601C2×C4—84no—
602C2×C4#39418yes—
603C2×C4#39818yes—
604C22C2×#39411yescharacteristic
605C22C2×#39811yescharacteristic
606C22#239811yescharacteristic
607C22#240411yescharacteristic
608C22#240511yescharacteristic
609C22#241512yes—
610C22#241612yes—
611C22#241714yes—
612C22#242614yes—
613C22#242914yes—
614C22#243411yescharacteristic
615C22#243611yescharacteristic
616C22#244114yes—
617C22#244414yes—
618C22#244614yes—
619C22#245212yes—
620C22#245312yes—
621C22#245814yes—
622C22#247314yes—
623C22#248411yescharacteristic
624C22#248512yes—
625C22#248612yes—
626C22#250311yescharacteristic
627C22#250411yescharacteristic
628C22#250612yes—
629C22#250812yes—
630C22#251914yes—
631C22#253314yes—
632C22#253611yescharacteristic
633C22#253611yescharacteristic
634C22#253711yescharacteristic
635C22#254314yes—
636C22#254611yescharacteristic
637C22#254711yescharacteristic
638C22#254711yescharacteristic
639C22#254811yescharacteristic
640C22#256211yescharacteristic
641C22#257014yes—
642C22#258311yescharacteristic
643C22#258411yescharacteristic
644C22#258714yes—
645C22#259014yes—
646C22#259111yescharacteristic
647C22#261611yescharacteristic
648C22#261711yescharacteristic
649C22#261811yescharacteristic
650C22#262511yescharacteristic
651C22#263211yescharacteristic
652C22#263411yescharacteristic
653C22#263911yescharacteristic
654C22#264211yescharacteristic
655C22#266011yescharacteristic
656C22#268212yes—
657C22#269014yes—
658C22#270214yes—
659C22#270414yes—
660C22#271314yes—
661C22#272412yes—
662C22#272514yes—
663C22#272712yes—
664C22#272914yes—
665C22#276614yes—
666C22#277214yes—
667C22#277414yes—
668C22#277614yes—
669C22#280812yes—
670C22#281711yescharacteristic
671C22#282011yescharacteristic
672C22#284711yescharacteristic
673C22#285411yescharacteristic
674C22#286211yescharacteristic
675C4—28no—
676C4—28no—
677C4—48no—
678C4—44no—
679C4—88no—
680C4—84no—
681C4—84no—
682C4—84no—
683C2#1482111yescharacteristic
684C2#1488311yescharacteristic
685C2#1491311yescharacteristic
686C2#1509011yescharacteristic
687C2#1512911yescharacteristic
688C2#1514911yescharacteristic
689C2#1518811yescharacteristic
690C2#1520711yescharacteristic
691C2#1524211yescharacteristic
692C2#1551814yes—
693C2#1562014yes—
694C2#1588814yes—
695C2#1599914yes—
696C2#1636611yescharacteristic
697C2#1660811yescharacteristic
698C2#1696311yescharacteristic
699C2#1699311yescharacteristic
700C2#1701011yescharacteristic
701C2#1706911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Maximal subgroups

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

subgroupindex
C22×#3892
C2×#14422
C2×#14412
C2×C4⋊#952
#75572
#75562
#75542