Finite Group Databasebeta

← #158501

Subgroups — #158501

Order 512.

3064 conjugacy classes of subgroups.

The subgroup lattice has 713 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C22×#389C211yesmaximal, characteristic
3C2×#1442C212yesmaximal
4C2×#1441C212yesmaximal
5C2×#1441C212yesmaximal
6#7557C212yesmaximal
7#7557C214yesmaximal
8#7554C211yesmaximal, characteristic
9C23×C4⋊C4C2211yescharacteristic
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C42C2211yescharacteristic
16C2×#389—24no—
17C2×#389—24no—
18C2×#389—28no—
19C2×#389—28no—
20C22×#95C2212yes—
21C22×#95C2214yes—
22C22×#95C2212yes—
23C22×#95C2214yes—
24C22×#95C2214yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2214yes—
28C22×#95C2212yes—
29#1442—28no—
30#1441—28no—
31#1441—28no—
32C24×C4C2312yes—
33C24×C4C2312yes—
34C24×C4C2314yes—
35C24×C4C2312yes—
36C24×C4C2312yes—
37C24×C4C2311yescharacteristic
38C24×C4C2311yescharacteristic
39C24×C4C2311yescharacteristic
40C22×C4⋊C4—24no—
41C22×C4⋊C4—22no—
42C22×C4⋊C4—24no—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—24no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4—24no—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—24no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—28no—
64C22×C4⋊C4—42no—
65C22×C4⋊C4—42no—
66C22×C4⋊C4—44no—
67C22×C4⋊C4D414yes—
68C22×C4⋊C4D418yes—
69C22×C4⋊C4Q814yes—
70C22×C42—24no—
71C22×C42—24no—
72C22×C42—42no—
73C22×C42D414yes—
74#389—232no—
75#389—232no—
76C2×#95—24no—
77C2×#95—24no—
78C2×#95—24no—
79C2×#95—24no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—24no—
83C2×#95—28no—
84C2×#95—28no—
85C2×#95—28no—
86C2×#95—28no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—28no—
90C2×#95—28no—
91C2×#95—28no—
92C2×#95—24no—
93C2×#95—28no—
94C2×#95—24no—
95C2×#95—44no—
96C2×#95—44no—
97C2×#95—44no—
98C2×#95—44no—
99C2×#95—42no—
100C2×#95—42no—
101C2×#95D418yes—
102C2×#95Q818yes—
103C25C2411yescharacteristic
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—22no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—24no—
127C23×C4—24no—
128C23×C4—22no—
129C23×C4—24no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—21no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—21no—
137C23×C4—22no—
138C23×C4—24no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—24no—
145C23×C4—24no—
146C23×C4—24no—
147C23×C4—24no—
148C23×C4—24no—
149C23×C4—22no—
150C23×C4—22no—
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—24no—
160C23×C4—24no—
161C23×C4—24no—
162C23×C4—22no—
163C23×C4—24no—
164C23×C4—24no—
165C23×C4—24no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—24no—
170C23×C4—24no—
171C23×C4—24no—
172C23×C4—24no—
173C23×C4C2×D414yes—
174C23×C4C2×D414yes—
175C23×C4C2×D414yes—
176C23×C4C2×D414yes—
177C23×C4C2×D414yes—
178C23×C4C2×D412yes—
179C23×C4C2×D414yes—
180C23×C4C2×D412yes—
181C23×C4C2×D412yes—
182C23×C4C2×D414yes—
183C23×C4C2×D412yes—
184C23×C4C2×Q818yes—
185C23×C4C2×Q814yes—
186C23×C4C2×Q812yes—
187C23×C4C2×Q814yes—
188C23×C4#4114yes—
189C23×C4#4114yes—
190C23×C4#4114yes—
191C23×C4#4112yes—
192C23×C4#4114yes—
193C23×C4#4112yes—
194C2×C4⋊C4—28no—
195C2×C4⋊C4—28no—
196C2×C4⋊C4—216no—
197C2×C4⋊C4—216no—
198C2×C4⋊C4—28no—
199C2×C4⋊C4—28no—
200C2×C4⋊C4—216no—
201C2×C4⋊C4—28no—
202C2×C4⋊C4—216no—
203C2×C4⋊C4—28no—
204C2×C4⋊C4—28no—
205C2×C4⋊C4—28no—
206C2×C4⋊C4—216no—
207C2×C4⋊C4—216no—
208C2×C4⋊C4—216no—
209C2×C4⋊C4—216no—
210C2×C4⋊C4—416no—
211C2×C4⋊C4—416no—
212C2×C4⋊C4—416no—
213C2×C4⋊C4—416no—
214C2×C4⋊C4—44no—
215C2×C4⋊C4—44no—
216C2×C4⋊C4—48no—
217C2×C4⋊C4—44no—
218C2×C4⋊C4—44no—
219C2×C4⋊C4—48no—
220C2×C4⋊C4—48no—
221C2×C4⋊C4—48no—
222C2×C4⋊C4—48no—
223C2×C4⋊C4—48no—
224C2×C42—28no—
225C2×C42—28no—
226C2×C42—44no—
227C2×C42—416no—
228#95—216no—
229#95—216no—
230#95—216no—
231#95—416no—
232#95—416no—
233#95—416no—
234#95—48no—
235#95—416no—
236#95—48no—
237C24C22×D411yescharacteristic
238C24C22×D412yes—
239C24C22×D412yes—
240C24C22×D411yescharacteristic
241C24C22×Q811yescharacteristic
242C24C22×Q812yes—
243C24C2×#4111yescharacteristic
244C24C2×#4112yes—
245C24C2×#4112yes—
246C24C2×#4111yescharacteristic
247C24C2×#4112yes—
248C24C2×#4112yes—
249C24H(5,𝔽2)12yes—
250C24H(5,𝔽2)11yescharacteristic
251C24H(5,𝔽2)12yes—
252C242−1+411yescharacteristic
253C242−1+412yes—
254C242−1+412yes—
255C242−1+412yes—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—28no—
273C22×C4—28no—
274C22×C4—28no—
275C22×C4—28no—
276C22×C4—28no—
277C22×C4—28no—
278C22×C4—28no—
279C22×C4—28no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—24no—
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—24no—
295C22×C4—24no—
296C22×C4—28no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—28no—
306C22×C4—24no—
307C22×C4—28no—
308C22×C4—28no—
309C22×C4—28no—
310C22×C4—28no—
311C22×C4—28no—
312C22×C4—28no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—28no—
324C22×C4—24no—
325C22×C4—28no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—28no—
329C22×C4—28no—
330C22×C4—28no—
331C22×C4—28no—
332C22×C4—28no—
333C22×C4—28no—
334C22×C4—28no—
335C22×C4—28no—
336C22×C4—28no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—44no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—44no—
355C22×C4—44no—
356C22×C4—44no—
357C22×C4—42no—
358C22×C4—44no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—44no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—44no—
367C22×C4—42no—
368C22×C4—44no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—44no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—44no—
379C22×C4—44no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—44no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—44no—
386C22×C4—44no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—44no—
394C22×C4—44no—
395C22×C4—44no—
396C22×C4—44no—
397C22×C4—44no—
398C22×C4—44no—
399C22×C4—44no—
400C22×C4—44no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4—44no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—44no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4#12014yes—
434C22×C4#12014yes—
435C22×C4#12118yes—
436C22×C4#12118yes—
437C22×C4#12114yes—
438C22×C4C22⋊Q818yes—
439C22×C4C22⋊Q818yes—
440C22×C4C22⋊Q814yes—
441C22×C4#12318yes—
442C22×C4#12414yes—
443C22×C4#12414yes—
444C22×C4C4⋊Q814yes—
445C22×C4C4⋊Q818yes—
446C4⋊C4—232no—
447C4⋊C4—232no—
448C4⋊C4—416no—
449C4⋊C4—416no—
450C4⋊C4—432no—
451C4⋊C4—432no—
452C42—416no—
453C23C2×#12011yescharacteristic
454C23C2×#12011yescharacteristic
455C23C2×#12111yescharacteristic
456C23C2×#12112yes—
457C23C2×#12112yes—
458C23C2×C22⋊Q811yescharacteristic
459C23C2×C22⋊Q812yes—
460C23C2×C22⋊Q812yes—
461C23C2×#12312yes—
462C23#52511yescharacteristic
463C23#52511yescharacteristic
464C23#52512yes—
465C23#52512yes—
466C23C2×#12411yescharacteristic
467C23C2×#12411yescharacteristic
468C23#52914yes—
469C23C2×C4⋊Q811yescharacteristic
470C23C2×C4⋊Q812yes—
471C23#53314yes—
472C23#53411yescharacteristic
473C23#53511yescharacteristic
474C23#53512yes—
475C23#53611yescharacteristic
476C23#53611yescharacteristic
477C23#53611yescharacteristic
478C23#53612yes—
479C23#53711yescharacteristic
480C23#53712yes—
481C23#53712yes—
482C23#53712yes—
483C23#53812yes—
484C23#53912yes—
485C23#53912yes—
486C23#53912yes—
487C23#53914yes—
488C23#54114yes—
489C23#54114yes—
490C23#54412yes—
491C23#54414yes—
492C23D4214yes—
493C23#54612yes—
494C23#54614yes—
495C23#54714yes—
496C23#54714yes—
497C23#54712yes—
498C23#54814yes—
499C23#54814yes—
500C23D4×Q811yescharacteristic
501C23D4×Q812yes—
502C23D4×Q814yes—
503C23#55011yescharacteristic
504C23#55212yes—
505C23#55312yes—
506C23#55314yes—
507C23#55312yes—
508C23#55412yes—
509C23#55414yes—
510C23#55412yes—
511C23#55411yescharacteristic
512C23#55512yes—
513C23#55612yes—
514C23#55612yes—
515C23#55611yescharacteristic
516C23#55612yes—
517C23#55712yes—
518C23#55712yes—
519C23#55712yes—
520C23#55712yes—
521C23#56214yes—
522C23#56312yes—
523C23#56412yes—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—216no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—216no—
538C2×C4—216no—
539C2×C4—216no—
540C2×C4—28no—
541C2×C4—28no—
542C2×C4—24no—
543C2×C4—28no—
544C2×C4—216no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—28no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—48no—
563C2×C4—48no—
564C2×C4—48no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—48no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—48no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—48no—
582C2×C4—48no—
583C2×C4—48no—
584C2×C4—48no—
585C2×C4—44no—
586C2×C4—48no—
587C2×C4—48no—
588C2×C4—48no—
589C2×C4—48no—
590C2×C4—48no—
591C2×C4—48no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4—84no—
603C2×C4—84no—
604C2×C4—84no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4—84no—
608C2×C4—84no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4#39418yes—
613C2×C4#39518yes—
614C22C2×#39411yescharacteristic
615C22C2×#39511yescharacteristic
616C22#239811yescharacteristic
617C22#240311yescharacteristic
618C22#240611yescharacteristic
619C22#240611yescharacteristic
620C22#241412yes—
621C22#241614yes—
622C22#241712yes—
623C22#242514yes—
624C22#242914yes—
625C22#243411yescharacteristic
626C22#243511yescharacteristic
627C22#243611yescharacteristic
628C22#243611yescharacteristic
629C22#243914yes—
630C22#244014yes—
631C22#244314yes—
632C22#244614yes—
633C22#244914yes—
634C22#245314yes—
635C22#246614yes—
636C22#246914yes—
637C22#248512yes—
638C22#248712yes—
639C22#253511yescharacteristic
640C22#253812yes—
641C22#253811yescharacteristic
642C22#254612yes—
643C22#254611yescharacteristic
644C22#254711yescharacteristic
645C22#255014yes—
646C22#256211yescharacteristic
647C22#256311yescharacteristic
648C22#256811yescharacteristic
649C22#258111yescharacteristic
650C22#258112yes—
651C22#258311yescharacteristic
652C22#258411yescharacteristic
653C22#258412yes—
654C22#258714yes—
655C22#259014yes—
656C22#259111yescharacteristic
657C22#261511yescharacteristic
658C22#261611yescharacteristic
659C22#261811yescharacteristic
660C22#262711yescharacteristic
661C22#263311yescharacteristic
662C22#263411yescharacteristic
663C22#263911yescharacteristic
664C22#264211yescharacteristic
665C22#266011yescharacteristic
666C22#267614yes—
667C22#268114yes—
668C22#270414yes—
669C22#271914yes—
670C22#272014yes—
671C22#272514yes—
672C22#272612yes—
673C22#272614yes—
674C22#272712yes—
675C22#278314yes—
676C22#280214yes—
677C22#280214yes—
678C22#280512yes—
679C22#281012yes—
680C22#281611yescharacteristic
681C22#282211yescharacteristic
682C22#284711yescharacteristic
683C22#284811yescharacteristic
684C22#286211yescharacteristic
685C4—28no—
686C4—28no—
687C4—48no—
688C4—48no—
689C4—44no—
690C4—88no—
691C4—84no—
692C4—84no—
693C2#1471911yescharacteristic
694C2#1472011yescharacteristic
695C2#1486811yescharacteristic
696C2#1488411yescharacteristic
697C2#1515811yescharacteristic
698C2#1518111yescharacteristic
699C2#1518811yescharacteristic
700C2#1520711yescharacteristic
701C2#1523011yescharacteristic
702C2#1534914yes—
703C2#1536114yes—
704C2#1561814yes—
705C2#1596914yes—
706C2#1625311yescharacteristic
707C2#1660711yescharacteristic
708C2#1663411yescharacteristic
709C2#1699211yescharacteristic
710C2#1700811yescharacteristic
711C2#1707411yescharacteristic
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
#75572
#75542