Finite Group Databasebeta

← #158597

Subgroups — #158597

Order 512.

2908 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#384C211yesmaximal, characteristic
2C2×#1445C212yesmaximal
3C2×#1445C212yesmaximal
4C2×#1442C212yesmaximal
5C2×#1441C212yesmaximal
6C2×#1436C211yesmaximal, characteristic
7#7557C212yesmaximal
8#7557C212yesmaximal
9#7554C211yesmaximal, characteristic
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2212yes—
12C23×C4⋊C4C2212yes—
13C23×C4⋊C4C2212yes—
14C23×C42C2211yescharacteristic
15C2×#384—24no—
16C2×#384—28no—
17C22×#95C2214yes—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2211yescharacteristic
21C22×#95C2211yescharacteristic
22C22×#95C2211yescharacteristic
23C22×#95C2214yes—
24C22×#95C2214yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2214yes—
29#1445—28no—
30#1445—28no—
31#1442—28no—
32#1441—28no—
33#1436—24no—
34C24×C4C2314yes—
35C24×C4C2311yescharacteristic
36C24×C4C2311yescharacteristic
37C24×C4C2311yescharacteristic
38C24×C4C2314yes—
39C24×C4C2311yescharacteristic
40C24×C4C2311yescharacteristic
41C24×C4C2311yescharacteristic
42C24×C4C2311yescharacteristic
43C22×C4⋊C4—22no—
44C22×C4⋊C4—24no—
45C22×C4⋊C4—28no—
46C22×C4⋊C4—28no—
47C22×C4⋊C4—24no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—24no—
54C22×C4⋊C4—24no—
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—44no—
62C22×C4⋊C4—44no—
63C22×C4⋊C4D414yes—
64C22×C4⋊C4D418yes—
65C22×C42—24no—
66C22×C42—24no—
67C22×C42—24no—
68C22×C42D414yes—
69#384—232no—
70C2×#95—22no—
71C2×#95—22no—
72C2×#95—24no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—24no—
76C2×#95—22no—
77C2×#95—22no—
78C2×#95—22no—
79C2×#95—28no—
80C2×#95—24no—
81C2×#95—28no—
82C2×#95—28no—
83C2×#95—28no—
84C2×#95—28no—
85C2×#95—28no—
86C2×#95—28no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—28no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—44no—
97C2×#95—44no—
98C2×#95—44no—
99C2×#95—44no—
100C2×#95D414yes—
101C2×#95D414yes—
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—21no—
117C23×C4—21no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—24no—
125C23×C4—24no—
126C23×C4—21no—
127C23×C4—24no—
128C23×C4—24no—
129C23×C4—24no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—24no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—24no—
136C23×C4—24no—
137C23×C4—24no—
138C23×C4—24no—
139C23×C4—21no—
140C23×C4—24no—
141C23×C4—24no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—24no—
145C23×C4—24no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—24no—
149C23×C4—24no—
150C23×C4—24no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—24no—
156C23×C4—24no—
157C23×C4—24no—
158C23×C4—24no—
159C23×C4—24no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—24no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—24no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—24no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—24no—
174C23×C4—24no—
175C23×C4—24no—
176C23×C4C2×D418yes—
177C23×C4C2×D412yes—
178C23×C4C2×D412yes—
179C23×C4C2×D412yes—
180C23×C4C2×D412yes—
181C23×C4C2×D412yes—
182C23×C4C2×D412yes—
183C23×C4C2×D414yes—
184C23×C4C2×D412yes—
185C23×C4C2×D412yes—
186C23×C4C2×D412yes—
187C23×C4C2×D412yes—
188C23×C4C2×D412yes—
189C23×C4C2×D412yes—
190C23×C4C2×Q818yes—
191C23×C4C2×Q814yes—
192C23×C4#4112yes—
193C23×C4#4114yes—
194C23×C4#4112yes—
195C23×C4#4112yes—
196C23×C4#4114yes—
197C23×C4#4114yes—
198C23×C4#4114yes—
199C2×C4⋊C4—216no—
200C2×C4⋊C4—216no—
201C2×C4⋊C4—216no—
202C2×C4⋊C4—216no—
203C2×C4⋊C4—28no—
204C2×C4⋊C4—216no—
205C2×C4⋊C4—216no—
206C2×C4⋊C4—416no—
207C2×C4⋊C4—416no—
208C2×C4⋊C4—416no—
209C2×C4⋊C4—416no—
210C2×C4⋊C4—48no—
211C2×C4⋊C4—48no—
212C2×C4⋊C4—48no—
213C2×C4⋊C4—48no—
214C2×C4⋊C4—48no—
215C2×C4⋊C4—48no—
216C2×C4⋊C4—48no—
217C2×C4⋊C4—44no—
218C2×C4⋊C4—48no—
219C2×C4⋊C4—44no—
220C2×C4⋊C4—48no—
221C2×C42—232no—
222C2×C42—28no—
223C2×C42—28no—
224C2×C42—28no—
225#95—28no—
226#95—28no—
227#95—216no—
228#95—416no—
229#95—416no—
230#95—416no—
231#95—44no—
232#95—48no—
233#95—48no—
234#95—44no—
235#95—44no—
236#95—416no—
237C24C22×D411yescharacteristic
238C24C22×D412yes—
239C24C22×D411yescharacteristic
240C24C22×D411yescharacteristic
241C24C22×D411yescharacteristic
242C24C22×Q812yes—
243C24C2×#4111yescharacteristic
244C24C2×#4112yes—
245C24C2×#4111yescharacteristic
246C24C2×#4111yescharacteristic
247C24C2×#4112yes—
248C24C2×#4112yes—
249C24C2×#4112yes—
250C24H(5,𝔽2)12yes—
251C24H(5,𝔽2)12yes—
252C242−1+412yes—
253C242−1+412yes—
254C242−1+412yes—
255C242−1+412yes—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—28no—
263C22×C4—28no—
264C22×C4—28no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—28no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—28no—
273C22×C4—28no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—28no—
283C22×C4—28no—
284C22×C4—28no—
285C22×C4—28no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—28no—
291C22×C4—28no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—24no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—28no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—28no—
308C22×C4—22no—
309C22×C4—28no—
310C22×C4—28no—
311C22×C4—24no—
312C22×C4—28no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—28no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—28no—
319C22×C4—28no—
320C22×C4—28no—
321C22×C4—28no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—28no—
327C22×C4—28no—
328C22×C4—28no—
329C22×C4—28no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—44no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—44no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—44no—
351C22×C4—41no—
352C22×C4—44no—
353C22×C4—44no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—44no—
357C22×C4—41no—
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—44no—
367C22×C4—44no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—44no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—44no—
376C22×C4—44no—
377C22×C4—44no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—44no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4—44no—
386C22×C4—44no—
387C22×C4—42no—
388C22×C4—44no—
389C22×C4—44no—
390C22×C4—42no—
391C22×C4—44no—
392C22×C4—44no—
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—42no—
402C22×C4—42no—
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—42no—
421C22×C4—42no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4#12014yes—
436C22×C4#12114yes—
437C22×C4#12118yes—
438C22×C4#12114yes—
439C22×C4#12114yes—
440C22×C4C22⋊Q818yes—
441C22×C4#12318yes—
442C22×C4#12318yes—
443C22×C4#12314yes—
444C22×C4#12314yes—
445C22×C4#12414yes—
446C22×C4#12414yes—
447C22×C4#12518yes—
448C22×C4#12618yes—
449C22×C4#12714yes—
450C22×C4C4⋊Q814yes—
451C4⋊C4—432no—
452C4⋊C4—432no—
453C4⋊C4—432no—
454C4⋊C4—416no—
455C42—232no—
456C23C2×#12011yescharacteristic
457C23C2×#12111yescharacteristic
458C23C2×#12111yescharacteristic
459C23C2×#12111yescharacteristic
460C23C2×#12112yes—
461C23C2×C22⋊Q812yes—
462C23C2×#12311yescharacteristic
463C23C2×#12311yescharacteristic
464C23C2×#12312yes—
465C23C2×#12312yes—
466C23#52514yes—
467C23C2×#12411yescharacteristic
468C23C2×#12411yescharacteristic
469C23C2×#12512yes—
470C23C2×#12612yes—
471C23C2×#12711yescharacteristic
472C23C2×C4⋊Q811yescharacteristic
473C23#53211yescharacteristic
474C23#53211yescharacteristic
475C23#53211yescharacteristic
476C23#53314yes—
477C23#53511yescharacteristic
478C23#53511yescharacteristic
479C23#53512yes—
480C23#53612yes—
481C23#53611yescharacteristic
482C23#53611yescharacteristic
483C23#53611yescharacteristic
484C23#53611yescharacteristic
485C23#53614yes—
486C23#53612yes—
487C23#53914yes—
488C23#53914yes—
489C23#54012yes—
490C23#54112yes—
491C23#54112yes—
492C23#54114yes—
493C23#54214yes—
494C23#54414yes—
495C23D4212yes—
496C23D4212yes—
497C23#54612yes—
498C23#54612yes—
499C23#54712yes—
500C23#54712yes—
501C23#54712yes—
502C23#54712yes—
503C23#54712yes—
504C23#54712yes—
505C23#54814yes—
506C23D4×Q812yes—
507C23D4×Q814yes—
508C23D4×Q812yes—
509C23#55012yes—
510C23#55012yes—
511C23#55212yes—
512C23#55212yes—
513C23#55214yes—
514C23#55214yes—
515C23#55212yes—
516C23#55212yes—
517C23#55314yes—
518C23#55414yes—
519C23#55612yes—
520C23#55612yes—
521C23#55712yes—
522C23#55712yes—
523C23#55912yes—
524C23#55912yes—
525C23#56314yes—
526C23#56314yes—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—216no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—216no—
539C2×C4—216no—
540C2×C4—216no—
541C2×C4—216no—
542C2×C4—216no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—28no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—48no—
565C2×C4—42no—
566C2×C4—48no—
567C2×C4—48no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—48no—
571C2×C4—48no—
572C2×C4—48no—
573C2×C4—48no—
574C2×C4—48no—
575C2×C4—48no—
576C2×C4—48no—
577C2×C4—48no—
578C2×C4—48no—
579C2×C4—48no—
580C2×C4—48no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—48no—
584C2×C4—48no—
585C2×C4—48no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—81no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—84no—
592C2×C4—81no—
593C2×C4—84no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—84no—
603C2×C4—84no—
604C2×C4—84no—
605C2×C4—84no—
606C2×C4—84no—
607C2×C4—84no—
608C2×C4—84no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—84no—
614C2×C4—84no—
615C2×C4—84no—
616C2×C4—84no—
617C2×C4—84no—
618C2×C4—84no—
619C2×C4#39418yes—
620C2×C4#39718yes—
621C2×C4#39818yes—
622C22C2×#39411yescharacteristic
623C22C2×#39711yescharacteristic
624C22C2×#39811yescharacteristic
625C22#240811yescharacteristic
626C22#240811yescharacteristic
627C22#241314yes—
628C22#242314yes—
629C22#242914yes—
630C22#243411yescharacteristic
631C22#243611yescharacteristic
632C22#244114yes—
633C22#244314yes—
634C22#244512yes—
635C22#244512yes—
636C22#244614yes—
637C22#244914yes—
638C22#247314yes—
639C22#248114yes—
640C22#248414yes—
641C22#248611yescharacteristic
642C22#248611yescharacteristic
643C22#248611yescharacteristic
644C22#248611yescharacteristic
645C22#249612yes—
646C22#249612yes—
647C22#249912yes—
648C22#250112yes—
649C22#250211yescharacteristic
650C22#250311yescharacteristic
651C22#250311yescharacteristic
652C22#250411yescharacteristic
653C22#250612yes—
654C22#250612yes—
655C22#251114yes—
656C22#254112yes—
657C22#254212yes—
658C22#254412yes—
659C22#254611yescharacteristic
660C22#254611yescharacteristic
661C22#254711yescharacteristic
662C22#254711yescharacteristic
663C22#254811yescharacteristic
664C22#254811yescharacteristic
665C22#256512yes—
666C22#257014yes—
667C22#261411yescharacteristic
668C22#261911yescharacteristic
669C22#262111yescharacteristic
670C22#262111yescharacteristic
671C22#262311yescharacteristic
672C22#262311yescharacteristic
673C22#264011yescharacteristic
674C22#264211yescharacteristic
675C22#266011yescharacteristic
676C22#267414yes—
677C22#267714yes—
678C22#271314yes—
679C22#271614yes—
680C22#271814yes—
681C22#272014yes—
682C22#272114yes—
683C22#272114yes—
684C22#279114yes—
685C22#279314yes—
686C22#279414yes—
687C22#279414yes—
688C22#282111yescharacteristic
689C22#282111yescharacteristic
690C22#284911yescharacteristic
691C22#285611yescharacteristic
692C22#286211yescharacteristic
693C4—28no—
694C4—28no—
695C4—28no—
696C4—44no—
697C4—88no—
698C4—82no—
699C4—88no—
700C4—82no—
701C4—82no—
702C2#1477611yescharacteristic
703C2#1478611yescharacteristic
704C2#1507311yescharacteristic
705C2#1512711yescharacteristic
706C2#1515011yescharacteristic
707C2#1515111yescharacteristic
708C2#1518511yescharacteristic
709C2#1518811yescharacteristic
710C2#1524211yescharacteristic
711C2#1538814yes—
712C2#1543414yes—
713C2#1576514yes—
714C2#1578914yes—
715C2#1650611yescharacteristic
716C2#1650711yescharacteristic
717C2#1706011yescharacteristic
718C2#1706111yescharacteristic
719C2#1706311yescharacteristic
720C2#1706311yescharacteristic
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×#3842
C2×#14452
C2×#14422
C2×#14412
C2×#14362
#75572
#75542