Finite Group Databasebeta

← #160397

Subgroups — #160397

Order 512.

2188 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7557C212yesmaximal
2#7557C212yesmaximal
3#7557C212yesmaximal
4#7557C211yesmaximal, characteristic
5#7557C211yesmaximal, characteristic
6#7557C211yesmaximal, characteristic
7#7556C212yesmaximal
8#7556C212yesmaximal
9#7556C212yesmaximal
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2211yescharacteristic
12C22×#95C2211yescharacteristic
13C22×#95C2212yes—
14C22×#95C2212yes—
15C22×#95C2212yes—
16C22×#95C2212yes—
17C22×#95C2211yescharacteristic
18C22×#95C2212yes—
19C22×#95C2211yescharacteristic
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2211yescharacteristic
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C24×C4C2311yescharacteristic
32C24×C4C2311yescharacteristic
33C24×C4C2312yes—
34C24×C4C2312yes—
35C24×C4C2312yes—
36C24×C4C2312yes—
37C24×C4C2312yes—
38C24×C4C2312yes—
39C24×C4C2311yescharacteristic
40C22×C4⋊C4—24no—
41C22×C4⋊C4—24no—
42C22×C4⋊C4—24no—
43C22×C4⋊C4—41no—
44C22×C4⋊C4—41no—
45C22×C4⋊C4—42no—
46C22×C4⋊C4—42no—
47C22×C4⋊C4—42no—
48C22×C4⋊C4—42no—
49C22×C4⋊C4—42no—
50C22×C4⋊C4—42no—
51C22×C4⋊C4Q814yes—
52C2×#95—24no—
53C2×#95—24no—
54C2×#95—24no—
55C2×#95—24no—
56C2×#95—24no—
57C2×#95—24no—
58C2×#95—24no—
59C2×#95—24no—
60C2×#95—24no—
61C2×#95—24no—
62C2×#95—24no—
63C2×#95—24no—
64C2×#95—24no—
65C2×#95—22no—
66C2×#95—24no—
67C2×#95—22no—
68C2×#95—42no—
69C2×#95—42no—
70C2×#95—42no—
71C2×#95—42no—
72C2×#95—42no—
73C2×#95—41no—
74C2×#95—42no—
75C2×#95—41no—
76C2×#95—42no—
77C2×#95—41no—
78C2×#95—41no—
79C2×#95—41no—
80C2×#95—41no—
81C2×#95—42no—
82C2×#95—42no—
83C2×#95—42no—
84C2×#95—42no—
85C2×#95—42no—
86C2×#95—42no—
87C2×#95—42no—
88C2×#95—42no—
89C2×#95—42no—
90C2×#95—41no—
91C2×#95—42no—
92C2×#95—42no—
93C2×#95—42no—
94C2×#95—42no—
95C2×#95—41no—
96C2×#95—42no—
97C2×#95—42no—
98C2×#95—42no—
99C2×#95—42no—
100C2×#95—42no—
101C2×#95—42no—
102C2×#95—42no—
103C2×#95—42no—
104C2×#95Q818yes—
105C25C2411yescharacteristic
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—21no—
115C23×C4—21no—
116C23×C4—22no—
117C23×C4—22no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—22no—
122C23×C4—21no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—22no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4C2×Q812yes—
213C23×C4C2×Q812yes—
214C23×C4C2×Q814yes—
215C23×C4C2×Q814yes—
216C23×C4C2×Q812yes—
217C23×C4C2×Q814yes—
218C23×C4#4114yes—
219C23×C4#4114yes—
220C23×C4#4114yes—
221C23×C4#4114yes—
222C23×C4#4114yes—
223C23×C4#4112yes—
224C23×C4#4112yes—
225C2×C4⋊C4—44no—
226C2×C4⋊C4—44no—
227C2×C4⋊C4—44no—
228C2×C4⋊C4—48no—
229C2×C4⋊C4—48no—
230C2×C4⋊C4—48no—
231C2×C4⋊C4—48no—
232C2×C4⋊C4—48no—
233C2×C4⋊C4—48no—
234C2×C4⋊C4—48no—
235C2×C4⋊C4—48no—
236C2×C4⋊C4—48no—
237#95—48no—
238#95—44no—
239#95—48no—
240#95—48no—
241#95—48no—
242#95—48no—
243#95—44no—
244#95—44no—
245#95—44no—
246#95—48no—
247#95—48no—
248#95—48no—
249#95—48no—
250#95—44no—
251#95—48no—
252#95—44no—
253#95—48no—
254#95—48no—
255#95—48no—
256C24C22×Q811yescharacteristic
257C24C22×Q812yes—
258C24C2×#4111yescharacteristic
259C24C2×#4112yes—
260C24C2×#4112yes—
261C24C2×#4111yescharacteristic
262C24C2×#4112yes—
263C24C2×#4112yes—
264C24C2×#4112yes—
265C24H(5,𝔽2)11yescharacteristic
266C24H(5,𝔽2)12yes—
267C24H(5,𝔽2)12yes—
268C24H(5,𝔽2)12yes—
269C24H(5,𝔽2)12yes—
270C24H(5,𝔽2)11yescharacteristic
271C24H(5,𝔽2)12yes—
272C24H(5,𝔽2)11yescharacteristic
273C242−1+411yescharacteristic
274C242−1+412yes—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
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—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—41no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—41no—
517C22×C4—42no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4#12514yes—
549C22×C4#12518yes—
550C4⋊C4—416no—
551C4⋊C4—432no—
552C23C2×#12511yescharacteristic
553C23C2×#12512yes—
554C23#52912yes—
555C23#52912yes—
556C23#52912yes—
557C23#53311yescharacteristic
558C23#53312yes—
559C23#53311yescharacteristic
560C23#53312yes—
561C23#53812yes—
562C23#53812yes—
563C23#53812yes—
564C23#53812yes—
565C23#53811yescharacteristic
566C23#53811yescharacteristic
567C23#53812yes—
568C23#53812yes—
569C23#53812yes—
570C23#53912yes—
571C23#53912yes—
572C23#53911yescharacteristic
573C23#53911yescharacteristic
574C23#53912yes—
575C23#54012yes—
576C23#54012yes—
577C23#54012yes—
578C23#54012yes—
579C23#54012yes—
580C23#54012yes—
581C23#54112yes—
582C23#54212yes—
583C23#54212yes—
584C23#54212yes—
585C23#54212yes—
586C23#54212yes—
587C23#54312yes—
588C23#54311yescharacteristic
589C23#54311yescharacteristic
590C23#54311yescharacteristic
591C23#54412yes—
592C23#54412yes—
593C23#54411yescharacteristic
594C23#54412yes—
595C23#55111yescharacteristic
596C23#55112yes—
597C23#55112yes—
598C23#55112yes—
599C23#55112yes—
600C23#55111yescharacteristic
601C23#55112yes—
602C23#55112yes—
603C23#55112yes—
604C23#55212yes—
605C23#55312yes—
606C23#55312yes—
607C23#55312yes—
608C23#55312yes—
609C23#55312yes—
610C23#55312yes—
611C23#55312yes—
612C23#55412yes—
613C23#55412yes—
614C23#55412yes—
615C23#55412yes—
616C23#55412yes—
617C23#55412yes—
618C23#55412yes—
619C23#55412yes—
620C23#55511yescharacteristic
621C23#55612yes—
622C23#55612yes—
623C23#55712yes—
624C23Q8211yescharacteristic
625C23Q8212yes—
626C23#55912yes—
627C23#56012yes—
628C23#56012yes—
629C23#56011yescharacteristic
630C23#56012yes—
631C23#56011yescharacteristic
632C23#56012yes—
633C23H(3,𝔽4)11yescharacteristic
634C23H(3,𝔽4)12yes—
635C23#56212yes—
636C23#56212yes—
637C23#56212yes—
638C23#56311yescharacteristic
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—28no—
642C2×C4—24no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—42no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—44no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4—82no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4—82no—
736C2×C4—82no—
737C2×C4—82no—
738C2×C4—82no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4—82no—
744C2×C4—82no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4—82no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C22#250512yes—
759C22#250512yes—
760C22#250712yes—
761C22#250712yes—
762C22#250712yes—
763C22#250912yes—
764C22#252012yes—
765C22#252212yes—
766C22#252212yes—
767C22#253112yes—
768C22#256911yescharacteristic
769C22#256911yescharacteristic
770C22#256912yes—
771C22#257012yes—
772C22#257211yescharacteristic
773C22#257312yes—
774C22#257612yes—
775C22#258612yes—
776C22#258611yescharacteristic
777C22#258712yes—
778C22#258812yes—
779C22#258912yes—
780C22#259712yes—
781C22#260512yes—
782C22#260811yescharacteristic
783C22#264611yescharacteristic
784C22#264712yes—
785C22#265112yes—
786C22#265312yes—
787C22#265412yes—
788C22#266511yescharacteristic
789C22#266511yescharacteristic
790C22#266612yes—
791C22#266712yes—
792C22#273512yes—
793C22#273912yes—
794C22#274012yes—
795C22#274112yes—
796C22#274212yes—
797C22#274612yes—
798C22#274811yescharacteristic
799C22#274812yes—
800C22#274811yescharacteristic
801C22#274912yes—
802C22#274912yes—
803C22#275212yes—
804C22#275212yes—
805C22#275312yes—
806C22#275312yes—
807C22#275512yes—
808C22#275712yes—
809C22#275712yes—
810C22#276312yes—
811C22#276312yes—
812C22#276812yes—
813C22#277712yes—
814C22#277812yes—
815C22#277812yes—
816C22#278012yes—
817C22#278012yes—
818C22#278211yescharacteristic
819C22#278412yes—
820C22#278612yes—
821C22#278812yes—
822C22#278911yescharacteristic
823C22#279012yes—
824C22#279212yes—
825C22#279211yescharacteristic
826C22#279212yes—
827C22#279511yescharacteristic
828C22#279812yes—
829C22#280012yes—
830C22#280012yes—
831C22#280412yes—
832C22#280612yes—
833C22#280612yes—
834C22#280911yescharacteristic
835C22#281111yescharacteristic
836C22#282412yes—
837C22#282412yes—
838C22#282812yes—
839C22#282811yescharacteristic
840C22#282812yes—
841C22#282912yes—
842C22#283011yescharacteristic
843C22#284112yes—
844C22#284211yescharacteristic
845C4—44no—
846C4—48no—
847C4—84no—
848C4—84no—
849C4—84no—
850C4—82no—
851C4—82no—
852C4—84no—
853C4—84no—
854C2#1611712yes—
855C2#1612012yes—
856C2#1616612yes—
857C2#1616711yescharacteristic
858C2#1618611yescharacteristic
859C2#1623012yes—
860C2#1671112yes—
861C2#1671312yes—
862C2#1678212yes—
863C2#1690411yescharacteristic
864C2#1690512yes—
865C2#1692112yes—
866C2#1693311yescharacteristic
867C2#1699712yes—
868C2#1700311yescharacteristic
869C2#1723212yes—
870C2#1727311yescharacteristic
871C2#1729312yes—
872C2#1730611yescharacteristic
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
#75572
#75562