Finite Group Databasebeta

← #763132

Subgroups — #763132

Order 512.

1874 conjugacy classes of subgroups.

The subgroup lattice has 671 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16906C214yesmaximal
2#15235C212yesmaximal
3#15231C212yesmaximal
4#15152C212yesmaximal
5#15146C212yesmaximal
6#14867C214yesmaximal
7#14030C212yesmaximal
8#13982C212yesmaximal
9#13955C212yesmaximal
10#13911C211yesmaximal, characteristic
11#13911C211yesmaximal, characteristic
12#13911C211yesmaximal, characteristic
13#13910C211yesmaximal, characteristic
14#13909C212yesmaximal
15C4×#382C211yesmaximal, characteristic
16C4×#384C211yesmaximal, characteristic
17C4×#384C211yesmaximal, characteristic
18C2×#400C2214yes—
19C2×#389C2212yes—
20C2×#389C2212yes—
21C2×#384C2211yescharacteristic
22C2×#384C2211yescharacteristic
23C2×#384C2211yescharacteristic
24C2×#384C2211yescharacteristic
25C2×#384C2212yes—
26C2×#382C2211yescharacteristic
27C2×#382C2212yes—
28C2×#382C2211yescharacteristic
29C2×#382C2212yes—
30C2×#382C2212yes—
31C2×C4×C4⋊C4C2212yes—
32C2×C4×C4⋊C4C2212yes—
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2212yes—
38C2×C4×C4⋊C4C2212yes—
39C2×C4×C4⋊C4C2212yes—
40C2×C43C2211yescharacteristic
41#1445C2214yes—
42#1444C2214yes—
43#1443C2214yes—
44#1443C2214yes—
45#1442C2214yes—
46#1442C2214yes—
47#1442C2214yes—
48#1442C2214yes—
49#1442C2214yes—
50#1442C2214yes—
51#1442C2214yes—
52#1442C2214yes—
53#1441C2214yes—
54#1441C2214yes—
55#1441C2214yes—
56#1436C2214yes—
57#1436C2214yes—
58C4⋊#95C2212yes—
59C4⋊#95C2212yes—
60C4⋊#95C2212yes—
61C4⋊#95C2212yes—
62C4⋊#95C2212yes—
63C4⋊#95C2212yes—
64C4⋊#95C2212yes—
65C4⋊#95C2211yescharacteristic
66C4⋊#95C2212yes—
67C4⋊#95C2212yes—
68C4⋊#95C2212yes—
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2211yescharacteristic
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2211yescharacteristic
77#1434C2212yes—
78#1434C2212yes—
79#1434C2214yes—
80#1434C2214yes—
81C4×#95C2212yes—
82C4×#95C2212yes—
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2312yes—
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2312yes—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2312yes—
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2312yes—
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2314yes—
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2314yes—
103C22×C42C2312yes—
104C22×C42C2312yes—
105C22×C42C2312yes—
106C22×C42C2312yes—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2314yes—
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115#400—48no—
116#389—28no—
117#389—44no—
118#384—24no—
119#384—24no—
120#384—24no—
121#384—24no—
122#384—44no—
123#382—28no—
124#382—24no—
125#382—24no—
126#382—44no—
127#382—44no—
128C4×C4⋊C4—28no—
129C4×C4⋊C4—24no—
130C4×C4⋊C4—24no—
131C4×C4⋊C4—24no—
132C4×C4⋊C4—24no—
133C4×C4⋊C4—28no—
134C4×C4⋊C4—44no—
135C4×C4⋊C4—44no—
136C4×C4⋊C4—44no—
137C2×#95C2312yes—
138C2×#95C2314yes—
139C2×#95C2312yes—
140C2×#95C2312yes—
141C2×#95C2312yes—
142C2×#95C2312yes—
143C2×#95C2312yes—
144C2×#95C2312yes—
145C2×#95C2312yes—
146C2×#95C2312yes—
147C2×#95C2312yes—
148C2×#95C2314yes—
149C2×#95C2314yes—
150C2×#95C2314yes—
151C2×#95C2312yes—
152C2×#95C2312yes—
153C2×#95C2314yes—
154C2×#95C2314yes—
155C2×#95C2314yes—
156C2×#95C2314yes—
157C2×#95C2312yes—
158C2×#95C2312yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2312yes—
165C2×#95C2314yes—
166C2×#95C2312yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C43Q818yes—
171C23×C4C2412yes—
172C23×C4C2414yes—
173C23×C4C2414yes—
174C23×C4C2412yes—
175C23×C4C2412yes—
176C23×C4C2412yes—
177C23×C4C2412yes—
178C23×C4C2412yes—
179C23×C4C2411yescharacteristic
180C23×C4C2412yes—
181C23×C4C2412yes—
182C23×C4C2411yescharacteristic
183C23×C4C2411yescharacteristic
184C23×C4C2411yescharacteristic
185C23×C4C2411yescharacteristic
186C23×C4C2411yescharacteristic
187C23×C4C2411yescharacteristic
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—24no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4—24no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—28no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4—42no—
237C2×C4⋊C4—42no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4—42no—
240C2×C4⋊C4—42no—
241C2×C4⋊C4—44no—
242C2×C4⋊C4—44no—
243C2×C4⋊C4—44no—
244C2×C4⋊C4—44no—
245C2×C4⋊C4—44no—
246C2×C4⋊C4#4114yes—
247C2×C4⋊C4#4114yes—
248C2×C42—22no—
249C2×C42—22no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42—22no—
254C2×C42—22no—
255C2×C42—22no—
256C2×C42—24no—
257C2×C42—24no—
258C2×C42—24no—
259C2×C42—24no—
260C2×C42—24no—
261C2×C42—24no—
262C2×C42—24no—
263C2×C42—24no—
264C2×C42—24no—
265C2×C42—24no—
266C2×C42—24no—
267C2×C42—24no—
268C2×C42—28no—
269C2×C42—41no—
270C2×C42—41no—
271C2×C42—44no—
272C2×C42—44no—
273C2×C42C2×Q814yes—
274C2×C42C2×Q814yes—
275C2×C42C2×Q814yes—
276C2×C42C2×Q814yes—
277C2×C42C2×Q814yes—
278C2×C42C2×Q814yes—
279C2×C42C2×Q814yes—
280C2×C42#4114yes—
281C2×C42#4114yes—
282C2×C42#4114yes—
283C2×C42#4114yes—
284#95—24no—
285#95—24no—
286#95—24no—
287#95—28no—
288#95—24no—
289#95—24no—
290#95—24no—
291#95—28no—
292#95—28no—
293#95—24no—
294#95—24no—
295#95—24no—
296#95—24no—
297#95—28no—
298#95—28no—
299#95—24no—
300#95—24no—
301#95—42no—
302#95—42no—
303#95—44no—
304#95—44no—
305#95—44no—
306#95—42no—
307#95—42no—
308#95—44no—
309#95—44no—
310#95—44no—
311#95—44no—
312#95—44no—
313#95—44no—
314#95—44no—
315#95—44no—
316#95—44no—
317C24C2511yescharacteristic
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4C22×Q812yes—
409C22×C4C22×Q812yes—
410C22×C4C22×Q812yes—
411C22×C4C22×Q812yes—
412C22×C4C22×Q812yes—
413C22×C4C22×Q812yes—
414C22×C4C22×Q812yes—
415C22×C4C2×#4114yes—
416C22×C4C2×#4114yes—
417C22×C4C2×#4112yes—
418C22×C4C2×#4112yes—
419C22×C4C2×#4112yes—
420C22×C4C2×#4112yes—
421C22×C4C2×#4112yes—
422C22×C4C2×#4112yes—
423C22×C4C2×#4112yes—
424C22×C4C2×#4112yes—
425C22×C4C2×#4112yes—
426C22×C4C2×#4112yes—
427C22×C4C2×#4112yes—
428C22×C4C2×#4112yes—
429C22×C4C2×#4112yes—
430C22×C4C2×#4112yes—
431C22×C4H(5,𝔽2)12yes—
432C22×C4H(5,𝔽2)12yes—
433C22×C4H(5,𝔽2)12yes—
434C22×C42−1+412yes—
435C22×C42−1+412yes—
436C22×C42−1+412yes—
437C4⋊C4—28no—
438C4⋊C4—28no—
439C4⋊C4—48no—
440C4⋊C4—48no—
441C4⋊C4—48no—
442C4⋊C4—48no—
443C4⋊C4—48no—
444C4⋊C4—48no—
445C4⋊C4—44no—
446C4⋊C4—44no—
447C4⋊C4—48no—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—48no—
451C4⋊C4—44no—
452C4⋊C4—44no—
453C4⋊C4—48no—
454C4⋊C4—48no—
455C4⋊C4—88no—
456C4⋊C4—88no—
457C42—28no—
458C42—28no—
459C42—28no—
460C42—28no—
461C42—44no—
462C42—48no—
463C42—48no—
464C42—48no—
465C42—48no—
466C42—88no—
467C42#125116yes—
468C42#125116yes—
469C23C23×Q811yescharacteristic
470C23C22×#4111yescharacteristic
471C23C22×#4111yescharacteristic
472C23C22×#4111yescharacteristic
473C23C22×#4111yescharacteristic
474C23C22×#4111yescharacteristic
475C23C22×#4111yescharacteristic
476C23C2×H(5,𝔽2)11yescharacteristic
477C23C2×H(5,𝔽2)11yescharacteristic
478C23C2×H(5,𝔽2)11yescharacteristic
479C23C2×2−1+411yescharacteristic
480C23C2×2−1+411yescharacteristic
481C23C2×2−1+411yescharacteristic
482C23#58511yescharacteristic
483C23#58511yescharacteristic
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—44no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—44no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—44no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4C2×#12514yes—
586C2×C4C2×#12514yes—
587C2×C4C2×#12514yes—
588C2×C4C2×#12514yes—
589C2×C4C2×#12514yes—
590C2×C4C2×#12514yes—
591C2×C4#53314yes—
592C2×C4#54414yes—
593C2×C4#54414yes—
594C2×C4#54414yes—
595C2×C4#55214yes—
596C2×C4#55314yes—
597C2×C4#55514yes—
598C2×C4#55614yes—
599C2×C4#55614yes—
600C2×C4#55614yes—
601C2×C4#55914yes—
602C2×C4#55914yes—
603C22C22×#12511yescharacteristic
604C22C22×#12511yescharacteristic
605C22C2×#53311yescharacteristic
606C22C2×#54411yescharacteristic
607C22C2×#54411yescharacteristic
608C22C2×#54411yescharacteristic
609C22#345811yescharacteristic
610C22C2×#55211yescharacteristic
611C22C2×#55311yescharacteristic
612C22C2×#55511yescharacteristic
613C22C2×#55611yescharacteristic
614C22C2×#55611yescharacteristic
615C22C2×#55611yescharacteristic
616C22#347511yescharacteristic
617C22#347511yescharacteristic
618C22C2×#55911yescharacteristic
619C22C2×#55911yescharacteristic
620C22#348011yescharacteristic
621C22#348011yescharacteristic
622C22#350611yescharacteristic
623C22#350611yescharacteristic
624C22#350711yescharacteristic
625C22#350711yescharacteristic
626C22#350811yescharacteristic
627C22#350911yescharacteristic
628C22#351111yescharacteristic
629C22#351111yescharacteristic
630C22#351911yescharacteristic
631C22#352011yescharacteristic
632C22#352211yescharacteristic
633C22#352311yescharacteristic
634C22#354611yescharacteristic
635C22#354711yescharacteristic
636C22#355411yescharacteristic
637C22#355511yescharacteristic
638C4—24no—
639C4—24no—
640C4—24no—
641C4—24no—
642C4—44no—
643C4—44no—
644C4—42no—
645C4—82no—
646C4—84no—
647C4—82no—
648C4—82no—
649C4—82no—
650C4—82no—
651C4—82no—
652C4—84no—
653C4#257018yes—
654C4#257118yes—
655C2C2×#257011yescharacteristic
656C2C2×#257111yescharacteristic
657C2#3494811yescharacteristic
658C2#3518111yescharacteristic
659C2#3523911yescharacteristic
660C2#3528611yescharacteristic
661C2#3762411yescharacteristic
662C2#5942611yescharacteristic
663C2#5942711yescharacteristic
664C2#5944211yescharacteristic
665C2#5944311yescharacteristic
666C2#5963911yescharacteristic
667C2#5964011yescharacteristic
668C2#5967811yescharacteristic
669C2#5967911yescharacteristic
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
#169062
#152352
#152312
#151522
#151462
#148672
#140302
#139822
#139552
#139112
#139102
#139092
C4×#3822
C4×#3842