Finite Group Databasebeta

← #678413

Subgroups — #678413

Order 512.

2162 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2570C211yesmaximal, characteristic
2C2×#2370C211yesmaximal, characteristic
3#15888C214yesmaximal
4#15626C214yesmaximal
5#15239C211yesmaximal, characteristic
6#15196C211yesmaximal, characteristic
7#15196C211yesmaximal, characteristic
8#15153C211yesmaximal, characteristic
9#14791C214yesmaximal
10#14709C211yesmaximal, characteristic
11#14160C211yesmaximal, characteristic
12#14051C211yesmaximal, characteristic
13#14049C211yesmaximal, characteristic
14#14035C214yesmaximal
15#13910C211yesmaximal, characteristic
16#13909C211yesmaximal, characteristic
17#13909C211yesmaximal, characteristic
18C4×#384C211yesmaximal, characteristic
19C4×#389C211yesmaximal, characteristic
20C22×#125C2211yescharacteristic
21#2570—28no—
22C2×#400C2212yes—
23C2×#400C2214yes—
24C2×#398C2212yes—
25#2370—28no—
26C2×#389C2212yes—
27C2×#389C2212yes—
28C2×#389C2214yes—
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#387C2212yes—
34C2×#387C2212yes—
35C2×#387C2212yes—
36C2×#387C2212yes—
37C2×#387C2214yes—
38C2×#384C2211yescharacteristic
39C2×#384C2211yescharacteristic
40C2×#384C2211yescharacteristic
41C2×#384C2211yescharacteristic
42C2×#382C2211yescharacteristic
43C2×#382C2211yescharacteristic
44C2×#382C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2214yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C43C2211yescharacteristic
56#1445C2214yes—
57#1445C2214yes—
58#1444C2214yes—
59#1444C2214yes—
60#1444C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1436C2214yes—
70#1436C2214yes—
71#1436C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74#1436C2212yes—
75#1436C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2214yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90#1434C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C2×#125—24no—
94C2×#125—24no—
95C2×#125Q818yes—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C22×C42C2312yes—
124C22×C42C2312yes—
125C22×C42C2312yes—
126C22×C42C2311yescharacteristic
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C22×C42C2312yes—
130C22×C42C2312yes—
131C22×C42C2312yes—
132C22×C42C2311yescharacteristic
133#400—28no—
134#400—48no—
135#398—28no—
136#389—28no—
137#389—28no—
138#389—216no—
139#389—24no—
140#389—24no—
141#389—24no—
142#389—24no—
143#387—28no—
144#387—28no—
145#387—28no—
146#387—28no—
147#387—48no—
148#384—24no—
149#384—24no—
150#384—24no—
151#384—24no—
152#382—24no—
153#382—24no—
154#382—24no—
155C4×C4⋊C4—24no—
156C4×C4⋊C4—24no—
157C4×C4⋊C4—24no—
158C4×C4⋊C4—24no—
159C4×C4⋊C4—24no—
160C4×C4⋊C4—24no—
161C4×C4⋊C4—24no—
162C4×C4⋊C4—28no—
163C4×C4⋊C4—48no—
164C4×C4⋊C4D418yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C43—24no—
200C23×C4C2412yes—
201C23×C4C2412yes—
202C23×C4C2412yes—
203C23×C4C2412yes—
204C23×C4C2412yes—
205C23×C4C2412yes—
206C23×C4C2411yescharacteristic
207C23×C4C2411yescharacteristic
208C23×C4C2411yescharacteristic
209C23×C4C2412yes—
210C23×C4C2412yes—
211C23×C4C2412yes—
212C23×C4C2412yes—
213C23×C4C2412yes—
214C23×C4C2411yescharacteristic
215C23×C4C2411yescharacteristic
216C23×C4C2411yescharacteristic
217C23×C4C2412yes—
218C23×C4C2411yescharacteristic
219#125—232no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—28no—
245C2×C4⋊C4—28no—
246C2×C4⋊C4—28no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—28no—
253C2×C4⋊C4—28no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—44no—
268C2×C4⋊C4—44no—
269C2×C4⋊C4—44no—
270C2×C4⋊C4—44no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—44no—
274C2×C4⋊C4—44no—
275C2×C4⋊C4—44no—
276C2×C4⋊C4C2×D414yes—
277C2×C4⋊C4C2×D414yes—
278C2×C4⋊C4C2×Q818yes—
279C2×C4⋊C4C2×Q818yes—
280C2×C4⋊C4C2×Q814yes—
281C2×C4⋊C4C2×Q814yes—
282C2×C4⋊C4#4114yes—
283C2×C4⋊C4#4118yes—
284C2×C42—24no—
285C2×C42—22no—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42—22no—
289C2×C42—24no—
290C2×C42—24no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—24no—
294C2×C42—24no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—24no—
303C2×C42—28no—
304C2×C42—22no—
305C2×C42—22no—
306C2×C42—24no—
307C2×C42—24no—
308C2×C42—24no—
309C2×C42—42no—
310C2×C42—44no—
311C2×C42—44no—
312C2×C42—44no—
313C2×C42C2×D414yes—
314C2×C42C2×D414yes—
315C2×C42C2×D414yes—
316C2×C42C2×Q814yes—
317C2×C42#4114yes—
318C2×C42#4114yes—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—24no—
329#95—24no—
330#95—24no—
331#95—24no—
332#95—24no—
333#95—24no—
334#95—28no—
335#95—24no—
336#95—28no—
337#95—24no—
338#95—28no—
339#95—28no—
340#95—28no—
341#95—24no—
342#95—28no—
343#95—24no—
344#95—28no—
345#95—44no—
346#95—44no—
347#95—44no—
348#95—44no—
349#95—44no—
350#95—44no—
351#95C2×D414yes—
352#95C2×D414yes—
353C24C2511yescharacteristic
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4C22×D412yes—
434C22×C4C22×D412yes—
435C22×C4C22×D412yes—
436C22×C4C22×D412yes—
437C22×C4C22×D412yes—
438C22×C4C22×D412yes—
439C22×C4C22×D412yes—
440C22×C4C22×Q814yes—
441C22×C4C22×Q814yes—
442C22×C4C22×Q812yes—
443C22×C4C22×Q812yes—
444C22×C4C22×Q812yes—
445C22×C4C2×#4114yes—
446C22×C4C2×#4114yes—
447C22×C4C2×#4112yes—
448C22×C4C2×#4112yes—
449C22×C4C2×#4114yes—
450C22×C4C2×#4114yes—
451C22×C4C2×#4114yes—
452C22×C4C2×#4112yes—
453C22×C4C2×#4112yes—
454C22×C4C2×#4112yes—
455C22×C4H(5,𝔽2)14yes—
456C22×C42−1+414yes—
457C22×C42−1+412yes—
458C22×C42−1+412yes—
459C4⋊C4—216no—
460C4⋊C4—216no—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C4⋊C4—28no—
464C4⋊C4—28no—
465C4⋊C4—216no—
466C4⋊C4—44no—
467C4⋊C4—48no—
468C4⋊C4—416no—
469C4⋊C4—416no—
470C4⋊C4—416no—
471C4⋊C4—48no—
472C4⋊C4—48no—
473C4⋊C4—48no—
474C4⋊C4—44no—
475C4⋊C4—44no—
476C4⋊C4—44no—
477C4⋊C4—44no—
478C4⋊C4—44no—
479C4⋊C4—48no—
480C4⋊C4—84no—
481C4⋊C4—84no—
482C4⋊C4—84no—
483C42—216no—
484C42—28no—
485C42—28no—
486C42—28no—
487C42—48no—
488C42—44no—
489C42—44no—
490C42—48no—
491C42—44no—
492C42—84no—
493C42—84no—
494C42—84no—
495C42C22⋊Q8116yes—
496C23C23×D411yescharacteristic
497C23C23×Q811yescharacteristic
498C23C22×#4111yescharacteristic
499C23C22×#4111yescharacteristic
500C23C22×#4111yescharacteristic
501C23C22×#4112yes—
502C23C2×H(5,𝔽2)12yes—
503C23C2×2−1+411yescharacteristic
504C23C2×2−1+411yescharacteristic
505C23C2×2−1+412yes—
506C23#58512yes—
507C2×C4—24no—
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—24no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—28no—
537C2×C4—28no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—28no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4C2×C22⋊Q814yes—
602C2×C4C2×C22⋊Q814yes—
603C2×C4C2×C22⋊Q814yes—
604C2×C4#52914yes—
605C2×C4#53214yes—
606C2×C4#54114yes—
607C2×C4#54714yes—
608C2×C4#54814yes—
609C2×C4#55218yes—
610C2×C4#55714yes—
611C2×C4#55714yes—
612C22C22×C22⋊Q811yescharacteristic
613C22C2×#52911yescharacteristic
614C22C2×#53211yescharacteristic
615C22#344911yescharacteristic
616C22C2×#54111yescharacteristic
617C22C2×#54711yescharacteristic
618C22C2×#54811yescharacteristic
619C22C2×#55212yes—
620C22#347512yes—
621C22C2×#55711yescharacteristic
622C22C2×#55711yescharacteristic
623C22Q8×#4112yes—
624C22#348112yes—
625C22#349212yes—
626C22#349811yescharacteristic
627C22#349911yescharacteristic
628C22#350312yes—
629C22#350612yes—
630C22#350912yes—
631C22#351612yes—
632C22#352212yes—
633C22#355512yes—
634C22#355912yes—
635C4—24no—
636C4—24no—
637C4—28no—
638C4—24no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—44no—
644C4—44no—
645C4—44no—
646C4—44no—
647C4—82no—
648C4—82no—
649C4—82no—
650C4—82no—
651C4—82no—
652C4—82no—
653C4#245318yes—
654C2C2×#245311yescharacteristic
655C2#3494711yescharacteristic
656C2#3553211yescharacteristic
657C2#3618111yescharacteristic
658C2#3625412yes—
659C2#3649611yescharacteristic
660C2#3916211yescharacteristic
661C2#3948311yescharacteristic
662C2#3990112yes—
663C2#5944512yes—
664C2#5967012yes—
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
C2×#25702
C2×#23702
#158882
#156262
#152392
#151962
#151532
#147912
#147092
#141602
#140512
#140492
#140352
#139102
#139092
C4×#3842
C4×#3892