Finite Group Databasebeta

← #480760

Subgroups — #480760

Order 512.

1127 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic
2#17364C211yesmaximal, characteristic
3#17362C211yesmaximal, characteristic
4#11579C214yesmaximal, complemented
5#11576C214yesmaximal, complemented
6#11517C214yesmaximal, complemented
7C22×C4×D4C2211yescharacteristic
8C23×C4⋊C4C411yescharacteristic
9#2920—21no—
10C2×#407—21no—
11#2487—21no—
12#2487—21no—
13#2487—21no—
14#2487—21no—
15#2487C412yes—
16#2487C412yes—
17#2487C2212yes—
18#2487C2212yes—
19C2×#400—21no—
20C2×#399—21no—
21C2×#389—21no—
22C2×#386C412yes—
23C2×#385C2212yes—
24C2×#380—21no—
25C2×#380C411yescharacteristic
26#1466—21no—
27#1466C2212yes—
28#1465—21no—
29#1465C2212yes—
30#1463—21no—
31#1462—21no—
32#1462C2212yes—
33#1462C2212yes—
34#1460—21no—
35#1460C2212yes—
36#1459—21no—
37#1459C2212yes—
38#1326C22116yescomplemented
39C23×D4C2×C411yescharacteristic
40C24×C4C2×C411yescharacteristic
41C24×C4C2×C412yes—
42C24×C4D411yescharacteristic
43C22×M16—41no—
44C2×C4×D4—41no—
45C2×C4×D4—41no—
46C2×C4×D4—41no—
47C2×C4×D4—41no—
48C2×C4×D4C2×C411yescharacteristic
49C2×C4×D4C2×C411yescharacteristic
50C2×C4×D4D411yescharacteristic
51C2×C4×D4D411yescharacteristic
52C2×C4×D4D411yescharacteristic
53C2×C4×D4D411yescharacteristic
54C2×C4×D4C2311yescharacteristic
55C2×C4×D4C2311yescharacteristic
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—41no—
63C22×C4⋊C4—41no—
64C22×C4⋊C4—41no—
65C22×C4⋊C4—41no—
66C22×C4⋊C4C2×C412yes—
67C22×C4⋊C4C2×C412yes—
68C22×C4⋊C4D411yescharacteristic
69C22×C22⋊C4—22no—
70C22×C22⋊C4C2×C412yes—
71C22×C22⋊C4D411yescharacteristic
72C22×C22⋊C4C2311yescharacteristic
73C22×C42D411yescharacteristic
74#432—22no—
75#432—41no—
76#431—22no—
77#431—41no—
78#423—41no—
79#407—22no—
80#407—22no—
81#407—22no—
82#407—41no—
83#407—41no—
84C2×C22⋊C8—22no—
85C2×C22⋊C8—41no—
86C4×M16—41no—
87#400—22no—
88#400—22no—
89#400—22no—
90#400—22no—
91#399—22no—
92#399—22no—
93#399—22no—
94#399—22no—
95#389—22no—
96#389—22no—
97#389—22no—
98#389—22no—
99#386—22no—
100#386—22no—
101#386C2×C414yes—
102#386C2×C414yes—
103#385—22no—
104#385—22no—
105#385C2×C414yes—
106#385C2314yes—
107#380—21no—
108#380—21no—
109#380—22no—
110#380—22no—
111#380—22no—
112#380—22no—
113#380C2×C412yes—
114#380C2×C412yes—
115C2×#95—21no—
116C2×#95—22no—
117C2×#95—22no—
118#324—22no—
119#324—22no—
120#323—22no—
121#323—22no—
122#323—22no—
123#323—22no—
124#323C2314yes—
125#323C2314yes—
126C25C22⋊C411yescharacteristic
127C25C22×C411yescharacteristic
128C22×D4—24no—
129C22×D4—41no—
130C22×D4—41no—
131C22×D4—42no—
132C22×D4C22⋊C411yescharacteristic
133C22×D4C22⋊C411yescharacteristic
134C22×D4C22×C411yescharacteristic
135C22×D4C22×C411yescharacteristic
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—44no—
148C23×C4—44no—
149C23×C4—42no—
150C23×C4—42no—
151C23×C4—84no—
152C23×C4C22⋊C411yescharacteristic
153C23×C4C22⋊C411yescharacteristic
154C23×C4C22⋊C411yescharacteristic
155C23×C4C22⋊C411yescharacteristic
156C23×C4C22⋊C411yescharacteristic
157C23×C4C22⋊C411yescharacteristic
158C23×C4C22⋊C411yescharacteristic
159C23×C4C22×C411yescharacteristic
160C23×C4C22×C411yescharacteristic
161C23×C4C22×C414yes—
162C23×C4C2×D411yescharacteristic
163C23×C4C2×D411yescharacteristic
164C23×C4C2×D411yescharacteristic
165C23×C4C2×D411yescharacteristic
166C2×M16—42no—
167C2×M16—42no—
168C2×M16—42no—
169C2×M16—84no—
170C22×C8—42no—
171C4×D4—41no—
172C4×D4—41no—
173C4×D4—41no—
174C4×D4—41no—
175C4×D4—41no—
176C4×D4—41no—
177C4×D4—41no—
178C4×D4—41no—
179C4×D4—41no—
180C4×D4—41no—
181C4×D4—41no—
182C4×D4—41no—
183C4×D4—41no—
184C4×D4—41no—
185C4×D4—41no—
186C4×D4—41no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—44no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4—41no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—42no—
209C2×C4⋊C4—42no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—84no—
213C2×C4⋊C4C22⋊C411yescharacteristic
214C2×C4⋊C4C22⋊C411yescharacteristic
215C2×C4⋊C4C2×D411yescharacteristic
216C2×C4⋊C4C2×D411yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—24no—
219C2×C22⋊C4—24no—
220C2×C22⋊C4—44no—
221C2×C22⋊C4—41no—
222C2×C22⋊C4—41no—
223C2×C22⋊C4—41no—
224C2×C22⋊C4—41no—
225C2×C22⋊C4—84no—
226C2×C22⋊C4C22⋊C411yescharacteristic
227C2×C22⋊C4C22⋊C411yescharacteristic
228C2×C22⋊C4C22×C414yes—
229C2×C22⋊C4C22×C411yescharacteristic
230C2×C22⋊C4C2×D411yescharacteristic
231C2×C22⋊C4C2×D411yescharacteristic
232C2×C22⋊C4C2×D411yescharacteristic
233C2×C22⋊C4C2×D411yescharacteristic
234C2×C22⋊C4C2411yescharacteristic
235C2×C42—21no—
236C2×C42—21no—
237C2×C42—21no—
238C2×C42—21no—
239C2×C42C22⋊C411yescharacteristic
240C2×C42C22⋊C411yescharacteristic
241C2×C42C2×D411yescharacteristic
242C2×C42C2×D411yescharacteristic
243C4⋊C8—42no—
244C4⋊C8—42no—
245C22⋊C8—24no—
246C22⋊C8—24no—
247C22⋊C8—42no—
248C22⋊C8—42no—
249C22⋊C8—42no—
250C22⋊C8—42no—
251#97—42no—
252C4×C8—42no—
253#95—24no—
254#95—22no—
255#95—22no—
256#95—24no—
257#95—24no—
258#95—24no—
259C24—22no—
260C24—21no—
261C24—21no—
262C24—22no—
263C24—22no—
264C24—21no—
265C24—21no—
266C24—41no—
267C24—42no—
268C24—42no—
269C24—42no—
270C24—42no—
271C24C2×C22⋊C411yescharacteristic
272C24C2×C22⋊C411yescharacteristic
273C24C2×C22⋊C411yescharacteristic
274C24C2×C22⋊C411yescharacteristic
275C24C23×C411yescharacteristic
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—48no—
288C2×D4—48no—
289C2×D4#10114yes—
290C22×C4—24no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—41no—
319C22×C4—44no—
320C22×C4—44no—
321C22×C4—44no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—44no—
331C22×C4—44no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—44no—
336C22×C4—44no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—44no—
340C22×C4—44no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—44no—
344C22×C4—82no—
345C22×C4—82no—
346C22×C4—82no—
347C22×C4—84no—
348C22×C4—84no—
349C22×C4—88no—
350C22×C4—88no—
351C22×C4#9911yescharacteristic
352C22×C4#9911yescharacteristic
353C22×C4#9911yescharacteristic
354C22×C4#9911yescharacteristic
355C22×C4C2×C22⋊C411yescharacteristic
356C22×C4C2×C22⋊C411yescharacteristic
357C22×C4C2×C22⋊C411yescharacteristic
358C22×C4C2×C22⋊C411yescharacteristic
359C22×C4C2×C22⋊C411yescharacteristic
360C22×C4C2×C22⋊C411yescharacteristic
361C22×C4C2×C22⋊C411yescharacteristic
362C22×C4C2×C22⋊C411yescharacteristic
363C22×C4C22×D411yescharacteristic
364C22×C4C22×D411yescharacteristic
365M16—84no—
366M16—84no—
367M16—84no—
368C2×C8—44no—
369C2×C8—44no—
370C2×C8—84no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—44no—
376C4⋊C4—44no—
377C4⋊C4—44no—
378C4⋊C4—44no—
379C4⋊C4—42no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—42no—
383C4⋊C4—84no—
384C4⋊C4—84no—
385C22⋊C4—28no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—44no—
395C22⋊C4—84no—
396C22⋊C4—84no—
397C42—21no—
398C42—21no—
399C42—21no—
400C42—21no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—21no—
405C23—21no—
406C23—21no—
407C23—22no—
408C23—22no—
409C23—24no—
410C23—24no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—42no—
421C23—42no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—42no—
427C23—42no—
428C23—48no—
429C23—48no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—48no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—81no—
440C23—81no—
441C23—84no—
442C23C2×#9911yescharacteristic
443C23C2×#9911yescharacteristic
444C23C2×#10112yes—
445C23C2×#10112yes—
446C23C22×C22⋊C411yescharacteristic
447C23#56812yes—
448D4—44no—
449D4—44no—
450D4—44no—
451D4—44no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—81no—
499C2×C4—81no—
500C2×C4—81no—
501C2×C4—81no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—88no—
505C2×C4—84no—
506C2×C4—88no—
507C2×C4—84no—
508C2×C4—88no—
509C2×C4#35214yes—
510C2×C4C2×#9911yescharacteristic
511C2×C4C2×#9911yescharacteristic
512C2×C4C2×#9911yescharacteristic
513C2×C4C2×#9911yescharacteristic
514C2×C4C2×#10112yes—
515C8—84no—
516C8—84no—
517C22—24no—
518C22—24no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—48no—
534C22—48no—
535C22—42no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—81no—
546C22—84no—
547C22—84no—
548C22—81no—
549C22C2×#35212yes—
550C22#212212yes—
551C22#287911yescharacteristic
552C22C22×#9911yescharacteristic
553C22C22×#10111yescharacteristic
554C4—21no—
555C4—21no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—84no—
565C4—84no—
566C4C2×#35212yes—
567C4C2×#35212yes—
568C2—21no—
569C2—21no—
570C2—22no—
571C2—22no—
572C2—42no—
573C2—42no—
574C2—42no—
575C2—81no—
576C2#1739711yescharacteristic
577C2C22×#35211yescharacteristic
578C2C2×#212211yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC23×D4C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #11579C2semidirect
5. #11576C2semidirect
6. #11517C2semidirect
38. #1326C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#24872
#173642
#173622
#115792
#115762
#115172