Finite Group Databasebeta

← #480855

Subgroups — #480855

Order 512.

825 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35678C211yesmaximal, characteristic
2#17371C211yesmaximal, characteristic, complemented
3#17371C211yesmaximal, characteristic, complemented
4#11571C212yesmaximal, complemented
5#11567C212yesmaximal, complemented
6#11554C212yesmaximal, complemented
7#11550C212yesmaximal, complemented
8#11534C212yesmaximal, complemented
9#11530C212yesmaximal, complemented
10C2×#540C411yescharacteristic
11C2×#519C2211yescharacteristic
12#2983—21no—
13#2983—21no—
14#2565C411yescharacteristic
15#2565C2211yescharacteristic
16#2548C411yescharacteristic
17#2548C2211yescharacteristic
18#2500C2211yescharacteristic
19#2500C2211yescharacteristic
20#2476—21no—
21#2476—21no—
22#2476—21no—
23#2476—21no—
24#2458—21no—
25#2458—21no—
26#2458—21no—
27#2458—21no—
28#2436C411yescharacteristic
29#2436C411yescharacteristic
30#2326C411yescharacteristic
31#2326C2211yescharacteristic
32C4×#124C411yescharacteristic
33C4×#124C2211yescharacteristic
34#2298C411yescharacteristic
35#1467—21no—
36#1467C2212yes—
37#1467C2212yes—
38#1467C2212yes—
39#1464—21no—
40#1464—21no—
41#1464—21no—
42#1464C2212yes—
43#1461—21no—
44#1461C2212yes—
45#1458—21no—
46#1458C2212yes—
47#1325C2214yes—
48#1324C2214yes—
49#1318C2214yes—
50#1318C2214yes—
51C23×Q8C2×C411yescharacteristic
52#540—44no—
53C2×#127C2×C411yescharacteristic
54C2×#125C2×C411yescharacteristic
55C2×#124C2×C411yescharacteristic
56C2×#124C2×C411yescharacteristic
57C2×#124C2×C411yescharacteristic
58C2×#124C2×C411yescharacteristic
59C2×#123—21no—
60C2×#123—21no—
61C2×#121—21no—
62C2×#121—21no—
63C2×#121C2×C411yescharacteristic
64C2×#121C2×C411yescharacteristic
65#519—44no—
66C2×C4×Q8C2×C411yescharacteristic
67C2×C4×Q8C2×C411yescharacteristic
68C2×C4×Q8D411yescharacteristic
69C2×C4×Q8D411yescharacteristic
70C2×C4×Q8D411yescharacteristic
71C2×C4×Q8D411yescharacteristic
72C2×C4×Q8C2311yescharacteristic
73C2×C4×Q8C2311yescharacteristic
74C2×C4×D4C2×C411yescharacteristic
75C2×C4×D4C2×C411yescharacteristic
76C2×#117C2×C411yescharacteristic
77C2×#117D411yescharacteristic
78C2×#117D411yescharacteristic
79C2×#117D411yescharacteristic
80C2×#117D411yescharacteristic
81C2×#117C2311yescharacteristic
82#446—44no—
83#446—44no—
84#432—22no—
85#432—22no—
86#432—22no—
87#432—22no—
88#431—22no—
89#431—22no—
90#398—21no—
91#398—21no—
92#398—21no—
93#398—21no—
94#394—21no—
95#394—21no—
96#394—21no—
97#394—21no—
98#394—21no—
99#394—21no—
100#394—21no—
101#394—21no—
102#393—21no—
103#393—21no—
104#393—21no—
105#393—21no—
106#391C2×C411yescharacteristic
107#391C2×C411yescharacteristic
108#391C2×C411yescharacteristic
109#391C2×C411yescharacteristic
110#390—21no—
111#390—21no—
112#390—21no—
113#390—21no—
114#390C2×C411yescharacteristic
115#390C2×C411yescharacteristic
116#390C2311yescharacteristic
117#390C2311yescharacteristic
118#388—21no—
119#388—21no—
120#388—21no—
121#388—21no—
122#388—21no—
123#388—21no—
124#388—21no—
125#388—21no—
126#388—21no—
127#388—21no—
128#388—21no—
129#388—21no—
130#388—21no—
131#388—21no—
132#387—21no—
133#387—21no—
134#387—21no—
135#387—21no—
136#387—21no—
137#387—21no—
138#386—21no—
139#386—21no—
140#386—21no—
141#386—21no—
142#385—21no—
143#385—21no—
144#385—21no—
145#385—21no—
146#384C2×C411yescharacteristic
147#384C2311yescharacteristic
148#382C2×C411yescharacteristic
149#382C2311yescharacteristic
150C4×C4⋊C4C2×C411yescharacteristic
151C4×C4⋊C4C2×C411yescharacteristic
152C4×C22⋊C4—21no—
153C4×C22⋊C4—21no—
154C4×C22⋊C4—21no—
155C4×C22⋊C4—21no—
156C4×C22⋊C4C2×C411yescharacteristic
157C4×C22⋊C4C2×C411yescharacteristic
158#376C2×C411yescharacteristic
159C43C2×C411yescharacteristic
160#324—22no—
161#324—22no—
162#324—22no—
163#324—22no—
164#324C2314yes—
165#324C2314yes—
166#323—22no—
167#323—22no—
168C22×Q8—42no—
169C22×Q8—42no—
170C22×Q8—42no—
171C22×Q8C22⋊C411yescharacteristic
172C22×Q8C22⋊C411yescharacteristic
173C22×Q8C22×C411yescharacteristic
174C22×Q8C22×C411yescharacteristic
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4C22×C411yescharacteristic
180C22×D4C22×C411yescharacteristic
181C23×C4—21no—
182C23×C4—21no—
183C23×C4C22⋊C411yescharacteristic
184C23×C4C22⋊C411yescharacteristic
185C23×C4C22×C411yescharacteristic
186#127—42no—
187#125—42no—
188#124—42no—
189#124—42no—
190#124—42no—
191#124—42no—
192#123—44no—
193#123—44no—
194#121—44no—
195#121—44no—
196#121—42no—
197#121—42no—
198C4×Q8—24no—
199C4×Q8—24no—
200C4×Q8—42no—
201C4×Q8—42no—
202C4×Q8—42no—
203C4×Q8—42no—
204C4×Q8—42no—
205C4×Q8—42no—
206C4×D4—42no—
207C4×D4—42no—
208#117—24no—
209#117—42no—
210#117—42no—
211#117—42no—
212#117—42no—
213#117—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4C22⋊C411yescharacteristic
223C2×C4⋊C4C22⋊C411yescharacteristic
224C2×C4⋊C4C22⋊C411yescharacteristic
225C2×C4⋊C4C22⋊C411yescharacteristic
226C2×C4⋊C4C22⋊C411yescharacteristic
227C2×C4⋊C4C22⋊C411yescharacteristic
228C2×C4⋊C4C22×C411yescharacteristic
229C2×C4⋊C4C22×C411yescharacteristic
230C2×C4⋊C4C22×C411yescharacteristic
231C2×C4⋊C4C2×D411yescharacteristic
232C2×C4⋊C4C2×D411yescharacteristic
233C2×C4⋊C4C2×D411yescharacteristic
234C2×C4⋊C4C2×D411yescharacteristic
235C2×C4⋊C4C2411yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4C22⋊C411yescharacteristic
259C2×C22⋊C4C22⋊C411yescharacteristic
260C2×C22⋊C4C2×D411yescharacteristic
261C2×C22⋊C4C2×D411yescharacteristic
262C2×C42—21no—
263C2×C42—21no—
264C2×C42C22⋊C411yescharacteristic
265C2×C42C22⋊C411yescharacteristic
266C2×C42C22⋊C411yescharacteristic
267C2×C42C22⋊C411yescharacteristic
268C2×C42C22×C411yescharacteristic
269C2×C42C22×C411yescharacteristic
270C2×C42C22×C411yescharacteristic
271C2×C42C22×C411yescharacteristic
272C2×C42C22×C411yescharacteristic
273C2×C42C22×C411yescharacteristic
274C2×C42C2×D411yescharacteristic
275C2×C42C2×D411yescharacteristic
276C2×C42C2×D411yescharacteristic
277C2×C42C2×D411yescharacteristic
278C2×C42C2×D411yescharacteristic
279C2×C42C2×D411yescharacteristic
280C4⋊C8—42no—
281C4⋊C8—42no—
282C4⋊C8—42no—
283C4⋊C8—42no—
284C4⋊C8—42no—
285C4⋊C8—42no—
286C22⋊C8—24no—
287C22⋊C8—24no—
288#97—42no—
289#97—42no—
290#97—42no—
291#97—42no—
292C4×C8—42no—
293C4×C8—42no—
294#95—21no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—21no—
306#95—21no—
307#95—21no—
308#95—21no—
309#95—21no—
310#95—21no—
311#95—21no—
312C24—21no—
313C24—21no—
314C24C2×C22⋊C411yescharacteristic
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×Q8—41no—
324C2×Q8—41no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—416no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4—81no—
339C2×D4—81no—
340C2×D4—81no—
341C2×D4—81no—
342C2×D4—81no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4—81no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—81no—
364C22×C4—81no—
365C22×C4—81no—
366C22×C4—81no—
367C22×C4C2×C22⋊C411yescharacteristic
368C22×C4C2×C22⋊C411yescharacteristic
369C22×C4C2×C22⋊C411yescharacteristic
370C22×C4C2×C22⋊C411yescharacteristic
371C22×C4C2×C22⋊C411yescharacteristic
372C22×C4C2×C22⋊C411yescharacteristic
373C22×C4C2×C22⋊C411yescharacteristic
374C22×C4C2×C22⋊C411yescharacteristic
375C22×C4C2×C22⋊C411yescharacteristic
376C22×C4C2×C22⋊C411yescharacteristic
377C22×C4C2×C22⋊C411yescharacteristic
378C22×C4C23×C411yescharacteristic
379C22×C4C22×D411yescharacteristic
380C22×C4C22×D411yescharacteristic
381C2×C8—44no—
382C2×C8—44no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4—81no—
399C4⋊C4—81no—
400C4⋊C4—81no—
401C4⋊C4—81no—
402C4⋊C4—81no—
403C4⋊C4—81no—
404C4⋊C4#9914yes—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—41no—
408C22⋊C4—41no—
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—81no—
422C22⋊C4—81no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—81no—
428C22⋊C4—81no—
429C22⋊C4—81no—
430C22⋊C4—81no—
431C42—22no—
432C42—22no—
433C42—22no—
434C42—22no—
435C42—22no—
436C42—22no—
437C42—22no—
438C42—22no—
439C42—22no—
440C42—22no—
441C42—41no—
442C42—41no—
443C42—41no—
444C42—41no—
445C42—41no—
446C42—41no—
447C42—81no—
448C42—81no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23C22×C22⋊C411yescharacteristic
469Q8—44no—
470Q8—44no—
471Q8—44no—
472Q8—44no—
473D4—82no—
474D4—82no—
475D4—162no—
476D4—162no—
477D4—162no—
478D4—162no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—162no—
530C2×C4—162no—
531C2×C4C2×#9912yes—
532C2×C4C2×#9912yes—
533C2×C4C2×#9912yes—
534C2×C4#41312yes—
535C2×C4#56812yes—
536C8—84no—
537C8—84no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22#287911yescharacteristic
560C22C22×#9911yescharacteristic
561C22C2×#41311yescharacteristic
562C4—22no—
563C4—22no—
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C2—21no—
583C2—21no—
584C2—81no—
585C2—161no—
586C2—161no—
587C2#1740011yescharacteristic
588C2#3336211yescharacteristic
589C2#3337011yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC2×#540C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×#519 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #17371C2semidirect
3. #17371C2semidirect
4. #11571C2semidirect
5. #11567C2semidirect
6. #11554C2semidirect
7. #11550C2semidirect
8. #11534C2semidirect
9. #11530C2semidirect

Maximal subgroups

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

subgroupindex
#356782
#173712
#115712
#115672
#115542
#115502
#115342
#115302