Finite Group Databasebeta

← #480842

Subgroups — #480842

Order 512.

855 conjugacy classes of subgroups.

The subgroup lattice has 605 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35454C211yesmaximal, characteristic
2#17372C211yesmaximal, characteristic, complemented
3#17370C211yesmaximal, characteristic, complemented
4#11579C212yesmaximal, complemented
5#11559C212yesmaximal, complemented
6#11548C212yesmaximal, complemented
7#11542C212yesmaximal, complemented
8#11527C212yesmaximal, complemented
9#11526C212yesmaximal, complemented
10C22×#126C411yescharacteristic
11C2×#520C2211yescharacteristic
12#2983—21no—
13#2975—21no—
14#2534C411yescharacteristic
15#2534C2211yescharacteristic
16#2487C411yescharacteristic
17#2487C2211yescharacteristic
18#2484C2211yescharacteristic
19#2482C2211yescharacteristic
20#2481—21no—
21#2481—21no—
22#2479—21no—
23#2479—21no—
24#2469—21no—
25#2469—21no—
26#2467—21no—
27#2467—21no—
28#2406C411yescharacteristic
29#2404C411yescharacteristic
30#2321C411yescharacteristic
31#2321C2211yescharacteristic
32#2313C411yescharacteristic
33C4×#123C411yescharacteristic
34C4×#123C2211yescharacteristic
35#1466—21no—
36#1466C2212yes—
37#1465C2212yes—
38#1465C2212yes—
39#1464—21no—
40#1464C2212yes—
41#1463—21no—
42#1463—21no—
43#1461—21no—
44#1460C2212yes—
45#1458—21no—
46#1458C2212yes—
47#1326C2214yes—
48#1326C2214yes—
49#1317C2214yes—
50#1316C2214yes—
51C22×#41C2×C411yescharacteristic
52C2×#126—21no—
53C2×#126—21no—
54C2×#126—21no—
55C2×#126—21no—
56C2×#126—44no—
57C2×#123C2×C411yescharacteristic
58C2×#123C2×C411yescharacteristic
59C2×#120C2×C411yescharacteristic
60C2×#120C2×C411yescharacteristic
61#520—44no—
62C2×C4×Q8D411yescharacteristic
63C2×C4×Q8D411yescharacteristic
64C2×C4×D4C2×C411yescharacteristic
65C2×C4×D4C2×C411yescharacteristic
66C2×C4×D4D411yescharacteristic
67C2×C4×D4D411yescharacteristic
68C2×C4×D4C2311yescharacteristic
69C2×C4×D4C2311yescharacteristic
70C2×#117D411yescharacteristic
71C2×#117D411yescharacteristic
72C2×#117C2311yescharacteristic
73C22×C4⋊C4C2×C411yescharacteristic
74C22×C4⋊C4C2×C411yescharacteristic
75C22×C4⋊C4C2×C411yescharacteristic
76C22×C4⋊C4D411yescharacteristic
77C22×C4⋊C4D411yescharacteristic
78C22×C22⋊C4C2×C411yescharacteristic
79C22×C22⋊C4C2×C411yescharacteristic
80C22×C22⋊C4C2×C411yescharacteristic
81C22×C42C2×C411yescharacteristic
82#446—44no—
83#436—44no—
84#432—22no—
85#432—22no—
86#431—22no—
87#431—22no—
88#407—22no—
89#407—22no—
90#400—21no—
91#400—21no—
92#400—21no—
93#399—21no—
94#399—21no—
95#399—21no—
96#398—21no—
97#397—21no—
98#396—21no—
99#396—21no—
100#395—21no—
101#394—21no—
102#394—21no—
103#394—21no—
104#393—21no—
105#392—21no—
106#390—21no—
107#390—21no—
108#389—21no—
109#389—21no—
110#388—21no—
111#388—21no—
112#388—21no—
113#388—21no—
114#388—21no—
115#388—21no—
116#388—21no—
117#388—21no—
118#388—21no—
119#388—21no—
120#387—21no—
121#387—21no—
122#387—21no—
123#387—21no—
124#387—21no—
125#387—21no—
126#387—21no—
127#387—21no—
128#386—21no—
129#386—21no—
130#386—21no—
131#386—21no—
132#386—21no—
133#386—21no—
134#386C2×C411yescharacteristic
135#386C2×C411yescharacteristic
136#386C2×C411yescharacteristic
137#386C2×C411yescharacteristic
138#385—21no—
139#385—21no—
140#385C2×C411yescharacteristic
141#385C2×C411yescharacteristic
142#385C2311yescharacteristic
143#385C2311yescharacteristic
144#381C2×C411yescharacteristic
145#381C2×C411yescharacteristic
146#381C2×C411yescharacteristic
147#381C2311yescharacteristic
148#380—21no—
149#380—21no—
150#380C2×C411yescharacteristic
151#380C2×C411yescharacteristic
152#379C2×C411yescharacteristic
153#379C2311yescharacteristic
154C4×C4⋊C4—21no—
155C4×C4⋊C4—21no—
156C4×C22⋊C4—21no—
157C4×C22⋊C4—21no—
158C4×C22⋊C4C2×C411yescharacteristic
159C4×C22⋊C4C2×C411yescharacteristic
160#324—22no—
161#324—22no—
162#324—22no—
163#324—22no—
164#323—22no—
165#323—22no—
166#323C2314yes—
167#323C2314yes—
168C25C22×C411yescharacteristic
169C2×#41—42no—
170C2×#41—42no—
171C2×#41—42no—
172C22×Q8C22⋊C411yescharacteristic
173C22×D4—21no—
174C22×D4—21no—
175C22×D4C22⋊C411yescharacteristic
176C22×D4C22×C411yescharacteristic
177C22×D4C22×C411yescharacteristic
178C23×C4C22⋊C411yescharacteristic
179C23×C4C22⋊C411yescharacteristic
180C23×C4C22⋊C411yescharacteristic
181C23×C4C22⋊C411yescharacteristic
182C23×C4C22×C411yescharacteristic
183C23×C4C22×C411yescharacteristic
184C23×C4C22×C411yescharacteristic
185C23×C4C22×C411yescharacteristic
186C23×C4C22×C411yescharacteristic
187C23×C4C22×C411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C2×M16—42no—
191C2×M16—42no—
192#126—44no—
193#126—44no—
194#126—44no—
195#126—44no—
196#123—42no—
197#123—42no—
198#120—42no—
199#120—42no—
200C4×Q8—24no—
201C4×Q8—42no—
202C4×D4—24no—
203C4×D4—42no—
204C4×D4—42no—
205C4×D4—42no—
206C4×D4—42no—
207C4×D4—42no—
208#117—42no—
209#117—42no—
210#117—42no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
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⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4—42no—
227C2×C4⋊C4—42no—
228C2×C4⋊C4C22⋊C411yescharacteristic
229C2×C4⋊C4C22⋊C411yescharacteristic
230C2×C4⋊C4C22⋊C411yescharacteristic
231C2×C4⋊C4C22⋊C411yescharacteristic
232C2×C4⋊C4C22⋊C411yescharacteristic
233C2×C4⋊C4C22⋊C411yescharacteristic
234C2×C4⋊C4C2×D411yescharacteristic
235C2×C4⋊C4C2×D411yescharacteristic
236C2×C4⋊C4C2×D411yescharacteristic
237C2×C4⋊C4C2×D411yescharacteristic
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—42no—
257C2×C22⋊C4—42no—
258C2×C22⋊C4—42no—
259C2×C22⋊C4C22⋊C411yescharacteristic
260C2×C22⋊C4C22⋊C411yescharacteristic
261C2×C22⋊C4C22×C411yescharacteristic
262C2×C22⋊C4C22×C411yescharacteristic
263C2×C22⋊C4C22×C411yescharacteristic
264C2×C22⋊C4C22×C411yescharacteristic
265C2×C22⋊C4C22×C411yescharacteristic
266C2×C22⋊C4C2×D411yescharacteristic
267C2×C22⋊C4C2×D411yescharacteristic
268C2×C22⋊C4C2411yescharacteristic
269C2×C42—21no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42—42no—
274C2×C42C22⋊C411yescharacteristic
275C2×C42C22⋊C411yescharacteristic
276C2×C42C2×D411yescharacteristic
277C2×C42C2×D411yescharacteristic
278C2×C42C2×D411yescharacteristic
279C2×C42C2×D411yescharacteristic
280C4⋊C8—42no—
281C4⋊C8—42no—
282C4⋊C8—42no—
283C4⋊C8—42no—
284C22⋊C8—24no—
285C22⋊C8—24no—
286C22⋊C8—42no—
287C22⋊C8—42no—
288#97—42no—
289#97—42no—
290C4×C8—42no—
291C4×C8—42no—
292#95—21no—
293#95—21no—
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—22no—
314C24—41no—
315C24—41no—
316C24—81no—
317C24—81no—
318C24C2×C22⋊C411yescharacteristic
319C24C2×C22⋊C411yescharacteristic
320C24C23×C411yescharacteristic
321#41—416no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—41no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—81no—
337C2×D4—81no—
338C2×D4—81no—
339C2×D4—81no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—81no—
368C22×C4—81no—
369C22×C4—81no—
370C22×C4—81no—
371C22×C4—81no—
372C22×C4—81no—
373C22×C4—81no—
374C22×C4—81no—
375C22×C4C2×C22⋊C411yescharacteristic
376C22×C4C2×C22⋊C411yescharacteristic
377C22×C4C2×C22⋊C411yescharacteristic
378C22×C4C2×C22⋊C411yescharacteristic
379C22×C4C2×C22⋊C411yescharacteristic
380C22×C4C2×C22⋊C411yescharacteristic
381C22×C4C2×C22⋊C411yescharacteristic
382C22×C4C2×C22⋊C411yescharacteristic
383C22×C4C2×C22⋊C411yescharacteristic
384C22×C4C2×C22⋊C411yescharacteristic
385C22×C4C22×D411yescharacteristic
386C22×C4C22×D411yescharacteristic
387M16—162no—
388M16—162no—
389C2×C8—44no—
390C2×C8—44no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—81no—
407C4⋊C4—81no—
408C4⋊C4—81no—
409C4⋊C4—81no—
410C4⋊C4—81no—
411C4⋊C4—81no—
412C4⋊C4#9914yes—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
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—41no—
432C22⋊C4—41no—
433C22⋊C4—81no—
434C22⋊C4—81no—
435C22⋊C4—81no—
436C22⋊C4—81no—
437C22⋊C4—81no—
438C22⋊C4—81no—
439C22⋊C4—81no—
440C22⋊C4—81no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—22no—
445C42—41no—
446C42—41no—
447C42—42no—
448C42—42no—
449C42—81no—
450C42—81no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—82no—
473C23—82no—
474C23—82no—
475C23—162no—
476C23—162no—
477C23C22×C22⋊C411yescharacteristic
478C23#56812yes—
479Q8—44no—
480D4—44no—
481D4—44no—
482D4—44no—
483D4—162no—
484D4—162no—
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—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—44no—
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—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—161no—
541C2×C4—161no—
542C2×C4C2×#9912yes—
543C2×C4C2×#9912yes—
544C2×C4C2×#9912yes—
545C2×C4#41312yes—
546C8—84no—
547C8—84no—
548C22—21no—
549C22—21no—
550C22—22no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—164no—
573C22#287911yescharacteristic
574C22C22×#9911yescharacteristic
575C22C2×#41311yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C2—21no—
596C2—21no—
597C2—42no—
598C2—81no—
599C2—81no—
600C2—161no—
601C2#1740011yescharacteristic
602C2#3335011yescharacteristic
603C2#3335111yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radical#2404C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×#520 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #17372C2semidirect
3. #17370C2semidirect
4. #11579C2semidirect
5. #11559C2semidirect
6. #11548C2semidirect
7. #11542C2semidirect
8. #11527C2semidirect
9. #11526C2semidirect

Maximal subgroups

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

subgroupindex
#354542
#173722
#173702
#115792
#115592
#115482
#115422
#115272
#115262