Finite Group Databasebeta

← #482460

Subgroups — #482460

Order 512.

896 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35748C211yesmaximal, characteristic
2#20725C211yesmaximal, characteristic
3#17368C211yesmaximal, characteristic
4#11901C212yesmaximal, complemented
5#11897C212yesmaximal, complemented
6#11813C212yesmaximal, complemented
7#11810C212yesmaximal, complemented
8#11788C212yesmaximal, complemented
9#11784C212yesmaximal, complemented
10C2×Q82C411yescharacteristic, complemented
11C2×#520C2211yescharacteristic
12#2973—21no—
13#2628C411yescharacteristic, complemented
14#2628C411yescharacteristic, complemented
15#2628C2211yescharacteristic
16#2580C411yescharacteristic, complemented
17#2580C2211yescharacteristic
18#2580C2211yescharacteristic
19#2542C411yescharacteristic, complemented
20#2542C2211yescharacteristic
21#2542C2211yescharacteristic
22#2452—21no—
23#2452—21no—
24#2452—21no—
25#2440—21no—
26#2440—21no—
27#2440—21no—
28#2396C411yescharacteristic, complemented
29#2396C411yescharacteristic, complemented
30#2396C2211yescharacteristic
31#2351C411yescharacteristic, complemented
32Q8×C4⋊C4—21no—
33#2341—21no—
34#2313—21no—
35#1820C2212yes—
36#1799—21no—
37#1799C2212yes—
38#1782—21no—
39C4×#99—21no—
40C4×#99C2212yes—
41#1467—21no—
42#1465C2212yes—
43#1464C2212yes—
44#1463—21no—
45#1459C2212yes—
46C2×#324—21no—
47#1352C2214yes—
48#1352C2214yes—
49#1352C2214yes—
50#1351C2214yes—
51C22×#41D411yescharacteristic
52Q82—44no—
53C2×C4⋊Q8—21no—
54C2×C4⋊Q8—21no—
55C2×C4⋊Q8—21no—
56C2×C4⋊Q8C2×C411yescharacteristic
57C2×C4⋊Q8C2×C411yescharacteristic
58C2×C4⋊Q8C2×C411yescharacteristic
59C2×C22⋊Q8—21no—
60C2×C22⋊Q8—21no—
61C2×C22⋊Q8—21no—
62C2×C22⋊Q8—21no—
63C2×C22⋊Q8—21no—
64C2×C22⋊Q8—21no—
65#520—44no—
66C2×C4×Q8—21no—
67C2×C4×Q8—21no—
68C2×C4×Q8C2×C411yescharacteristic
69C2×C4×Q8C2×C411yescharacteristic
70C2×C4×Q8C2×C411yescharacteristic
71C2×C4×Q8C2×C411yescharacteristic
72C2×C4×Q8D411yescharacteristic
73C2×C4×D4C2×C411yescharacteristic
74C2×C4×D4D411yescharacteristic
75C2×C4×D4D411yescharacteristic
76C2×C4×D4D411yescharacteristic
77C2×C4×D4C2311yescharacteristic
78C2×C4×D4C2311yescharacteristic
79C2×#117C2×C411yescharacteristic
80C2×#117C2×C411yescharacteristic
81C2×#117C2311yescharacteristic
82C22×C4⋊C4D411yescharacteristic
83C22×C4⋊C4D411yescharacteristic
84C22×C4⋊C4D411yescharacteristic
85#435—44no—
86#432—22no—
87C2×#99—22no—
88C2×#99—22no—
89#407—22no—
90C2×C22⋊C8—22no—
91#400C2×C411yescharacteristic
92#400C2×C411yescharacteristic
93#400C2×C411yescharacteristic
94#399C2×C411yescharacteristic
95#399C2×C411yescharacteristic
96#399C2×C411yescharacteristic
97#399C2×C411yescharacteristic
98#399C2×C411yescharacteristic
99#399C2×C411yescharacteristic
100#399C2311yescharacteristic
101#399C2311yescharacteristic
102#399C2311yescharacteristic
103#398—21no—
104#398—21no—
105#398—21no—
106#396—21no—
107#396—21no—
108#396—21no—
109#395—21no—
110#395—21no—
111#395—21no—
112#395C2×C411yescharacteristic
113#393—21no—
114#393—21no—
115#393—21no—
116#393C2×C411yescharacteristic
117#393C2×C411yescharacteristic
118#393C2311yescharacteristic
119#390—21no—
120#390—21no—
121#390—21no—
122#390—21no—
123#390—21no—
124#390—21no—
125#389—21no—
126#389—21no—
127#389—21no—
128#389—21no—
129#389—21no—
130#389—21no—
131#389—21no—
132#389—21no—
133#389—21no—
134#387—44no—
135#385—21no—
136#385—21no—
137#385—21no—
138#385—21no—
139#385—21no—
140#385—21no—
141#384—21no—
142#384—21no—
143#384—21no—
144#382C2×C411yescharacteristic
145#382C2×C411yescharacteristic
146#382C2×C411yescharacteristic
147#381—22no—
148#380—21no—
149#380—21no—
150#380—21no—
151#380—22no—
152C4×C4⋊C4—21no—
153C4×C4⋊C4—21no—
154C4×C4⋊C4—21no—
155C4×C4⋊C4C2×C411yescharacteristic
156C4×C4⋊C4C2×C411yescharacteristic
157C4×C4⋊C4C2×C411yescharacteristic
158C4×C22⋊C4—21no—
159C4×C22⋊C4—21no—
160C4×C22⋊C4—21no—
161C4×C22⋊C4—22no—
162#342—22no—
163#342C2314yes—
164#324—22no—
165#324—22no—
166#324—22no—
167#323C2314yes—
168C2×#41—24no—
169C2×#41—42no—
170C2×#41—42no—
171C22×Q8—21no—
172C22×Q8—21no—
173C22×Q8—21no—
174C22×Q8C22⋊C411yescharacteristic
175C22×Q8C22×C411yescharacteristic
176C22×D4C22⋊C411yescharacteristic
177C22×D4C2×D411yescharacteristic
178C22×D4C2×D411yescharacteristic
179C23×C4C22⋊C411yescharacteristic
180C23×C4C22⋊C411yescharacteristic
181C23×C4C22⋊C411yescharacteristic
182C23×C4C22⋊C411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C2×M16—42no—
189C22×C8—42no—
190C4⋊Q8—42no—
191C4⋊Q8—42no—
192C4⋊Q8—42no—
193C4⋊Q8—44no—
194C4⋊Q8—44no—
195C4⋊Q8—44no—
196C22⋊Q8—82no—
197C22⋊Q8—82no—
198C22⋊Q8—82no—
199C22⋊Q8—82no—
200C22⋊Q8—82no—
201C22⋊Q8—82no—
202C4×Q8—24no—
203C4×Q8—42no—
204C4×Q8—42no—
205C4×Q8—42no—
206C4×Q8—42no—
207C4×Q8—44no—
208C4×Q8—44no—
209C4×D4—24no—
210C4×D4—42no—
211C4×D4—42no—
212C4×D4—42no—
213C4×D4—42no—
214C4×D4—42no—
215#117—42no—
216#117—42no—
217#117—42no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—42no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4C22⋊C411yescharacteristic
245C2×C4⋊C4C22⋊C411yescharacteristic
246C2×C4⋊C4C22⋊C411yescharacteristic
247C2×C4⋊C4C22⋊C411yescharacteristic
248C2×C4⋊C4C22⋊C411yescharacteristic
249C2×C4⋊C4C22⋊C411yescharacteristic
250C2×C4⋊C4C22×C411yescharacteristic
251C2×C4⋊C4C22×C411yescharacteristic
252C2×C4⋊C4C22×C411yescharacteristic
253C2×C4⋊C4C22×C411yescharacteristic
254C2×C4⋊C4C2×D411yescharacteristic
255C2×C4⋊C4C2×D411yescharacteristic
256C2×C4⋊C4C2×D411yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—24no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4C22⋊C411yescharacteristic
271C2×C22⋊C4C22⋊C411yescharacteristic
272C2×C22⋊C4C22×C411yescharacteristic
273C2×C22⋊C4C22×C411yescharacteristic
274C2×C22⋊C4C2×D411yescharacteristic
275C2×C22⋊C4C2411yescharacteristic
276C2×C42—21no—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—42no—
283C2×C42C22⋊C411yescharacteristic
284C2×C42C22⋊C411yescharacteristic
285C2×C42C22×C411yescharacteristic
286C2×C42C22×C411yescharacteristic
287C2×C42C22×C411yescharacteristic
288C2×C42C2×D411yescharacteristic
289C4⋊C8—42no—
290#99—44no—
291#99—44no—
292C22⋊C8—24no—
293C22⋊C8—42no—
294C22⋊C8—42no—
295#97—42no—
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—42no—
310#95—42no—
311#95—44no—
312#95C22×C411yescharacteristic
313#95C22×C411yescharacteristic
314#95C22×C411yescharacteristic
315#95C22×C411yescharacteristic
316C24C2×C22⋊C411yescharacteristic
317C24C2×C22⋊C411yescharacteristic
318C24C22×D411yescharacteristic
319#41—416no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—42no—
324C2×Q8—42no—
325C2×Q8—41no—
326C2×Q8—42no—
327C2×Q8—42no—
328C2×Q8—81no—
329C2×Q8—81no—
330C2×Q8—81no—
331C2×Q8—81no—
332C2×Q8—81no—
333C2×Q8—81no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4#13714yes—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—44no—
367C22×C4—81no—
368C22×C4—81no—
369C22×C4—81no—
370C22×C4—81no—
371C22×C4—81no—
372C22×C4—81no—
373C22×C4C2×C22⋊C411yescharacteristic
374C22×C4C2×C22⋊C411yescharacteristic
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×C4C23×C411yescharacteristic
384C22×C4C22×D411yescharacteristic
385M16—162no—
386C2×C8—44no—
387C2×C8—162no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
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—42no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4—42no—
415C4⋊C4—42no—
416C4⋊C4—81no—
417C4⋊C4—81no—
418C4⋊C4—81no—
419C4⋊C4—81no—
420C4⋊C4—81no—
421C4⋊C4—81no—
422C4⋊C4—162no—
423C4⋊C4#9914yes—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—42no—
431C22⋊C4—42no—
432C22⋊C4—42no—
433C22⋊C4—42no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—44no—
437C22⋊C4—44no—
438C22⋊C4—81no—
439C22⋊C4—81no—
440C22⋊C4—81no—
441C22⋊C4—81no—
442C22⋊C4—81no—
443C22⋊C4—81no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—22no—
448C42—41no—
449C42—41no—
450C42—42no—
451C42—42no—
452C42—42no—
453C42—42no—
454C42—42no—
455C42—42no—
456C42—162no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23#41912yes—
471C23C22×C22⋊C411yescharacteristic
472C23C2×#13712yes—
473Q8—28no—
474Q8—42no—
475Q8—42no—
476Q8—162no—
477Q8—162no—
478Q8—162no—
479D4—44no—
480D4—44no—
481D4—44no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
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—41no—
500C2×C4—41no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—41no—
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—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4—84no—
537C2×C4—84no—
538C2×C4—84no—
539C2×C4—161no—
540C2×C4—161no—
541C2×C4C2×#9912yes—
542C2×C4C2×#9912yes—
543C2×C4C2×#9912yes—
544C2×C4#41912yes—
545C2×C4#42112yes—
546C8—84no—
547C22—21no—
548C22—21no—
549C22—22no—
550C22—22no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C22×#9911yescharacteristic
565C22C2×#41911yescharacteristic
566C22C2×#42111yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—22no—
572C4—42no—
573C4—41no—
574C4—42no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—164no—
588C2—21no—
589C2—21no—
590C2—42no—
591C2—42no—
592C2—81no—
593C2#1757811yescharacteristic
594C2#3334911yescharacteristic
595C2#3335911yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC22×#41D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
4. #11901C2semidirect
5. #11897C2semidirect
6. #11813C2semidirect
7. #11810C2semidirect
8. #11788C2semidirect
9. #11784C2semidirect
10. C2×Q82C4semidirect
13. #2628C4semidirect
14. #2628C4semidirect
16. #2580C4semidirect
19. #2542C4semidirect
28. #2396C4semidirect
29. #2396C4semidirect
31. #2351C4semidirect

Maximal subgroups

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

subgroupindex
#357482
#207252
#173682
#119012
#118972
#118132
#118102
#117882
#117842