Finite Group Databasebeta

← #481809

Subgroups — #481809

Order 512.

903 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
1#35846C211yesmaximal, characteristic
2#20397C211yesmaximal, characteristic
3#17368C211yesmaximal, characteristic
4#11792C212yesmaximal, complemented
5#11782C212yesmaximal, complemented
6#11768C212yesmaximal, complemented
7#11764C212yesmaximal, complemented
8#11739C212yesmaximal, complemented
9#11735C212yesmaximal, complemented
10C2×#556C411yescharacteristic
11C2×#520C2211yescharacteristic
12#2973—21no—
13C2×#413—21no—
14#2873—21no—
15#2638C411yescharacteristic
16#2638C2211yescharacteristic
17#2621C411yescharacteristic
18#2583C411yescharacteristic
19#2583C2211yescharacteristic
20#2581C2211yescharacteristic
21#2546C2211yescharacteristic
22#2484C411yescharacteristic
23#2484C2211yescharacteristic
24#2478—21no—
25#2478—21no—
26#2466—21no—
27#2466—21no—
28#2447—21no—
29#2432—21no—
30#2396C411yescharacteristic
31#2395C411yescharacteristic
32#2395C2211yescharacteristic
33#2365—21no—
34#2360—21no—
35#2357C411yescharacteristic
36C4×#101—21no—
37C4×#101C2212yes—
38C4×#100—21no—
39C4×#100C2212yes—
40C2×#343C2212yes—
41#1467C2212yes—
42#1465—21no—
43#1464—21no—
44#1463C2212yes—
45#1459C2212yes—
46C2×#324—21no—
47#1354C2214yes—
48#1353C2214yes—
49#1346C2214yes—
50#1346C2214yes—
51C22×#41D411yescharacteristic
52C22×M16—22no—
53#556—44no—
54C2×C4⋊Q8—21no—
55C2×C4⋊Q8C2×C411yescharacteristic
56C2×#126—21no—
57C2×#126—21no—
58C2×#124—21no—
59C2×C22⋊Q8—21no—
60C2×C22⋊Q8C2×C411yescharacteristic
61C2×C22⋊Q8C2×C411yescharacteristic
62#520—44no—
63C2×C4×Q8—21no—
64C2×C4×Q8C2×C411yescharacteristic
65C2×C4×Q8D411yescharacteristic
66C2×C4×Q8C2311yescharacteristic
67C2×C4×D4C2×C411yescharacteristic
68C2×C4×D4C2×C411yescharacteristic
69C2×C4×D4D411yescharacteristic
70C2×C4×D4D411yescharacteristic
71C2×C4×D4D411yescharacteristic
72C2×C4×D4C2311yescharacteristic
73C2×#117C2×C411yescharacteristic
74C2×#117C2×C411yescharacteristic
75C2×#117C2×C411yescharacteristic
76C2×#117D411yescharacteristic
77C2×#117D411yescharacteristic
78C22×C4⋊C4C2×C411yescharacteristic
79C22×C4⋊C4D411yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81#435—44no—
82#432—22no—
83#413—28no—
84C2×#101—22no—
85C2×#100—22no—
86#407—22no—
87C2×C22⋊C8—22no—
88#405—44no—
89C4×M16—22no—
90C4×M16—22no—
91#400C2×C411yescharacteristic
92#400C2×C411yescharacteristic
93#400C2311yescharacteristic
94#399C2×C411yescharacteristic
95#398—21no—
96#398—21no—
97#398C2×C411yescharacteristic
98#398C2×C411yescharacteristic
99#398C2×C411yescharacteristic
100#398C2×C411yescharacteristic
101#398C2311yescharacteristic
102#398C2311yescharacteristic
103#397—21no—
104#397—21no—
105#397—21no—
106#397—21no—
107#397—21no—
108#397C2×C411yescharacteristic
109#397C2×C411yescharacteristic
110#396—21no—
111#395C2×C411yescharacteristic
112#395C2×C411yescharacteristic
113#395C2311yescharacteristic
114#394—21no—
115#394—21no—
116#394—21no—
117#394—21no—
118#393C2×C411yescharacteristic
119#391—21no—
120#391—21no—
121#391—21no—
122#390—21no—
123#389—21no—
124#389—21no—
125#389—21no—
126#389—21no—
127#389—21no—
128#389—21no—
129#389—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#387—21no—
139#387—21no—
140#385—21no—
141#385—21no—
142#385—21no—
143#385—21no—
144#385—21no—
145#385—21no—
146#385—21no—
147#385—21no—
148#382C2×C411yescharacteristic
149#381—21no—
150#381—21no—
151#381C2×C411yescharacteristic
152#381C2×C411yescharacteristic
153C4×C4⋊C4—21no—
154C4×C4⋊C4—21no—
155C4×C4⋊C4—21no—
156C4×C4⋊C4—21no—
157C4×C4⋊C4C2×C411yescharacteristic
158C4×C22⋊C4—21no—
159C4×C22⋊C4—21no—
160C4×C22⋊C4—21no—
161C4×C22⋊C4C2×C411yescharacteristic
162C4×C22⋊C4C2×C411yescharacteristic
163#343—22no—
164#343C2314yes—
165#324—22no—
166#324—22no—
167#324C2314yes—
168#323—22no—
169C2×#41—24no—
170C2×#41—42no—
171C2×#41—42no—
172C22×Q8—21no—
173C22×Q8C22×C411yescharacteristic
174C22×Q8C2×D411yescharacteristic
175C22×D4C22⋊C411yescharacteristic
176C22×D4C22⋊C411yescharacteristic
177C22×D4C2×D411yescharacteristic
178C23×C4C22⋊C411yescharacteristic
179C23×C4C22⋊C411yescharacteristic
180C23×C4C22⋊C411yescharacteristic
181C23×C4C22⋊C411yescharacteristic
182C23×C4C22×C411yescharacteristic
183C23×C4C22×C411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C2×M16—28no—
188C2×M16—24no—
189C2×M16—44no—
190C2×M16—42no—
191C2×M16—42no—
192C22×C8—42no—
193C22×C8—42no—
194C4⋊Q8—42no—
195C4⋊Q8—44no—
196#126—44no—
197#126—44no—
198#124—44no—
199C22⋊Q8—44no—
200C22⋊Q8—42no—
201C22⋊Q8—42no—
202C4×Q8—42no—
203C4×Q8—42no—
204C4×Q8—42no—
205C4×Q8—44no—
206C4×D4—24no—
207C4×D4—24no—
208C4×D4—42no—
209C4×D4—42no—
210C4×D4—42no—
211C4×D4—42no—
212#117—24no—
213#117—42no—
214#117—42no—
215#117—42no—
216#117—42no—
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—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—42no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4C22⋊C411yescharacteristic
237C2×C4⋊C4C22⋊C411yescharacteristic
238C2×C4⋊C4C22⋊C411yescharacteristic
239C2×C4⋊C4C22⋊C411yescharacteristic
240C2×C4⋊C4C22×C411yescharacteristic
241C2×C4⋊C4C22×C411yescharacteristic
242C2×C4⋊C4C22×C411yescharacteristic
243C2×C4⋊C4C22×C411yescharacteristic
244C2×C4⋊C4C22×C411yescharacteristic
245C2×C4⋊C4C2×D411yescharacteristic
246C2×C4⋊C4C2×D411yescharacteristic
247C2×C4⋊C4C2×D411yescharacteristic
248C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
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×C42—21no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42C22⋊C411yescharacteristic
274C2×C42C22⋊C411yescharacteristic
275C2×C42C22×C411yescharacteristic
276C2×C42C2×D411yescharacteristic
277C2×C42C2×D411yescharacteristic
278C2×C42C2×D411yescharacteristic
279C4⋊C8—42no—
280#101—28no—
281#100—28no—
282C22⋊C8—24no—
283C22⋊C8—42no—
284C22⋊C8—42no—
285#97—42no—
286#97—42no—
287#97—42no—
288C4×C8—42no—
289C4×C8—42no—
290#95—21no—
291#95—21no—
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#95C22×C411yescharacteristic
312#95C22×C411yescharacteristic
313#95C22×C411yescharacteristic
314#95C22×C411yescharacteristic
315C24C2×C22⋊C411yescharacteristic
316C24C2×C22⋊C411yescharacteristic
317C24C2×C22⋊C411yescharacteristic
318#41—48no—
319#41—48no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—41no—
323C2×Q8—42no—
324C2×Q8—42no—
325C2×Q8—41no—
326C2×Q8—42no—
327C2×Q8—81no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—81no—
360C22×C4—81no—
361C22×C4—81no—
362C22×C4—81no—
363C22×C4—81no—
364C22×C4—81no—
365C22×C4#10414yes—
366C22×C4C2×C22⋊C411yescharacteristic
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×C4C23×C411yescharacteristic
376C22×C4C22×D411yescharacteristic
377C22×C4C22×D411yescharacteristic
378M16—28no—
379M16—48no—
380M16—44no—
381M16—162no—
382C2×C8—44no—
383C2×C8—48no—
384C2×C8—44no—
385C2×C8—162no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—42no—
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—81no—
413C4⋊C4—81no—
414C4⋊C4—81no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
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—81no—
430C22⋊C4—81no—
431C22⋊C4—81no—
432C22⋊C4#9914yes—
433C42—22no—
434C42—22no—
435C42—22no—
436C42—22no—
437C42—41no—
438C42—41no—
439C42—42no—
440C42—42no—
441C42—42no—
442C42—42no—
443C42—81no—
444C42—81no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23C2×#9912yes—
459C23C2×#10412yes—
460C23C22×C22⋊C411yescharacteristic
461Q8—44no—
462Q8—84no—
463Q8—82no—
464D4—44no—
465D4—44no—
466D4—44no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
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—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—161no—
523C2×C4—161no—
524C2×C4C2×#9912yes—
525C2×C4C2×#9912yes—
526C2×C4C2×#10412yes—
527C2×C4C2×#10412yes—
528C2×C4#57512yes—
529C8—48no—
530C8—84no—
531C22—21no—
532C22—21no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—42no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22C22×#9911yescharacteristic
549C22#289611yescharacteristic
550C22C22×#10411yescharacteristic
551C4—22no—
552C4—22no—
553C4—22no—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C2—21no—
572C2—21no—
573C2—42no—
574C2—42no—
575C2—81no—
576C2#1754211yescharacteristic
577C2#3335011yescharacteristic
578C2#3337211yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC22×#41D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#520 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11792C2semidirect
5. #11782C2semidirect
6. #11768C2semidirect
7. #11764C2semidirect
8. #11739C2semidirect
9. #11735C2semidirect

Maximal subgroups

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

subgroupindex
#358462
#203972
#173682
#117922
#117822
#117682
#117642
#117392
#117352