Finite Group Databasebeta

← #482461

Subgroups — #482461

Order 512.

848 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36031C211yesmaximal, characteristic
2#20731C211yesmaximal, characteristic
3#17370C211yesmaximal, characteristic
4#11907C212yesmaximal, complemented
5#11905C212yesmaximal, complemented
6#11817C212yesmaximal, complemented
7#11814C212yesmaximal, complemented
8#11793C212yesmaximal, complemented
9#11790C212yesmaximal, complemented
10C2×#554C411yescharacteristic
11C2×#520C2211yescharacteristic
12#2975—21no—
13#2921—21no—
14#2628C411yescharacteristic
15#2627C411yescharacteristic
16#2627C2211yescharacteristic
17#2581C2211yescharacteristic
18#2568C2211yescharacteristic
19#2564C411yescharacteristic
20#2564C2211yescharacteristic
21#2487C411yescharacteristic
22#2487C2211yescharacteristic
23#2453—21no—
24#2450—21no—
25#2450—21no—
26#2442—21no—
27#2438—21no—
28#2438—21no—
29#2396C411yescharacteristic
30C2×#400C411yescharacteristic
31C2×#400C2211yescharacteristic
32#2349—21no—
33#2349C411yescharacteristic
34#2339—21no—
35#1821C2212yes—
36#1801C2212yes—
37#1800—21no—
38#1785—21no—
39C4×#101—21no—
40C4×#100C2212yes—
41#1465—21no—
42#1465C2212yes—
43#1463—21no—
44#1463C2212yes—
45#1461C2212yes—
46#1458—21no—
47#1354C2214yes—
48#1353C2214yes—
49#1353C2214yes—
50#1353C2214yes—
51C22×#41D411yescharacteristic
52#554—44no—
53C2×C4⋊Q8C2×C411yescharacteristic
54C2×#125—21no—
55C2×C22⋊Q8—21no—
56C2×C22⋊Q8—21no—
57C2×C22⋊Q8C2×C411yescharacteristic
58C2×C22⋊Q8C2×C411yescharacteristic
59#520—44no—
60C2×C4×Q8C2×C411yescharacteristic
61C2×C4×Q8D411yescharacteristic
62C2×C4×Q8C2311yescharacteristic
63C2×C4×D4—21no—
64C2×C4×D4—21no—
65C2×C4×D4C2×C411yescharacteristic
66C2×C4×D4C2×C411yescharacteristic
67C2×C4×D4D411yescharacteristic
68C2×C4×D4D411yescharacteristic
69C2×C4×D4D411yescharacteristic
70C2×C4×D4C2311yescharacteristic
71C2×#117C2×C411yescharacteristic
72C2×#117D411yescharacteristic
73C2×#117D411yescharacteristic
74C22×C4⋊C4C2×C411yescharacteristic
75C22×C4⋊C4C2×C411yescharacteristic
76C22×C4⋊C4C2×C411yescharacteristic
77C22×C4⋊C4D411yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79#436—44no—
80#433—44no—
81#431—22no—
82#423—22no—
83C2×#101—22no—
84C2×#100—22no—
85#407—22no—
86#407—22no—
87#407—22no—
88C4×M16—22no—
89#400—21no—
90#400—21no—
91#400—21no—
92#400—21no—
93#400C2×C411yescharacteristic
94#400C2×C411yescharacteristic
95#400C2×C411yescharacteristic
96#400C2×C411yescharacteristic
97#400C2×C411yescharacteristic
98#400C2×C411yescharacteristic
99#400C2311yescharacteristic
100#400C2311yescharacteristic
101#400C2311yescharacteristic
102#399C2×C411yescharacteristic
103#399C2×C411yescharacteristic
104#399C2×C411yescharacteristic
105#398—21no—
106#398—21no—
107#398—21no—
108#398—21no—
109#398—21no—
110#396—21no—
111#395—21no—
112#395C2×C411yescharacteristic
113#395C2×C411yescharacteristic
114#395C2311yescharacteristic
115#393—21no—
116#393C2×C411yescharacteristic
117#391—21no—
118#391—21no—
119#391—21no—
120#391—21no—
121#389—21no—
122#389—21no—
123#389—21no—
124#389—21no—
125#389—21no—
126#387—21no—
127#387—21no—
128#387—21no—
129#387—21no—
130#386—21no—
131#386—21no—
132#386—21no—
133#386—21no—
134#385—21no—
135#385—21no—
136#385—21no—
137#385—21no—
138#385—21no—
139#385—21no—
140#385—21no—
141#385—21no—
142#382—21no—
143#382C2×C411yescharacteristic
144#381—21no—
145#381—21no—
146#380—21no—
147#380—21no—
148#380—21no—
149#380—21no—
150#380—21no—
151#380C2×C411yescharacteristic
152#380C2×C411yescharacteristic
153C4×C4⋊C4—21no—
154C4×C4⋊C4C2×C411yescharacteristic
155C4×C22⋊C4—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95C2×C411yescharacteristic
161C2×#95C2×C411yescharacteristic
162#343—22no—
163#343C2314yes—
164#324—22no—
165#324—22no—
166#324C2314yes—
167#323—22no—
168C2×#41—24no—
169C2×#41—42no—
170C2×#41—42no—
171C22×Q8—21no—
172C22×Q8C22×C411yescharacteristic
173C22×Q8C2×D411yescharacteristic
174C22×D4C22⋊C411yescharacteristic
175C22×D4C22⋊C411yescharacteristic
176C22×D4C2×D411yescharacteristic
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4C22⋊C411yescharacteristic
182C23×C4C22⋊C411yescharacteristic
183C23×C4C22⋊C411yescharacteristic
184C23×C4C22⋊C411yescharacteristic
185C23×C4C22×C411yescharacteristic
186C23×C4C22×C411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C2×M16—24no—
191C2×M16—42no—
192C2×M16—42no—
193C4⋊Q8—42no—
194#125—44no—
195C22⋊Q8—44no—
196C22⋊Q8—42no—
197C22⋊Q8—44no—
198C22⋊Q8—42no—
199C4×Q8—42no—
200C4×Q8—42no—
201C4×Q8—42no—
202C4×D4—24no—
203C4×D4—24no—
204C4×D4—42no—
205C4×D4—42no—
206C4×D4—42no—
207C4×D4—42no—
208C4×D4—44no—
209C4×D4—44no—
210#117—24no—
211#117—42no—
212#117—42no—
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—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—42no—
230C2×C4⋊C4—42no—
231C2×C4⋊C4—42no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4C22⋊C411yescharacteristic
235C2×C4⋊C4C22⋊C411yescharacteristic
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⋊C4C2×D411yescharacteristic
244C2×C4⋊C4C2×D411yescharacteristic
245C2×C4⋊C4C2×D411yescharacteristic
246C2×C4⋊C4C2411yescharacteristic
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⋊C4C22⋊C411yescharacteristic
256C2×C22⋊C4C22⋊C411yescharacteristic
257C2×C22⋊C4C22⋊C411yescharacteristic
258C2×C22⋊C4C22⋊C411yescharacteristic
259C2×C22⋊C4C22×C411yescharacteristic
260C2×C22⋊C4C2×D411yescharacteristic
261C2×C42—21no—
262C2×C42—21no—
263C2×C42C22⋊C411yescharacteristic
264C2×C42C22⋊C411yescharacteristic
265C2×C42C22×C411yescharacteristic
266C2×C42C2×D411yescharacteristic
267C2×C42C2×D411yescharacteristic
268C2×C42C2×D411yescharacteristic
269C4⋊C8—44no—
270C4⋊C8—42no—
271#101—44no—
272#100—44no—
273C22⋊C8—24no—
274C22⋊C8—44no—
275C22⋊C8—42no—
276C22⋊C8—42no—
277#97—42no—
278C4×C8—42no—
279C4×C8—42no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—21no—
287#95—21no—
288#95—21no—
289#95—21no—
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#95C22×C411yescharacteristic
306#95C22×C411yescharacteristic
307#95C22×C411yescharacteristic
308#95C22×C411yescharacteristic
309C24C2×C22⋊C411yescharacteristic
310C24C2×C22⋊C411yescharacteristic
311C24C2×C22⋊C411yescharacteristic
312#41—416no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—42no—
317C2×Q8—81no—
318C2×Q8—81no—
319C2×Q8—81no—
320C2×Q8#13714yes—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—41no—
329C2×D4—41no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—81no—
358C22×C4—81no—
359C22×C4—81no—
360C22×C4—81no—
361C22×C4—81no—
362C22×C4—81no—
363C22×C4—81no—
364C22×C4—81no—
365C22×C4—81no—
366C22×C4—81no—
367C22×C4—81no—
368C22×C4—81no—
369C22×C4—81no—
370C22×C4—81no—
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×C4C2×C22⋊C411yescharacteristic
379C22×C4C2×C22⋊C411yescharacteristic
380C22×C4C23×C411yescharacteristic
381C22×C4C22×D411yescharacteristic
382C22×C4C22×D411yescharacteristic
383M16—44no—
384M16—44no—
385M16—162no—
386M16—162no—
387C2×C8—44no—
388C2×C8—44no—
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—41no—
401C4⋊C4—41no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—81no—
410C4⋊C4—81no—
411C4⋊C4—81no—
412C4⋊C4—81no—
413C4⋊C4—81no—
414C4⋊C4—81no—
415C4⋊C4—81no—
416C4⋊C4—81no—
417C4⋊C4—81no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—42no—
426C22⋊C4—42no—
427C22⋊C4—81no—
428C22⋊C4—81no—
429C22⋊C4—81no—
430C22⋊C4—81no—
431C22⋊C4#9914yes—
432C42—22no—
433C42—22no—
434C42—22no—
435C42—22no—
436C42—41no—
437C42—41no—
438C42—42no—
439C42—42no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23C2×#9912yes—
454C23#42112yes—
455C23C22×C22⋊C411yescharacteristic
456Q8—44no—
457Q8—82no—
458Q8—162no—
459D4—28no—
460D4—44no—
461D4—44no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
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—82no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4—82no—
516C2×C4—161no—
517C2×C4—161no—
518C2×C4—162no—
519C2×C4—162no—
520C2×C4—162no—
521C2×C4—162no—
522C2×C4C2×#9912yes—
523C2×C4C2×#9912yes—
524C2×C4#41912yes—
525C2×C4#41912yes—
526C2×C4C2×#13712yes—
527C8—84no—
528C8—84no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—81no—
546C22C22×#9911yescharacteristic
547C22C2×#41911yescharacteristic
548C22C2×#42111yescharacteristic
549C4—22no—
550C4—22no—
551C4—22no—
552C4—22no—
553C4—22no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C2—21no—
570C2—21no—
571C2—42no—
572C2—42no—
573C2—81no—
574C2#1757811yescharacteristic
575C2#3335011yescharacteristic
576C2#3337011yescharacteristic
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. #11907C2semidirect
5. #11905C2semidirect
6. #11817C2semidirect
7. #11814C2semidirect
8. #11793C2semidirect
9. #11790C2semidirect

Maximal subgroups

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

subgroupindex
#360312
#207312
#173702
#119072
#119052
#118172
#118142
#117932
#117902