Finite Group Databasebeta

← #414887

Subgroups — #414887

Order 512.

1292 conjugacy classes of subgroups.

The subgroup lattice has 575 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2859C211yesmaximal, characteristic
2C2×#1989C212yesmaximal
3C2×#1989C212yesmaximal
4C4×#389C211yesmaximal, characteristic
5#11268C212yesmaximal
6#11267C211yesmaximal, characteristic
7#11267C211yesmaximal, characteristic
8#11208C212yesmaximal
9#11207C211yesmaximal, characteristic
10#11207C211yesmaximal, characteristic
11#10832C211yesmaximal, characteristic
12C22×#125C2212yes—
13C22×C4⋊C8C2212yes—
14#2859—28no—
15C2×#389—21no—
16C2×#389—21no—
17C2×#389—21no—
18C2×#389—21no—
19C2×#389C2211yescharacteristic
20C2×#389C2211yescharacteristic
21C2×#384C2211yescharacteristic
22C2×#384C2211yescharacteristic
23C2×#382C2212yes—
24C2×C4×C4⋊C4—21no—
25C2×C4×C4⋊C4C2211yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×C43C2211yescharacteristic
28#1989—28no—
29#1989—28no—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#340C2212yes—
38C2×#336C2211yescharacteristic
39C2×#336C2211yescharacteristic
40C2×#336C2212yes—
41#1436—21no—
42#1436—21no—
43C4⋊#95C2211yescharacteristic
44C4⋊#95C2211yescharacteristic
45C4×#95—21no—
46C23×C8C2312yes—
47C23×C8C2312yes—
48C2×#125—24no—
49C2×#125—24no—
50C2×#125—24no—
51C2×#125—24no—
52C2×#125—24no—
53C2×#125D418yes—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4C2312yes—
63C22×C4⋊C4C2312yes—
64C22×C4⋊C4C2311yescharacteristic
65C22×C4⋊C4C2311yescharacteristic
66C22×C4⋊C4C2311yescharacteristic
67C22×C4⋊C4C2311yescharacteristic
68C22×C42—21no—
69C22×C42—21no—
70C22×C42D411yescharacteristic
71C22×C42D411yescharacteristic
72C22×C42D411yescharacteristic
73C22×C42D411yescharacteristic
74C22×C42C2311yescharacteristic
75C22×C42C2311yescharacteristic
76C22×C42C2311yescharacteristic
77C2×C4⋊C8—24no—
78C2×C4⋊C8—24no—
79C2×C4⋊C8—24no—
80#389—28no—
81#389—28no—
82#389—28no—
83#389—28no—
84#389—22no—
85#389—22no—
86#389Q814yes—
87#389Q814yes—
88#384—24no—
89#384—24no—
90#382—24no—
91#382—24no—
92C4×C4⋊C4—22no—
93C4×C4⋊C4—24no—
94C4×C4⋊C4—44no—
95C4×C4⋊C4D414yes—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C43—24no—
107#340—24no—
108#340—24no—
109#340—24no—
110#340—24no—
111#340—24no—
112#340—24no—
113#340—24no—
114#340—24no—
115#336—22no—
116#336—22no—
117#336—24no—
118C23×C4—21no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D411yescharacteristic
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C23×C4C2411yescharacteristic
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145#125—216no—
146#125—216no—
147#125—48no—
148#125—48no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—28no—
171C2×C4⋊C4—28no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—44no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4C2×D414yes—
196C2×C4⋊C4C2×D414yes—
197C2×C4⋊C4C2×D412yes—
198C2×C4⋊C4C2×D412yes—
199C2×C4⋊C4C2×Q812yes—
200C2×C4⋊C4C2×Q812yes—
201C2×C4⋊C4C2×Q812yes—
202C2×C4⋊C4C2×Q812yes—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—24no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—41no—
217C2×C42—41no—
218C2×C42—41no—
219C2×C42—41no—
220C2×C42—42no—
221C2×C42—42no—
222C2×C42—42no—
223C2×C42—42no—
224C2×C42—42no—
225C2×C42C2×D412yes—
226C2×C42C2×D414yes—
227C2×C42C2×Q812yes—
228C2×C42C2×Q812yes—
229C2×C42#4112yes—
230C2×C42#4112yes—
231C2×C42#4114yes—
232C2×C42#4112yes—
233C4⋊C8—48no—
234#95—28no—
235#95—28no—
236#95—24no—
237#95—24no—
238#95—24no—
239#95—42no—
240#95—42no—
241#95—42no—
242#95—42no—
243#95—42no—
244C24C22×D411yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4#12012yes—
316C22×C4#12012yes—
317C22×C4#12112yes—
318C22×C4#12112yes—
319C22×C4C22⋊Q812yes—
320C22×C4C22⋊Q812yes—
321C22×C4C22⋊Q812yes—
322C22×C4C22⋊Q812yes—
323C22×C4#12412yes—
324C22×C4#12412yes—
325C22×C4#13512yes—
326C22×C4#13512yes—
327C22×C4AGL(1,ℤ/8)12yes—
328C22×C4#13712yes—
329C22×C4C22×D411yescharacteristic
330C22×C4C22×D412yes—
331C22×C4C22×Q811yescharacteristic
332C22×C4C22×Q811yescharacteristic
333C22×C4C2×#4112yes—
334C22×C4C2×#4111yescharacteristic
335C22×C4C2×#4111yescharacteristic
336C22×C4C2×#4111yescharacteristic
337C22×C42−1+412yes—
338C22×C42−1+412yes—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C2×C8—42no—
350C2×C8—42no—
351C2×C8—42no—
352C2×C8—42no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—24no—
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—48no—
364C4⋊C4—48no—
365C4⋊C4—48no—
366C4⋊C4—48no—
367C4⋊C4—48no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—416no—
376C4⋊C4—416no—
377C4⋊C4—48no—
378C4⋊C4C4⋊Q814yes—
379C42—24no—
380C42—24no—
381C42—24no—
382C42—24no—
383C42—44no—
384C42—44no—
385C42—44no—
386C42—44no—
387C42—48no—
388C42—84no—
389C42#12118yes—
390C42#12318yes—
391C23C2×#12011yescharacteristic
392C23C2×#12111yescharacteristic
393C23C2×C22⋊Q811yescharacteristic
394C23C2×C22⋊Q811yescharacteristic
395C23C2×#12411yescharacteristic
396C23#53611yescharacteristic
397C23#53611yescharacteristic
398C23C2×#13511yescharacteristic
399C23C2×#13511yescharacteristic
400C23C2×AGL(1,ℤ/8)11yescharacteristic
401C23C2×#13711yescharacteristic
402C23#57511yescharacteristic
403C23#57511yescharacteristic
404C23#57511yescharacteristic
405C23#57511yescharacteristic
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4#39414yes—
487C2×C4#39414yes—
488C2×C4#47814yes—
489C2×C4#47914yes—
490C2×C4C2×#12112yes—
491C2×C4C2×#12312yes—
492C2×C4C2×C4⋊Q811yescharacteristic
493C2×C4#53211yescharacteristic
494C2×C4#53311yescharacteristic
495C2×C4#53311yescharacteristic
496C2×C4#53612yes—
497C2×C4#54112yes—
498C2×C4#54812yes—
499C2×C4#54812yes—
500C2×C4D4×Q812yes—
501C2×C4D4×Q812yes—
502C2×C4#55612yes—
503C2×C4#55612yes—
504C2×C4#55712yes—
505C2×C4#55712yes—
506C8—82no—
507C8—82no—
508C22C2×#39411yescharacteristic
509C22#240911yescharacteristic
510C22#240911yescharacteristic
511C22#256811yescharacteristic
512C22#256811yescharacteristic
513C22#262111yescharacteristic
514C22#285711yescharacteristic
515C22#300211yescharacteristic
516C22#300211yescharacteristic
517C22#300611yescharacteristic
518C22#300711yescharacteristic
519C22#303511yescharacteristic
520C22#303511yescharacteristic
521C22#303611yescharacteristic
522C22#303711yescharacteristic
523C22C2×#47811yescharacteristic
524C22C2×#47911yescharacteristic
525C22#307611yescharacteristic
526C22#307611yescharacteristic
527C22#307711yescharacteristic
528C22#307811yescharacteristic
529C22#308011yescharacteristic
530C22#308011yescharacteristic
531C22#313111yescharacteristic
532C22#313511yescharacteristic
533C22#314111yescharacteristic
534C22#314211yescharacteristic
535C22#322811yescharacteristic
536C22#323111yescharacteristic
537C22#323211yescharacteristic
538C22#323211yescharacteristic
539C22#323411yescharacteristic
540C22#323611yescharacteristic
541C22#324011yescharacteristic
542C22#324011yescharacteristic
543C4—24no—
544C4—24no—
545C4—24no—
546C4—24no—
547C4—44no—
548C4—42no—
549C4—42no—
550C4—82no—
551C4—84no—
552C4—84no—
553C4—82no—
554C4—82no—
555C4#244612yes—
556C4#244612yes—
557C4#254512yes—
558C4#254612yes—
559C2#1518011yescharacteristic
560C2#2350411yescharacteristic
561C2#2350811yescharacteristic
562C2#2430411yescharacteristic
563C2#2430511yescharacteristic
564C2#2430611yescharacteristic
565C2#2430711yescharacteristic
566C2#2922011yescharacteristic
567C2#2922111yescharacteristic
568C2#2922311yescharacteristic
569C2#2922711yescharacteristic
570C2#2987011yescharacteristic
571C2#2987111yescharacteristic
572C2#3319911yescharacteristic
573C2#3320011yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#28592
C2×#19892
C4×#3892
#112682
#112672
#112082
#112072
#108322