Finite Group Databasebeta

← #468159

Subgroups — #468159

Order 512.

1176 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2859C211yesmaximal, characteristic
2C2×#2059C212yesmaximal
3#14699C211yesmaximal, characteristic
4#11385C212yesmaximal
5#11325C212yesmaximal
6#11324C211yesmaximal, characteristic
7#11323C211yesmaximal, characteristic
8#11268C212yesmaximal
9#11207C211yesmaximal, characteristic
10#11207C211yesmaximal, characteristic
11#10795C211yesmaximal, characteristic
12C22×#125C2212yes—
13C22×#107C2212yes—
14C22×#106C2212yes—
15#2859—28no—
16C2×#389—21no—
17C2×#389—21no—
18C2×#389—21no—
19C2×#389—21no—
20C2×#389C2211yescharacteristic
21C2×#389C2211yescharacteristic
22C2×#387—21no—
23C2×#384C2211yescharacteristic
24C2×#384C2211yescharacteristic
25C2×#382C2212yes—
26C2×C43C2211yescharacteristic
27#2059—28no—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#336C2211yescharacteristic
35C2×#336C2211yescharacteristic
36C2×#336C2212yes—
37C2×#336C2212yes—
38#1436—21no—
39#1436—21no—
40C4⋊#95C2211yescharacteristic
41C4⋊#95C2211yescharacteristic
42C4⋊#95C2211yescharacteristic
43C4⋊#95C2211yescharacteristic
44#1434—21no—
45C23×C8C2312yes—
46C23×C8C2312yes—
47C2×#125—24no—
48C2×#125—42no—
49C2×#125—42no—
50C2×#125—42no—
51C2×#125—42no—
52C2×#125D418yes—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C4⋊C4C2312yes—
65C22×C4⋊C4C2311yescharacteristic
66C22×C4⋊C4C2311yescharacteristic
67C22×C42D411yescharacteristic
68C22×C42D411yescharacteristic
69C22×C42D411yescharacteristic
70C22×C42D411yescharacteristic
71C22×C42C2311yescharacteristic
72C22×C42C2311yescharacteristic
73C22×C42C2311yescharacteristic
74C2×#107—24no—
75C2×#107—42no—
76C2×#107—42no—
77C2×#106—24no—
78C2×#106—42no—
79C2×#106—42no—
80#389—28no—
81#389—28no—
82#389—28no—
83#389—28no—
84#389—22no—
85#389—24no—
86#389Q814yes—
87#387—44no—
88#384—24no—
89#384—24no—
90#382—24no—
91#382—24no—
92C2×#95—21no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C43—24no—
105#340—24no—
106#340—24no—
107#340—42no—
108#340—42no—
109#340—42no—
110#340—42no—
111#336—24no—
112#336—22no—
113#336—22no—
114#336Q818yes—
115C23×C4—22no—
116C23×C4—22no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4C2×D411yescharacteristic
122C23×C4C2×D411yescharacteristic
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D411yescharacteristic
127C23×C4C2411yescharacteristic
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
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×C8C2×Q814yes—
141C22×C8C2×Q814yes—
142#125—48no—
143#125—48no—
144#125—48no—
145#125—48no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—28no—
165C2×C4⋊C4—28no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—44no—
185C2×C4⋊C4—44no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—42no—
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⋊C4—42no—
196C2×C4⋊C4C2×D414yes—
197C2×C4⋊C4C2×D414yes—
198C2×C4⋊C4C2×Q812yes—
199C2×C4⋊C4C2×Q812yes—
200C2×C42—22no—
201C2×C42—22no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—21no—
207C2×C42—21no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
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×C42C2×D414yes—
221C2×C42C2×Q812yes—
222C2×C42C2×Q814yes—
223C2×C42#4112yes—
224#107—48no—
225#106—48no—
226#95—28no—
227#95—28no—
228#95—24no—
229#95—42no—
230#95—42no—
231#95—42no—
232#95—42no—
233#95—42no—
234#95—42no—
235#95—42no—
236#95—42no—
237#95—42no—
238C24C22×D411yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
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—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4#12012yes—
314C22×C4#12012yes—
315C22×C4C22⋊Q812yes—
316C22×C4C22⋊Q812yes—
317C22×C4C4⋊Q812yes—
318C22×C4C4⋊Q812yes—
319C22×C4#13512yes—
320C22×C4#13512yes—
321C22×C4AGL(1,ℤ/8)12yes—
322C22×C4#13712yes—
323C22×C4C22×D412yes—
324C22×C4C22×Q812yes—
325C22×C4C22×Q811yescharacteristic
326C22×C4C2×#4111yescharacteristic
327C22×C4H(5,𝔽2)11yescharacteristic
328C22×C4H(5,𝔽2)11yescharacteristic
329C22×C4H(5,𝔽2)12yes—
330C22×C42−1+411yescharacteristic
331C22×C42−1+411yescharacteristic
332C22×C42−1+412yes—
333C2×C8—24no—
334C2×C8—24no—
335C2×C8—24no—
336C2×C8—24no—
337C2×C8—24no—
338C2×C8—24no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—24no—
354C4⋊C4—48no—
355C4⋊C4—48no—
356C4⋊C4—48no—
357C4⋊C4—48no—
358C4⋊C4—416no—
359C4⋊C4—416no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—42no—
367C4⋊C4—48no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—84no—
373C42—24no—
374C42—24no—
375C42—24no—
376C42—24no—
377C42—24no—
378C42—24no—
379C42—44no—
380C42—44no—
381C42—44no—
382C42—44no—
383C23C2×#12011yescharacteristic
384C23C2×C22⋊Q811yescharacteristic
385C23C2×C4⋊Q811yescharacteristic
386C23#53511yescharacteristic
387C23#53511yescharacteristic
388C23#53611yescharacteristic
389C23#53611yescharacteristic
390C23C2×#13511yescharacteristic
391C23C2×#13511yescharacteristic
392C23C2×AGL(1,ℤ/8)11yescharacteristic
393C23C2×#13711yescharacteristic
394C23#57511yescharacteristic
395C23#57511yescharacteristic
396C23#57511yescharacteristic
397C23#57511yescharacteristic
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
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—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4—81no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—81no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
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#47814yes—
481C2×C4#47914yes—
482C2×C4#53412yes—
483C2×C4#53412yes—
484C2×C4#54211yescharacteristic
485C2×C4#54211yescharacteristic
486C2×C4#54412yes—
487C2×C4#54412yes—
488C2×C4#54411yescharacteristic
489C2×C4#54411yescharacteristic
490C2×C4#54812yes—
491C2×C4D4×Q812yes—
492C2×C4D4×Q812yes—
493C2×C4D4×Q812yes—
494C2×C4#55412yes—
495C2×C4Q8212yes—
496C2×C4#56312yes—
497C2×C4#56312yes—
498C8—44no—
499C8—44no—
500C22#240911yescharacteristic
501C22#243411yescharacteristic
502C22#256711yescharacteristic
503C22#261311yescharacteristic
504C22#262811yescharacteristic
505C22#266011yescharacteristic
506C22#282111yescharacteristic
507C22#300211yescharacteristic
508C22#300211yescharacteristic
509C22#300611yescharacteristic
510C22#300711yescharacteristic
511C22C2×#47811yescharacteristic
512C22C2×#47911yescharacteristic
513C22#308011yescharacteristic
514C22#308011yescharacteristic
515C22#316011yescharacteristic
516C22#316211yescharacteristic
517C22#316511yescharacteristic
518C22#316611yescharacteristic
519C22#320711yescharacteristic
520C22#321011yescharacteristic
521C22#321211yescharacteristic
522C22#321211yescharacteristic
523C22#321411yescharacteristic
524C22#321611yescharacteristic
525C22#321911yescharacteristic
526C22#321911yescharacteristic
527C22#323211yescharacteristic
528C22#323211yescharacteristic
529C22#323311yescharacteristic
530C22#323311yescharacteristic
531C22#323411yescharacteristic
532C22#323511yescharacteristic
533C22#323611yescharacteristic
534C22#323711yescharacteristic
535C4—24no—
536C4—24no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4—42no—
541C4—82no—
542C4—84no—
543C4—84no—
544C4—82no—
545C4—161no—
546C4—161no—
547C4#272912yes—
548C4#272912yes—
549C4#273412yes—
550C4#273412yes—
551C2#1660311yescharacteristic
552C2#2430511yescharacteristic
553C2#2430711yescharacteristic
554C2#2581411yescharacteristic
555C2#2581811yescharacteristic
556C2#2920711yescharacteristic
557C2#2921411yescharacteristic
558C2#2962811yescharacteristic
559C2#2962911yescharacteristic
560C2#2998611yescharacteristic
561C2#2998811yescharacteristic
562C2#3030811yescharacteristic
563C2#3031211yescharacteristic
564C2#3284111yescharacteristic
565C2#3284311yescharacteristic
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×#20592
#146992
#113852
#113252
#113242
#113232
#112682
#112072
#107952