Finite Group Databasebeta

← #470000

Subgroups — #470000

Order 512.

1166 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2863C211yesmaximal, characteristic
2C2×#2084C211yesmaximal, characteristic
3C2×#2072C211yesmaximal, characteristic
4#14712C211yesmaximal, characteristic
5#11327C212yesmaximal
6#11292C212yesmaximal
7#11207C211yesmaximal, characteristic
8#11122C212yesmaximal
9#11067C212yesmaximal
10#11050C211yesmaximal, characteristic
11#10795C211yesmaximal, characteristic
12C22×#106C2212yes—
13C22×#103C2212yes—
14C22×#103C2212yes—
15#2863—24no—
16#2863—24no—
17C2×#391C2211yescharacteristic
18C2×#391C2211yescharacteristic
19C2×#391C2211yescharacteristic
20C2×#389—21no—
21C2×#389—21no—
22C2×#389C2211yescharacteristic
23C2×#389C2211yescharacteristic
24C2×#389C2211yescharacteristic
25C2×#389C2212yes—
26C2×#387—21no—
27C2×#387—21no—
28C2×#387—21no—
29C2×#384C2211yescharacteristic
30C2×#384C2211yescharacteristic
31C2×#383—21no—
32C2×C43C2211yescharacteristic
33#2084—24no—
34#2072—24no—
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#340C2212yes—
38C2×#340C2212yes—
39C2×#340C2212yes—
40C2×#336C2212yes—
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2212yes—
44C4⋊#95—21no—
45C4⋊#95—21no—
46C4⋊#95C2212yes—
47C23×Q8C2311yescharacteristic
48C23×C8C2312yes—
49C23×C8C2312yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2312yes—
63C22×C42D411yescharacteristic
64C22×C42D411yescharacteristic
65C22×C42D411yescharacteristic
66C22×C42D411yescharacteristic
67C22×C42C2311yescharacteristic
68C22×C42C2311yescharacteristic
69C22×C42C2311yescharacteristic
70C2×#106—24no—
71C2×#106—42no—
72C2×#106—42no—
73C2×#103—24no—
74C2×#103—24no—
75C2×#103—24no—
76C2×#103—42no—
77C2×#103—42no—
78C2×#103—42no—
79#391—22no—
80#391—22no—
81#391—22no—
82#391—22no—
83#391—22no—
84#391D414yes—
85#389—22no—
86#389—22no—
87#389—22no—
88#389—22no—
89#389—22no—
90#389—42no—
91#389—42no—
92#389—44no—
93#389—44no—
94#389D414yes—
95#387—28no—
96#387—28no—
97#387—28no—
98#384—24no—
99#384—22no—
100#384—22no—
101#383—28no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—21no—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—21no—
110C2×#95—21no—
111C2×#95—22no—
112C2×#95—22no—
113C2×#95—22no—
114C43—22no—
115C43—22no—
116#340—24no—
117#340—24no—
118#340—24no—
119#340—24no—
120#340—42no—
121#336—24no—
122#336—22no—
123#336—22no—
124#336—42no—
125C22×Q8—21no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—21no—
129C22×Q8—21no—
130C22×Q8—21no—
131C22×Q8—22no—
132C22×Q8—22no—
133C22×Q8—21no—
134C22×Q8C2×D412yes—
135C23×C4—22no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—22no—
141C23×C4C2×D411yescharacteristic
142C23×C4C2×D411yescharacteristic
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2411yescharacteristic
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—22no—
158C22×C8—22no—
159C22×C8—22no—
160C22×C8—22no—
161C22×C8#4114yes—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
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⋊C4—42no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—44no—
202C2×C4⋊C4—44no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—42no—
205C2×C4⋊C4—44no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—42no—
208C2×C4⋊C4C2×D412yes—
209C2×C4⋊C4C2×D412yes—
210C2×C4⋊C4C2×D412yes—
211C2×C4⋊C4#4114yes—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—21no—
227C2×C42—22no—
228C2×C42—21no—
229C2×C42—21no—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—22no—
233C2×C42—41no—
234C2×C42—41no—
235C2×C42SD1614yes—
236C2×C42C2×D412yes—
237C2×C42C2×D412yes—
238#106—48no—
239#103—48no—
240#103—48no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—24no—
245#95—24no—
246#95—24no—
247#95—24no—
248#95—24no—
249#95—24no—
250#95—44no—
251#95—44no—
252#95—44no—
253C24C22×D411yescharacteristic
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—24no—
257C2×Q8—24no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8—42no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4#12012yes—
345C22×C4#12012yes—
346C22×C4C2×SD1612yes—
347C22×C4C2×SD1612yes—
348C22×C4C2×SD1612yes—
349C22×C4#13512yes—
350C22×C4AGL(1,ℤ/8)12yes—
351C22×C4#13712yes—
352C22×C4#13712yes—
353C22×C4#13712yes—
354C22×C4C22×D411yescharacteristic
355C22×C4C22×D411yescharacteristic
356C22×C4C2×#4112yes—
357C22×C4C2×#4112yes—
358C22×C4H(5,𝔽2)11yescharacteristic
359C22×C4H(5,𝔽2)11yescharacteristic
360C22×C4H(5,𝔽2)11yescharacteristic
361C22×C42−1+411yescharacteristic
362C22×C42−1+412yes—
363C22×C42−1+412yes—
364C2×C8—24no—
365C2×C8—24no—
366C2×C8—24no—
367C2×C8—42no—
368C2×C8—42no—
369C2×C8—42no—
370C2×C8—42no—
371C2×C8—42no—
372C2×C8—42no—
373C2×C8—42no—
374C2×C8—42no—
375C2×C8—42no—
376C2×C8—42no—
377C2×C8—42no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—24no—
384C4⋊C4—48no—
385C4⋊C4—48no—
386C4⋊C4—48no—
387C4⋊C4—48no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—48no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C4⋊C4—84no—
400C4⋊C4—88no—
401C4⋊C4—84no—
402C42—24no—
403C42—24no—
404C42—28no—
405C42—44no—
406C42—44no—
407C42—41no—
408C42—41no—
409C42—41no—
410C42—41no—
411C42—42no—
412C42—42no—
413C42—44no—
414C23C2×#12011yescharacteristic
415C23#52511yescharacteristic
416C23#53211yescharacteristic
417C23#53511yescharacteristic
418C23#53611yescharacteristic
419C23#53611yescharacteristic
420C23#53711yescharacteristic
421C23C22×SD1611yescharacteristic
422C23C2×#13511yescharacteristic
423C23C2×AGL(1,ℤ/8)11yescharacteristic
424C23C2×#13711yescharacteristic
425C23C2×#13711yescharacteristic
426C23C2×#13711yescharacteristic
427C23#57511yescharacteristic
428C23#57511yescharacteristic
429Q8—44no—
430Q8—44no—
431Q8—82no—
432Q8—82no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—82no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—82no—
497C2×C4—81no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—81no—
501C2×C4—81no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4—82no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4#44814yes—
516C2×C4#45214yes—
517C2×C4#53511yescharacteristic
518C2×C4#53511yescharacteristic
519C2×C4#53711yescharacteristic
520C2×C4#53711yescharacteristic
521C2×C4#53912yes—
522C2×C4#54112yes—
523C2×C4#54112yes—
524C2×C4#54212yes—
525C2×C4#54712yes—
526C2×C4#54712yes—
527C2×C4#54712yes—
528C2×C4#54812yes—
529C2×C4#55112yes—
530C2×C4#55312yes—
531C2×C4#56312yes—
532C2×C4#56312yes—
533C8—44no—
534C8—82no—
535C22#240611yescharacteristic
536C22#243211yescharacteristic
537C22#260311yescharacteristic
538C22#261511yescharacteristic
539C22#263711yescharacteristic
540C22#266411yescharacteristic
541C22#282111yescharacteristic
542C22C2×#44811yescharacteristic
543C22C2×#45211yescharacteristic
544C22#300611yescharacteristic
545C22#300711yescharacteristic
546C22#310111yescharacteristic
547C22#310511yescharacteristic
548C22#311311yescharacteristic
549C22#311711yescharacteristic
550C22#316711yescharacteristic
551C22#317211yescharacteristic
552C22#318011yescharacteristic
553C22#318511yescharacteristic
554C22#320811yescharacteristic
555C22#321211yescharacteristic
556C22#321611yescharacteristic
557C22#321811yescharacteristic
558C22#322911yescharacteristic
559C22#322911yescharacteristic
560C22#323111yescharacteristic
561C22#323211yescharacteristic
562C22#323611yescharacteristic
563C22#323811yescharacteristic
564C22#323911yescharacteristic
565C22#324011yescharacteristic
566C22#324611yescharacteristic
567C22#324811yescharacteristic
568C22#325211yescharacteristic
569C22#325411yescharacteristic
570C4—24no—
571C4—24no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—82no—
577C4—82no—
578C4—84no—
579C4—82no—
580C4—82no—
581C4—162no—
582C4#271812yes—
583C4#272212yes—
584C4#272312yes—
585C4#272512yes—
586C2#1667311yescharacteristic
587C2#2406311yescharacteristic
588C2#2406711yescharacteristic
589C2#2567211yescharacteristic
590C2#2567911yescharacteristic
591C2#2949211yescharacteristic
592C2#2950111yescharacteristic
593C2#2966111yescharacteristic
594C2#2966511yescharacteristic
595C2#3014711yescharacteristic
596C2#3014811yescharacteristic
597C2#3037711yescharacteristic
598C2#3038211yescharacteristic
599C2#3283711yescharacteristic
600C2#3283911yescharacteristic
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×#28632
C2×#20842
C2×#20722
#147122
#113272
#112922
#112072
#111222
#110672
#110502
#107952