Finite Group Databasebeta

← #416669

Subgroups — #416669

Order 512.

1184 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2864C211yesmaximal, characteristic
2C2×#1847C211yesmaximal, characteristic
3C2×#1836C211yesmaximal, characteristic
4#14712C211yesmaximal, characteristic
5#11328C212yesmaximal
6#11327C212yesmaximal
7#11220C212yesmaximal
8#11219C212yesmaximal
9#10843C211yesmaximal, characteristic
10#10843C211yesmaximal, characteristic
11#10693C211yesmaximal, characteristic
12C22×#107C2212yes—
13C22×#106C2212yes—
14C22×#97C2211yescharacteristic
15C22×#97C2211yescharacteristic
16#2864—24no—
17#2864—24no—
18C2×#389—21no—
19C2×#389—21no—
20C2×#389C2211yescharacteristic
21C2×#389C2211yescharacteristic
22C2×#389C2211yescharacteristic
23C2×#389C2211yescharacteristic
24C2×#389C2212yes—
25C2×#387—21no—
26C2×#387—21no—
27C2×#387—21no—
28C2×#387—21no—
29C2×#384C2211yescharacteristic
30C2×#384C2211yescharacteristic
31C2×#382C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×C43C2211yescharacteristic
34#1847—24no—
35#1836—24no—
36C2×#340C2212yes—
37C2×#340C2212yes—
38C2×#340C2212yes—
39C2×#340C2212yes—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#336C2212yes—
43C2×#336C2212yes—
44C4⋊#95—21no—
45C4⋊#95—21no—
46C4⋊#95C2212yes—
47C23×C8C2312yes—
48C23×C8C2312yes—
49C22×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C42D411yescharacteristic
65C22×C42D411yescharacteristic
66C22×C42D411yescharacteristic
67C22×C42D411yescharacteristic
68C22×C42C2311yescharacteristic
69C22×C42C2311yescharacteristic
70C22×C42C2311yescharacteristic
71C2×#107—24no—
72C2×#107—24no—
73C2×#107—42no—
74C2×#106—24no—
75C2×#106—24no—
76C2×#106—42no—
77C2×#97—22no—
78C2×#97—22no—
79C2×#97—22no—
80C2×#97—22no—
81C2×#97Q814yes—
82C2×#97Q814yes—
83#389—22no—
84#389—22no—
85#389—22no—
86#389—22no—
87#389—22no—
88#389—22no—
89#389—22no—
90#389—22no—
91#389—42no—
92#389—42no—
93#389—44no—
94#389—44no—
95#387—28no—
96#387—28no—
97#387—28no—
98#387—28no—
99#384—22no—
100#384—22no—
101#384—22no—
102#384Q814yes—
103#382—22no—
104#382—22no—
105#382D414yes—
106#382D414yes—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—21no—
110C2×#95—21no—
111C2×#95—21no—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—22no—
118C43—22no—
119C43—22no—
120#340—24no—
121#340—24no—
122#340—24no—
123#340—24no—
124#340—42no—
125#340—42no—
126#336—24no—
127#336—24no—
128C23×C4—22no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—22no—
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D411yescharacteristic
138C23×C4C2×D411yescharacteristic
139C23×C4C2×D411yescharacteristic
140C23×C4C2411yescharacteristic
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8C2×Q814yes—
152C22×C8C2×Q814yes—
153C22×C8#4114yes—
154C22×C8#4114yes—
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—22no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—24no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
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⋊C4—42no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—44no—
201C2×C4⋊C4—44no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—44no—
205C2×C4⋊C4C2×D412yes—
206C2×C4⋊C4C2×D412yes—
207C2×C4⋊C4C2×D412yes—
208C2×C4⋊C4C2×D412yes—
209C2×C4⋊C4C2×Q814yes—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—41no—
227C2×C42—41no—
228C2×C42—41no—
229C2×C42—41no—
230C2×C42C2×D412yes—
231C2×C42C2×D412yes—
232C2×C42C2×Q812yes—
233C2×C42C2×Q812yes—
234C2×C42C2×Q812yes—
235C2×C42#4112yes—
236#107—48no—
237#106—48no—
238#97—28no—
239#97—28no—
240#95—24no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—24no—
245#95—24no—
246#95—24no—
247#95—24no—
248#95—44no—
249#95—44no—
250#95—44no—
251C24C22×D411yescharacteristic
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—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—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—42no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—42no—
300C22×C4—42no—
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—42no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4#12012yes—
327C22×C4#12012yes—
328C22×C4C22⋊Q812yes—
329C22×C4C22⋊Q812yes—
330C22×C4C4⋊Q812yes—
331C22×C4C4⋊Q812yes—
332C22×C4AGL(1,ℤ/8)12yes—
333C22×C4AGL(1,ℤ/8)12yes—
334C22×C4#13712yes—
335C22×C4#13712yes—
336C22×C4C22×D411yescharacteristic
337C22×C4C22×D411yescharacteristic
338C22×C4C22×Q811yescharacteristic
339C22×C4C22×Q811yescharacteristic
340C22×C4C22×Q811yescharacteristic
341C22×C4C2×#4111yescharacteristic
342C22×C4C2×#4112yes—
343C22×C4C2×#4112yes—
344C22×C4H(5,𝔽2)12yes—
345C22×C42−1+412yes—
346C2×C8—24no—
347C2×C8—24no—
348C2×C8—24no—
349C2×C8—24no—
350C2×C8—24no—
351C2×C8—24no—
352C2×C8—24no—
353C2×C8—24no—
354C2×C8—24no—
355C2×C8—42no—
356C2×C8—42no—
357C2×C8—42no—
358C2×C8—42no—
359C2×C8#12518yes—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—48no—
367C4⋊C4—48no—
368C4⋊C4—48no—
369C4⋊C4—48no—
370C4⋊C4—48no—
371C4⋊C4—48no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—42no—
379C4⋊C4—42no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—84no—
383C4⋊C4—84no—
384C4⋊C4—88no—
385C42—44no—
386C42—44no—
387C42—44no—
388C42—44no—
389C42—42no—
390C42—42no—
391C42—42no—
392C42—42no—
393C42C22⋊Q814yes—
394C42C22⋊Q814yes—
395C42C4⋊Q814yes—
396C42C4⋊Q814yes—
397C23C2×#12011yescharacteristic
398C23C2×C22⋊Q811yescharacteristic
399C23C2×C4⋊Q811yescharacteristic
400C23#53211yescharacteristic
401C23#53211yescharacteristic
402C23#53511yescharacteristic
403C23#53611yescharacteristic
404C23C2×AGL(1,ℤ/8)11yescharacteristic
405C23C2×AGL(1,ℤ/8)11yescharacteristic
406C23C2×#13711yescharacteristic
407C23C2×#13711yescharacteristic
408C23#57511yescharacteristic
409C23#57511yescharacteristic
410C23#57511yescharacteristic
411C23#57511yescharacteristic
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—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
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—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—81no—
468C2×C4—82no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—82no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—82no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—82no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4—82no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4#39514yes—
495C2×C4#39514yes—
496C2×C4C2×C22⋊Q811yescharacteristic
497C2×C4C2×C22⋊Q811yescharacteristic
498C2×C4C2×#12512yes—
499C2×C4C2×C4⋊Q811yescharacteristic
500C2×C4C2×C4⋊Q811yescharacteristic
501C2×C4#53312yes—
502C2×C4#54412yes—
503C2×C4#54412yes—
504C2×C4#54612yes—
505C2×C4#54712yes—
506C2×C4#54812yes—
507C2×C4#55012yes—
508C2×C4#55212yes—
509C2×C4#55312yes—
510C2×C4#55412yes—
511C2×C4#55712yes—
512C8—28no—
513C8—44no—
514C22C2×#39511yescharacteristic
515C22#243111yescharacteristic
516C22#243211yescharacteristic
517C22#256511yescharacteristic
518C22#256611yescharacteristic
519C22#266011yescharacteristic
520C22#285911yescharacteristic
521C22#300611yescharacteristic
522C22#300611yescharacteristic
523C22#300711yescharacteristic
524C22#300711yescharacteristic
525C22#307711yescharacteristic
526C22#307711yescharacteristic
527C22#307811yescharacteristic
528C22#307811yescharacteristic
529C22#316511yescharacteristic
530C22#316511yescharacteristic
531C22#316611yescharacteristic
532C22#316611yescharacteristic
533C22#317111yescharacteristic
534C22#317111yescharacteristic
535C22#317211yescharacteristic
536C22#317211yescharacteristic
537C22#318011yescharacteristic
538C22#318011yescharacteristic
539C22#318111yescharacteristic
540C22#318111yescharacteristic
541C22#321711yescharacteristic
542C22#321811yescharacteristic
543C22#321911yescharacteristic
544C22#321911yescharacteristic
545C22#323811yescharacteristic
546C22#323911yescharacteristic
547C22#324011yescharacteristic
548C22#324011yescharacteristic
549C4—24no—
550C4—24no—
551C4—42no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4—82no—
556C4—82no—
557C4—84no—
558C4—82no—
559C4—82no—
560C4—162no—
561C4#244112yes—
562C4#244212yes—
563C4#255012yes—
564C4#255212yes—
565C2#1522811yescharacteristic
566C2#2355411yescharacteristic
567C2#2355411yescharacteristic
568C2#2560411yescharacteristic
569C2#2560511yescharacteristic
570C2#2567811yescharacteristic
571C2#2567911yescharacteristic
572C2#2918111yescharacteristic
573C2#2918211yescharacteristic
574C2#2919511yescharacteristic
575C2#2919611yescharacteristic
576C2#3030911yescharacteristic
577C2#3031111yescharacteristic
578C2#3325911yescharacteristic
579C2#3325911yescharacteristic
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×#28642
C2×#18472
C2×#18362
#147122
#113282
#113272
#112202
#112192
#108432
#106932