Finite Group Databasebeta

← #4930255

Subgroups — #4930255

Order 512.

2594 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic
2C2×#2446C212yesmaximal
3C2×#2276C211yesmaximal, characteristic
4#15122C212yesmaximal
5#15122C212yesmaximal
6#15106C212yesmaximal
7#15090C212yesmaximal
8#14861C214yesmaximal
9#14844C214yesmaximal
10#14274C211yesmaximal, characteristic
11#14155C211yesmaximal, characteristic
12#14150C211yesmaximal, characteristic
13#14142C212yesmaximal
14#14024C212yesmaximal
15#14021C212yesmaximal
16#13942C211yesmaximal, characteristic
17#13848C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C4⋊Q8C2212yes—
20C22×C4×Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23#2546—28no—
24#2446—216no—
25C2×#400C2214yes—
26C2×#398C2214yes—
27C2×#398C2214yes—
28C2×#391C2212yes—
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#391C2212yes—
32C2×#391C2212yes—
33C2×#391C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#387C2214yes—
38C2×#387C2214yes—
39C2×#382C2211yescharacteristic
40#2276—28no—
41C2×C4×C4⋊C4C2212yes—
42C2×C4×C4⋊C4C2212yes—
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2212yes—
50C2×#376C2212yes—
51C2×#376C2211yescharacteristic
52#1445C2212yes—
53#1445C2212yes—
54#1445C2212yes—
55#1445C2212yes—
56#1445C2212yes—
57#1445C2212yes—
58#1444C2211yescharacteristic
59#1444C2212yes—
60#1444C2211yescharacteristic
61#1443C2214yes—
62#1443C2214yes—
63#1442C2214yes—
64#1442C2211yescharacteristic
65#1442C2214yes—
66#1442C2212yes—
67#1442C2211yescharacteristic
68#1441C2214yes—
69#1441C2212yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2212yes—
73#1436C2214yes—
74#1436C2214yes—
75#1436C2214yes—
76#1436C2214yes—
77#1436C2214yes—
78C4⋊#95C2214yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81#1434C2212yes—
82#1434C2214yes—
83#1434C2212yes—
84#1434C2214yes—
85C4×#95C2212yes—
86C23×Q8C2312yes—
87C23×Q8C2311yescharacteristic
88C2×C4⋊Q8—28no—
89C2×C4⋊Q8—28no—
90C2×C4⋊Q8—28no—
91C2×C4⋊Q8—24no—
92C2×C4⋊Q8—24no—
93C2×C4⋊Q8—24no—
94C2×C4×Q8—24no—
95C2×C4×Q8—24no—
96C2×C4×Q8—24no—
97C2×C4×Q8—24no—
98C2×C4×Q8—24no—
99C2×C4×Q8—24no—
100C2×C4×Q8—24no—
101C2×C4×Q8D418yes—
102C2×C4×Q8D418yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C42C2312yes—
121C22×C42C2312yes—
122C22×C42C2312yes—
123C22×C42C2312yes—
124C22×C42C2311yescharacteristic
125C22×C42C2312yes—
126C22×C42C2311yescharacteristic
127C22×C42C2312yes—
128C22×C42C2312yes—
129C22×C42C2312yes—
130C22×C42C2311yescharacteristic
131#400—216no—
132#398—216no—
133#398—216no—
134#391—28no—
135#391—28no—
136#391—28no—
137#391—28no—
138#391—28no—
139#391—28no—
140#389—28no—
141#389—28no—
142#389—28no—
143#387—216no—
144#387—216no—
145#382—24no—
146C4×C4⋊C4—24no—
147C4×C4⋊C4—24no—
148C4×C4⋊C4—28no—
149C4×C4⋊C4—28no—
150C4×C4⋊C4—28no—
151C4×C4⋊C4—28no—
152C4×C4⋊C4—24no—
153C4×C4⋊C4—24no—
154C4×C4⋊C4—24no—
155#376—28no—
156#376—24no—
157C2×#95C2312yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2312yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2311yescharacteristic
171C2×#95C2312yes—
172C2×#95C2311yescharacteristic
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2311yescharacteristic
181C2×#95C2311yescharacteristic
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2311yescharacteristic
187C2×#95C2312yes—
188C2×#95C2311yescharacteristic
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C22×Q8—24no—
193C22×Q8—24no—
194C22×Q8—22no—
195C22×Q8—22no—
196C22×Q8—22no—
197C22×Q8—22no—
198C22×Q8—24no—
199C22×Q8—24no—
200C22×Q8—24no—
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8C2×D414yes—
204C22×Q8C2×D414yes—
205C22×Q8#4114yes—
206C23×C4C2414yes—
207C23×C4C2414yes—
208C23×C4C2412yes—
209C23×C4C2411yescharacteristic
210C23×C4C2412yes—
211C23×C4C2411yescharacteristic
212C23×C4C2412yes—
213C23×C4C2412yes—
214C23×C4C2411yescharacteristic
215C23×C4C2411yescharacteristic
216C23×C4C2412yes—
217C23×C4C2412yes—
218C23×C4C2412yes—
219C23×C4C2412yes—
220C23×C4C2411yescharacteristic
221C23×C4C2411yescharacteristic
222C23×C4C2411yescharacteristic
223C4⋊Q8—432no—
224C4⋊Q8—416no—
225C4×Q8—232no—
226C4×Q8—232no—
227C4×Q8—232no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—28no—
249C2×C4⋊C4—28no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—28no—
252C2×C4⋊C4—28no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—28no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—28no—
258C2×C4⋊C4—28no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4C2×D414yes—
273C2×C4⋊C4C2×D418yes—
274C2×C4⋊C4C2×D414yes—
275C2×C4⋊C4C2×D418yes—
276C2×C4⋊C4#4114yes—
277C2×C42—24no—
278C2×C42—24no—
279C2×C42—22no—
280C2×C42—22no—
281C2×C42—24no—
282C2×C42—24no—
283C2×C42—24no—
284C2×C42—22no—
285C2×C42—24no—
286C2×C42—24no—
287C2×C42—22no—
288C2×C42—24no—
289C2×C42—24no—
290C2×C42—24no—
291C2×C42—24no—
292C2×C42—24no—
293C2×C42—24no—
294C2×C42—24no—
295C2×C42—24no—
296C2×C42—24no—
297C2×C42—44no—
298C2×C42—44no—
299C2×C42—44no—
300C2×C42C2×D418yes—
301C2×C42C2×D414yes—
302C2×C42C2×D418yes—
303C2×C42C2×D414yes—
304C2×C42#4114yes—
305C2×C42#4114yes—
306C2×C42#4114yes—
307#95—22no—
308#95—24no—
309#95—24no—
310#95—22no—
311#95—22no—
312#95—24no—
313#95—22no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—28no—
318#95—28no—
319#95—28no—
320#95—28no—
321#95—28no—
322#95—28no—
323#95—28no—
324#95—28no—
325#95—28no—
326#95—22no—
327#95—22no—
328#95—24no—
329#95—24no—
330#95—28no—
331#95—28no—
332#95—28no—
333#95—28no—
334#95—24no—
335#95—24no—
336#95—28no—
337#95—28no—
338#95—24no—
339#95—42no—
340#95—44no—
341#95—44no—
342C24C2511yescharacteristic
343C2×Q8—28no—
344C2×Q8—28no—
345C2×Q8—28no—
346C2×Q8—28no—
347C2×Q8—28no—
348C2×Q8—28no—
349C2×Q8—48no—
350C2×Q8—48no—
351C2×Q8—48no—
352C2×Q8—48no—
353C2×Q8—48no—
354C2×Q8—48no—
355C2×Q8—48no—
356C2×Q8#121116yes—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4C22×D414yes—
433C22×C4C22×D412yes—
434C22×C4C22×D412yes—
435C22×C4C22×D414yes—
436C22×C4C22×D414yes—
437C22×C4C22×D414yes—
438C22×C4C22×D412yes—
439C22×C4C22×D412yes—
440C22×C4C22×D412yes—
441C22×C4C22×D412yes—
442C22×C4C2×#4112yes—
443C22×C4C2×#4114yes—
444C22×C4C2×#4112yes—
445C22×C4C2×#4114yes—
446C22×C4C2×#4112yes—
447C22×C4C2×#4112yes—
448C22×C4C2×#4112yes—
449C22×C4C2×#4112yes—
450C22×C4C2×#4112yes—
451C22×C4C2×#4112yes—
452C22×C4C2×#4112yes—
453C22×C4C2×#4112yes—
454C22×C4C2×#4112yes—
455C22×C42−1+414yes—
456C22×C42−1+414yes—
457C22×C42−1+414yes—
458C4⋊C4—28no—
459C4⋊C4—28no—
460C4⋊C4—216no—
461C4⋊C4—216no—
462C4⋊C4—216no—
463C4⋊C4—28no—
464C4⋊C4—216no—
465C4⋊C4—28no—
466C4⋊C4—28no—
467C4⋊C4—48no—
468C4⋊C4—48no—
469C4⋊C4—416no—
470C4⋊C4—416no—
471C4⋊C4—416no—
472C4⋊C4—48no—
473C4⋊C4—48no—
474C4⋊C4—48no—
475C42—216no—
476C42—216no—
477C42—28no—
478C42—216no—
479C42—28no—
480C42—48no—
481C42—48no—
482C42—84no—
483C42—84no—
484C42—84no—
485C42#123116yes—
486C23C23×D411yescharacteristic
487C23C23×D411yescharacteristic
488C23C22×#4111yescharacteristic
489C23C22×#4111yescharacteristic
490C23C22×#4111yescharacteristic
491C23C22×#4111yescharacteristic
492C23C22×#4111yescharacteristic
493C23C2×2−1+412yes—
494C23C2×2−1+412yes—
495C23C2×2−1+412yes—
496C23#58512yes—
497Q8—232no—
498Q8—816no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—28no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—28no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—44no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—42no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4C2×#12118yes—
591C2×C4C2×#12114yes—
592C2×C4C2×#12314yes—
593C2×C4C2×#12314yes—
594C2×C4C2×#12314yes—
595C2×C4#52514yes—
596C2×C4#52914yes—
597C2×C4#52914yes—
598C2×C4#53214yes—
599C2×C4#53214yes—
600C22C22×#12111yescharacteristic
601C22C22×#12311yescharacteristic
602C22C2×#52511yescharacteristic
603C22C2×#52911yescharacteristic
604C22C2×#52911yescharacteristic
605C22C2×#53211yescharacteristic
606C22C2×#53211yescharacteristic
607C22#348612yes—
608C22#348611yescharacteristic
609C22#348611yescharacteristic
610C22#348912yes—
611C22#349512yes—
612C22#349911yescharacteristic
613C22#350011yescharacteristic
614C22#350712yes—
615C22#350712yes—
616C22#350912yes—
617C22#350912yes—
618C22#350912yes—
619C22#351512yes—
620C22#351612yes—
621C22#352312yes—
622C22#352312yes—
623C4—28no—
624C4—24no—
625C4—24no—
626C4—44no—
627C4—44no—
628C4—42no—
629C4—44no—
630C4—42no—
631C4—44no—
632C4—44no—
633C4—42no—
634C4—44no—
635C4—42no—
636C4—84no—
637C4—82no—
638C4—84no—
639C4#285418yes—
640C2#3561911yescharacteristic
641C2#3563712yes—
642C2#3565612yes—
643C2#3567411yescharacteristic
644C2#3570011yescharacteristic
645C2#3571211yescharacteristic
646C2#3573711yescharacteristic
647C2#3574911yescharacteristic
648C2#3587012yes—
649C2#3593812yes—
650C2C2×#285411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#24462
C2×#22762
#151222
#151062
#150902
#148612
#148442
#142742
#141552
#141502
#141422
#140242
#140212
#139422
#138482