Finite Group Databasebeta

← #4389783

Subgroups — #4389783

Order 512.

2418 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2822C211yesmaximal, characteristic
2C2×#2581C211yesmaximal, characteristic
3C2×#2565C211yesmaximal, characteristic
4C2×#2584C211yesmaximal, characteristic
5C2×#2634C211yesmaximal, characteristic
6C2×#2634C211yesmaximal, characteristic
7#16964C212yesmaximal
8#16813C212yesmaximal
9#15856C214yesmaximal
10#15804C214yesmaximal
11#15804C214yesmaximal
12#15804C214yesmaximal
13#15173C212yesmaximal
14#15153C212yesmaximal
15#13781C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×#125C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20#2822—28no—
21#2634—28no—
22#2634—28no—
23#2584—28no—
24#2581—28no—
25#2565—28no—
26C2×#400C2212yes—
27C2×#400C2212yes—
28C2×#400C2212yes—
29C2×#400C2212yes—
30C2×#400C2212yes—
31C2×#400C2212yes—
32C2×#400C2212yes—
33C2×#398C2212yes—
34C2×#398C2212yes—
35C2×#398C2212yes—
36C2×#398C2212yes—
37C2×#398C2214yes—
38C2×#398C2212yes—
39C2×#398C2214yes—
40C2×#395C2212yes—
41C2×#395C2212yes—
42C2×#395C2212yes—
43C2×#395C2212yes—
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2212yes—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#389C2212yes—
51C2×#389C2212yes—
52C2×#387C2214yes—
53C2×#387C2214yes—
54C2×#387C2214yes—
55C2×#387C2214yes—
56C2×#384C2211yescharacteristic
57C2×#383C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61#1445C2214yes—
62#1445C2214yes—
63#1445C2214yes—
64#1445C2214yes—
65#1445C2214yes—
66#1445C2214yes—
67#1445C2214yes—
68#1445C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75C4⋊#95C2214yes—
76C4⋊#95C2214yes—
77C4⋊#95C2214yes—
78C4⋊#95C2214yes—
79#1434C2212yes—
80C4×#95C2212yes—
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C2×#125—24no—
84C2×#125—24no—
85C2×#125—24no—
86C2×#125—24no—
87C2×#125—24no—
88C2×#125—24no—
89C2×C4×Q8—24no—
90C2×C4×Q8—24no—
91C2×C4×Q8—24no—
92C2×C4×Q8—24no—
93C2×C4×Q8—24no—
94C2×C4×Q8—24no—
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2312yes—
98C22×C4⋊C4C2312yes—
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C42C2312yes—
119C22×C42C2312yes—
120C22×C42C2314yes—
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124#400—28no—
125#400—28no—
126#400—28no—
127#400—28no—
128#400—28no—
129#400—28no—
130#400—28no—
131#398—216no—
132#398—216no—
133#398—28no—
134#398—28no—
135#398—28no—
136#398—28no—
137#398—28no—
138#395—28no—
139#395—28no—
140#395—28no—
141#395—28no—
142#391—28no—
143#391—24no—
144#391—24no—
145#389—28no—
146#389—28no—
147#389—28no—
148#389—28no—
149#389—28no—
150#387—216no—
151#387—216no—
152#387—216no—
153#387—216no—
154#384—24no—
155#383D418yes—
156#382—24no—
157#382D418yes—
158C4×C4⋊C4D418yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2312yes—
162C2×#95C2314yes—
163C2×#95C2312yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C22×Q8—22no—
188C22×Q8—22no—
189C22×Q8—22no—
190C22×Q8—22no—
191C22×Q8—22no—
192C22×Q8—22no—
193C22×Q8—24no—
194C22×Q8—24no—
195C22×Q8—42no—
196C22×Q8—42no—
197C23×C4C2412yes—
198C23×C4C2412yes—
199C23×C4C2412yes—
200C23×C4C2412yes—
201C23×C4C2412yes—
202C23×C4C2412yes—
203C23×C4C2414yes—
204C23×C4C2412yes—
205C23×C4C2414yes—
206C23×C4C2412yes—
207C23×C4C2412yes—
208C23×C4C2411yescharacteristic
209C23×C4C2411yescharacteristic
210C23×C4C2411yescharacteristic
211C23×C4C2412yes—
212#125—416no—
213#125—416no—
214C4×Q8—416no—
215C4×Q8—416no—
216C2×C4⋊C4—28no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—28no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4—28no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—28no—
261C2×C4⋊C4—28no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—216no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—28no—
268C2×C4⋊C4—44no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—44no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—44no—
274C2×C4⋊C4—44no—
275C2×C4⋊C4—44no—
276C2×C4⋊C4—44no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4C2×D418yes—
279C2×C4⋊C4C2×D418yes—
280C2×C42—24no—
281C2×C42—24no—
282C2×C42—24no—
283C2×C42—24no—
284C2×C42—24no—
285C2×C42—24no—
286C2×C42—28no—
287C2×C42—42no—
288C2×C42—42no—
289C2×C42—44no—
290C2×C42—44no—
291C2×C42C2×D414yes—
292C2×C42C2×D414yes—
293C2×C42C2×D414yes—
294C2×C42C2×D414yes—
295C2×C42C2×D414yes—
296#95—28no—
297#95—28no—
298#95—28no—
299#95—28no—
300#95—28no—
301#95—28no—
302#95—28no—
303#95—28no—
304#95—28no—
305#95—28no—
306#95—28no—
307#95—28no—
308#95—24no—
309#95—24no—
310#95—24no—
311#95—24no—
312#95—28no—
313#95—28no—
314#95—28no—
315#95—28no—
316#95—44no—
317#95—44no—
318#95C2×D418yes—
319#95C2×D418yes—
320#95C2×D418yes—
321#95C2×D418yes—
322#95C2×D418yes—
323#95C2×D418yes—
324C24C2511yescharacteristic
325C2×Q8—28no—
326C2×Q8—28no—
327C2×Q8—48no—
328C2×Q8—48no—
329C2×Q8—48no—
330C2×Q8—48no—
331C2×Q8—44no—
332C2×Q8—44no—
333C2×Q8—44no—
334C2×Q8—44no—
335C22×C4—24no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4C22×D418yes—
402C22×C4C22×D418yes—
403C22×C4C22×D414yes—
404C22×C4C22×D412yes—
405C22×C4C22×D412yes—
406C22×C4C22×D412yes—
407C22×C4C22×D412yes—
408C22×C4C22×D412yes—
409C22×C4C22×D412yes—
410C22×C4C22×D412yes—
411C22×C4C22×D412yes—
412C22×C4C22×D412yes—
413C22×C4C22×D414yes—
414C22×C42−1+414yes—
415C22×C42−1+414yes—
416C22×C42−1+418yes—
417C4⋊C4—216no—
418C4⋊C4—48no—
419C4⋊C4—48no—
420C4⋊C4—416no—
421C4⋊C4—416no—
422C4⋊C4—416no—
423C4⋊C4—48no—
424C4⋊C4—48no—
425C4⋊C4—48no—
426C4⋊C4—44no—
427C4⋊C4—44no—
428C4⋊C4—48no—
429C4⋊C4—44no—
430C4⋊C4—44no—
431C4⋊C4—48no—
432C4⋊C4—48no—
433C4⋊C4—44no—
434C4⋊C4—44no—
435C4⋊C4—48no—
436C4⋊C4—416no—
437C4⋊C4—84no—
438C4⋊C4—84no—
439C4⋊C4—88no—
440C42—44no—
441C42—44no—
442C42—48no—
443C42—48no—
444C42—88no—
445C42#127116yes—
446C23C23×D411yescharacteristic
447C23C23×D411yescharacteristic
448C23C23×D411yescharacteristic
449C23C2×2−1+414yes—
450C23C2×2−1+412yes—
451C23C2×2−1+412yes—
452C23#58512yes—
453C23#58512yes—
454Q8—416no—
455Q8—416no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—28no—
470C2×C4—28no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—28no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—28no—
481C2×C4—28no—
482C2×C4—24no—
483C2×C4—28no—
484C2×C4—28no—
485C2×C4—28no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4C2×#12714yes—
535C2×C4C2×#12714yes—
536C2×C4C2×#12714yes—
537C2×C4#53618yes—
538C22C22×#12711yescharacteristic
539C22C2×#53612yes—
540C22#348511yescharacteristic
541C22#348511yescharacteristic
542C22#348611yescharacteristic
543C22#348611yescharacteristic
544C22#348912yes—
545C22#348912yes—
546C22#348912yes—
547C22#348912yes—
548C22#349912yes—
549C22#349912yes—
550C22#355514yes—
551C22#355614yes—
552C22#356314yes—
553C22#356414yes—
554C4—24no—
555C4—24no—
556C4—28no—
557C4—24no—
558C4—44no—
559C4—44no—
560C4—48no—
561C4—44no—
562C4—48no—
563C4—82no—
564C4—82no—
565C4—82no—
566C4—82no—
567C4—82no—
568C4—82no—
569C2#3531711yescharacteristic
570C2#3563411yescharacteristic
571C2#3563411yescharacteristic
572C2#4141112yes—
573C2#4281112yes—
574C2#4777014yes—
575C2#5089212yes—
576C2#5120612yes—
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×#28222
C2×#25812
C2×#25652
C2×#25842
C2×#26342
#169642
#168132
#158562
#158042
#151732
#151532
#137812