Finite Group Databasebeta

← #4422102

Subgroups — #4422102

Order 512.

2154 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2581C211yesmaximal, characteristic
2C2×#2584C211yesmaximal, characteristic
3C2×#2634C211yesmaximal, characteristic
4C2×#2356C211yesmaximal, characteristic
5#17078C212yesmaximal
6#16993C212yesmaximal
7#16677C212yesmaximal
8#16663C212yesmaximal
9#15895C214yesmaximal
10#15874C214yesmaximal
11#15156C212yesmaximal
12#15090C212yesmaximal
13#14903C212yesmaximal
14#14901C212yesmaximal
15#14664C211yesmaximal, characteristic
16#14356C211yesmaximal, characteristic
17#14346C211yesmaximal, characteristic
18C22×#125C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21#2634—28no—
22#2584—28no—
23#2581—28no—
24C2×#400C2212yes—
25C2×#400C2211yescharacteristic
26C2×#400C2211yescharacteristic
27C2×#400C2212yes—
28C2×#398C2212yes—
29C2×#398C2211yescharacteristic
30C2×#398C2211yescharacteristic
31C2×#395C2211yescharacteristic
32C2×#395C2211yescharacteristic
33C2×#395C2211yescharacteristic
34C2×#395C2211yescharacteristic
35C2×#395C2212yes—
36#2356—28no—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#387C2214yes—
45C2×#387C2214yes—
46C2×#387C2212yes—
47C2×#387C2212yes—
48C2×#383C2211yescharacteristic
49C2×#383C2212yes—
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×#376C2212yes—
55#1446C2212yes—
56#1445C2212yes—
57#1445C2214yes—
58#1445C2212yes—
59#1445C2212yes—
60#1445C2214yes—
61#1444C2214yes—
62#1444C2214yes—
63#1444C2212yes—
64#1443C2214yes—
65#1443C2214yes—
66#1442C2214yes—
67#1442C2212yes—
68#1442C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2212yes—
74#1441C2212yes—
75#1441C2214yes—
76#1441C2212yes—
77#1441C2212yes—
78#1441C2212yes—
79#1441C2212yes—
80C4⋊#95C2214yes—
81C4⋊#95C2212yes—
82C4⋊#95C2214yes—
83#1434C2214yes—
84#1434C2214yes—
85#1434C2212yes—
86#1434C2214yes—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C2×#125—24no—
90C2×#125—24no—
91C2×#125—24no—
92C2×C4×Q8—24no—
93C2×C4×Q8—24no—
94C2×C4×Q8—24no—
95C2×C4×Q8—24no—
96C2×C4×Q8—24no—
97C2×C4×Q8D418yes—
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C42C2312yes—
120C22×C42C2314yes—
121C22×C42C2312yes—
122C22×C42C2312yes—
123C22×C42C2311yescharacteristic
124#400—28no—
125#400—24no—
126#400—24no—
127#400—28no—
128#398—28no—
129#398—24no—
130#398—24no—
131#395—28no—
132#395—24no—
133#395—24no—
134#395—24no—
135#395—24no—
136#391—28no—
137#391—28no—
138#389—28no—
139#389—28no—
140#389—28no—
141#389—28no—
142#389—28no—
143#387—216no—
144#387—216no—
145#387—28no—
146#387—28no—
147#383—24no—
148#383—28no—
149#382—24no—
150#382—24no—
151C4×C4⋊C4—28no—
152C4×C4⋊C4D418yes—
153#376—28no—
154C2×#95C2311yescharacteristic
155C2×#95C2312yes—
156C2×#95C2311yescharacteristic
157C2×#95C2312yes—
158C2×#95C2312yes—
159C2×#95C2312yes—
160C2×#95C2314yes—
161C2×#95C2312yes—
162C2×#95C2312yes—
163C2×#95C2312yes—
164C2×#95C2312yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C22×Q8—22no—
192C22×Q8—22no—
193C22×Q8—22no—
194C22×Q8—22no—
195C22×Q8—22no—
196C22×Q8—24no—
197C22×Q8—42no—
198C22×Q8—42no—
199C22×Q8—42no—
200C22×Q8C2×D414yes—
201C23×C4C2411yescharacteristic
202C23×C4C2411yescharacteristic
203C23×C4C2412yes—
204C23×C4C2411yescharacteristic
205C23×C4C2411yescharacteristic
206C23×C4C2412yes—
207C23×C4C2414yes—
208C23×C4C2412yes—
209C23×C4C2414yes—
210C23×C4C2412yes—
211C23×C4C2412yes—
212C23×C4C2412yes—
213C23×C4C2412yes—
214C23×C4C2411yescharacteristic
215C23×C4C2411yescharacteristic
216C23×C4C2411yescharacteristic
217C23×C4C2412yes—
218#125—416no—
219C4×Q8—232no—
220C4×Q8—416no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—28no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—28no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—28no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4—42no—
264C2×C4⋊C4—44no—
265C2×C4⋊C4—44no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—44no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—44no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—44no—
274C2×C4⋊C4—44no—
275C2×C4⋊C4—44no—
276C2×C4⋊C4C2×D418yes—
277C2×C4⋊C4C2×D414yes—
278C2×C4⋊C4C2×D418yes—
279C2×C42—24no—
280C2×C42—24no—
281C2×C42—24no—
282C2×C42—24no—
283C2×C42—28no—
284C2×C42—24no—
285C2×C42—28no—
286C2×C42—28no—
287C2×C42—44no—
288C2×C42C2×D418yes—
289C2×C42C2×D418yes—
290C2×C42C2×D414yes—
291C2×C42C2×D414yes—
292C2×C42#4114yes—
293#95—24no—
294#95—28no—
295#95—28no—
296#95—24no—
297#95—24no—
298#95—24no—
299#95—24no—
300#95—28no—
301#95—22no—
302#95—22no—
303#95—24no—
304#95—28no—
305#95—28no—
306#95—28no—
307#95—24no—
308#95—24no—
309#95—24no—
310#95—24no—
311#95—24no—
312#95—24no—
313#95—24no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—28no—
318#95—28no—
319#95—44no—
320#95—44no—
321#95—44no—
322#95—44no—
323#95—44no—
324#95—44no—
325#95—44no—
326#95—44no—
327#95—44no—
328#95C2×D414yes—
329#95C2×D414yes—
330C24C2511yescharacteristic
331C2×Q8—28no—
332C2×Q8—28no—
333C2×Q8—48no—
334C2×Q8—48no—
335C2×Q8—48no—
336C2×Q8—44no—
337C2×Q8—44no—
338C2×Q8—44no—
339C2×Q8—48no—
340C2×Q8—44no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4C22×D414yes—
419C22×C4C22×D414yes—
420C22×C4C22×D414yes—
421C22×C4C22×D412yes—
422C22×C4C22×D412yes—
423C22×C4C22×D412yes—
424C22×C4C22×D412yes—
425C22×C4C22×D412yes—
426C22×C4C22×D412yes—
427C22×C4C22×D414yes—
428C22×C4C2×#4112yes—
429C22×C4C2×#4112yes—
430C22×C4C2×#4112yes—
431C22×C42−1+414yes—
432C22×C42−1+418yes—
433C4⋊C4—28no—
434C4⋊C4—216no—
435C4⋊C4—216no—
436C4⋊C4—48no—
437C4⋊C4—48no—
438C4⋊C4—48no—
439C4⋊C4—48no—
440C4⋊C4—416no—
441C4⋊C4—48no—
442C4⋊C4—48no—
443C4⋊C4—48no—
444C4⋊C4—44no—
445C4⋊C4—44no—
446C4⋊C4—44no—
447C4⋊C4—44no—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—44no—
451C4⋊C4—84no—
452C4⋊C4—88no—
453C4⋊C4—84no—
454C42—216no—
455C42—48no—
456C42—48no—
457C42—416no—
458C42#121116yes—
459C23C23×D411yescharacteristic
460C23C23×D411yescharacteristic
461C23C22×#4111yescharacteristic
462C23C2×2−1+414yes—
463C23C2×2−1+412yes—
464C23#58512yes—
465C23#58512yes—
466C23#58512yes—
467Q8—416no—
468Q8—416no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—28no—
483C2×C4—28no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4C2×#12114yes—
558C2×C4C2×#12114yes—
559C2×C4C2×#12114yes—
560C2×C4#53618yes—
561C22C22×#12111yescharacteristic
562C22C2×#53612yes—
563C22#344912yes—
564C22#348511yescharacteristic
565C22#348611yescharacteristic
566C22#348711yescharacteristic
567C22#348711yescharacteristic
568C22#348912yes—
569C22#349312yes—
570C22#349512yes—
571C22#349912yes—
572C22#350912yes—
573C22#355514yes—
574C22#356314yes—
575C22#356414yes—
576C22#356514yes—
577C4—24no—
578C4—24no—
579C4—28no—
580C4—24no—
581C4—44no—
582C4—44no—
583C4—44no—
584C4—44no—
585C4—84no—
586C4—82no—
587C4—82no—
588C4—81no—
589C4—81no—
590C4—82no—
591C4—81no—
592C4—81no—
593C4—84no—
594C2#3515011yescharacteristic
595C2#3531611yescharacteristic
596C2#3566111yescharacteristic
597C2#4141112yes—
598C2#4231212yes—
599C2#4231312yes—
600C2#4289112yes—
601C2#5148414yes—
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×#25812
C2×#25842
C2×#26342
C2×#23562
#170782
#169932
#166772
#166632
#158952
#158742
#151562
#150902
#149032
#149012
#146642
#143562
#143462