Finite Group Databasebeta

← #614525

Subgroups — #614525

Order 512.

2134 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2514C211yesmaximal, characteristic
2C2×#2508C211yesmaximal, characteristic
3#15240C211yesmaximal, characteristic
4#15231C211yesmaximal, characteristic
5#15184C211yesmaximal, characteristic
6#15151C211yesmaximal, characteristic
7#15049C214yesmaximal
8#14844C214yesmaximal
9#14707C211yesmaximal, characteristic
10#14703C211yesmaximal, characteristic
11#14703C211yesmaximal, characteristic
12#14703C211yesmaximal, characteristic
13#14689C211yesmaximal, characteristic
14#14223C214yesmaximal
15#14051C211yesmaximal, characteristic
16#14003C211yesmaximal, characteristic
17#13914C214yesmaximal
18C4×#384C211yesmaximal, characteristic
19C42×C4⋊C4C211yesmaximal, characteristic
20#2514—28no—
21#2508—28no—
22C2×#401C2212yes—
23C2×#400C2212yes—
24C2×#400C2212yes—
25C2×#398C2214yes—
26C2×#398C2212yes—
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#387C2212yes—
40C2×#387C2212yes—
41C2×#384C2211yescharacteristic
42C2×#384C2211yescharacteristic
43C2×#383C2212yes—
44C2×#382C2212yes—
45C2×#382C2211yescharacteristic
46C2×#382C2211yescharacteristic
47C2×#382C2211yescharacteristic
48C2×#382C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2214yes—
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C43C2211yescharacteristic
57C2×C43C2211yescharacteristic
58C2×C43C2211yescharacteristic
59#1445C2214yes—
60#1445C2214yes—
61#1445C2214yes—
62#1443C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1436C2214yes—
69#1436C2214yes—
70#1436C2214yes—
71#1436C2214yes—
72#1436C2214yes—
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2211yescharacteristic
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2214yes—
82#1434C2214yes—
83#1434C2214yes—
84#1434C2214yes—
85#1434C2214yes—
86#1434C2214yes—
87#1434C2214yes—
88#1434C2214yes—
89C4×#95C2212yes—
90C4×#95C2211yescharacteristic
91C4×#95C2211yescharacteristic
92C4×#95C2212yes—
93C23×Q8C2311yescharacteristic
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2314yes—
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C42C2312yes—
112C22×C42C2311yescharacteristic
113C22×C42C2312yes—
114C22×C42C2312yes—
115C22×C42C2312yes—
116C22×C42C2312yes—
117C22×C42C2312yes—
118C22×C42C2312yes—
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C22×C42C2312yes—
124C22×C42C2311yescharacteristic
125C22×C42C2311yescharacteristic
126#401—28no—
127#400—28no—
128#400—28no—
129#398—28no—
130#398—216no—
131#391—24no—
132#391—24no—
133#391—24no—
134#391—24no—
135#391—24no—
136#391—24no—
137#391—24no—
138#389—24no—
139#389—24no—
140#389—24no—
141#389—24no—
142#389—24no—
143#387—28no—
144#387—28no—
145#384—24no—
146#384—24no—
147#383—28no—
148#382—24no—
149#382—24no—
150#382—24no—
151#382—24no—
152#382—28no—
153C4×C4⋊C4—28no—
154C4×C4⋊C4—24no—
155C4×C4⋊C4—24no—
156C4×C4⋊C4—28no—
157C4×C4⋊C4—24no—
158C4×C4⋊C4—216no—
159C4×C4⋊C4D418yes—
160C2×#95C2312yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2312yes—
164C2×#95C2314yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C43—24no—
199C43—24no—
200C43—24no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8—22no—
204C22×Q8—22no—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8—22no—
208C23×C4C2412yes—
209C23×C4C2412yes—
210C23×C4C2412yes—
211C23×C4C2412yes—
212C23×C4C2412yes—
213C23×C4C2412yes—
214C23×C4C2412yes—
215C23×C4C2411yescharacteristic
216C23×C4C2411yescharacteristic
217C23×C4C2411yescharacteristic
218C23×C4C2411yescharacteristic
219C23×C4C2412yes—
220C23×C4C2412yes—
221C23×C4C2412yes—
222C23×C4C2411yescharacteristic
223C23×C4C2411yescharacteristic
224C23×C4C2412yes—
225C23×C4C2412yes—
226C23×C4C2411yescharacteristic
227C2×C4⋊C4—22no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—24no—
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—24no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—28no—
242C2×C4⋊C4—28no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—28no—
247C2×C4⋊C4—28no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4—28no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—44no—
264C2×C4⋊C4—44no—
265C2×C4⋊C4—44no—
266C2×C4⋊C4—44no—
267C2×C4⋊C4C2×D414yes—
268C2×C4⋊C4C2×D414yes—
269C2×C4⋊C4#4118yes—
270C2×C4⋊C4#4114yes—
271C2×C42—24no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—24no—
277C2×C42—22no—
278C2×C42—24no—
279C2×C42—24no—
280C2×C42—22no—
281C2×C42—22no—
282C2×C42—22no—
283C2×C42—22no—
284C2×C42—22no—
285C2×C42—24no—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42—24no—
289C2×C42—24no—
290C2×C42—24no—
291C2×C42—24no—
292C2×C42—24no—
293C2×C42—22no—
294C2×C42—24no—
295C2×C42—24no—
296C2×C42—24no—
297C2×C42—22no—
298C2×C42—28no—
299C2×C42—28no—
300C2×C42—24no—
301C2×C42—22no—
302C2×C42—24no—
303C2×C42—24no—
304C2×C42—42no—
305C2×C42—42no—
306C2×C42—42no—
307C2×C42C2×D414yes—
308C2×C42C2×D414yes—
309C2×C42C2×D414yes—
310C2×C42#4114yes—
311C2×C42#4114yes—
312C2×C42#4118yes—
313C2×C42#4114yes—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—24no—
329#95—24no—
330#95—24no—
331#95—24no—
332#95—24no—
333#95—24no—
334#95—24no—
335#95—24no—
336#95—28no—
337#95—28no—
338#95—28no—
339#95—28no—
340#95—28no—
341#95—28no—
342#95—28no—
343#95—28no—
344#95—28no—
345#95—28no—
346#95—28no—
347#95—28no—
348#95—44no—
349#95—44no—
350#95C2×D414yes—
351#95C2×D414yes—
352C24C2511yescharacteristic
353C2×Q8—44no—
354C2×Q8—44no—
355C2×Q8—44no—
356C2×Q8—44no—
357C2×Q8—44no—
358C2×Q8—44no—
359C2×Q8—44no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
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—24no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4C22×D412yes—
444C22×C4C22×D412yes—
445C22×C4C22×D412yes—
446C22×C4C22×D412yes—
447C22×C4C22×D412yes—
448C22×C4C22×D412yes—
449C22×C4C22×D412yes—
450C22×C4C2×#4114yes—
451C22×C4C2×#4114yes—
452C22×C4C2×#4114yes—
453C22×C4C2×#4114yes—
454C22×C4C2×#4114yes—
455C22×C4C2×#4114yes—
456C22×C4C2×#4114yes—
457C22×C4C2×#4114yes—
458C22×C4C2×#4114yes—
459C22×C4C2×#4114yes—
460C22×C4C2×#4112yes—
461C22×C4C2×#4112yes—
462C22×C4C2×#4112yes—
463C22×C4C2×#4112yes—
464C22×C42−1+414yes—
465C22×C42−1+412yes—
466C22×C42−1+412yes—
467C4⋊C4—216no—
468C4⋊C4—28no—
469C4⋊C4—28no—
470C4⋊C4—28no—
471C4⋊C4—416no—
472C4⋊C4—416no—
473C4⋊C4—48no—
474C4⋊C4—48no—
475C4⋊C4—44no—
476C4⋊C4—44no—
477C4⋊C4—44no—
478C4⋊C4—44no—
479C4⋊C4—44no—
480C4⋊C4—44no—
481C4⋊C4—84no—
482C4⋊C4—84no—
483C4⋊C4—84no—
484C42—216no—
485C42—28no—
486C42—28no—
487C42—28no—
488C42—28no—
489C42—216no—
490C42—28no—
491C42—28no—
492C42—48no—
493C42—48no—
494C42—48no—
495C42—44no—
496C42—48no—
497C42—48no—
498C42—48no—
499C23C23×D411yescharacteristic
500C23C22×#4111yescharacteristic
501C23C22×#4112yes—
502C23C22×#4112yes—
503C23C22×#4111yescharacteristic
504C23C22×#4111yescharacteristic
505C23C22×#4111yescharacteristic
506C23C2×2−1+411yescharacteristic
507C23C2×2−1+411yescharacteristic
508C23C2×2−1+412yes—
509C23#58512yes—
510Q8—88no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—28no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4#52918yes—
608C2×C4#52914yes—
609C2×C4#53214yes—
610C2×C4#53214yes—
611C2×C4#53214yes—
612C2×C4#54114yes—
613C2×C4#54714yes—
614C2×C4#54814yes—
615C2×C4#55218yes—
616C2×C4#55214yes—
617C2×C4#55214yes—
618C22C2×#52912yes—
619C22C2×#52911yescharacteristic
620C22C2×#53211yescharacteristic
621C22C2×#53211yescharacteristic
622C22C2×#53211yescharacteristic
623C22#344412yes—
624C22C2×#54111yescharacteristic
625C22#346112yes—
626C22C2×#54711yescharacteristic
627C22C2×#54811yescharacteristic
628C22C2×#55211yescharacteristic
629C22C2×#55212yes—
630C22C2×#55211yescharacteristic
631C22#347512yes—
632C22#347512yes—
633C22#348212yes—
634C22#349512yes—
635C22#349911yescharacteristic
636C22#350011yescharacteristic
637C22#350712yes—
638C22#350912yes—
639C22#351812yes—
640C22#352312yes—
641C4—24no—
642C4—24no—
643C4—28no—
644C4—28no—
645C4—44no—
646C4—42no—
647C4—42no—
648C4—42no—
649C4—44no—
650C4—44no—
651C4—42no—
652C4—82no—
653C4—82no—
654C4—82no—
655C4—82no—
656C4—82no—
657C4—82no—
658C4—82no—
659C4#251918yes—
660C2C2×#251911yescharacteristic
661C2#3478012yes—
662C2#3518712yes—
663C2#3531811yescharacteristic
664C2#3618111yescharacteristic
665C2#3618511yescharacteristic
666C2#3619912yes—
667C2#3638012yes—
668C2#3650811yescharacteristic
669C2#3653411yescharacteristic
670C2#3663111yescharacteristic
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×#25142
C2×#25082
#152402
#152312
#151842
#151512
#150492
#148442
#147072
#147032
#146892
#142232
#140512
#140032
#139142
C4×#3842
C42×C4⋊C42