Finite Group Databasebeta

← #6542099

Subgroups — #6542099

Order 512.

1323 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39641C211yesmaximal, characteristic
2#34488C211yesmaximal, characteristic
3#30103C212yesmaximal
4#29866C211yesmaximal, characteristic
5#29587C212yesmaximal
6#29407C212yesmaximal
7#29274C211yesmaximal, characteristic
8#28689C211yesmaximal, characteristic
9#27377C212yesmaximal
10#27364C212yesmaximal
11#26882C212yesmaximal
12#26867C212yesmaximal
13#26278C211yesmaximal, characteristic
14#26276C211yesmaximal, characteristic
15#25840C211yesmaximal, characteristic
16#25840C211yesmaximal, characteristic
17#23843C212yesmaximal
18#23779C211yesmaximal, characteristic
19#23161C211yesmaximal, characteristic
20#23157C211yesmaximal, characteristic
21#23068C211yesmaximal, characteristic
22#23062C211yesmaximal, characteristic
23#22829C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C2×#500C2211yescharacteristic
26C2×#500C2211yescharacteristic
27C2×#475C2211yescharacteristic
28C2×#475C2211yescharacteristic
29#2868C2211yescharacteristic
30#2791—22no—
31#2791—22no—
32#2647C2212yes—
33#2546—21no—
34#2546—21no—
35#2546C2211yescharacteristic
36#2546C2211yescharacteristic
37#2507C2212yes—
38#2507C2212yes—
39#2446—21no—
40#2446—21no—
41#2382—22no—
42#2370C2212yes—
43#2365—21no—
44#2365C2211yescharacteristic
45#2365C2211yescharacteristic
46#2365C2211yescharacteristic
47#2355C2211yescharacteristic
48#2355C2212yes—
49#2351—21no—
50Q8×C4⋊C4C2211yescharacteristic
51#2336—22no—
52#2330C2212yes—
53#2330C2212yes—
54#2327—21no—
55#2320—21no—
56#2320C2212yes—
57C4×C4⋊Q8C2211yescharacteristic
58C4×#125C2211yescharacteristic
59#2295C2211yescharacteristic
60#2295C2211yescharacteristic
61#2101C2212yes—
62#2101C2211yescharacteristic
63#2100C2212yes—
64#2099C2212yes—
65#2097C2211yescharacteristic
66#2088C2211yescharacteristic
67#2086C2211yescharacteristic
68#2084C2212yes—
69#2084C2212yes—
70#2084C2212yes—
71#2083C2212yes—
72#2083C2212yes—
73#2083C2212yes—
74#2072C2212yes—
75#2072C2212yes—
76#2068C2211yescharacteristic
77#2066C2211yescharacteristic
78#2059C2212yes—
79#2059C2212yes—
80#2059C2211yescharacteristic
81#2059C2212yes—
82#2059C2212yes—
83#2059C2212yes—
84#2026C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1988C2211yescharacteristic
88#1988C2211yescharacteristic
89#1988C2211yescharacteristic
90#1988C2211yescharacteristic
91#1984C2211yescharacteristic
92#1984C2211yescharacteristic
93#1948C2211yescharacteristic
94#1947C2212yes—
95#1947C2212yes—
96#1947C2211yescharacteristic
97#1943C2212yes—
98#1942C2212yes—
99#1935C2212yes—
100#1933C2212yes—
101#1928C2212yes—
102#1927C2212yes—
103#1921C2212yes—
104#1921C2212yes—
105#1921C2212yes—
106#1920C2212yes—
107#1919C2212yes—
108#1919C2212yes—
109#1919C2212yes—
110#1919C2212yes—
111#1918C2212yes—
112#1918C2212yes—
113#1918C2212yes—
114#1918C2212yes—
115#1917C2212yes—
116#1916C2212yes—
117#1863C2212yes—
118#1863C2212yes—
119#1863C2212yes—
120#1863C2212yes—
121#1840C2212yes—
122#1831C2211yescharacteristic
123#1776C2212yes—
124#1776C2212yes—
125C4×#107C2212yes—
126C4×#107C2211yescharacteristic
127C4×#106C2212yes—
128C4×#106C2211yescharacteristic
129#1770C2211yescharacteristic
130C8×C4⋊C4C2211yescharacteristic
131C4×C4⋊C8C2211yescharacteristic
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134#1746C2212yes—
135#557—24no—
136#557—24no—
137C2×C4⋊Q8—21no—
138C2×C4⋊Q8—21no—
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8—21no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×#125—22no—
146C2×#125C2311yescharacteristic
147C2×#125C2312yes—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8C2312yes—
155C2×C4×Q8C2311yescharacteristic
156C2×C4×Q8C2311yescharacteristic
157#500—24no—
158#500—24no—
159#475—24no—
160#475—24no—
161C2×#107C2311yescharacteristic
162C2×#107C2312yes—
163C2×#107C2312yes—
164C2×#107C2312yes—
165C2×#107C2312yes—
166C2×#107C2312yes—
167C2×#107C2311yescharacteristic
168C2×#106C2312yes—
169C2×#106C2312yes—
170C2×#106C2311yescharacteristic
171C2×#106C2312yes—
172C2×#106C2311yescharacteristic
173C2×C4⋊C8C2311yescharacteristic
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×#103C2312yes—
178C2×#103C2312yes—
179C2×#103C2311yescharacteristic
180C2×#103C2311yescharacteristic
181C2×#103C2311yescharacteristic
182C2×#103C2311yescharacteristic
183C2×#97C2312yes—
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2312yes—
187#400—22no—
188#400—22no—
189#398—22no—
190#398—22no—
191#398—22no—
192#398—22no—
193#398—22no—
194#398—22no—
195#398—22no—
196#398—22no—
197#391—21no—
198#391—21no—
199#391—21no—
200#391—21no—
201#391—21no—
202#391—21no—
203#391D411yescharacteristic
204#391D411yescharacteristic
205#391C2311yescharacteristic
206#391C2312yes—
207#391C2311yescharacteristic
208#389—21no—
209#389—22no—
210#389—22no—
211#389—21no—
212#389—22no—
213#389—22no—
214#389—22no—
215#389—22no—
216#389—22no—
217#389—22no—
218#389D411yescharacteristic
219#389D411yescharacteristic
220#389C2311yescharacteristic
221#389C2311yescharacteristic
222#389C2312yes—
223#389C2311yescharacteristic
224#389C2312yes—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#389C2311yescharacteristic
230#389C2312yes—
231#389C2312yes—
232#387—22no—
233#387—22no—
234#387—22no—
235#387—21no—
236#387—21no—
237#387—21no—
238#387—21no—
239#387—22no—
240#387—22no—
241#387—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387D412yes—
253#387D412yes—
254#384—21no—
255#384—21no—
256#384C2311yescharacteristic
257#384C2312yes—
258#384C2312yes—
259#384C2312yes—
260#383—22no—
261#382—22no—
262#382—21no—
263#382—22no—
264#382C2311yescharacteristic
265C4×C4⋊C4—21no—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—22no—
272C4×C4⋊C4C2311yescharacteristic
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2312yes—
283#376—21no—
284#376C2312yes—
285C43C2311yescharacteristic
286#340C2311yescharacteristic
287#340C2311yescharacteristic
288#340C2311yescharacteristic
289#340C2311yescharacteristic
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2311yescharacteristic
295#340C2311yescharacteristic
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#336C2312yes—
309#336C2311yescharacteristic
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2312yes—
315#336C2311yescharacteristic
316#336C2312yes—
317#336C2312yes—
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8C2×D411yescharacteristic
322C22×Q8C2411yescharacteristic
323C22×C8C2412yes—
324C22×C8C2411yescharacteristic
325C22×C8C2411yescharacteristic
326C22×C8C2412yes—
327C22×C8C2411yescharacteristic
328C22×C8C2411yescharacteristic
329C4⋊Q8—28no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—82no—
336C4⋊Q8—82no—
337C4⋊Q8—82no—
338C4⋊Q8—82no—
339C4⋊Q8#4114yes—
340#125—216no—
341#125—24no—
342#125—24no—
343#125—22no—
344#125—22no—
345C4×Q8—28no—
346C4×Q8—24no—
347C4×Q8—24no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—82no—
352C4×Q8—82no—
353C4×Q8—82no—
354C4×Q8—82no—
355C4×Q8—82no—
356C4×Q8#4114yes—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D412yes—
390C2×C4⋊C4C2×D412yes—
391C2×C4⋊C4C2×D412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2411yescharacteristic
397C2×C4⋊C4C2411yescharacteristic
398C2×C4⋊C4C2411yescharacteristic
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2411yescharacteristic
402C2×C4⋊C4C2411yescharacteristic
403C2×C42—22no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2412yes—
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2412yes—
422C2×C42C2411yescharacteristic
423#107—22no—
424#107—24no—
425#107—24no—
426#107—24no—
427#107—24no—
428#107—22no—
429#107—24no—
430#106—22no—
431#106—24no—
432#106—24no—
433#106—22no—
434#106—24no—
435C4⋊C8—22no—
436C4⋊C8—22no—
437C4⋊C8—22no—
438C4⋊C8—22no—
439#103—24no—
440#103—24no—
441#103—22no—
442#103—22no—
443#103—22no—
444#103—22no—
445#97—24no—
446C4×C8—24no—
447C4×C8—22no—
448C4×C8—22no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—22no—
456#95—22no—
457#95—21no—
458#95—21no—
459#95—22no—
460#95—22no—
461#95—21no—
462#95—21no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95C2×D412yes—
479#95C2×D412yes—
480#95C2×D412yes—
481#95C2×D412yes—
482#95C2×D412yes—
483#95C2×D412yes—
484#95C2×D412yes—
485C2×Q8—22no—
486C2×Q8—24no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8C2×#4112yes—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4C22×D412yes—
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D412yes—
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D412yes—
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D412yes—
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C2511yescharacteristic
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C82−1+412yes—
543C2×C82−1+412yes—
544C4⋊C4—28no—
545C4⋊C4—28no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—28no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—22no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—24no—
556C4⋊C4—21no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—22no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—22no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—81no—
582C4⋊C4—81no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4—82no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4C2×#4112yes—
598C4⋊C4C2×#4114yes—
599C4⋊C42−1+412yes—
600C4⋊C42−1+412yes—
601C42—28no—
602C42—24no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—41no—
615C42—42no—
616C42—42no—
617C42—42no—
618C42—82no—
619C42—82no—
620C42—82no—
621C42—82no—
622C42—82no—
623C42—82no—
624C42C2×#4112yes—
625C42C2×#4112yes—
626C23C23×D411yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—44no—
630Q8—48no—
631Q8—41no—
632Q8—41no—
633Q8—84no—
634Q8—84no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4#52512yes—
697C2×C4#52512yes—
698C2×C4#57612yes—
699C2×C4#57712yes—
700C2×C4#57812yes—
701C2×C4C22×#4111yescharacteristic
702C2×C4C22×#4111yescharacteristic
703C2×C4C2×2−1+411yescharacteristic
704C2×C4C2×2−1+411yescharacteristic
705C2×C4C2×2−1+411yescharacteristic
706C2×C4C2×2−1+411yescharacteristic
707C8—22no—
708C8—22no—
709C8—42no—
710C8—42no—
711C8—41no—
712C8—41no—
713C22C2×#52511yescharacteristic
714C22#348611yescharacteristic
715C22#349911yescharacteristic
716C22C2×#57611yescharacteristic
717C22C2×#57711yescharacteristic
718C22C2×#57811yescharacteristic
719C22#358611yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—41no—
724C4—42no—
725C4—42no—
726C4—44no—
727C4—41no—
728C4—42no—
729C4—42no—
730C4—41no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—82no—
738C4—82no—
739C4—82no—
740C4—81no—
741C4#311914yes—
742C4#350911yescharacteristic
743C4#350911yescharacteristic
744C4#352311yescharacteristic
745C4#352311yescharacteristic
746C2#3574911yescharacteristic
747C2C2×#311911yescharacteristic
748C2#6059411yescharacteristic
749C2#6185711yescharacteristic
750C2#6186911yescharacteristic
751C2#6248811yescharacteristic
752C2#6252211yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#396412
#344882
#301032
#298662
#295872
#294072
#292742
#286892
#273772
#273642
#268822
#268672
#262782
#262762
#258402
#238432
#237792
#231612
#231572
#230682
#230622
#228292