Finite Group Databasebeta

← #6591285

Subgroups — #6591285

Order 512.

1314 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36535C211yesmaximal, characteristic
2#36286C211yesmaximal, characteristic
3#33290C211yesmaximal, characteristic
4#33202C211yesmaximal, characteristic
5#33200C211yesmaximal, characteristic
6#28193C212yesmaximal
7#27738C211yesmaximal, characteristic
8#27737C211yesmaximal, characteristic
9#27734C212yesmaximal
10#26515C212yesmaximal
11#26513C211yesmaximal, characteristic
12#26512C211yesmaximal, characteristic
13#25001C212yesmaximal
14#25000C212yesmaximal
15#24687C212yesmaximal
16#24683C211yesmaximal, characteristic
17#24682C211yesmaximal, characteristic
18#23070C212yesmaximal
19#23069C211yesmaximal, characteristic
20#23068C211yesmaximal, characteristic
21#22744C212yesmaximal
22#21712C211yesmaximal, characteristic
23C42×Q16C211yesmaximal, characteristic
24C2×#479C2212yes—
25C2×#477C2211yescharacteristic
26C2×#475C2211yescharacteristic
27C2×#446C2212yes—
28C2×C4×Q16C2211yescharacteristic
29C2×C4×Q16C2211yescharacteristic
30C2×C4×Q16C2211yescharacteristic
31#2864—21no—
32#2863—21no—
33#2862C2211yescharacteristic
34#2859C2211yescharacteristic
35#2605—22no—
36#2590—22no—
37#2588—22no—
38#2588—22no—
39#2581C2212yes—
40#2581C2212yes—
41#2571C2211yescharacteristic
42#2570—21no—
43#2570C2212yes—
44#2568C2211yescharacteristic
45#2567C2211yescharacteristic
46#2565C2212yes—
47#2552C2211yescharacteristic
48#2550—21no—
49#2511—21no—
50#2451—21no—
51#2370C2212yes—
52#2369C2211yescharacteristic
53#2365C2211yescharacteristic
54#2356C2212yes—
55#2355C2211yescharacteristic
56#2355C2211yescharacteristic
57#2355C2212yes—
58#2355C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#125—21no—
61#2295—21no—
62C42×Q8C2211yescharacteristic
63C42×Q8C2211yescharacteristic
64#2101C2212yes—
65#2101C2212yes—
66#2100C2212yes—
67#2099C2212yes—
68#2087C2212yes—
69#2087C2212yes—
70#2074C2212yes—
71#2074C2212yes—
72#2072C2212yes—
73#2072C2212yes—
74#2056C2212yes—
75#2056C2212yes—
76#1991C2212yes—
77#1991C2212yes—
78#1990C2211yescharacteristic
79#1990C2211yescharacteristic
80#1990C2211yescharacteristic
81#1990C2211yescharacteristic
82#1989C2212yes—
83#1988C2211yescharacteristic
84#1987C2211yescharacteristic
85#1984C2212yes—
86#1949C2212yes—
87#1949C2212yes—
88#1949C2212yes—
89#1949C2212yes—
90#1949C2212yes—
91#1948C2211yescharacteristic
92#1947C2211yescharacteristic
93#1947C2212yes—
94#1947C2212yes—
95#1939C2211yescharacteristic
96#1939C2211yescharacteristic
97#1939C2212yes—
98#1935C2212yes—
99#1935C2212yes—
100#1935C2212yes—
101#1935C2212yes—
102#1928C2212yes—
103#1928C2212yes—
104#1927C2212yes—
105#1927C2212yes—
106#1921C2212yes—
107#1920C2212yes—
108#1919C2212yes—
109#1918C2212yes—
110#1842C2211yescharacteristic
111#1836C2212yes—
112#1836C2212yes—
113#1835C2212yes—
114#1835C2212yes—
115#1805C2212yes—
116#1805C2212yes—
117#1805C2212yes—
118#1803C2211yescharacteristic
119#1803C2211yescharacteristic
120#1776C2212yes—
121#1776C2212yes—
122C4×#107C2211yescharacteristic
123C4×#107C2211yescharacteristic
124C4×#107C2211yescharacteristic
125#1770C2211yescharacteristic
126#1770C2211yescharacteristic
127#1770C2212yes—
128C4×#103C2211yescharacteristic
129C4×#103C2211yescharacteristic
130C4×#103C2211yescharacteristic
131C4×#103C2211yescharacteristic
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134C42×C8C2211yescharacteristic
135C22×Q16C2311yescharacteristic
136C2×C4⋊Q8D411yescharacteristic
137C2×C4⋊Q8C2311yescharacteristic
138C2×C4⋊Q8C2311yescharacteristic
139C2×#125—21no—
140C2×#125C2312yes—
141C2×C4×Q8—21no—
142C2×C4×Q8C2311yescharacteristic
143C2×C4×Q8C2311yescharacteristic
144C2×C4×Q8C2311yescharacteristic
145C2×C4×Q8C2311yescharacteristic
146C2×C4×Q8C2311yescharacteristic
147C2×C4×Q8C2311yescharacteristic
148C2×C4×Q8C2312yes—
149#479—28no—
150#477—24no—
151#475—24no—
152#446—28no—
153C4×Q16—24no—
154C4×Q16—24no—
155C4×Q16—24no—
156C2×#107C2312yes—
157C2×#107C2312yes—
158C2×#107C2311yescharacteristic
159C2×#107C2311yescharacteristic
160C2×#107C2311yescharacteristic
161C2×#106C2312yes—
162C2×#106C2312yes—
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169C2×#103C2312yes—
170C2×#103C2312yes—
171C2×#103C2312yes—
172C2×#103C2312yes—
173C2×#103C2311yescharacteristic
174C2×#103C2311yescharacteristic
175C2×#103C2311yescharacteristic
176C2×#103C2311yescharacteristic
177C2×#103C2311yescharacteristic
178C2×#103C2311yescharacteristic
179C2×#97C2312yes—
180C2×#97C2312yes—
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187#400—22no—
188#400—22no—
189#400—22no—
190#400—22no—
191#400—22no—
192#398—22no—
193#398—22no—
194#398—22no—
195#398—22no—
196#395—22no—
197#395—22no—
198#395—22no—
199#391—22no—
200#391—22no—
201#391—21no—
202#391—21no—
203#391—21no—
204#391—21no—
205#391—21no—
206#391—21no—
207#391—21no—
208#391—22no—
209#391D412yes—
210#391C2312yes—
211#391C2312yes—
212#391C2312yes—
213#391C2312yes—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—22no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389D411yescharacteristic
225#389D412yes—
226#389D411yescharacteristic
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#387—22no—
232#387—22no—
233#387—22no—
234#387—22no—
235#387—22no—
236#387—22no—
237#387—22no—
238#387—22no—
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#384D411yescharacteristic
251#384C2312yes—
252#384C2312yes—
253#384C2311yescharacteristic
254#384C2311yescharacteristic
255#383—22no—
256#382—21no—
257#382—21no—
258#382—21no—
259#382C2312yes—
260#382C2312yes—
261#382C2312yes—
262#382C2312yes—
263#382C2312yes—
264C4×C4⋊C4—21no—
265C4×C4⋊C4—22no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—22no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—22no—
276C4×C4⋊C4C2311yescharacteristic
277C4×C4⋊C4C2311yescharacteristic
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2312yes—
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2311yescharacteristic
289#376—22no—
290C43—21no—
291C43—21no—
292C43C2311yescharacteristic
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#336C2312yes—
316#336C2312yes—
317#336C2312yes—
318#336C2312yes—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8C2×D412yes—
322C22×Q8C2411yescharacteristic
323C22×Q8C2411yescharacteristic
324C2×Q16—22no—
325C2×Q16—22no—
326C2×Q16—22no—
327C22×C8C2411yescharacteristic
328C22×C8C2411yescharacteristic
329C22×C8C2412yes—
330C22×C8C2412yes—
331C22×C8C2411yescharacteristic
332C22×C8C2411yescharacteristic
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—42no—
338#125—24no—
339#125—24no—
340#125—44no—
341C4×Q8—24no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—24no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—44no—
354C4×Q8#4114yes—
355C4×Q8#4114yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D412yes—
380C2×C4⋊C4C2×D412yes—
381C2×C4⋊C4C2×D412yes—
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2411yescharacteristic
389C2×C4⋊C4C2411yescharacteristic
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2411yescharacteristic
396C2×C4⋊C4C2411yescharacteristic
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—22no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2412yes—
418C2×C42C2412yes—
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422#107—22no—
423#107—22no—
424#107—22no—
425#107—24no—
426#107—24no—
427#106—24no—
428#106—24no—
429C4⋊C8—24no—
430C4⋊C8—24no—
431C4⋊C8—24no—
432C4⋊C8—22no—
433C4⋊C8—22no—
434C4⋊C8—24no—
435#103—22no—
436#103—22no—
437#103—24no—
438#103—24no—
439#103—24no—
440#103—24no—
441#103—22no—
442#103—22no—
443#103—22no—
444#103—22no—
445#97—24no—
446#97—24no—
447C4×C8—22no—
448C4×C8—22no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8#4114yes—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
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#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95C2×D412yes—
486#95C2×D412yes—
487#95C2×D412yes—
488#95C2×D412yes—
489C2×Q8—24no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—81no—
507C2×Q8—81no—
508C2×Q8C2×#4112yes—
509C2×Q8C2×#4112yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C2511yescharacteristic
533Q16—28no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8C2×#4112yes—
551C2×C8C2×#4112yes—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—81no—
595C4⋊C4—81no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4C2×#4112yes—
602C4⋊C4C2×#4112yes—
603C42—24no—
604C42—24no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—41no—
612C42—41no—
613C42—44no—
614C42—42no—
615C42—42no—
616C42—42no—
617C42—42no—
618C42—42no—
619C42—42no—
620C42—81no—
621C42—81no—
622C42—81no—
623C42—81no—
624C42—82no—
625C42—82no—
626C42—82no—
627C42C2×#4112yes—
628C42C2×#4112yes—
629C42C2×#4112yes—
630C422−1+412yes—
631C422−1+412yes—
632C422−1+412yes—
633C23C23×D411yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—84no—
643Q8—84no—
644Q8—162no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4#54712yes—
704C2×C4#54712yes—
705C2×C4#54812yes—
706C2×C4#54812yes—
707C2×C4#54812yes—
708C2×C4#54812yes—
709C2×C4#57512yes—
710C2×C4#57812yes—
711C2×C4C22×#4111yescharacteristic
712C2×C4C22×#4111yescharacteristic
713C2×C4C22×#4111yescharacteristic
714C2×C4C2×2−1+411yescharacteristic
715C2×C4C2×2−1+411yescharacteristic
716C2×C4C2×2−1+411yescharacteristic
717C8—22no—
718C8—22no—
719C8—42no—
720C8—42no—
721C8—41no—
722C8—41no—
723C22C2×#54711yescharacteristic
724C22C2×#54811yescharacteristic
725C22C2×#54811yescharacteristic
726C22C2×#57511yescharacteristic
727C22C2×#57811yescharacteristic
728C22#358411yescharacteristic
729C22#358411yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—81no—
744C4—81no—
745C4—82no—
746C4—81no—
747C4—82no—
748C4—82no—
749C4—81no—
750C4—82no—
751C4#337714yes—
752C4#344411yescharacteristic
753C4#350911yescharacteristic
754C4#350911yescharacteristic
755C4#350911yescharacteristic
756C2#3615111yescharacteristic
757C2#6125111yescharacteristic
758C2#6128611yescharacteristic
759C2C2×#337711yescharacteristic
760C2#6131611yescharacteristic
761C2#6132811yescharacteristic
762C2#6133111yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ 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
#365352
#362862
#332902
#332022
#332002
#281932
#277382
#277372
#277342
#265152
#265132
#265122
#250012
#250002
#246872
#246832
#246822
#230702
#230692
#230682
#227442
#217122
C42×Q162