Finite Group Databasebeta

← #6833915

Subgroups — #6833915

Order 512.

1246 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39769C211yesmaximal, characteristic
2#39625C211yesmaximal, characteristic
3#33289C211yesmaximal, characteristic
4#32432C212yesmaximal
5#32315C212yesmaximal
6#32228C212yesmaximal
7#31461C212yesmaximal
8#29984C211yesmaximal, characteristic
9#29866C211yesmaximal, characteristic
10#29097C212yesmaximal
11#28801C212yesmaximal
12#28048C212yesmaximal
13#27823C211yesmaximal, characteristic
14#27746C212yesmaximal
15#27737C211yesmaximal, characteristic
16#26506C211yesmaximal, characteristic
17#26440C211yesmaximal, characteristic
18#24818C211yesmaximal, characteristic
19#24683C211yesmaximal, characteristic
20#23068C211yesmaximal, characteristic
21#22970C211yesmaximal, characteristic
22#21673C211yesmaximal, characteristic
23#21276C211yesmaximal, characteristic
24C2×#475C2211yescharacteristic
25C2×#475C2211yescharacteristic
26C2×C4×Q16C2211yescharacteristic
27#2868C2211yescharacteristic
28#2868C2211yescharacteristic
29#2794—22no—
30#2794—22no—
31#2792—22no—
32#2734—22no—
33#2660—21no—
34#2642—21no—
35#2570C2212yes—
36#2570C2212yes—
37#2568C2211yescharacteristic
38#2568C2211yescharacteristic
39#2567C2212yes—
40#2552C2211yescharacteristic
41#2551—21no—
42#2551C2211yescharacteristic
43#2551C2212yes—
44#2550—21no—
45#2511C2212yes—
46#2511C2212yes—
47#2507C2212yes—
48#2451C2212yes—
49#2446—21no—
50#2446—21no—
51#2365C2211yescharacteristic
52#2365C2211yescharacteristic
53#2355C2211yescharacteristic
54Q8×C4⋊C4C2211yescharacteristic
55#2330—21no—
56#2327—21no—
57C4×#125C2211yescharacteristic
58#2295C2211yescharacteristic
59#2295C2211yescharacteristic
60#2101C2212yes—
61#2101C2212yes—
62#2100C2212yes—
63#2099C2212yes—
64#2095C2212yes—
65#2086C2212yes—
66#2086C2212yes—
67#2085C2212yes—
68#2084C2212yes—
69#2084C2212yes—
70#2074C2212yes—
71#2072C2212yes—
72#2072C2212yes—
73#2072C2212yes—
74#2066C2212yes—
75#2057C2212yes—
76#2057C2212yes—
77#2056C2212yes—
78#2024C2212yes—
79#2024C2212yes—
80#1993C2212yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2212yes—
85#1990C2211yescharacteristic
86#1990C2212yes—
87#1988C2211yescharacteristic
88#1988C2212yes—
89#1988C2211yescharacteristic
90#1969C2211yescharacteristic
91#1969C2211yescharacteristic
92#1949C2212yes—
93#1947C2211yescharacteristic
94#1947C2211yescharacteristic
95#1947C2212yes—
96#1944C2212yes—
97#1942C2211yescharacteristic
98#1942C2211yescharacteristic
99#1939C2211yescharacteristic
100#1939C2211yescharacteristic
101#1935C2212yes—
102#1935C2212yes—
103#1935C2212yes—
104#1933C2211yescharacteristic
105#1933C2211yescharacteristic
106#1933C2211yescharacteristic
107#1933C2211yescharacteristic
108#1928C2212yes—
109#1927C2212yes—
110#1920C2212yes—
111#1919C2212yes—
112#1918C2212yes—
113#1918C2212yes—
114#1916C2212yes—
115#1916C2212yes—
116#1878C2212yes—
117#1863C2212yes—
118#1836C2212yes—
119#1834C2212yes—
120#1834C2212yes—
121#1831C2211yescharacteristic
122#1805C2212yes—
123#1803C2211yescharacteristic
124#1803C2211yescharacteristic
125#1776C2212yes—
126C4×#107C2211yescharacteristic
127#1771C2212yes—
128#1771C2212yes—
129#1770C2211yescharacteristic
130#1770C2211yescharacteristic
131#1763C2212yes—
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134C42×C8C2211yescharacteristic
135C22×Q16C2311yescharacteristic
136C2×C4⋊Q8—21no—
137C2×C4⋊Q8—22no—
138C2×C4⋊Q8—21no—
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8—21no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2312yes—
145C2×C4⋊Q8C2312yes—
146C2×#125—21no—
147C2×#125D411yescharacteristic
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2312yes—
153#475—24no—
154#475—24no—
155C4×Q16—24no—
156C2×#107C2311yescharacteristic
157C2×#107C2311yescharacteristic
158C2×#107C2312yes—
159C2×#107C2311yescharacteristic
160C2×#107C2312yes—
161C2×#106C2312yes—
162C2×#106C2312yes—
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×#103C2312yes—
168C2×#103C2312yes—
169C2×#103C2311yescharacteristic
170C2×#103C2311yescharacteristic
171C2×#103C2311yescharacteristic
172C2×#103C2311yescharacteristic
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#103C2311yescharacteristic
176C2×#103C2311yescharacteristic
177C2×#97C2312yes—
178C2×#97C2312yes—
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185#400—22no—
186#400—22no—
187#400—22no—
188#400—22no—
189#400—22no—
190#400—22no—
191#400—22no—
192#400—22no—
193#398—22no—
194#398—22no—
195#398—22no—
196#398—22no—
197#398—22no—
198#398—22no—
199#395—22no—
200#395—22no—
201#395—22no—
202#395—22no—
203#395—22no—
204#395—22no—
205#391—21no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—21no—
210#391—21no—
211#391—22no—
212#391C2311yescharacteristic
213#391C2312yes—
214#391C2312yes—
215#391C2312yes—
216#391C2311yescharacteristic
217#391C2311yescharacteristic
218#391C2311yescharacteristic
219#389—22no—
220#389—22no—
221#389—22no—
222#389—21no—
223#389—21no—
224#389—22no—
225#389—22no—
226#389D411yescharacteristic
227#389D411yescharacteristic
228#389C2311yescharacteristic
229#389C2312yes—
230#389C2311yescharacteristic
231#389C2312yes—
232#389C2312yes—
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2312yes—
236#389C2312yes—
237#387—22no—
238#387—22no—
239#387—22no—
240#387—22no—
241#387—21no—
242#387—21no—
243#387—21no—
244#387—21no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387D412yes—
255#387D412yes—
256#384—21no—
257#384—21no—
258#384—21no—
259#384—21no—
260#384—21no—
261#384C2312yes—
262#384C2312yes—
263#384C2312yes—
264#384C2312yes—
265#384C2311yescharacteristic
266#384C2311yescharacteristic
267#382—21no—
268#382D411yescharacteristic
269#382C2312yes—
270#382C2312yes—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2312yes—
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2312yes—
284#376—21no—
285#376—21no—
286C43C2311yescharacteristic
287#340C2312yes—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2311yescharacteristic
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2311yescharacteristic
304#340C2311yescharacteristic
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2312yes—
315C22×Q8—21no—
316C22×Q8—21no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8C2411yescharacteristic
320C22×Q8C2411yescharacteristic
321C2×Q16—22no—
322C2×Q16—22no—
323C2×Q16—41no—
324C22×C8C2411yescharacteristic
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2411yescharacteristic
328C22×C8C2411yescharacteristic
329C22×C8C2411yescharacteristic
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—42no—
335C4⋊Q8—42no—
336C4⋊Q8—42no—
337C4⋊Q8—42no—
338C4⋊Q8—44no—
339C4⋊Q8—82no—
340C4⋊Q8—82no—
341C4⋊Q8—82no—
342C4⋊Q8—82no—
343C4⋊Q8—84no—
344#125—24no—
345#125—82no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—42no—
350C4×Q8—42no—
351C4×Q8—82no—
352C4×Q8—82no—
353C4×Q8#4114yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D412yes—
387C2×C4⋊C4C2×D412yes—
388C2×C4⋊C4C2×D412yes—
389C2×C4⋊C4C2×D412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2411yescharacteristic
397C2×C4⋊C4C2411yescharacteristic
398C2×C4⋊C4C2411yescharacteristic
399C2×C4⋊C4C2411yescharacteristic
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2412yes—
413C2×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415C2×C42C2412yes—
416C2×C42C2411yescharacteristic
417#107—22no—
418#107—22no—
419#107—42no—
420#107—42no—
421#107—41no—
422#106—24no—
423#106—24no—
424C4⋊C8—24no—
425C4⋊C8—22no—
426C4⋊C8—22no—
427C4⋊C8—42no—
428#103—22no—
429#103—24no—
430#103—24no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—41no—
435#103—42no—
436#103—41no—
437#103—42no—
438#97—24no—
439#97—42no—
440C4×C8—22no—
441C4×C8—22no—
442C4×C8—22no—
443C4×C8—22no—
444C4×C8—41no—
445C4×C8—41no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—22no—
457#95—22no—
458#95—21no—
459#95—21no—
460#95—22no—
461#95—21no—
462#95—21no—
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#95C2×D412yes—
479#95C2×D412yes—
480#95C2×D412yes—
481#95C2×D412yes—
482#95C2×D412yes—
483#95C2×D412yes—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—44no—
502C2×Q8—82no—
503C2×Q8—82no—
504C2×Q8—82no—
505C2×Q8—82no—
506C2×Q8—82no—
507C2×Q8C2×#4112yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C2511yescharacteristic
531Q16—44no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C82−1+412yes—
549C2×C82−1+412yes—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—21no—
571C4⋊C4—22no—
572C4⋊C4—21no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
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⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4—81no—
600C4⋊C4—82no—
601C4⋊C4—81no—
602C4⋊C4—82no—
603C4⋊C4—82no—
604C4⋊C4—82no—
605C4⋊C4C2×#4112yes—
606C42—24no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—21no—
611C42—21no—
612C42—22no—
613C42—22no—
614C42—21no—
615C42—21no—
616C42—22no—
617C42—22no—
618C42—42no—
619C42—42no—
620C42—42no—
621C42—82no—
622C42—82no—
623C42—82no—
624C42—82no—
625C42#13714yes—
626C42C2×#4112yes—
627C422−1+412yes—
628C23C23×D411yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—84no—
638Q8—84no—
639Q8—164no—
640Q8—164no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
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—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4#54812yes—
700C2×C4#54812yes—
701C2×C4C2×#13712yes—
702C2×C4C2×#13712yes—
703C2×C4C2×#13712yes—
704C2×C4#57612yes—
705C2×C4#57712yes—
706C2×C4#57812yes—
707C2×C4C22×#4111yescharacteristic
708C2×C4C2×2−1+411yescharacteristic
709C2×C4C2×2−1+411yescharacteristic
710C2×C4C2×2−1+411yescharacteristic
711C2×C4#58511yescharacteristic
712C2×C4#58511yescharacteristic
713C8—22no—
714C8—22no—
715C8—41no—
716C8—42no—
717C8—42no—
718C8—41no—
719C22C2×#54811yescharacteristic
720C22#349911yescharacteristic
721C22#350011yescharacteristic
722C22C22×#13711yescharacteristic
723C22C2×#57611yescharacteristic
724C22C2×#57711yescharacteristic
725C22C2×#57811yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—82no—
742C4—81no—
743C4—82no—
744C4—82no—
745C4—82no—
746C4—81no—
747C4#337514yes—
748C4#346111yescharacteristic
749C4#349511yescharacteristic
750C4#355511yescharacteristic
751C4#356311yescharacteristic
752C2#3942711yescharacteristic
753C2C2×#337511yescharacteristic
754C2#6133011yescharacteristic
755C2#6247811yescharacteristic
756C2#6248811yescharacteristic
757C2#6253611yescharacteristic
758C2#6255011yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ 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
#397692
#396252
#332892
#324322
#323152
#322282
#314612
#299842
#298662
#290972
#288012
#280482
#278232
#277462
#277372
#265062
#264402
#248182
#246832
#230682
#229702
#216732
#212762