Finite Group Databasebeta

← #6542108

Subgroups — #6542108

Order 512.

1310 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39643C211yesmaximal, characteristic
2#34491C211yesmaximal, characteristic
3#30100C212yesmaximal
4#29867C211yesmaximal, characteristic
5#29585C212yesmaximal
6#29403C212yesmaximal
7#29273C211yesmaximal, characteristic
8#28688C211yesmaximal, characteristic
9#27389C212yesmaximal
10#27366C212yesmaximal
11#26872C212yesmaximal
12#26859C212yesmaximal
13#26283C211yesmaximal, characteristic
14#26277C211yesmaximal, characteristic
15#25841C211yesmaximal, characteristic
16#25837C211yesmaximal, characteristic
17#23842C212yesmaximal
18#23777C211yesmaximal, characteristic
19#23163C211yesmaximal, characteristic
20#23158C211yesmaximal, characteristic
21#23069C211yesmaximal, characteristic
22#23062C211yesmaximal, characteristic
23#22829C211yesmaximal, characteristic
24C2×Q82C2211yescharacteristic
25C2×#500C2211yescharacteristic
26C2×#498C2211yescharacteristic
27C2×#477C2211yescharacteristic
28C2×#475C2211yescharacteristic
29#2862C2211yescharacteristic
30#2799—22no—
31#2755—22no—
32#2647C2212yes—
33#2582—21no—
34#2568—21no—
35#2567C2211yescharacteristic
36#2546C2211yescharacteristic
37#2511—21no—
38#2509C2212yes—
39#2508C2212yes—
40#2446—21no—
41#2381—22no—
42#2369C2211yescharacteristic
43#2369C2211yescharacteristic
44#2365—21no—
45#2365C2211yescharacteristic
46#2365C2212yes—
47#2356—21no—
48#2356C2212yes—
49#2355C2211yescharacteristic
50#2355C2211yescharacteristic
51#2331—21no—
52#2331C2212yes—
53#2331C2212yes—
54#2327—22no—
55#2320—21no—
56#2320C2212yes—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59#2295C2211yescharacteristic
60#2295C2211yescharacteristic
61#2101C2212yes—
62#2101C2212yes—
63#2100C2211yescharacteristic
64#2099C2212yes—
65#2095C2211yescharacteristic
66#2087C2211yescharacteristic
67#2087C2211yescharacteristic
68#2085C2212yes—
69#2085C2212yes—
70#2085C2212yes—
71#2085C2212yes—
72#2085C2212yes—
73#2085C2212yes—
74#2074C2212yes—
75#2074C2212yes—
76#2068C2211yescharacteristic
77#2068C2211yescharacteristic
78#2058C2212yes—
79#2058C2212yes—
80#2058C2212yes—
81#2057C2211yescharacteristic
82#2057C2212yes—
83#2057C2212yes—
84#2024C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1988C2211yescharacteristic
88#1987C2211yescharacteristic
89#1987C2211yescharacteristic
90#1987C2211yescharacteristic
91#1984C2211yescharacteristic
92#1984C2211yescharacteristic
93#1949C2212yes—
94#1949C2212yes—
95#1948C2211yescharacteristic
96#1948C2211yescharacteristic
97#1944C2212yes—
98#1942C2212yes—
99#1935C2212yes—
100#1933C2212yes—
101#1927C2212yes—
102#1927C2212yes—
103#1921C2212yes—
104#1921C2212yes—
105#1921C2212yes—
106#1920C2212yes—
107#1920C2212yes—
108#1919C2212yes—
109#1919C2212yes—
110#1919C2212yes—
111#1919C2212yes—
112#1919C2212yes—
113#1918C2212yes—
114#1918C2212yes—
115#1917C2212yes—
116#1916C2212yes—
117#1865C2212yes—
118#1865C2212yes—
119#1863C2212yes—
120#1863C2212yes—
121#1840C2212yes—
122#1831C2211yescharacteristic
123#1776C2212yes—
124#1776C2212yes—
125C4×#107C2212yes—
126C4×#107C2211yescharacteristic
127C4×#107C2211yescharacteristic
128C4×#106C2212yes—
129#1770C2211yescharacteristic
130C8×C4⋊C4C2211yescharacteristic
131C4×C4⋊C8C2211yescharacteristic
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134#1746C2212yes—
135Q82—24no—
136Q82—24no—
137C2×C4⋊Q8—21no—
138C2×C4⋊Q8—22no—
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8C2311yescharacteristic
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2312yes—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—22no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153#500—24no—
154#498—24no—
155#477—24no—
156#475—24no—
157C2×#107C2312yes—
158C2×#107C2311yescharacteristic
159C2×#107C2311yescharacteristic
160C2×#107C2312yes—
161C2×#107C2312yes—
162C2×#107C2311yescharacteristic
163C2×#107C2311yescharacteristic
164C2×#106C2312yes—
165C2×#106C2312yes—
166C2×#106C2312yes—
167C2×#106C2312yes—
168C2×#106C2312yes—
169C2×C4⋊C8C2311yescharacteristic
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2311yescharacteristic
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#103C2311yescharacteristic
176C2×#103C2311yescharacteristic
177C2×#103C2311yescharacteristic
178C2×#103C2311yescharacteristic
179C2×#97C2312yes—
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2312yes—
183#400—22no—
184#400—22no—
185#400—22no—
186#400—22no—
187#400—22no—
188#398—22no—
189#398—22no—
190#398—22no—
191#398—22no—
192#395—22no—
193#391—21no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—22no—
198#391—21no—
199#391—21no—
200#391—21no—
201#391—21no—
202#391—21no—
203#391—21no—
204#391—22no—
205#391—22no—
206#391—22no—
207#391—22no—
208#391—22no—
209#391—22no—
210#391D411yescharacteristic
211#391D411yescharacteristic
212#391C2311yescharacteristic
213#391C2312yes—
214#391C2311yescharacteristic
215#389—21no—
216#389—21no—
217#389—22no—
218#389—21no—
219#389—21no—
220#389D411yescharacteristic
221#389D411yescharacteristic
222#389C2312yes—
223#389C2311yescharacteristic
224#389C2311yescharacteristic
225#389C2312yes—
226#389C2312yes—
227#389C2311yescharacteristic
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#389C2311yescharacteristic
232#389C2312yes—
233#389C2312yes—
234#387—22no—
235#387—22no—
236#387—22no—
237#387—22no—
238#387—21no—
239#387—21no—
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#387D412yes—
252#387D412yes—
253#384—21no—
254#384C2311yescharacteristic
255#384C2311yescharacteristic
256#383—22no—
257#383—22no—
258#382—21no—
259#382—22no—
260#382—22no—
261#382C2312yes—
262#382C2312yes—
263#382C2312yes—
264C4×C4⋊C4—21no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4C2311yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2312yes—
282#376—21no—
283#376—22no—
284#376C2312yes—
285C43C2311yescharacteristic
286#340C2311yescharacteristic
287#340C2311yescharacteristic
288#340C2311yescharacteristic
289#340C2312yes—
290#340C2312yes—
291#340C2311yescharacteristic
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#336C2311yescharacteristic
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2312yes—
315#336C2311yescharacteristic
316#336C2312yes—
317#336C2312yes—
318C22×Q8—22no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8C2×D411yescharacteristic
324C22×Q8C2411yescharacteristic
325C22×C8C2411yescharacteristic
326C22×C8C2412yes—
327C22×C8C2411yescharacteristic
328C22×C8C2412yes—
329C22×C8C2411yescharacteristic
330C22×C8C2411yescharacteristic
331C4⋊Q8—216no—
332C4⋊Q8—28no—
333C4⋊Q8—24no—
334C4⋊Q8—24no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—82no—
343C4⋊Q8#4114yes—
344C4×Q8—28no—
345C4×Q8—24no—
346C4×Q8—24no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—82no—
351C4×Q8—82no—
352C4×Q8—82no—
353C4×Q8—84no—
354C4×Q8#4114yes—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D412yes—
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D412yes—
383C2×C4⋊C4C2×D412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2411yescharacteristic
389C2×C4⋊C4C2411yescharacteristic
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C42—21no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2412yes—
411C2×C42C2411yescharacteristic
412C2×C42C2411yescharacteristic
413C2×C42C2412yes—
414C2×C42C2411yescharacteristic
415#107—22no—
416#107—22no—
417#107—24no—
418#107—24no—
419#107—24no—
420#107—22no—
421#107—22no—
422#106—24no—
423#106—24no—
424#106—24no—
425#106—24no—
426#106—24no—
427C4⋊C8—22no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431#103—24no—
432#103—24no—
433#103—22no—
434#103—22no—
435#103—22no—
436#103—22no—
437#97—24no—
438C4×C8—24no—
439C4×C8—22no—
440C4×C8—22no—
441#95—21no—
442#95—21no—
443#95—22no—
444#95—22no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—22no—
449#95—22no—
450#95—21no—
451#95—22no—
452#95—22no—
453#95—21no—
454#95—21no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—21no—
461#95—21no—
462#95—22no—
463#95—22no—
464#95—21no—
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#95C2×D412yes—
475#95C2×D412yes—
476#95C2×D412yes—
477#95C2×D412yes—
478#95C2×D412yes—
479#95C2×D412yes—
480#95C2×D412yes—
481C2×Q8—28no—
482C2×Q8—24no—
483C2×Q8—22no—
484C2×Q8—24no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—81no—
497C2×Q8—82no—
498C2×Q8—81no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×Q8—82no—
502C2×Q8—81no—
503C2×Q8—81no—
504C2×Q8C2×#4112yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D412yes—
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D412yes—
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D412yes—
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D412yes—
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C2511yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C82−1+412yes—
545C2×C82−1+412yes—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—81no—
580C4⋊C4—82no—
581C4⋊C4—81no—
582C4⋊C4—82no—
583C4⋊C4—82no—
584C4⋊C4—81no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4—81no—
588C4⋊C4—81no—
589C4⋊C4—81no—
590C4⋊C4—82no—
591C4⋊C4—82no—
592C4⋊C4—82no—
593C4⋊C4C2×#4114yes—
594C4⋊C4C2×#4112yes—
595C4⋊C42−1+412yes—
596C4⋊C42−1+412yes—
597C42—28no—
598C42—24no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—41no—
610C42—41no—
611C42—44no—
612C42—42no—
613C42—42no—
614C42—42no—
615C42—82no—
616C42—82no—
617C42—82no—
618C42—82no—
619C42—82no—
620C42C2×#4112yes—
621C42C2×#4112yes—
622C23C23×D411yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—44no—
626Q8—41no—
627Q8—41no—
628Q8—84no—
629Q8—84no—
630Q8—88no—
631Q8—84no—
632Q8—162no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4#52512yes—
696C2×C4#52512yes—
697C2×C4#57712yes—
698C2×C4#57812yes—
699C2×C4C22×#4111yescharacteristic
700C2×C4C22×#4111yescharacteristic
701C2×C4C2×2−1+411yescharacteristic
702C2×C4C2×2−1+411yescharacteristic
703C2×C4C2×2−1+411yescharacteristic
704C2×C4C2×2−1+411yescharacteristic
705C8—22no—
706C8—22no—
707C8—42no—
708C8—42no—
709C8—41no—
710C8—41no—
711C22C2×#52511yescharacteristic
712C22#348611yescharacteristic
713C22#349911yescharacteristic
714C22C2×#57711yescharacteristic
715C22C2×#57811yescharacteristic
716C22#358411yescharacteristic
717C22#358511yescharacteristic
718C4—22no—
719C4—41no—
720C4—42no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—44no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4—82no—
736C4—82no—
737C4—81no—
738C4—82no—
739C4#312114yes—
740C4#350911yescharacteristic
741C4#350911yescharacteristic
742C4#352311yescharacteristic
743C4#352311yescharacteristic
744C2#3574911yescharacteristic
745C2C2×#312111yescharacteristic
746C2#6059211yescharacteristic
747C2#6185411yescharacteristic
748C2#6186411yescharacteristic
749C2#6249611yescharacteristic
750C2#6252111yescharacteristic
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
#396432
#344912
#301002
#298672
#295852
#294032
#292732
#286882
#273892
#273662
#268722
#268592
#262832
#262772
#258412
#258372
#238422
#237772
#231632
#231582
#230692
#230622
#228292