Finite Group Databasebeta

← #6559890

Subgroups — #6559890

Order 512.

1266 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#39642C211yesmaximal, characteristic
2#38984C211yesmaximal, characteristic
3#30393C212yesmaximal
4#30280C211yesmaximal, characteristic
5#29589C212yesmaximal
6#29528C212yesmaximal
7#29349C211yesmaximal, characteristic
8#29218C211yesmaximal, characteristic
9#28970C212yesmaximal
10#28947C212yesmaximal
11#28684C211yesmaximal, characteristic
12#28677C211yesmaximal, characteristic
13#28647C211yesmaximal, characteristic
14#28638C211yesmaximal, characteristic
15#28050C212yesmaximal
16#28030C212yesmaximal
17#23838C211yesmaximal, characteristic
18#23793C212yesmaximal
19#23221C211yesmaximal, characteristic
20#23217C211yesmaximal, characteristic
21#23163C211yesmaximal, characteristic
22#23156C211yesmaximal, characteristic
23#20571C211yesmaximal, characteristic
24C2×#498C2211yescharacteristic
25C2×#498C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#487C2211yescharacteristic
28C2×#446C2211yescharacteristic
29C2×C8×Q8C2211yescharacteristic
30#2868C2211yescharacteristic
31#2862C2211yescharacteristic
32#2767—22no—
33#2762—22no—
34#2713—22no—
35#2713—22no—
36#2647C2212yes—
37#2645C2212yes—
38#2581—21no—
39#2568—21no—
40#2568C2211yescharacteristic
41#2567C2211yescharacteristic
42#2567C2211yescharacteristic
43#2552—21no—
44#2552—21no—
45#2546C2211yescharacteristic
46#2514—21no—
47#2511—21no—
48#2511—21no—
49#2511C2212yes—
50#2506C2212yes—
51#2506C2212yes—
52#2451C2212yes—
53#2446—21no—
54#2369C2211yescharacteristic
55#2369C2211yescharacteristic
56#2365C2211yescharacteristic
57#2365C2211yescharacteristic
58#2330C2212yes—
59#2320C2212yes—
60C4×C4⋊Q8C2211yescharacteristic
61C4×#125C2211yescharacteristic
62#2295C2211yescharacteristic
63#2100C2212yes—
64#2100C2212yes—
65#2096C2212yes—
66#2096C2212yes—
67#2096C2212yes—
68#2096C2212yes—
69#2088C2212yes—
70#2088C2212yes—
71#2088C2212yes—
72#2088C2212yes—
73#2085C2211yescharacteristic
74#2085C2211yescharacteristic
75#2084C2211yescharacteristic
76#2083C2211yescharacteristic
77#2074C2212yes—
78#2068C2212yes—
79#2068C2212yes—
80#2066C2212yes—
81#2066C2212yes—
82#2059C2211yescharacteristic
83#2059C2211yescharacteristic
84#2058C2211yescharacteristic
85#2057C2211yescharacteristic
86#2026C2212yes—
87#1990C2212yes—
88#1988C2211yescharacteristic
89#1988C2211yescharacteristic
90#1987C2211yescharacteristic
91#1987C2211yescharacteristic
92#1987C2211yescharacteristic
93#1987C2211yescharacteristic
94#1981C2211yescharacteristic
95#1981C2211yescharacteristic
96#1944C2212yes—
97#1943C2212yes—
98#1943C2212yes—
99#1941C2212yes—
100#1941C2212yes—
101#1941C2212yes—
102#1935C2212yes—
103#1935C2212yes—
104#1935C2212yes—
105#1933C2212yes—
106#1933C2212yes—
107#1933C2212yes—
108#1933C2212yes—
109#1933C2212yes—
110#1928C2212yes—
111#1927C2212yes—
112#1920C2212yes—
113#1920C2212yes—
114#1919C2212yes—
115#1919C2212yes—
116#1865C2212yes—
117#1863C2212yes—
118#1834C2212yes—
119#1776C2212yes—
120C4×#107C2211yescharacteristic
121C4×#107C2211yescharacteristic
122C4×#106C2211yescharacteristic
123C4×#106C2211yescharacteristic
124C4×#106C2212yes—
125#1771C2212yes—
126#1770C2211yescharacteristic
127C8×C4⋊C4C2212yes—
128C8×C4⋊C4C2211yescharacteristic
129#1768C2212yes—
130C4×C4⋊C8C2211yescharacteristic
131#1763C2212yes—
132C4×#103C2212yes—
133#1746C2212yes—
134#1744C2211yescharacteristic
135C2×C4⋊Q8—21no—
136C2×C4⋊Q8—21no—
137C2×C4⋊Q8—21no—
138C2×C4⋊Q8C2311yescharacteristic
139C2×C4⋊Q8C2311yescharacteristic
140C2×C4⋊Q8C2311yescharacteristic
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143C2×#125—22no—
144C2×#125—22no—
145C2×#125C2311yescharacteristic
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8C2312yes—
149C2×C4×Q8C2311yescharacteristic
150#498—24no—
151#498—24no—
152#487—24no—
153#487—24no—
154#446—24no—
155C8×Q8—24no—
156C2×#107C2311yescharacteristic
157C2×#107C2311yescharacteristic
158C2×#107C2311yescharacteristic
159C2×#107C2311yescharacteristic
160C2×#106C2311yescharacteristic
161C2×#106C2311yescharacteristic
162C2×#106C2311yescharacteristic
163C2×#106C2312yes—
164C2×#106C2312yes—
165C2×#106C2312yes—
166C2×#106C2312yes—
167C2×#106C2311yescharacteristic
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2311yescharacteristic
172C2×#103C2312yes—
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#103C2312yes—
176C2×#103C2312yes—
177C2×#103C2312yes—
178C2×#103C2312yes—
179C2×#103C2312yes—
180C2×#97C2312yes—
181C2×#97C2312yes—
182C2×C4×C8C2312yes—
183C2×C4×C8C2312yes—
184C2×C4×C8C2312yes—
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187#401—22no—
188#400—22no—
189#400—22no—
190#400—22no—
191#400—22no—
192#400—22no—
193#400—22no—
194#400—22no—
195#400—22no—
196#400—22no—
197#400—22no—
198#398—22no—
199#398—22no—
200#398—22no—
201#398—22no—
202#398—22no—
203#398—22no—
204#395—22no—
205#395—22no—
206#395—22no—
207#391—21no—
208#391—21no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—22no—
216#391—22no—
217#391—22no—
218#391D411yescharacteristic
219#391D411yescharacteristic
220#391C2312yes—
221#391C2312yes—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—22no—
230#389—22no—
231#389D411yescharacteristic
232#389D411yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#387—22no—
247#387—22no—
248#387—21no—
249#387—21no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387D412yes—
260#387D412yes—
261#384—21no—
262#384—21no—
263#384—21no—
264#384—21no—
265#384C2311yescharacteristic
266#384C2312yes—
267#384C2312yes—
268#383—22no—
269#382—21no—
270#382—21no—
271#382—21no—
272#382—22no—
273#382C2311yescharacteristic
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2311yescharacteristic
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2312yes—
289#376C2312yes—
290C43C2311yescharacteristic
291#340C2311yescharacteristic
292#340C2311yescharacteristic
293#340C2311yescharacteristic
294#340C2311yescharacteristic
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2311yescharacteristic
302#340C2311yescharacteristic
303#340C2311yescharacteristic
304#340C2311yescharacteristic
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#336C2311yescharacteristic
312#336C2311yescharacteristic
313#336C2311yescharacteristic
314#336C2311yescharacteristic
315#336C2312yes—
316#336C2312yes—
317#336C2312yes—
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8C2×D411yescharacteristic
323C22×Q8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2411yescharacteristic
327C22×C8C2411yescharacteristic
328C22×C8C2411yescharacteristic
329C22×C8C2411yescharacteristic
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—41no—
340C4⋊Q8—82no—
341C4⋊Q8—82no—
342C4⋊Q8—82no—
343#125—22no—
344#125—22no—
345#125—84no—
346#125—84no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—24no—
350C4×Q8—42no—
351C4×Q8—82no—
352C4×Q8—82no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
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—22no—
370C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D412yes—
384C2×C4⋊C4C2×D412yes—
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2411yescharacteristic
396C2×C4⋊C4C2411yescharacteristic
397C2×C4⋊C4C2411yescharacteristic
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—22no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2412yes—
411C2×C42C2412yes—
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415#107—22no—
416#107—22no—
417#107—22no—
418#107—41no—
419#106—24no—
420#106—24no—
421#106—24no—
422#106—24no—
423#106—22no—
424#106—22no—
425#106—22no—
426#106—41no—
427C4⋊C8—24no—
428C4⋊C8—24no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431#103—24no—
432#103—24no—
433#103—24no—
434#103—24no—
435#103—24no—
436#103—24no—
437#103—42no—
438#103—42no—
439#97—24no—
440#97—42no—
441C4×C8—24no—
442C4×C8—42no—
443C4×C8—42no—
444C4×C8#4114yes—
445C4×C8#4114yes—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—21no—
455#95—22no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—22no—
461#95—22no—
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#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—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—81no—
502C2×Q8—81no—
503C2×Q8—81no—
504C2×Q8—81no—
505C2×Q8—81no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4C22×D412yes—
519C22×C4C22×D412yes—
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C2511yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8C2×#4112yes—
544C2×C8C2×#4112yes—
545C2×C8C2×#4112yes—
546C2×C8C2×#4112yes—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—22no—
550C4⋊C4—24no—
551C4⋊C4—22no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—44no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—81no—
587C4⋊C4—81no—
588C4⋊C4—81no—
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—82no—
600C4⋊C42−1+412yes—
601C4⋊C42−1+412yes—
602C4⋊C42−1+412yes—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—22no—
615C42—44no—
616C42—42no—
617C42—42no—
618C42—42no—
619C42—42no—
620C42—82no—
621C42—82no—
622C42—82no—
623C42C2×#4112yes—
624C42C2×#4112yes—
625C23C23×D411yescharacteristic
626Q8—44no—
627Q8—42no—
628Q8—42no—
629Q8—42no—
630Q8—42no—
631Q8—84no—
632Q8—84no—
633Q8—162no—
634Q8—162no—
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—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4#53212yes—
696C2×C4#53212yes—
697C2×C4#57712yes—
698C2×C4#57712yes—
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×C4#58511yescharacteristic
707C8—22no—
708C8—22no—
709C8—22no—
710C8—22no—
711C8—42no—
712C8—42no—
713C22C2×#53211yescharacteristic
714C22#348611yescharacteristic
715C22#348911yescharacteristic
716C22C2×#57711yescharacteristic
717C22C2×#57711yescharacteristic
718C22C2×#57711yescharacteristic
719C22C2×#57811yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—42no—
724C4—42no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—82no—
733C4—82no—
734C4—82no—
735C4—82no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4#317814yes—
742C4#350711yescharacteristic
743C4#350711yescharacteristic
744C4#350911yescharacteristic
745C4#350911yescharacteristic
746C2#3593811yescharacteristic
747C2C2×#317811yescharacteristic
748C2#6071211yescharacteristic
749C2#6186911yescharacteristic
750C2#6187111yescharacteristic
751C2#6220211yescharacteristic
752C2#6220411yescharacteristic
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
#396422
#389842
#303932
#302802
#295892
#295282
#293492
#292182
#289702
#289472
#286842
#286772
#286472
#286382
#280502
#280302
#238382
#237932
#232212
#232172
#231632
#231562
#205712