Finite Group Databasebeta

← #7572953

Subgroups — #7572953

Order 512.

1282 conjugacy classes of subgroups.

The subgroup lattice has 745 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59672C211yesmaximal, characteristic
2#36447C211yesmaximal, characteristic
3#32509C212yesmaximal
4#32145C212yesmaximal
5#29314C211yesmaximal, characteristic
6#29178C211yesmaximal, characteristic
7#28827C211yesmaximal, characteristic
8#28792C211yesmaximal, characteristic
9#27994C212yesmaximal
10#27303C212yesmaximal
11#27295C212yesmaximal
12#26865C212yesmaximal
13#26508C211yesmaximal, characteristic
14#26507C211yesmaximal, characteristic
15#26108C211yesmaximal, characteristic
16#26047C212yesmaximal
17#26047C211yesmaximal, characteristic
18#23253C211yesmaximal, characteristic
19#22967C212yesmaximal
20#22965C211yesmaximal, characteristic
21#22965C211yesmaximal, characteristic
22C4×#479C211yesmaximal, characteristic
23C4×#477C211yesmaximal, characteristic
24C2×#479C2211yescharacteristic
25C2×#479C2212yes—
26C2×#477C2211yescharacteristic
27#2859—21no—
28#2859C2211yescharacteristic
29#2809—22no—
30#2571—21no—
31#2571C2211yescharacteristic
32#2565—22no—
33#2552—21no—
34#2552—21no—
35#2552C2211yescharacteristic
36#2552C2211yescharacteristic
37#2552C2211yescharacteristic
38#2552C2212yes—
39#2508—22no—
40#2508—21no—
41#2508C2212yes—
42#2508C2212yes—
43#2506—21no—
44#2506—22no—
45#2506C2212yes—
46#2506C2212yes—
47#2370—21no—
48#2370C2212yes—
49#2369C2211yescharacteristic
50#2369C2211yescharacteristic
51#2351C2212yes—
52Q8×C4⋊C4C2212yes—
53Q8×C4⋊C4C2211yescharacteristic
54Q8×C4⋊C4C2211yescharacteristic
55C4×C4⋊Q8C2211yescharacteristic
56C4×#125—21no—
57C4×#125C2211yescharacteristic
58C4×#125C2211yescharacteristic
59C42×Q8C2211yescharacteristic
60#2101C2212yes—
61#2099C2212yes—
62#2099C2212yes—
63#2088C2212yes—
64#2088C2212yes—
65#2086C2212yes—
66#2086C2212yes—
67#2086C2212yes—
68#2086C2212yes—
69#2085C2212yes—
70#2085C2212yes—
71#2083C2212yes—
72#2083C2212yes—
73#2059C2212yes—
74#2059C2212yes—
75#2059C2212yes—
76#1991C2212yes—
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1989C2211yescharacteristic
80#1987C2211yescharacteristic
81#1949C2211yescharacteristic
82#1949C2212yes—
83#1948C2211yescharacteristic
84#1948C2211yescharacteristic
85#1948C2212yes—
86#1947C2211yescharacteristic
87#1947C2211yescharacteristic
88#1947C2211yescharacteristic
89#1942C2212yes—
90#1942C2212yes—
91#1942C2212yes—
92#1942C2212yes—
93#1942C2212yes—
94#1941C2212yes—
95#1939C2211yescharacteristic
96#1939C2211yescharacteristic
97#1939C2212yes—
98#1921C2212yes—
99#1921C2212yes—
100#1921C2212yes—
101#1920C2211yescharacteristic
102#1920C2212yes—
103#1919C2212yes—
104#1918C2211yescharacteristic
105#1918C2212yes—
106#1918C2212yes—
107#1916C2212yes—
108#1916C2212yes—
109#1865C2211yescharacteristic
110#1865C2212yes—
111#1863C2212yes—
112#1863C2211yescharacteristic
113#1863C2212yes—
114#1863C2212yes—
115#1863C2212yes—
116#1845C2212yes—
117#1845C2211yescharacteristic
118#1834C2211yescharacteristic
119#1805C2211yescharacteristic
120#1803C2211yescharacteristic
121#1803C2212yes—
122C4×#107C2212yes—
123C4×#107C2211yescharacteristic
124C4×#106C2211yescharacteristic
125C8×C4⋊C4C2212yes—
126C8×C4⋊C4C2211yescharacteristic
127C8×C4⋊C4C2211yescharacteristic
128C4×C4⋊C8C2211yescharacteristic
129C4×C4⋊C8C2211yescharacteristic
130C4×#103C2212yes—
131C4×#103C2211yescharacteristic
132C4×#103C2211yescharacteristic
133C4×#103C2212yes—
134C4×#103C2212yes—
135C2×C4⋊Q8C2311yescharacteristic
136C2×#125—21no—
137C2×#125—21no—
138C2×#125—22no—
139C2×#125—22no—
140C2×#125—21no—
141C2×#125D411yescharacteristic
142C2×#125C2311yescharacteristic
143C2×#125C2312yes—
144C2×C4×Q8—21no—
145C2×C4×Q8C2311yescharacteristic
146C2×C4×Q8C2312yes—
147C2×C4×Q8C2312yes—
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150#479—24no—
151#479—28no—
152#477Q818yes—
153C2×#107C2312yes—
154C2×#107C2311yescharacteristic
155C2×#107C2312yes—
156C2×#107C2312yes—
157C2×#107C2312yes—
158C2×#107C2312yes—
159C2×#107C2311yescharacteristic
160C2×#107C2312yes—
161C2×#106C2312yes—
162C2×#106C2311yescharacteristic
163C2×#106C2311yescharacteristic
164C2×#106C2312yes—
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2311yescharacteristic
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2311yescharacteristic
170C2×C4⋊C8C2311yescharacteristic
171C2×#103C2311yescharacteristic
172C2×#103C2312yes—
173C2×#103C2311yescharacteristic
174C2×#103C2311yescharacteristic
175C2×#103C2312yes—
176C2×#103C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2312yes—
180C2×C4×C8C2312yes—
181C2×C4×C8C2312yes—
182#400—22no—
183#400—22no—
184#400—22no—
185#400—22no—
186#400—22no—
187#398—22no—
188#398—22no—
189#398—22no—
190#398—22no—
191#398—22no—
192#398—22no—
193#398—22no—
194#398—22no—
195#398—22no—
196#391—21no—
197#391—22no—
198#391—22no—
199#389—21no—
200#389—21no—
201#389—22no—
202#389—22no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—22no—
207#389—22no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—22no—
213#389—22no—
214#389—22no—
215#389—22no—
216#389D411yescharacteristic
217#389D411yescharacteristic
218#389C2311yescharacteristic
219#389C2311yescharacteristic
220#389C2312yes—
221#389C2312yes—
222#389C2312yes—
223#389C2312yes—
224#389C2312yes—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#387—22no—
232#387—22no—
233#387—22no—
234#387—21no—
235#387—21no—
236#387—22no—
237#387—22no—
238#387—22no—
239#387D412yes—
240#387D412yes—
241#384—22no—
242#384—21no—
243#384—21no—
244#384—22no—
245#384—21no—
246#384C2311yescharacteristic
247#384C2312yes—
248#384C2311yescharacteristic
249#384C2312yes—
250#384C2311yescharacteristic
251#382—21no—
252#382—21no—
253#382—22no—
254#382—22no—
255#382—22no—
256#382D411yescharacteristic
257#382C2311yescharacteristic
258#382C2312yes—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—21no—
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—22no—
271C4×C4⋊C4—22no—
272C4×C4⋊C4C2311yescharacteristic
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2312yes—
284C43—21no—
285C43C2311yescharacteristic
286#340C2312yes—
287#340C2312yes—
288#340C2312yes—
289#340C2311yescharacteristic
290#340C2312yes—
291#340C2311yescharacteristic
292#340C2311yescharacteristic
293#340C2311yescharacteristic
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2311yescharacteristic
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#336C2312yes—
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2311yescharacteristic
314#336C2311yescharacteristic
315C22×Q8—21no—
316C22×Q8C2411yescharacteristic
317C22×C8C2411yescharacteristic
318C22×C8C2411yescharacteristic
319C22×C8C2411yescharacteristic
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2411yescharacteristic
323C4⋊Q8—22no—
324C4⋊Q8C2×Q814yes—
325#125—24no—
326#125—22no—
327#125—24no—
328#125—42no—
329#125—41no—
330#125—44no—
331#125—44no—
332#125—82no—
333#125—84no—
334#125—84no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—24no—
338C4×Q8—24no—
339C4×Q8—22no—
340C4×Q8—41no—
341C4×Q8—42no—
342C4×Q8—42no—
343C4×Q8—41no—
344C4×Q8—82no—
345C4×Q8C2×Q814yes—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
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—21no—
379C2×C4⋊C4C2×D412yes—
380C2×C4⋊C4C2×D412yes—
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D412yes—
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2411yescharacteristic
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2411yescharacteristic
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2411yescharacteristic
398C2×C42—21no—
399C2×C42—22no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2411yescharacteristic
416C2×C42C2412yes—
417C2×C42C2411yescharacteristic
418C2×C42C2412yes—
419C2×C42C2411yescharacteristic
420#107—24no—
421#107—22no—
422#107—41no—
423#107—42no—
424#107—42no—
425#107—42no—
426#107—42no—
427#107C2×Q818yes—
428#106—24no—
429#106—22no—
430#106—42no—
431#106—41no—
432C4⋊C8—22no—
433C4⋊C8—24no—
434C4⋊C8—22no—
435C4⋊C8—42no—
436C4⋊C8—41no—
437C4⋊C8C2×Q814yes—
438#103—22no—
439#103—24no—
440#103—22no—
441#103—22no—
442#103C2×Q818yes—
443#103#4114yes—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—42no—
447C4×C8—42no—
448C4×C8—42no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—21no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—21no—
464#95—22no—
465#95—21no—
466#95—21no—
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—
480C2×Q8—24no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—81no—
485C2×Q8—81no—
486C2×Q8C22×Q812yes—
487C2×Q8C2×#4112yes—
488C2×Q82−1+412yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D412yes—
503C22×C4C22×D411yescharacteristic
504C22×C4C22×D412yes—
505C22×C4C22×D411yescharacteristic
506C22×C4C22×D412yes—
507C22×C4C22×D411yescharacteristic
508C22×C4C22×D412yes—
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C2511yescharacteristic
512C2×C8—21no—
513C2×C8—22no—
514C2×C8—21no—
515C2×C8—22no—
516C2×C8—21no—
517C2×C8—22no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—22no—
524C2×C8—21no—
525C2×C8—22no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C22×Q814yes—
529C2×C8C2×#4112yes—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—22no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—22no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—44no—
560C4⋊C4—42no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—44no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—44no—
574C4⋊C4—42no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C4⋊C4—82no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4—82no—
581C4⋊C4—82no—
582C4⋊C4—82no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4#13514yes—
590C4⋊C4C22×Q814yes—
591C4⋊C4C22×Q812yes—
592C4⋊C4C2×#4112yes—
593C42—24no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—21no—
598C42—22no—
599C42—21no—
600C42—22no—
601C42—21no—
602C42—22no—
603C42—22no—
604C42—21no—
605C42—41no—
606C42—42no—
607C42—44no—
608C42—42no—
609C42—44no—
610C42—42no—
611C42—42no—
612C42—42no—
613C42—44no—
614C42—42no—
615C42—42no—
616C42—82no—
617C42—82no—
618C42C22×Q812yes—
619C422−1+412yes—
620C23C23×D411yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—22no—
624Q8—84no—
625Q8#55714yes—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4D4×Q812yes—
687C2×C4D4×Q812yes—
688C2×C4C2×#13514yes—
689C2×C4C2×#13512yes—
690C2×C4#57612yes—
691C2×C4#57812yes—
692C2×C4C23×Q811yescharacteristic
693C2×C4C22×#4111yescharacteristic
694C2×C4C2×2−1+411yescharacteristic
695C2×C4C2×2−1+411yescharacteristic
696C2×C4#58511yescharacteristic
697C2×C4#58511yescharacteristic
698C8—24no—
699C8—22no—
700C8—41no—
701C8—42no—
702C8—41no—
703C8—41no—
704C22C2×D4×Q811yescharacteristic
705C22D4×#4111yescharacteristic
706C22#348911yescharacteristic
707C22C22×#13511yescharacteristic
708C22C2×#57611yescharacteristic
709C22C2×#57811yescharacteristic
710C22#358611yescharacteristic
711C4—24no—
712C4—24no—
713C4—22no—
714C4—22no—
715C4—41no—
716C4—42no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—44no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—82no—
728C4—81no—
729C4—82no—
730C4—82no—
731C4—81no—
732C4#338314yes—
733C4C2×#55711yescharacteristic
734C4#350411yescharacteristic
735C4#351511yescharacteristic
736C4#356311yescharacteristic
737C2#5915411yescharacteristic
738C2C2×#338311yescharacteristic
739C2#6138111yescharacteristic
740C2#6143611yescharacteristic
741C2#6155211yescharacteristic
742C2#6210411yescharacteristic
743C2#6220611yescharacteristic
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
#596722
#364472
#325092
#321452
#293142
#291782
#288272
#287922
#279942
#273032
#272952
#268652
#265082
#265072
#261082
#260472
#232532
#229672
#229652
C4×#4792
C4×#4772