Finite Group Databasebeta

← #7572983

Subgroups — #7572983

Order 512.

1255 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59467C211yesmaximal, characteristic
2#36584C211yesmaximal, characteristic
3#32519C212yesmaximal
4#32143C212yesmaximal
5#29321C211yesmaximal, characteristic
6#29176C211yesmaximal, characteristic
7#28836C211yesmaximal, characteristic
8#28792C211yesmaximal, characteristic
9#28009C212yesmaximal
10#27324C212yesmaximal
11#27308C212yesmaximal
12#26887C212yesmaximal
13#26513C211yesmaximal, characteristic
14#26509C211yesmaximal, characteristic
15#26108C211yesmaximal, characteristic
16#26057C212yesmaximal
17#26043C211yesmaximal, characteristic
18#23258C211yesmaximal, characteristic
19#22973C212yesmaximal
20#22970C211yesmaximal, characteristic
21#22964C211yesmaximal, characteristic
22#21615C211yesmaximal, characteristic
23C4×#479C211yesmaximal, characteristic
24C2×#479C2211yescharacteristic
25C2×#479C2212yes—
26C2×#475C2211yescharacteristic
27#2859—21no—
28#2859C2211yescharacteristic
29#2791—22no—
30#2590—22no—
31#2571—21no—
32#2571—21no—
33#2571C2211yescharacteristic
34#2571C2211yescharacteristic
35#2565—21no—
36#2552C2211yescharacteristic
37#2552C2211yescharacteristic
38#2552C2212yes—
39#2509—22no—
40#2509—22no—
41#2509C2212yes—
42#2509C2212yes—
43#2509C2212yes—
44#2507C2212yes—
45#2453—21no—
46#2453—21no—
47#2370C2212yes—
48#2365C2211yescharacteristic
49#2365C2211yescharacteristic
50#2351C2212yes—
51#2351C2212yes—
52Q8×C4⋊C4—21no—
53Q8×C4⋊C4C2211yescharacteristic
54Q8×C4⋊C4C2211yescharacteristic
55C4×C4⋊Q8C2211yescharacteristic
56C4×#125—21no—
57C4×#125C2211yescharacteristic
58C4×#125C2211yescharacteristic
59C42×Q8C2211yescharacteristic
60#2101C2212yes—
61#2101C2212yes—
62#2099C2212yes—
63#2088C2212yes—
64#2088C2212yes—
65#2088C2212yes—
66#2088C2212yes—
67#2088C2212yes—
68#2087C2212yes—
69#2085C2212yes—
70#2085C2212yes—
71#2085C2212yes—
72#2084C2212yes—
73#2059C2212yes—
74#2059C2212yes—
75#2059C2212yes—
76#1991C2212yes—
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1989C2211yescharacteristic
80#1988C2211yescharacteristic
81#1949C2212yes—
82#1949C2211yescharacteristic
83#1949C2212yes—
84#1948C2211yescharacteristic
85#1948C2211yescharacteristic
86#1947C2211yescharacteristic
87#1947C2211yescharacteristic
88#1947C2211yescharacteristic
89#1944C2212yes—
90#1944C2212yes—
91#1944C2212yes—
92#1943C2212yes—
93#1942C2212yes—
94#1941C2212yes—
95#1940C2212yes—
96#1939C2211yescharacteristic
97#1939C2211yescharacteristic
98#1921C2212yes—
99#1920C2211yescharacteristic
100#1920C2212yes—
101#1920C2212yes—
102#1920C2212yes—
103#1920C2212yes—
104#1919C2212yes—
105#1919C2212yes—
106#1918C2211yescharacteristic
107#1917C2212yes—
108#1916C2212yes—
109#1865C2211yescharacteristic
110#1865C2212yes—
111#1865C2212yes—
112#1865C2212yes—
113#1863C2211yescharacteristic
114#1863C2212yes—
115#1863C2212yes—
116#1847C2212yes—
117#1844C2211yescharacteristic
118#1834C2211yescharacteristic
119#1805C2211yescharacteristic
120#1803C2211yescharacteristic
121#1803C2212yes—
122#1776C2212yes—
123C4×#107C2211yescharacteristic
124C4×#106C2211yescharacteristic
125#1770C2212yes—
126#1770C2211yescharacteristic
127C8×C4⋊C4C2211yescharacteristic
128#1767C2211yescharacteristic
129C4×C4⋊C8C2211yescharacteristic
130#1763C2212yes—
131#1763C2212yes—
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134C4×#103C2212yes—
135C2×C4⋊Q8C2311yescharacteristic
136C2×#125—21no—
137C2×#125—21no—
138C2×#125D411yescharacteristic
139C2×#125C2311yescharacteristic
140C2×#125C2312yes—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8C2311yescharacteristic
145C2×C4×Q8C2312yes—
146C2×C4×Q8C2312yes—
147C2×C4×Q8C2311yescharacteristic
148C2×C4×Q8C2311yescharacteristic
149#479—28no—
150#479—24no—
151#475Q818yes—
152C2×#107C2312yes—
153C2×#107C2311yescharacteristic
154C2×#107C2312yes—
155C2×#107C2312yes—
156C2×#107C2311yescharacteristic
157C2×#106C2311yescharacteristic
158C2×#106C2312yes—
159C2×#106C2312yes—
160C2×#106C2312yes—
161C2×#106C2311yescharacteristic
162C2×#106C2312yes—
163C2×#106C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2311yescharacteristic
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2311yescharacteristic
170C2×#103C2312yes—
171C2×#103C2311yescharacteristic
172C2×#103C2311yescharacteristic
173C2×#103C2311yescharacteristic
174C2×#103C2312yes—
175C2×#103C2311yescharacteristic
176C2×#97C2312yes—
177C2×#97C2312yes—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2312yes—
181#400—22no—
182#400—22no—
183#400—22no—
184#400—22no—
185#400—22no—
186#400—22no—
187#400—22no—
188#400—22no—
189#398—22no—
190#398—22no—
191#398—22no—
192#398—22no—
193#398—22no—
194#398—22no—
195#391—21no—
196#391—21no—
197#391—21no—
198#389—21no—
199#389—21no—
200#389—22no—
201#389—22no—
202#389—22no—
203#389—22no—
204#389—22no—
205#389—22no—
206#389—22no—
207#389—22no—
208#389—21no—
209#389—22no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—22no—
215#389—22no—
216#389—22no—
217#389D411yescharacteristic
218#389D411yescharacteristic
219#389C2311yescharacteristic
220#389C2311yescharacteristic
221#389C2312yes—
222#389C2312yes—
223#389C2312yes—
224#389C2312yes—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#389C2312yes—
232#387—22no—
233#387—22no—
234#387—21no—
235#387—21no—
236#387—22no—
237#387—22no—
238#387—22no—
239#387—22no—
240#387—22no—
241#387—22no—
242#387D412yes—
243#387D412yes—
244#384—21no—
245#384—21no—
246#384—21no—
247#384—22no—
248#384C2311yescharacteristic
249#384C2312yes—
250#384C2311yescharacteristic
251#384C2311yescharacteristic
252#382—21no—
253#382—21no—
254#382—21no—
255#382—22no—
256#382—22no—
257#382D411yescharacteristic
258#382C2311yescharacteristic
259#382C2312yes—
260#382C2312yes—
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—22no—
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#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2311yescharacteristic
301#340C2311yescharacteristic
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
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—42no—
328#125—42no—
329#125—41no—
330#125—44no—
331#125—82no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—24no—
335C4×Q8—24no—
336C4×Q8—22no—
337C4×Q8—42no—
338C4×Q8—41no—
339C4×Q8—42no—
340C4×Q8—41no—
341C4×Q8—44no—
342C4×Q8—82no—
343C4×Q8—82no—
344C4×Q8C2×Q814yes—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D412yes—
381C2×C4⋊C4C2×D412yes—
382C2×C4⋊C4C2×D412yes—
383C2×C4⋊C4C2×D412yes—
384C2×C4⋊C4C2411yescharacteristic
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2411yescharacteristic
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2411yescharacteristic
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—22no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—21no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2411yescharacteristic
413C2×C42C2412yes—
414C2×C42C2411yescharacteristic
415C2×C42C2412yes—
416C2×C42C2411yescharacteristic
417#107—22no—
418#107—24no—
419#107—41no—
420#107—42no—
421#107—42no—
422#106—24no—
423#106—22no—
424#106—42no—
425#106—42no—
426#106—42no—
427#106—41no—
428#106C2×Q818yes—
429C4⋊C8—22no—
430C4⋊C8—24no—
431C4⋊C8—22no—
432C4⋊C8—42no—
433C4⋊C8—41no—
434C4⋊C8C2×Q814yes—
435#103—24no—
436#103—22no—
437#103—22no—
438#103—22no—
439#103C2×Q818yes—
440#103#4114yes—
441#97—42no—
442#97—42no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—42no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—22no—
450#95—22no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—21no—
460#95—21no—
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#95C2×D412yes—
474#95C2×D412yes—
475#95C2×D412yes—
476#95C2×D412yes—
477#95C2×D412yes—
478#95C2×D412yes—
479C2×Q8—24no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8C22×Q812yes—
486C2×Q8C2×#4112yes—
487C2×Q82−1+412yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4C22×D412yes—
501C22×C4C22×D412yes—
502C22×C4C22×D411yescharacteristic
503C22×C4C22×D411yescharacteristic
504C22×C4C22×D411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C22×D412yes—
507C22×C4C22×D412yes—
508C22×C4C22×D411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C2511yescharacteristic
511C2×C8—21no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—22no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—22no—
523C2×C8—21no—
524C2×C8—22no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8C22×Q814yes—
528C2×C8C2×#4112yes—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
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—42no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—81no—
574C4⋊C4—81no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C4⋊C4—82no—
578C4⋊C4—82no—
579C4⋊C4—82no—
580C4⋊C4—82no—
581C4⋊C4—82no—
582C4⋊C4—82no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4C22×Q814yes—
588C4⋊C4C22×Q812yes—
589C4⋊C4C2×#4112yes—
590C42—24no—
591C42—22no—
592C42—22no—
593C42—21no—
594C42—22no—
595C42—21no—
596C42—22no—
597C42—22no—
598C42—21no—
599C42—22no—
600C42—21no—
601C42—41no—
602C42—41no—
603C42—42no—
604C42—44no—
605C42—42no—
606C42—44no—
607C42—44no—
608C42—42no—
609C42—42no—
610C42—42no—
611C42—81no—
612C42—81no—
613C42—82no—
614C42—82no—
615C42C22×Q812yes—
616C422−1+412yes—
617C23C23×D411yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—48no—
622Q8#55714yes—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4D4×Q812yes—
686C2×C4D4×Q812yes—
687C2×C4#57512yes—
688C2×C4#57712yes—
689C2×C4C23×Q811yescharacteristic
690C2×C4C22×#4111yescharacteristic
691C2×C4C2×2−1+411yescharacteristic
692C2×C4C2×2−1+411yescharacteristic
693C2×C4#58511yescharacteristic
694C2×C4#58511yescharacteristic
695C8—24no—
696C8—22no—
697C8—41no—
698C8—42no—
699C8—41no—
700C8—41no—
701C22C2×D4×Q811yescharacteristic
702C22D4×#4111yescharacteristic
703C22#348911yescharacteristic
704C22C2×#57511yescharacteristic
705C22C2×#57711yescharacteristic
706C22#358411yescharacteristic
707C22#358611yescharacteristic
708C4—24no—
709C4—22no—
710C4—41no—
711C4—42no—
712C4—42no—
713C4—41no—
714C4—42no—
715C4—44no—
716C4—42no—
717C4—41no—
718C4—42no—
719C4—41no—
720C4—42no—
721C4—82no—
722C4—81no—
723C4—81no—
724C4—82no—
725C4—82no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4#338814yes—
730C4C2×#55711yescharacteristic
731C4#350411yescharacteristic
732C4#351511yescharacteristic
733C4#356311yescharacteristic
734C2#5915411yescharacteristic
735C2C2×#338811yescharacteristic
736C2#6138611yescharacteristic
737C2#6146011yescharacteristic
738C2#6149511yescharacteristic
739C2#6215411yescharacteristic
740C2#6218411yescharacteristic
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
#594672
#365842
#325192
#321432
#293212
#291762
#288362
#287922
#280092
#273242
#273082
#268872
#265132
#265092
#261082
#260572
#260432
#232582
#229732
#229702
#229642
#216152
C4×#4792