Finite Group Databasebeta

← #7604136

Subgroups — #7604136

Order 512.

1259 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic
2#59443C211yesmaximal, characteristic
3#32496C212yesmaximal
4#32495C212yesmaximal
5#29289C211yesmaximal, characteristic
6#28647C211yesmaximal, characteristic
7#28638C211yesmaximal, characteristic
8#28284C211yesmaximal, characteristic
9#28047C212yesmaximal
10#28040C212yesmaximal
11#27745C212yesmaximal
12#26319C211yesmaximal, characteristic
13#26317C211yesmaximal, characteristic
14#26282C211yesmaximal, characteristic
15#26279C211yesmaximal, characteristic
16#26105C212yesmaximal
17#25463C212yesmaximal
18#23073C212yesmaximal
19#22743C211yesmaximal, characteristic
20#22739C211yesmaximal, characteristic
21C4×#501C211yesmaximal, characteristic
22#21714C211yesmaximal, characteristic
23#21647C211yesmaximal, characteristic
24C2×#501C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#477C2212yes—
27C2×#446C2211yescharacteristic
28C2×C8×Q8C2211yescharacteristic
29#2805—22no—
30#2776—22no—
31#2581—22no—
32#2571C2212yes—
33#2570—21no—
34#2568—21no—
35#2568C2211yescharacteristic
36#2568C2211yescharacteristic
37#2567C2211yescharacteristic
38#2567C2211yescharacteristic
39#2565C2212yes—
40#2533—22no—
41#2514—21no—
42#2514C2212yes—
43#2511—21no—
44#2511—21no—
45#2511C2212yes—
46#2509C2212yes—
47#2509C2212yes—
48#2446—21no—
49#2365C2212yes—
50#2356—21no—
51#2356C2212yes—
52#2355C2211yescharacteristic
53#2355C2211yescharacteristic
54#2355C2211yescharacteristic
55Q8×C4⋊C4—21no—
56Q8×C4⋊C4C2211yescharacteristic
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×#125C2211yescharacteristic
62#2101C2212yes—
63#2100C2212yes—
64#2097C2212yes—
65#2097C2212yes—
66#2088C2212yes—
67#2086C2212yes—
68#2085C2212yes—
69#2083C2212yes—
70#2074C2212yes—
71#2074C2212yes—
72#2068C2212yes—
73#2068C2212yes—
74#2068C2212yes—
75#2068C2212yes—
76#2066C2212yes—
77#2066C2212yes—
78#1993C2211yescharacteristic
79#1992C2211yescharacteristic
80#1990C2211yescharacteristic
81#1989C2212yes—
82#1987C2211yescharacteristic
83#1987C2211yescharacteristic
84#1984C2211yescharacteristic
85#1984C2211yescharacteristic
86#1981C2211yescharacteristic
87#1981C2211yescharacteristic
88#1956C2211yescharacteristic
89#1949C2212yes—
90#1949C2212yes—
91#1949C2212yes—
92#1949C2212yes—
93#1948C2211yescharacteristic
94#1947C2211yescharacteristic
95#1947C2212yes—
96#1947C2211yescharacteristic
97#1947C2211yescharacteristic
98#1944C2211yescharacteristic
99#1944C2211yescharacteristic
100#1943C2211yescharacteristic
101#1943C2211yescharacteristic
102#1940C2212yes—
103#1940C2212yes—
104#1935C2212yes—
105#1935C2212yes—
106#1935C2212yes—
107#1935C2212yes—
108#1933C2212yes—
109#1933C2212yes—
110#1928C2212yes—
111#1928C2212yes—
112#1927C2212yes—
113#1927C2212yes—
114#1921C2212yes—
115#1921C2212yes—
116#1919C2212yes—
117#1918C2212yes—
118#1847C2211yescharacteristic
119#1842C2211yescharacteristic
120#1836C2212yes—
121#1835C2212yes—
122#1834C2211yescharacteristic
123#1803C2212yes—
124#1776C2212yes—
125C4×#107C2212yes—
126C4×#107C2211yescharacteristic
127C4×#107C2211yescharacteristic
128C4×#106C2211yescharacteristic
129C4×#106C2211yescharacteristic
130#1771C2212yes—
131#1771C2212yes—
132#1763C2212yes—
133#1763C2212yes—
134C4×#97C2211yescharacteristic
135C2×C4⋊Q8D411yescharacteristic
136C2×C4⋊Q8C2311yescharacteristic
137C2×C4⋊Q8C2311yescharacteristic
138C2×C4⋊Q8C2311yescharacteristic
139C2×#125C2311yescharacteristic
140C2×C4×Q8—21no—
141C2×C4×Q8—22no—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8C2312yes—
145C2×C4×Q8C2311yescharacteristic
146C2×C4×Q8C2311yescharacteristic
147#501—24no—
148#487—24no—
149#477—28no—
150#446—24no—
151C8×Q8—24no—
152C2×#107C2312yes—
153C2×#107C2312yes—
154C2×#107C2311yescharacteristic
155C2×#107C2311yescharacteristic
156C2×#107C2311yescharacteristic
157C2×#107C2311yescharacteristic
158C2×#107C2312yes—
159C2×#106C2311yescharacteristic
160C2×#106C2311yescharacteristic
161C2×#106C2311yescharacteristic
162C2×#106C2311yescharacteristic
163C2×#106C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2311yescharacteristic
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2312yes—
170C2×#103C2312yes—
171C2×#103C2312yes—
172C2×#103C2312yes—
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#103C2312yes—
176C2×#103C2312yes—
177C2×#103C2312yes—
178C2×#97C2312yes—
179C2×#97C2311yescharacteristic
180C2×#97C2311yescharacteristic
181C2×#97C2311yescharacteristic
182C2×#97C2311yescharacteristic
183C2×C4×C8C2312yes—
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186#401—22no—
187#400—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#395—22no—
201#395—22no—
202#391—21no—
203#391—21no—
204#391—21no—
205#391—21no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—22no—
210#391—21no—
211#391—21no—
212#391D411yescharacteristic
213#391D411yescharacteristic
214#391C2312yes—
215#391C2312yes—
216#391C2312yes—
217#391C2312yes—
218#391C2312yes—
219#389—21no—
220#389—22no—
221#389—22no—
222#389—22no—
223#389—22no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389D412yes—
229#389D412yes—
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#387—22no—
240#387—22no—
241#387—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—21no—
247#387—21no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#384—21no—
256#384—21no—
257#384D411yescharacteristic
258#384C2311yescharacteristic
259#384C2311yescharacteristic
260#384C2311yescharacteristic
261#384C2312yes—
262#383—22no—
263#383—22no—
264#382—22no—
265#382—21no—
266#382—21no—
267#382C2311yescharacteristic
268#382C2312yes—
269#382C2312yes—
270#382C2312yes—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
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⋊C4C2312yes—
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291#376—22no—
292C43C2311yescharacteristic
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2311yescharacteristic
300#340C2311yescharacteristic
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#336C2312yes—
314#336C2312yes—
315#336C2312yes—
316#336C2312yes—
317C22×Q8—21no—
318C22×Q8—21no—
319C22×Q8C2×D411yescharacteristic
320C22×Q8C2×D411yescharacteristic
321C22×Q8C2412yes—
322C22×C8C2411yescharacteristic
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2411yescharacteristic
326C22×C8C2411yescharacteristic
327C22×C8C2411yescharacteristic
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—42no—
334C4⋊Q8#4114yes—
335#125—22no—
336#125—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—24no—
342C4×Q8—24no—
343C4×Q8—44no—
344C4×Q8—44no—
345C4×Q8—82no—
346C4×Q8—84no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4C2×D411yescharacteristic
372C2×C4⋊C4C2×D411yescharacteristic
373C2×C4⋊C4C2×D412yes—
374C2×C4⋊C4C2×D412yes—
375C2×C4⋊C4C2×D412yes—
376C2×C4⋊C4C2×D412yes—
377C2×C4⋊C4C2×D412yes—
378C2×C4⋊C4C2×D412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2411yescharacteristic
381C2×C4⋊C4C2411yescharacteristic
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2411yescharacteristic
385C2×C4⋊C4C2411yescharacteristic
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2411yescharacteristic
389C2×C4⋊C4C2411yescharacteristic
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—22no—
396C2×C42—21no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2412yes—
405C2×C42C2412yes—
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408C2×C42C2411yescharacteristic
409#107—22no—
410#107—24no—
411#107—24no—
412#107—22no—
413#107—22no—
414#107—41no—
415#107—42no—
416#106—22no—
417#106—22no—
418#106—22no—
419#106—41no—
420#106—42no—
421C4⋊C8—24no—
422C4⋊C8—24no—
423C4⋊C8—22no—
424C4⋊C8—22no—
425C4⋊C8—24no—
426C4⋊C8—42no—
427#103—24no—
428#103—24no—
429#103—24no—
430#103—24no—
431#103—24no—
432#103—42no—
433#103—42no—
434#103—42no—
435#97—24no—
436#97—22no—
437#97—22no—
438#97—22no—
439#97—41no—
440C4×C8—24no—
441C4×C8—22no—
442C4×C8#4114yes—
443#95—21no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—21no—
448#95—22no—
449#95—22no—
450#95—21no—
451#95—22no—
452#95—21no—
453#95—22no—
454#95—21no—
455#95—21no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—21no—
460#95—21no—
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#95—22no—
479#95C2×D412yes—
480#95C2×D412yes—
481#95C2×D412yes—
482#95C2×D412yes—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—24no—
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—22no—
495C2×Q8—22no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—81no—
500C2×Q8—81no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4C22×D412yes—
514C22×C4C22×D412yes—
515C22×C4C22×D411yescharacteristic
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C2511yescharacteristic
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8C2×#4112yes—
540C2×C8C2×#4112yes—
541C2×C82−1+412yes—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—44no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—81no—
585C4⋊C4—81no—
586C4⋊C4—81no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4—82no—
590C4⋊C4—81no—
591C4⋊C4—82no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4C2×#4112yes—
595C4⋊C4C2×#4112yes—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—21no—
601C42—22no—
602C42—22no—
603C42—21no—
604C42—41no—
605C42—41no—
606C42—44no—
607C42—44no—
608C42—44no—
609C42—42no—
610C42—42no—
611C42—42no—
612C42—42no—
613C42—82no—
614C42—82no—
615C42—82no—
616C42C2×#4112yes—
617C42C2×#4112yes—
618C422−1+412yes—
619C422−1+412yes—
620C23C23×D411yescharacteristic
621Q8—48no—
622Q8—44no—
623Q8—44no—
624Q8—42no—
625Q8—42no—
626Q8—42no—
627Q8—42no—
628Q8—84no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
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—42no—
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—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4#54712yes—
690C2×C4#54712yes—
691C2×C4#54812yes—
692C2×C4#54812yes—
693C2×C4#57512yes—
694C2×C4#57812yes—
695C2×C4C22×#4111yescharacteristic
696C2×C4C22×#4111yescharacteristic
697C2×C4C2×2−1+411yescharacteristic
698C2×C4C2×2−1+411yescharacteristic
699C2×C4C2×2−1+411yescharacteristic
700C2×C4#58511yescharacteristic
701C8—22no—
702C8—22no—
703C8—22no—
704C8—42no—
705C8—42no—
706C8—41no—
707C22C2×#54711yescharacteristic
708C22C2×#54811yescharacteristic
709C22#349711yescharacteristic
710C22C2×#57511yescharacteristic
711C22C2×#57811yescharacteristic
712C22#358511yescharacteristic
713C22#358611yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—41no—
724C4—41no—
725C4—82no—
726C4—82no—
727C4—82no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4—82no—
734C4—81no—
735C4#334914yes—
736C4#348011yescharacteristic
737C4#350911yescharacteristic
738C4#352311yescharacteristic
739C4#355511yescharacteristic
740C2#5965311yescharacteristic
741C2C2×#334911yescharacteristic
742C2#6129111yescharacteristic
743C2#6131811yescharacteristic
744C2#6134211yescharacteristic
745C2#6239911yescharacteristic
746C2#6240411yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ 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
#598702
#594432
#324962
#324952
#292892
#286472
#286382
#282842
#280472
#280402
#277452
#263192
#263172
#262822
#262792
#261052
#254632
#230732
#227432
#227392
C4×#5012
#217142
#216472