Finite Group Databasebeta

← #6819942

Subgroups — #6819942

Order 512.

1182 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39999C212yesmaximal
2#33257C211yesmaximal, characteristic
3#32482C212yesmaximal
4#32481C212yesmaximal
5#32479C212yesmaximal
6#32476C212yesmaximal
7#30001C212yesmaximal
8#28268C211yesmaximal, characteristic
9#28268C211yesmaximal, characteristic
10#28015C211yesmaximal, characteristic
11#28015C211yesmaximal, characteristic
12#28012C211yesmaximal, characteristic
13#28012C211yesmaximal, characteristic
14#27995C211yesmaximal, characteristic
15#27994C211yesmaximal, characteristic
16#27993C211yesmaximal, characteristic
17#27992C211yesmaximal, characteristic
18#25001C212yesmaximal
19#25000C212yesmaximal
20#22727C211yesmaximal, characteristic
21#22727C211yesmaximal, characteristic
22C8×C4⋊Q8C211yesmaximal, characteristic
23#21276C211yesmaximal, characteristic
24C2×C8×Q8C2211yescharacteristic
25C2×C8×Q8C2211yescharacteristic
26C2×C4×Q16C2211yescharacteristic
27#2864C2212yes—
28#2794—22no—
29#2789—22no—
30#2758—22no—
31#2713—22no—
32#2655—22no—
33#2581C2212yes—
34#2581C2212yes—
35#2533—22no—
36#2528—22no—
37#2514C2212yes—
38#2514C2212yes—
39#2511C2212yes—
40#2511C2212yes—
41#2509C2212yes—
42#2508C2212yes—
43#2507C2212yes—
44#2506C2212yes—
45#2355C2212yes—
46#2355C2212yes—
47#2336—22no—
48C4×C4⋊Q8C2211yescharacteristic
49#2295C2212yes—
50#2101C2212yes—
51#2101C2212yes—
52#2100C2212yes—
53#2099C2212yes—
54#2088C2212yes—
55#2088C2212yes—
56#2087C2212yes—
57#2086C2212yes—
58#2074C2212yes—
59#2074C2212yes—
60#2072C2212yes—
61#2072C2212yes—
62#2068C2212yes—
63#2068C2212yes—
64#2066C2212yes—
65#2066C2212yes—
66#2066C2212yes—
67#2066C2212yes—
68#2066C2212yes—
69#2066C2212yes—
70#1984C2211yescharacteristic
71#1984C2211yescharacteristic
72#1969C2211yescharacteristic
73#1969C2211yescharacteristic
74#1969C2211yescharacteristic
75#1969C2211yescharacteristic
76#1969C2211yescharacteristic
77#1969C2211yescharacteristic
78#1949C2212yes—
79#1949C2212yes—
80#1949C2212yes—
81#1949C2212yes—
82#1948C2212yes—
83#1948C2212yes—
84#1942C2211yescharacteristic
85#1942C2211yescharacteristic
86#1942C2211yescharacteristic
87#1942C2211yescharacteristic
88#1942C2211yescharacteristic
89#1942C2211yescharacteristic
90#1942C2211yescharacteristic
91#1942C2211yescharacteristic
92#1942C2211yescharacteristic
93#1942C2211yescharacteristic
94#1941C2212yes—
95#1941C2212yes—
96#1939C2211yescharacteristic
97#1939C2211yescharacteristic
98#1939C2211yescharacteristic
99#1939C2211yescharacteristic
100#1933C2212yes—
101#1933C2212yes—
102#1928C2212yes—
103#1928C2212yes—
104#1927C2212yes—
105#1927C2212yes—
106#1921C2212yes—
107#1920C2212yes—
108#1919C2212yes—
109#1918C2212yes—
110#1846C2211yescharacteristic
111#1846C2211yescharacteristic
112#1846C2211yescharacteristic
113#1846C2211yescharacteristic
114#1845C2211yescharacteristic
115#1845C2211yescharacteristic
116#1842C2211yescharacteristic
117#1835C2212yes—
118#1805C2212yes—
119#1805C2212yes—
120C4×#107C2211yescharacteristic
121C4×#107C2211yescharacteristic
122C4×#107C2211yescharacteristic
123C4×#107C2211yescharacteristic
124C4×#107C2211yescharacteristic
125C8×C4⋊C4C2211yescharacteristic
126C8×C4⋊C4C2211yescharacteristic
127C8×C4⋊C4C2211yescharacteristic
128C8×C4⋊C4C2211yescharacteristic
129C4×#103C2212yes—
130C42×C8C2211yescharacteristic
131C22×Q16C2311yescharacteristic
132C2×C4⋊Q8D411yescharacteristic
133C2×#125—22no—
134C2×C4×Q8C2312yes—
135C2×C4×Q8C2311yescharacteristic
136C2×C4×Q8C2311yescharacteristic
137C8×Q8—24no—
138C8×Q8—24no—
139C4×Q16—24no—
140C2×#107C2311yescharacteristic
141C2×#107C2311yescharacteristic
142C2×#107C2311yescharacteristic
143C2×#107C2311yescharacteristic
144C2×#107C2311yescharacteristic
145C2×#107C2311yescharacteristic
146C2×#107C2311yescharacteristic
147C2×#107C2312yes—
148C2×#107C2312yes—
149C2×#106C2312yes—
150C2×#106C2312yes—
151C2×#106C2312yes—
152C2×#106C2312yes—
153C2×C4⋊C8C2311yescharacteristic
154C2×C4⋊C8C2311yescharacteristic
155C2×C4⋊C8C2311yescharacteristic
156C2×C4⋊C8C2311yescharacteristic
157C2×C4⋊C8C2311yescharacteristic
158C2×C4⋊C8C2311yescharacteristic
159C2×C4⋊C8C2311yescharacteristic
160C2×C4⋊C8C2311yescharacteristic
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2311yescharacteristic
163C2×#103C2312yes—
164C2×#103C2312yes—
165C2×#103C2312yes—
166C2×#103C2312yes—
167C2×#103C2312yes—
168C2×#103C2312yes—
169C2×#103C2312yes—
170C2×C4×C8C2311yescharacteristic
171C2×C4×C8C2311yescharacteristic
172C2×C4×C8C2311yescharacteristic
173C2×C4×C8C2311yescharacteristic
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180#401—22no—
181#401—22no—
182#400—22no—
183#400—22no—
184#400—22no—
185#400—22no—
186#400—22no—
187#400—22no—
188#400—22no—
189#400—22no—
190#400—22no—
191#400—22no—
192#400—22no—
193#400—22no—
194#398—22no—
195#398—22no—
196#398—22no—
197#398—22no—
198#395—22no—
199#395—22no—
200#391—22no—
201#391—22no—
202#391D411yescharacteristic
203#391D411yescharacteristic
204#391C2312yes—
205#391C2312yes—
206#391C2312yes—
207#391C2312yes—
208#391C2312yes—
209#391C2312yes—
210#389—22no—
211#389—22no—
212#389D411yescharacteristic
213#389D411yescharacteristic
214#389D411yescharacteristic
215#389D411yescharacteristic
216#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#389C2312yes—
222#389C2312yes—
223#389C2312yes—
224#389C2312yes—
225#389C2312yes—
226#387—22no—
227#387—22no—
228#387—22no—
229#387—22no—
230#387—22no—
231#387—22no—
232#387—22no—
233#387—22no—
234#387—22no—
235#387—22no—
236#387—22no—
237#387—22no—
238#387—22no—
239#387—22no—
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#384D411yescharacteristic
251#384C2312yes—
252#384C2312yes—
253#383—22no—
254#383—22no—
255#382—22no—
256#382C2312yes—
257#382C2312yes—
258#382C2312yes—
259#382C2312yes—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4—22no—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2312yes—
265C4×C4⋊C4C2312yes—
266C4×C4⋊C4C2312yes—
267C4×C4⋊C4C2312yes—
268C4×C4⋊C4C2311yescharacteristic
269C4×C4⋊C4C2311yescharacteristic
270C4×C4⋊C4C2311yescharacteristic
271C4×C4⋊C4C2311yescharacteristic
272#376—22no—
273C43C2311yescharacteristic
274#340C2312yes—
275#340C2312yes—
276#340C2312yes—
277#340C2312yes—
278#340C2312yes—
279#340C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#340C2312yes—
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#340C2312yes—
289#336C2311yescharacteristic
290#336C2311yescharacteristic
291#336C2311yescharacteristic
292#336C2311yescharacteristic
293#336C2311yescharacteristic
294#336C2311yescharacteristic
295#336C2311yescharacteristic
296#336C2311yescharacteristic
297C22×Q8C2×D411yescharacteristic
298C22×Q8C2×D411yescharacteristic
299C22×Q8C2412yes—
300C2×Q16—22no—
301C2×Q16—22no—
302C2×Q16—22no—
303C22×C8C2411yescharacteristic
304C22×C8C2411yescharacteristic
305C22×C8C2411yescharacteristic
306C22×C8C2411yescharacteristic
307C22×C8C2411yescharacteristic
308C22×C8C2411yescharacteristic
309C22×C8C2411yescharacteristic
310C22×C8C2411yescharacteristic
311C4⋊Q8—24no—
312#125—48no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—24no—
318C4×Q8—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4C2×D411yescharacteristic
335C2×C4⋊C4C2×D411yescharacteristic
336C2×C4⋊C4C2×D411yescharacteristic
337C2×C4⋊C4C2×D411yescharacteristic
338C2×C4⋊C4C2×D411yescharacteristic
339C2×C4⋊C4C2×D411yescharacteristic
340C2×C4⋊C4C2×D411yescharacteristic
341C2×C4⋊C4C2×D411yescharacteristic
342C2×C4⋊C4C2×D411yescharacteristic
343C2×C4⋊C4C2×D411yescharacteristic
344C2×C4⋊C4C2×D411yescharacteristic
345C2×C4⋊C4C2×D411yescharacteristic
346C2×C4⋊C4C2×D411yescharacteristic
347C2×C4⋊C4C2×D411yescharacteristic
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42C2×D411yescharacteristic
362C2×C42C2×D411yescharacteristic
363C2×C42C2×D411yescharacteristic
364C2×C42C2×D411yescharacteristic
365C2×C42C2411yescharacteristic
366C2×C42C2411yescharacteristic
367C2×C42C2411yescharacteristic
368C2×C42C2411yescharacteristic
369C2×C42C2411yescharacteristic
370C2×C42C2411yescharacteristic
371C2×C42C2411yescharacteristic
372#107—22no—
373#107—22no—
374#107—22no—
375#107—22no—
376#107—22no—
377#107—22no—
378#107—22no—
379#107—42no—
380#107—42no—
381#106—42no—
382#106—42no—
383#106—42no—
384#106—42no—
385C4⋊C8—22no—
386C4⋊C8—22no—
387C4⋊C8—22no—
388C4⋊C8—22no—
389C4⋊C8—22no—
390C4⋊C8—22no—
391C4⋊C8—41no—
392C4⋊C8—41no—
393C4⋊C8—41no—
394C4⋊C8—41no—
395#103—24no—
396#103—42no—
397#103—42no—
398#103—42no—
399#103—42no—
400#103—42no—
401#103—42no—
402C4×C8—22no—
403C4×C8—22no—
404C4×C8—22no—
405C4×C8—22no—
406C4×C8—22no—
407C4×C8—22no—
408C4×C8—22no—
409C4×C8—41no—
410C4×C8—41no—
411C4×C8#4114yes—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95C2×D411yescharacteristic
448#95C2×D411yescharacteristic
449#95C2×D411yescharacteristic
450#95C2×D411yescharacteristic
451#95C2×D411yescharacteristic
452#95C2×D411yescharacteristic
453#95C2×D411yescharacteristic
454#95C2×D411yescharacteristic
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—41no—
466C2×Q8—41no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4C22×D411yescharacteristic
476C22×C4C22×D411yescharacteristic
477C22×C4C22×D411yescharacteristic
478C22×C4C22×D411yescharacteristic
479C22×C4C22×D411yescharacteristic
480C22×C4C22×D411yescharacteristic
481C22×C4C22×D411yescharacteristic
482C22×C4C22×D411yescharacteristic
483C22×C4C22×D411yescharacteristic
484C22×C4C22×D411yescharacteristic
485C22×C4C22×D411yescharacteristic
486C22×C4C22×D411yescharacteristic
487C22×C4C22×D411yescharacteristic
488C22×C4C22×D411yescharacteristic
489C22×C4C2511yescharacteristic
490Q16—44no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8C2×#4112yes—
512C2×C8C2×#4112yes—
513C2×C82−1+412yes—
514C2×C82−1+412yes—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4—44no—
547C4⋊C4—44no—
548C4⋊C4—44no—
549C4⋊C4—82no—
550C4⋊C4—82no—
551C4⋊C4—82no—
552C4⋊C4—82no—
553C4⋊C4—82no—
554C4⋊C4—82no—
555C4⋊C4—82no—
556C4⋊C4—82no—
557C4⋊C4#13514yes—
558C42—22no—
559C42—22no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—41no—
573C42—41no—
574C42—44no—
575C42—44no—
576C42—82no—
577C42—82no—
578C42—82no—
579C42—82no—
580C42C2×#4112yes—
581C422−1+412yes—
582C23C23×D411yescharacteristic
583Q8—44no—
584Q8—44no—
585Q8—42no—
586Q8—42no—
587Q8—42no—
588Q8—42no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4#54712yes—
650C2×C4#54712yes—
651C2×C4C2×#13512yes—
652C2×C4C2×#13512yes—
653C2×C4C2×#13512yes—
654C2×C4#57812yes—
655C2×C4C22×#4111yescharacteristic
656C2×C4C2×2−1+411yescharacteristic
657C2×C4C2×2−1+411yescharacteristic
658C2×C4C2×2−1+411yescharacteristic
659C2×C4#58511yescharacteristic
660C2×C4#58511yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C8—41no—
666C8—41no—
667C8—41no—
668C8#54114yes—
669C22C2×#54711yescharacteristic
670C22#349711yescharacteristic
671C22#349711yescharacteristic
672C22C22×#13511yescharacteristic
673C22C2×#57811yescharacteristic
674C22#358411yescharacteristic
675C22#358411yescharacteristic
676C4—22no—
677C4—22no—
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—41no—
689C4—41no—
690C4—82no—
691C4—82no—
692C4—82no—
693C4—82no—
694C4—82no—
695C4—82no—
696C4—82no—
697C4—82no—
698C4C2×#54111yescharacteristic
699C4#351211yescharacteristic
700C4#355511yescharacteristic
701C4#355511yescharacteristic
702C2#3937911yescharacteristic
703C2#6123411yescharacteristic
704C2#6128611yescharacteristic
705C2#6236111yescharacteristic
706C2#6236411yescharacteristic
707C2#6237711yescharacteristic
708C2#6238011yescharacteristic
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
#399992
#332572
#324822
#324812
#324792
#324762
#300012
#282682
#280152
#280122
#279952
#279942
#279932
#279922
#250012
#250002
#227272
C8×C4⋊Q82
#212762