Finite Group Databasebeta

← #6548926

Subgroups — #6548926

Order 512.

1309 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#39183C211yesmaximal, characteristic
2#34491C211yesmaximal, characteristic
3#30005C212yesmaximal
4#29999C211yesmaximal, characteristic
5#29292C212yesmaximal
6#29289C211yesmaximal, characteristic
7#29187C212yesmaximal
8#29177C211yesmaximal, characteristic
9#26521C212yesmaximal
10#26512C211yesmaximal, characteristic
11#26445C211yesmaximal, characteristic
12#26443C212yesmaximal
13#26095C212yesmaximal
14#26088C211yesmaximal, characteristic
15#26039C212yesmaximal
16#26023C211yesmaximal, characteristic
17#23793C212yesmaximal
18#23779C211yesmaximal, characteristic
19#22743C211yesmaximal, characteristic
20#22725C211yesmaximal, characteristic
21#22721C211yesmaximal, characteristic
22#22525C211yesmaximal, characteristic
23Q8×#103C211yesmaximal, characteristic
24C2×Q82C2211yescharacteristic
25C2×#446C2211yescharacteristic
26C2×C8×Q8C2211yescharacteristic
27#2859C2211yescharacteristic
28#2802—22no—
29#2791—22no—
30#2647C2212yes—
31#2570C2212yes—
32#2565—21no—
33#2552—21no—
34#2552C2211yescharacteristic
35#2552C2212yes—
36#2552C2211yescharacteristic
37#2509—21no—
38#2453—21no—
39#2381—22no—
40#2369C2211yescharacteristic
41#2365—21no—
42#2365C2212yes—
43#2356—21no—
44#2356C2212yes—
45#2355C2211yescharacteristic
46#2355C2211yescharacteristic
47#2355C2211yescharacteristic
48Q8×C4⋊C4C2211yescharacteristic
49#2331—21no—
50#2331C2212yes—
51#2330C2212yes—
52#2327—22no—
53#2320—21no—
54#2320C2212yes—
55C4×C4⋊Q8C2211yescharacteristic
56C4×#125C2211yescharacteristic
57#2295C2211yescharacteristic
58#2295C2211yescharacteristic
59#2101C2211yescharacteristic
60#2100C2212yes—
61#2097C2211yescharacteristic
62#2096C2212yes—
63#2088C2211yescharacteristic
64#2088C2212yes—
65#2088C2212yes—
66#2088C2212yes—
67#2087C2212yes—
68#2087C2212yes—
69#2087C2212yes—
70#2086C2212yes—
71#2086C2212yes—
72#2086C2211yescharacteristic
73#2068C2212yes—
74#2068C2212yes—
75#2068C2211yescharacteristic
76#2068C2212yes—
77#2066C2212yes—
78#2066C2211yescharacteristic
79#2059C2211yescharacteristic
80#2059C2212yes—
81#2026C2212yes—
82#2026C2211yescharacteristic
83#1993C2212yes—
84#1990C2212yes—
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1989C2212yes—
88#1989C2212yes—
89#1989C2212yes—
90#1988C2212yes—
91#1987C2211yescharacteristic
92#1987C2211yescharacteristic
93#1987C2212yes—
94#1949C2212yes—
95#1949C2212yes—
96#1949C2212yes—
97#1949C2212yes—
98#1948C2211yescharacteristic
99#1948C2212yes—
100#1947C2211yescharacteristic
101#1947C2211yescharacteristic
102#1947C2212yes—
103#1947C2211yescharacteristic
104#1947C2212yes—
105#1940C2212yes—
106#1939C2212yes—
107#1939C2211yescharacteristic
108#1939C2211yescharacteristic
109#1921C2212yes—
110#1920C2212yes—
111#1919C2212yes—
112#1919C2212yes—
113#1919C2212yes—
114#1918C2212yes—
115#1846C2212yes—
116#1844C2211yescharacteristic
117#1843C2212yes—
118#1842C2211yescharacteristic
119#1836C2212yes—
120#1834C2211yescharacteristic
121#1805C2212yes—
122#1803C2211yescharacteristic
123#1803C2211yescharacteristic
124#1803C2212yes—
125#1776C2212yes—
126C4×#107C2211yescharacteristic
127C4×#106C2212yes—
128C4×#106C2211yescharacteristic
129#1768C2212yes—
130C4×C4⋊C8C2211yescharacteristic
131#1763C2212yes—
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134C4×#103C2212yes—
135Q82—24no—
136Q82Q818yes—
137C2×C4⋊Q8—22no—
138C2×C4⋊Q8—21no—
139C2×C4⋊Q8C2311yescharacteristic
140C2×C4⋊Q8C2312yes—
141C2×#125—21no—
142C2×#125—21no—
143C2×#125C2311yescharacteristic
144C2×#125C2312yes—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—22no—
148C2×C4×Q8—21no—
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2311yescharacteristic
152#446—24no—
153C8×Q8—24no—
154C2×#107C2312yes—
155C2×#107C2311yescharacteristic
156C2×#107C2312yes—
157C2×#107C2312yes—
158C2×#107C2311yescharacteristic
159C2×#106C2311yescharacteristic
160C2×#106C2312yes—
161C2×#106C2311yescharacteristic
162C2×#106C2312yes—
163C2×#106C2312yes—
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×#103C2311yescharacteristic
175C2×#103C2311yescharacteristic
176C2×#103C2311yescharacteristic
177C2×#103C2312yes—
178C2×#103C2312yes—
179C2×#103C2311yescharacteristic
180C2×#97C2312yes—
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2312yes—
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#391—21no—
195#391—21no—
196#391—22no—
197#391—21no—
198#391—22no—
199#391—22no—
200#391—22no—
201#391D411yescharacteristic
202#391D411yescharacteristic
203#391C2311yescharacteristic
204#391C2312yes—
205#391C2311yescharacteristic
206#389—21no—
207#389—21no—
208#389—22no—
209#389—21no—
210#389—21no—
211#389—22no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—22no—
216#389—22no—
217#389D411yescharacteristic
218#389D411yescharacteristic
219#389C2311yescharacteristic
220#389C2311yescharacteristic
221#389C2312yes—
222#389C2312yes—
223#389C2312yes—
224#389C2312yes—
225#389C2311yescharacteristic
226#389C2312yes—
227#389C2312yes—
228#389C2311yescharacteristic
229#387—22no—
230#387—22no—
231#387—22no—
232#387—22no—
233#387—21no—
234#387—21no—
235#387—21no—
236#387—21no—
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#387D412yes—
249#387D412yes—
250#384—21no—
251#384—22no—
252#384C2311yescharacteristic
253#384C2312yes—
254#384C2311yescharacteristic
255#384C2311yescharacteristic
256#384C2312yes—
257#383—22no—
258#383—22no—
259#382—21no—
260#382—21no—
261#382—22no—
262#382C2311yescharacteristic
263#382C2312yes—
264#382C2312yes—
265C4×C4⋊C4—21no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2311yescharacteristic
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2312yes—
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2312yes—
283C4×C4⋊C4C2311yescharacteristic
284#376—21no—
285#376—22no—
286#376C2312yes—
287C43C2311yescharacteristic
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2311yescharacteristic
293#340C2311yescharacteristic
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2311yescharacteristic
300#340C2311yescharacteristic
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2312yes—
312#336C2312yes—
313#336C2311yescharacteristic
314#336C2312yes—
315#336C2311yescharacteristic
316C22×Q8—22no—
317C22×Q8—21no—
318C22×Q8C2×D411yescharacteristic
319C22×Q8C2411yescharacteristic
320C22×C8C2411yescharacteristic
321C22×C8C2411yescharacteristic
322C22×C8C2412yes—
323C22×C8C2411yescharacteristic
324C22×C8C2412yes—
325C22×C8C2411yescharacteristic
326C4⋊Q8—216no—
327C4⋊Q8—28no—
328C4⋊Q8—22no—
329C4⋊Q8—24no—
330C4⋊Q8C2×Q814yes—
331C4⋊Q8C2×Q818yes—
332#125—22no—
333#125—24no—
334#125—41no—
335#125—42no—
336#125—82no—
337#125—82no—
338C4×Q8—28no—
339C4×Q8—22no—
340C4×Q8—24no—
341C4×Q8—82no—
342C4×Q8—84no—
343C4×Q8—82no—
344C4×Q8C2×Q814yes—
345C4×Q8C2×Q818yes—
346C4×Q8C2×Q814yes—
347C4×Q8#4114yes—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D412yes—
379C2×C4⋊C4C2×D412yes—
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D412yes—
382C2×C4⋊C4C2411yescharacteristic
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2411yescharacteristic
385C2×C4⋊C4C2411yescharacteristic
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2411yescharacteristic
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2411yescharacteristic
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2411yescharacteristic
393C2×C42—21no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2411yescharacteristic
409C2×C42C2412yes—
410C2×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412C2×C42C2412yes—
413#107—42no—
414#107—42no—
415#107—42no—
416#107—41no—
417#107—41no—
418#106—24no—
419#106—22no—
420#106—22no—
421#106—42no—
422#106—42no—
423C4⋊C8—22no—
424C4⋊C8—22no—
425C4⋊C8—24no—
426C4⋊C8—22no—
427C4⋊C8—24no—
428C4⋊C8—42no—
429C4⋊C8—41no—
430C4⋊C8—42no—
431C4⋊C8—42no—
432C4⋊C8—42no—
433#103—22no—
434#103—22no—
435#103—42no—
436#103—41no—
437#103—41no—
438#103—42no—
439#97—24no—
440C4×C8—22no—
441C4×C8—24no—
442C4×C8—22no—
443#95—21no—
444#95—21no—
445#95—22no—
446#95—22no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—22no—
451#95—22no—
452#95—21no—
453#95—21no—
454#95—22no—
455#95—21no—
456#95—22no—
457#95—22no—
458#95—21no—
459#95—21no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—21no—
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—
480#95C2×D412yes—
481C2×Q8—24no—
482C2×Q8—28no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—81no—
491C2×Q8—82no—
492C2×Q8—81no—
493C2×Q8—82no—
494C2×Q8C22⋊Q814yes—
495C2×Q8C22×Q812yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4C22×D411yescharacteristic
509C22×C4C22×D412yes—
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D412yes—
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D412yes—
515C22×C4C22×D412yes—
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D411yescharacteristic
518C22×C4C2511yescharacteristic
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×C8—21no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—22no—
534C2×C8—21no—
535C2×C8—22no—
536C2×C82−1+412yes—
537C4⋊C4—28no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—28no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4—81no—
574C4⋊C4—82no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C4⋊C4—82no—
578C4⋊C4—81no—
579C4⋊C4—82no—
580C4⋊C4—81no—
581C4⋊C4—82no—
582C4⋊C4—82no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4C22⋊Q818yes—
589C4⋊C4C22⋊Q814yes—
590C4⋊C4C22×Q812yes—
591C4⋊C4C22×Q814yes—
592C4⋊C42−1+412yes—
593C42—28no—
594C42—24no—
595C42—22no—
596C42—22no—
597C42—21no—
598C42—21no—
599C42—22no—
600C42—21no—
601C42—21no—
602C42—22no—
603C42—41no—
604C42—41no—
605C42—44no—
606C42—42no—
607C42—42no—
608C42—42no—
609C42—82no—
610C42—82no—
611C42—82no—
612C42—82no—
613C42—82no—
614C42C22×Q814yes—
615C42C22×Q812yes—
616C42C2×#4112yes—
617C42C2×#4114yes—
618C23C23×D411yescharacteristic
619Q8—28no—
620Q8—22no—
621Q8—22no—
622Q8—41no—
623Q8—41no—
624Q8—84no—
625Q8—88no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
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—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4C2×C22⋊Q814yes—
687C2×C4C2×C22⋊Q812yes—
688C2×C4C2×C22⋊Q814yes—
689C2×C4C2×C22⋊Q812yes—
690C2×C4#57712yes—
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—22no—
699C8—41no—
700C8—41no—
701C8—42no—
702C8—41no—
703C8—42no—
704C22C22×C22⋊Q811yescharacteristic
705C22#348911yescharacteristic
706C22#349711yescharacteristic
707C22C2×#57711yescharacteristic
708C22C2×#57811yescharacteristic
709C22#358411yescharacteristic
710C22#358511yescharacteristic
711C4—24no—
712C4—22no—
713C4—24no—
714C4—41no—
715C4—42no—
716C4—42no—
717C4—44no—
718C4—42no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—41no—
723C4—42no—
724C4—81no—
725C4—82no—
726C4—81no—
727C4—82no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4—82no—
732C4#308214yes—
733C4#350211yescharacteristic
734C4#350211yescharacteristic
735C4#352311yescharacteristic
736C4#352411yescharacteristic
737C2#3578611yescharacteristic
738C2C2×#308211yescharacteristic
739C2#6049611yescharacteristic
740C2#6218511yescharacteristic
741C2#6221711yescharacteristic
742C2#6237811yescharacteristic
743C2#6240411yescharacteristic
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
#391832
#344912
#300052
#299992
#292922
#292892
#291872
#291772
#265212
#265122
#264452
#264432
#260952
#260882
#260392
#260232
#237932
#237792
#227432
#227252
#227212
#225252
Q8×#1032