Finite Group Databasebeta

← #6586383

Subgroups — #6586383

Order 512.

1320 conjugacy classes of subgroups.

The subgroup lattice has 763 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36600C211yesmaximal, characteristic
2#36447C211yesmaximal, characteristic
3#33263C211yesmaximal, characteristic
4#33073C211yesmaximal, characteristic
5#33069C211yesmaximal, characteristic
6#28969C212yesmaximal
7#28955C212yesmaximal
8#28800C211yesmaximal, characteristic
9#28792C211yesmaximal, characteristic
10#26885C212yesmaximal
11#26884C212yesmaximal
12#26395C212yesmaximal
13#26391C212yesmaximal
14#26092C211yesmaximal, characteristic
15#26089C211yesmaximal, characteristic
16#26047C211yesmaximal, characteristic
17#26043C211yesmaximal, characteristic
18#22980C212yesmaximal
19#22973C212yesmaximal
20#22771C211yesmaximal, characteristic
21#22763C211yesmaximal, characteristic
22#21675C211yesmaximal, characteristic
23C4×#441C211yesmaximal, characteristic
24C2×#479C2212yes—
25C2×#479C2212yes—
26C2×#441C2211yescharacteristic
27C2×#441C2211yescharacteristic
28C2×C4×Q16C2211yescharacteristic
29#2859—21no—
30#2859—21no—
31#2859C2211yescharacteristic
32#2859C2211yescharacteristic
33#2585—22no—
34#2585—22no—
35#2571—21no—
36#2571C2211yescharacteristic
37#2570—21no—
38#2570—21no—
39#2552—21no—
40#2552C2211yescharacteristic
41#2552C2211yescharacteristic
42#2552C2211yescharacteristic
43#2508—22no—
44#2508C2212yes—
45#2506—22no—
46#2506C2212yes—
47#2453C2212yes—
48#2453C2212yes—
49#2370C2212yes—
50#2370C2212yes—
51#2355C2211yescharacteristic
52#2355C2211yescharacteristic
53#2351C2212yes—
54Q8×C4⋊C4C2212yes—
55Q8×C4⋊C4C2211yescharacteristic
56Q8×C4⋊C4C2211yescharacteristic
57C4×#125—21no—
58C4×#125—21no—
59C4×#125C2211yescharacteristic
60C42×Q8C2211yescharacteristic
61C42×Q8C2211yescharacteristic
62#2097C2212yes—
63#2095C2212yes—
64#2088C2212yes—
65#2086C2212yes—
66#2085C2212yes—
67#2084C2212yes—
68#2068C2212yes—
69#2066C2212yes—
70#2059C2212yes—
71#2059C2212yes—
72#2059C2212yes—
73#2059C2212yes—
74#1992C2212yes—
75#1991C2212yes—
76#1949C2212yes—
77#1948C2211yescharacteristic
78#1947C2212yes—
79#1947C2211yescharacteristic
80#1947C2211yescharacteristic
81#1947C2211yescharacteristic
82#1944C2212yes—
83#1944C2212yes—
84#1944C2212yes—
85#1943C2212yes—
86#1943C2212yes—
87#1942C2212yes—
88#1939C2211yescharacteristic
89#1939C2211yescharacteristic
90#1935C2212yes—
91#1933C2212yes—
92#1921C2212yes—
93#1921C2212yes—
94#1921C2212yes—
95#1921C2212yes—
96#1920C2212yes—
97#1920C2212yes—
98#1918C2212yes—
99#1918C2212yes—
100#1917C2212yes—
101#1917C2212yes—
102#1878C2212yes—
103#1878C2212yes—
104#1865C2212yes—
105#1865C2212yes—
106#1863C2212yes—
107#1863C2212yes—
108#1863C2212yes—
109#1863C2212yes—
110#1845C2211yescharacteristic
111#1844C2211yescharacteristic
112#1834C2211yescharacteristic
113#1834C2211yescharacteristic
114#1831C2211yescharacteristic
115#1803C2211yescharacteristic
116#1803C2211yescharacteristic
117#1803C2211yescharacteristic
118#1803C2211yescharacteristic
119#1776C2211yescharacteristic
120#1776C2211yescharacteristic
121C4×#106C2211yescharacteristic
122#1771C2212yes—
123#1770C2212yes—
124#1770C2211yescharacteristic
125C8×C4⋊C4C2211yescharacteristic
126#1763C2211yescharacteristic
127#1763C2211yescharacteristic
128#1763C2211yescharacteristic
129#1763C2211yescharacteristic
130#1763C2212yes—
131C4×#103C2211yescharacteristic
132C4×#103C2211yescharacteristic
133C4×#103C2212yes—
134C4×#97C2211yescharacteristic
135C22×Q16C2311yescharacteristic
136C2×#125—21no—
137C2×#125—22no—
138C2×#125—21no—
139C2×#125—21no—
140C2×#125D411yescharacteristic
141C2×#125C2312yes—
142C2×#125C2312yes—
143C2×C4×Q8C2312yes—
144C2×C4×Q8C2312yes—
145C2×C4×Q8C2311yescharacteristic
146C2×C4×Q8C2311yescharacteristic
147C2×C4×Q8C2311yescharacteristic
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2311yescharacteristic
151#479—28no—
152#479—28no—
153#441—24no—
154#441—24no—
155C4×Q16Q818yes—
156C2×#107C2312yes—
157C2×#107C2312yes—
158C2×#107C2312yes—
159C2×#107C2312yes—
160C2×#107C2312yes—
161C2×#107C2311yescharacteristic
162C2×#106C2312yes—
163C2×#106C2312yes—
164C2×#106C2311yescharacteristic
165C2×#106C2311yescharacteristic
166C2×#106C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2311yescharacteristic
170C2×C4⋊C8C2311yescharacteristic
171C2×#103C2312yes—
172C2×#103C2312yes—
173C2×#103C2311yescharacteristic
174C2×#103C2311yescharacteristic
175C2×#103C2312yes—
176C2×#103C2312yes—
177C2×#103C2311yescharacteristic
178C2×#103C2311yescharacteristic
179C2×#103C2311yescharacteristic
180C2×#103C2311yescharacteristic
181C2×#97C2311yescharacteristic
182C2×#97C2311yescharacteristic
183C2×#97C2312yes—
184C2×#97C2311yescharacteristic
185C2×#97C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2312yes—
188C2×C4×C8C2311yescharacteristic
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#398—22no—
199#398—22no—
200#398—22no—
201#391C2312yes—
202#391C2312yes—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—22no—
208#389—22no—
209#389—22no—
210#389—22no—
211#389—22no—
212#389—22no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—22no—
218#389—22no—
219#389—22no—
220#389—22no—
221#389D411yescharacteristic
222#389D411yescharacteristic
223#389C2312yes—
224#389C2312yes—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
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#387D412yes—
244#387D412yes—
245#384—21no—
246#384—21no—
247#384—21no—
248#384—21no—
249#384—22no—
250#384C2311yescharacteristic
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#384C2311yescharacteristic
254#384C2312yes—
255#382—21no—
256#382—21no—
257#382—21no—
258#382—21no—
259#382—21no—
260#382—22no—
261#382—22no—
262#382D411yescharacteristic
263#382C2312yes—
264C4×C4⋊C4—21no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—22no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—22no—
276C4×C4⋊C4—22no—
277C4×C4⋊C4—22no—
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2312yes—
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2311yescharacteristic
284C4×C4⋊C4C2311yescharacteristic
285C4×C4⋊C4C2311yescharacteristic
286C4×C4⋊C4C2311yescharacteristic
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2312yes—
290C43—21no—
291C43—21no—
292C43C2311yescharacteristic
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2311yescharacteristic
298#340C2311yescharacteristic
299#340C2312yes—
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2312yes—
315#336C2312yes—
316#336C2312yes—
317C22×Q8C2411yescharacteristic
318C22×Q8C2411yescharacteristic
319C2×Q16—22no—
320C2×Q16—22no—
321C2×Q16C2×Q814yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C22×C8C2411yescharacteristic
325C22×C8C2411yescharacteristic
326C22×C8C2411yescharacteristic
327C22×C8C2411yescharacteristic
328#125—24no—
329#125—24no—
330#125—42no—
331#125—42no—
332#125—42no—
333#125—44no—
334#125—44no—
335#125—82no—
336#125—84no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—24no—
342C4×Q8—24no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—42no—
346C4×Q8—41no—
347C4×Q8—41no—
348C4×Q8—41no—
349C4×Q8—41no—
350C4×Q8—42no—
351C4×Q8C2×Q814yes—
352C4×Q8C2×Q814yes—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D412yes—
390C2×C4⋊C4C2×D412yes—
391C2×C4⋊C4C2×D412yes—
392C2×C4⋊C4C2×D412yes—
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2411yescharacteristic
401C2×C4⋊C4C2411yescharacteristic
402C2×C4⋊C4C2411yescharacteristic
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2412yes—
426C2×C42C2412yes—
427C2×C42C2411yescharacteristic
428#107—24no—
429#107—24no—
430#107—42no—
431#107—42no—
432#107—42no—
433#107C2×Q814yes—
434#106—24no—
435#106—22no—
436#106—22no—
437#106—24no—
438#106—42no—
439C4⋊C8—24no—
440C4⋊C8—24no—
441C4⋊C8—22no—
442C4⋊C8—22no—
443#103—24no—
444#103—24no—
445#103—22no—
446#103—22no—
447#103—42no—
448#103—42no—
449#103C2×Q814yes—
450#103C2×Q814yes—
451#103#4114yes—
452#103#4114yes—
453#97—22no—
454#97—22no—
455#97—41no—
456#97—41no—
457#97—42no—
458C4×C8—22no—
459C4×C8—42no—
460C4×C8C2×Q814yes—
461#95—21no—
462#95—21no—
463#95—21no—
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#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95C2×D412yes—
486#95C2×D412yes—
487#95C2×D412yes—
488#95C2×D412yes—
489#95C2×D412yes—
490#95C2×D412yes—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C22×Q812yes—
500C2×Q8C22×Q812yes—
501C2×Q8C2×#4112yes—
502C2×Q8C2×#4112yes—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4C22×D412yes—
516C22×C4C22×D411yescharacteristic
517C22×C4C22×D412yes—
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C2511yescharacteristic
526Q16—28no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8C22×Q812yes—
542C2×C8C22×Q812yes—
543C2×C8C2×#4112yes—
544C2×C8C2×#4112yes—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—22no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—81no—
591C4⋊C4—81no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4—81no—
595C4⋊C4—81no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4C22×Q812yes—
602C4⋊C4C22×Q812yes—
603C4⋊C4C2×#4112yes—
604C4⋊C4C2×#4112yes—
605C42—24no—
606C42—24no—
607C42—22no—
608C42—22no—
609C42—21no—
610C42—21no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—21no—
615C42—21no—
616C42—22no—
617C42—41no—
618C42—41no—
619C42—42no—
620C42—42no—
621C42—44no—
622C42—44no—
623C42—42no—
624C42—42no—
625C42—42no—
626C42—42no—
627C42—42no—
628C42—42no—
629C42—81no—
630C42—82no—
631C42—81no—
632C42—82no—
633C42C22×Q812yes—
634C422−1+412yes—
635C23C23×D411yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—41no—
642Q8—41no—
643Q8#53314yes—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4D4×Q812yes—
707C2×C4D4×Q812yes—
708C2×C4#57512yes—
709C2×C4#57812yes—
710C2×C4C23×Q811yescharacteristic
711C2×C4C22×#4111yescharacteristic
712C2×C4C22×#4111yescharacteristic
713C2×C4C2×2−1+411yescharacteristic
714C2×C4#58511yescharacteristic
715C2×C4#58511yescharacteristic
716C8—22no—
717C8—22no—
718C8—22no—
719C8—22no—
720C8—42no—
721C8—42no—
722C22C2×D4×Q811yescharacteristic
723C22D4×#4111yescharacteristic
724C22D4×#4111yescharacteristic
725C22C2×#57511yescharacteristic
726C22C2×#57811yescharacteristic
727C22#358511yescharacteristic
728C22#358611yescharacteristic
729C4—24no—
730C4—22no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—41no—
737C4—42no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—81no—
745C4—82no—
746C4—82no—
747C4—81no—
748C4—82no—
749C4—82no—
750C4#339014yes—
751C4C2×#53311yescharacteristic
752C4#350411yescharacteristic
753C4#351511yescharacteristic
754C4#351511yescharacteristic
755C2#3613111yescharacteristic
756C2C2×#339011yescharacteristic
757C2#6138011yescharacteristic
758C2#6146211yescharacteristic
759C2#6146711yescharacteristic
760C2#6154211yescharacteristic
761C2#6155211yescharacteristic
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
#366002
#364472
#332632
#330732
#330692
#289692
#289552
#288002
#287922
#268852
#268842
#263952
#263912
#260922
#260892
#260472
#260432
#229802
#229732
#227712
#227632
#216752
C4×#4412