Finite Group Databasebeta

← #6586500

Subgroups — #6586500

Order 512.

1329 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35867C212yesmaximal
2#33261C211yesmaximal, characteristic
3#33077C212yesmaximal
4#28813C211yesmaximal, characteristic
5#28812C211yesmaximal, characteristic
6#27028C212yesmaximal
7#27021C212yesmaximal
8#27017C212yesmaximal
9#27016C212yesmaximal
10#26485C211yesmaximal, characteristic
11#26485C211yesmaximal, characteristic
12#26485C211yesmaximal, characteristic
13#26483C211yesmaximal, characteristic
14#26038C212yesmaximal
15#26034C212yesmaximal
16#23160C211yesmaximal, characteristic
17#23158C211yesmaximal, characteristic
18#23157C211yesmaximal, characteristic
19#23157C211yesmaximal, characteristic
20#22809C211yesmaximal, characteristic
21#22808C211yesmaximal, characteristic
22#21676C211yesmaximal, characteristic
23#20507C211yesmaximal, characteristic
24C2×#500C2211yescharacteristic
25C2×#500C2211yescharacteristic
26C2×#500C2211yescharacteristic
27C2×#499C2211yescharacteristic
28C2×C4×Q16C2211yescharacteristic
29C2×C4×Q16C2211yescharacteristic
30C2×C4×Q16C2211yescharacteristic
31#2666—22no—
32#2647C2212yes—
33#2612—22no—
34#2605—22no—
35#2590—22no—
36#2588—22no—
37#2551C2212yes—
38#2550C2212yes—
39#2453C2212yes—
40#2451—22no—
41#2451C2212yes—
42#2451C2212yes—
43#2451C2212yes—
44#2446—22no—
45#2402C2211yescharacteristic
46#2399—22no—
47#2370C2212yes—
48#2369C2212yes—
49#2365C2212yes—
50#2365C2212yes—
51#2356C2212yes—
52#2355C2212yes—
53#2276C2212yes—
54#2068C2212yes—
55#2068C2212yes—
56#2068C2212yes—
57#2066C2212yes—
58#2059C2212yes—
59#2058C2212yes—
60#2057C2212yes—
61#2057C2212yes—
62#2026C2212yes—
63#2024C2212yes—
64#2024C2212yes—
65#2024C2212yes—
66#1989C2212yes—
67#1988C2212yes—
68#1988C2212yes—
69#1987C2212yes—
70#1969C2211yescharacteristic
71#1969C2211yescharacteristic
72#1969C2211yescharacteristic
73#1969C2211yescharacteristic
74#1949C2212yes—
75#1947C2212yes—
76#1944C2212yes—
77#1943C2212yes—
78#1942C2211yescharacteristic
79#1942C2211yescharacteristic
80#1942C2211yescharacteristic
81#1942C2211yescharacteristic
82#1942C2211yescharacteristic
83#1942C2211yescharacteristic
84#1942C2211yescharacteristic
85#1942C2211yescharacteristic
86#1940C2211yescharacteristic
87#1940C2211yescharacteristic
88#1928C2212yes—
89#1928C2212yes—
90#1927C2212yes—
91#1927C2212yes—
92#1921C2212yes—
93#1921C2212yes—
94#1920C2212yes—
95#1919C2212yes—
96#1918C2212yes—
97#1918C2212yes—
98#1918C2212yes—
99#1918C2212yes—
100#1917C2211yescharacteristic
101#1917C2211yescharacteristic
102#1917C2211yescharacteristic
103#1917C2211yescharacteristic
104#1865C2212yes—
105#1863C2212yes—
106#1863C2212yes—
107#1863C2212yes—
108#1846C2211yescharacteristic
109#1845C2211yescharacteristic
110#1836C2212yes—
111#1832C2211yescharacteristic
112#1805C2212yes—
113#1803C2212yes—
114C4×#107C2211yescharacteristic
115C4×#107C2211yescharacteristic
116C4×#107C2211yescharacteristic
117C4×#107C2211yescharacteristic
118C4×#107C2211yescharacteristic
119C4×#107C2211yescharacteristic
120C4×#107C2211yescharacteristic
121C8×C4⋊C4C2211yescharacteristic
122C8×C4⋊C4C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124C8×C4⋊C4C2211yescharacteristic
125C8×C4⋊C4C2211yescharacteristic
126C8×C4⋊C4C2211yescharacteristic
127#1763C2212yes—
128#1763C2212yes—
129#1763C2212yes—
130#1726C2211yescharacteristic
131C22×Q16C2311yescharacteristic
132C2×C4⋊Q8—22no—
133C2×C4⋊Q8C2312yes—
134C2×C4⋊Q8C2312yes—
135C2×C4⋊Q8C2312yes—
136C2×#125C2312yes—
137C2×C4×Q8—22no—
138C2×C4×Q8—22no—
139C2×C4×Q8C2312yes—
140C2×C4×Q8C2312yes—
141C2×C4×Q8C2312yes—
142#500—24no—
143#500—24no—
144#500—24no—
145#499—24no—
146C4×Q16—24no—
147C4×Q16—24no—
148C4×Q16Q818yescomplemented
149C2×#107C2312yes—
150C2×#107C2312yes—
151C2×#107C2312yes—
152C2×#107C2311yescharacteristic
153C2×#107C2311yescharacteristic
154C2×#107C2311yescharacteristic
155C2×#107C2311yescharacteristic
156C2×#107C2312yes—
157C2×#107C2311yescharacteristic
158C2×#107C2311yescharacteristic
159C2×#107C2311yescharacteristic
160C2×#106C2312yes—
161C2×#106C2312yes—
162C2×C4⋊C8C2311yescharacteristic
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2311yescharacteristic
167C2×C4⋊C8C2311yescharacteristic
168C2×#103C2312yes—
169C2×#103C2312yes—
170C2×#103C2312yes—
171C2×#103C2312yes—
172C2×#103C2312yes—
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#97C2311yescharacteristic
176C2×#97C2311yescharacteristic
177C2×#97C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185#400—22no—
186#400—22no—
187#400—22no—
188#400D411yescharacteristic
189#400D411yescharacteristic
190#400D411yescharacteristic
191#400D411yescharacteristic
192#398—22no—
193#398—22no—
194#398—22no—
195#398—22no—
196#398—22no—
197#398—22no—
198#398—22no—
199#398D411yescharacteristic
200#398D411yescharacteristic
201#398D411yescharacteristic
202#398D411yescharacteristic
203#395—22no—
204#395—22no—
205#395—22no—
206#395—22no—
207#395—22no—
208#395—22no—
209#391—22no—
210#391—22no—
211#391—22no—
212#391—22no—
213#391—22no—
214#391—22no—
215#391—22no—
216#391—22no—
217#391C2312yes—
218#391C2312yes—
219#391C2312yes—
220#391C2312yes—
221#389—22no—
222#389—22no—
223#389—22no—
224#389—22no—
225#389—22no—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
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#384C2312yes—
249#383—22no—
250#382—22no—
251#382C2312yes—
252C4×C4⋊C4—22no—
253C4×C4⋊C4—22no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—22no—
257C4×C4⋊C4—22no—
258C4×C4⋊C4C2312yes—
259C4×C4⋊C4C2312yes—
260C4×C4⋊C4C2312yes—
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2312yes—
265C4×C4⋊C4C2311yescharacteristic
266C4×C4⋊C4C2311yescharacteristic
267C4×C4⋊C4C2311yescharacteristic
268C4×C4⋊C4C2311yescharacteristic
269C4×C4⋊C4C2311yescharacteristic
270C4×C4⋊C4C2311yescharacteristic
271#376—22no—
272#376—22no—
273#376C2311yescharacteristic
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
297#336C2311yescharacteristic
298#336C2311yescharacteristic
299#336C2311yescharacteristic
300#336C2311yescharacteristic
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8—22no—
304C22×Q8C2412yes—
305C2×Q16—22no—
306C2×Q16—22no—
307C2×Q16C2×Q814yes—
308C22×C8C2411yescharacteristic
309C22×C8C2411yescharacteristic
310C22×C8C2411yescharacteristic
311C22×C8C2411yescharacteristic
312C22×C8C2411yescharacteristic
313C22×C8C2411yescharacteristic
314C22×C8C2411yescharacteristic
315C22×C8C2411yescharacteristic
316C4⋊Q8—24no—
317C4⋊Q8—24no—
318C4⋊Q8—24no—
319C4⋊Q8—42no—
320C4⋊Q8—42no—
321C4⋊Q8—42no—
322C4⋊Q8—84no—
323#125—24no—
324#125—42no—
325C4×Q8—24no—
326C4×Q8—24no—
327C4×Q8—24no—
328C4×Q8—42no—
329C4×Q8—42no—
330C4×Q8—84no—
331C4×Q8—84no—
332C4×Q8C2×Q818yes—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4C2×D411yescharacteristic
352C2×C4⋊C4C2×D411yescharacteristic
353C2×C4⋊C4C2×D411yescharacteristic
354C2×C4⋊C4C2×D411yescharacteristic
355C2×C4⋊C4C2×D411yescharacteristic
356C2×C4⋊C4C2×D411yescharacteristic
357C2×C4⋊C4C2×D411yescharacteristic
358C2×C4⋊C4C2×D411yescharacteristic
359C2×C4⋊C4C2×D411yescharacteristic
360C2×C4⋊C4C2×D411yescharacteristic
361C2×C4⋊C4C2×D411yescharacteristic
362C2×C4⋊C4C2×D411yescharacteristic
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42C2411yescharacteristic
381C2×C42C2411yescharacteristic
382C2×C42C2411yescharacteristic
383C2×C42C2411yescharacteristic
384C2×C42C2411yescharacteristic
385C2×C42C2411yescharacteristic
386C2×C42C2411yescharacteristic
387#107—22no—
388#107—22no—
389#107—22no—
390#107—22no—
391#107—24no—
392#107—24no—
393#107—24no—
394#107—42no—
395#107C2×Q814yes—
396#107#4114yes—
397#107#4114yes—
398#106—24no—
399#106—42no—
400C4⋊C8—22no—
401C4⋊C8—22no—
402C4⋊C8—41no—
403C4⋊C8—41no—
404C4⋊C8—41no—
405C4⋊C8—41no—
406#103—24no—
407#103—24no—
408#103—42no—
409#103—42no—
410#103—42no—
411#103—42no—
412#103C2×Q818yes—
413#97—22no—
414#97—41no—
415#97—41no—
416C4×C8—22no—
417C4×C8—22no—
418C4×C8—22no—
419C4×C8—22no—
420C4×C8—22no—
421C4×C8—22no—
422C4×C8C2×Q814yes—
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#95—22no—
448#95C2×D411yescharacteristic
449#95C2×D411yescharacteristic
450#95C2×D411yescharacteristic
451#95C2×D411yescharacteristic
452#95C2×D411yescharacteristic
453#95C2×D411yescharacteristic
454#95C2×D411yescharacteristic
455#95C2×D411yescharacteristic
456#95C2×D411yescharacteristic
457#95C2×D411yescharacteristic
458#95C2×D411yescharacteristic
459#95C2×D411yescharacteristic
460#95C2×D411yescharacteristic
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—82no—
475C2×Q8—82no—
476C2×Q8—82no—
477C2×Q8—82no—
478C2×Q8C22×Q814yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4C22×D411yescharacteristic
488C22×C4C22×D411yescharacteristic
489C22×C4C22×D411yescharacteristic
490C22×C4C22×D411yescharacteristic
491C22×C4C22×D411yescharacteristic
492C22×C4C22×D411yescharacteristic
493C22×C4C22×D411yescharacteristic
494C22×C4C22×D411yescharacteristic
495C22×C4C22×D411yescharacteristic
496C22×C4C22×D411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C22×D411yescharacteristic
499C22×C4C22×D411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C2511yescharacteristic
502Q16—28no—
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×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8C22×Q812yes—
524C2×C8C22×Q812yes—
525C2×C8C2×#4112yes—
526C2×C8C2×#4112yes—
527C4⋊C4—28no—
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—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—82no—
560C4⋊C4—82no—
561C4⋊C4—82no—
562C4⋊C4—82no—
563C4⋊C4—82no—
564C4⋊C4—82no—
565C4⋊C4—82no—
566C4⋊C4—82no—
567C4⋊C4—82no—
568C4⋊C4C22×Q814yes—
569C4⋊C4C2×#4114yes—
570C4⋊C4C2×#4114yes—
571C42—28no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—44no—
585C42—44no—
586C42—44no—
587C42—44no—
588C42—82no—
589C42—82no—
590C42—82no—
591C42—82no—
592C42—82no—
593C42C22×Q812yes—
594C422−1+412yes—
595C23C23×D411yescharacteristic
596Q8—24no—
597Q8—24no—
598Q8—42no—
599Q8—42no—
600Q8—88no—
601Q8—88no—
602Q8—164no—
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—24no—
619C2×C4—24no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4D4×Q812yes—
665C2×C4D4×Q812yes—
666C2×C4#57612yes—
667C2×C4#57812yes—
668C2×C4#57812yes—
669C2×C4C23×Q811yescharacteristic
670C2×C4C22×#4111yescharacteristic
671C2×C4C22×#4111yescharacteristic
672C2×C4C2×2−1+411yescharacteristic
673C2×C4#58511yescharacteristic
674C2×C4#58511yescharacteristic
675C8—22no—
676C8—41no—
677C8—41no—
678C8—41no—
679C8—41no—
680C8—41no—
681C8—41no—
682C8#53314yes—
683C22C2×D4×Q811yescharacteristic
684C22D4×#4111yescharacteristic
685C22D4×#4111yescharacteristic
686C22C2×#57611yescharacteristic
687C22C2×#57811yescharacteristic
688C22C2×#57811yescharacteristic
689C22#358411yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—41no—
696C4—41no—
697C4—44no—
698C4—44no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—44no—
705C4—41no—
706C4—41no—
707C4—44no—
708C4—82no—
709C4—82no—
710C4—82no—
711C4—82no—
712C4C2×#53311yescharacteristic
713C4#350411yescharacteristic
714C4#351811yescharacteristic
715C4#351811yescharacteristic
716C2#3613211yescharacteristic
717C2#6137211yescharacteristic
718C2#6137311yescharacteristic
719C2#6147111yescharacteristic
720C2#6147811yescharacteristic
721C2#6148211yescharacteristic
722C2#6148411yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
148. C4×Q16Q8semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#358672
#332612
#330772
#288132
#288122
#270282
#270212
#270172
#270162
#264852
#264832
#260382
#260342
#231602
#231582
#231572
#228092
#228082
#216762
#205072