Finite Group Databasebeta

← #482971

Subgroups — #482971

Order 512.

775 conjugacy classes of subgroups.

The subgroup lattice has 741 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62251C211yesmaximal, characteristic
2#33487C211yesmaximal, characteristic, complemented
3#22717C211yesmaximal, characteristic, complemented
4#11895C211yesmaximal, characteristic, complemented
5#11894C211yesmaximal, characteristic, complemented
6#11893C211yesmaximal, characteristic, complemented
7#11891C211yesmaximal, characteristic, complemented
8#11866C211yesmaximal, characteristic, complemented
9#11864C211yesmaximal, characteristic, complemented
10#11751C211yesmaximal, characteristic, complemented
11#11750C211yesmaximal, characteristic, complemented
12#11711C211yesmaximal, characteristic, complemented
13#11710C211yesmaximal, characteristic, complemented
14#11709C211yesmaximal, characteristic, complemented
15C2×#1349C211yesmaximal, characteristic, complemented
16#3519—21no—
17#3341C411yescharacteristic
18#3339C411yescharacteristic
19#3339C411yescharacteristic
20#3338C411yescharacteristic
21#3305—21no—
22#3297—21no—
23#3297—21no—
24#3295—21no—
25#3287C411yescharacteristic
26#3280C411yescharacteristic
27#3280C411yescharacteristic
28D4×D8C411yescharacteristic
29#3247—21no—
30#3188—21no—
31#3188—21no—
32#3169C2211yescharacteristic
33#3168C2211yescharacteristic
34#3050C2211yescharacteristic
35#3050C2211yescharacteristic
36C2×#466C2211yescharacteristic
37C2×#466C2211yescharacteristic
38D4×M16—21no—
39C2×C8×D4C2211yescharacteristic
40#2168—21no—
41#2168—21no—
42#2168—21no—
43#2168—21no—
44#2163C2211yescharacteristic, complemented
45#2163C2211yescharacteristic, complemented
46#2112C2211yescharacteristic, complemented
47#2112C2211yescharacteristic, complemented
48C2×C22⋊C16C2211yescharacteristic, complemented
49C2×C22⋊C16C2211yescharacteristic, complemented
50#1950—21no—
51#1855—21no—
52#1855—21no—
53#1837C2211yescharacteristic, complemented
54#1810C2211yescharacteristic, complemented
55#1810C2211yescharacteristic, complemented
56C4×#108C2211yescharacteristic, complemented
57C2×#341C2211yescharacteristic, complemented
58C2×#341C2211yescharacteristic, complemented
59#1350C2211yescharacteristic, complemented
60#1350C2211yescharacteristic, complemented
61#1350C2211yescharacteristic, complemented
62#1350C2211yescharacteristic, complemented
63#1349C2211yescharacteristic
64#1349C2211yescharacteristic
65#1349C2211yescharacteristic
66#1349C2211yescharacteristic
67#1349C2211yescharacteristic, complemented
68#1349C2211yescharacteristic, complemented
69#1349C2211yescharacteristic, complemented
70#1349C2211yescharacteristic, complemented
71#1349C2211yescharacteristic, complemented
72#1349C2211yescharacteristic, complemented
73#1349C2211yescharacteristic, complemented
74#1349C2211yescharacteristic, complemented
75C2×#135C2×C411yescharacteristic
76C2×#135C2×C411yescharacteristic
77C22×D8C2×C411yescharacteristic
78C22×D8C2×C411yescharacteristic
79C22×M16—21no—
80C22×M16—21no—
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83#555—21no—
84#554—21no—
85#553—21no—
86#553—21no—
87#553—41no—
88#550—21no—
89#546—21no—
90#546—21no—
91#546—41no—
92#546—41no—
93D42—21no—
94D42—41no—
95#540—41no—
96#538—41no—
97#538—41no—
98#532—21no—
99#529—21no—
100#525—21no—
101#525—21no—
102C2×#121—21no—
103C2×#121—21no—
104#518—41no—
105C2×C4×D4D411yescharacteristic
106C2×M32—21no—
107C2×M32—21no—
108C22×C16—21no—
109C22×C16—21no—
110#500C2×C411yescharacteristic
111#499C2×C411yescharacteristic
112#495C2×C411yescharacteristic
113#493C2×C411yescharacteristic
114#488—21no—
115#486—21no—
116#484—21no—
117#484—21no—
118#482—21no—
119#482—21no—
120#482—21no—
121#482—21no—
122#481—21no—
123#481—21no—
124#478—21no—
125#478—21no—
126#477—21no—
127#476—21no—
128#467C2×C411yescharacteristic
129#467C2×C411yescharacteristic
130#467C2311yescharacteristic
131#466—21no—
132#466—21no—
133#466—21no—
134#466—21no—
135#466—21no—
136#466C2×C411yescharacteristic
137#466C2×C411yescharacteristic
138#466C2×C411yescharacteristic
139#466C2×C411yescharacteristic
140#466C2×C411yescharacteristic
141#466C2×C411yescharacteristic
142#466C2311yescharacteristic
143#466C2311yescharacteristic
144#466C2311yescharacteristic
145#465—21no—
146#465—21no—
147#465—21no—
148#465—21no—
149#465—21no—
150#463—21no—
151#463—21no—
152#460—21no—
153#459—21no—
154#450—21no—
155#450—21no—
156#449—21no—
157#449—21no—
158#449—21no—
159#449—21no—
160#447—21no—
161#447—21no—
162C4×Q16C2×C411yescharacteristic
163C4×SD16—21no—
164C4×D8—21no—
165C4×D8C2×C411yescharacteristic
166C4×D8C2×C411yescharacteristic
167C4×D8C2×C411yescharacteristic
168#436—41no—
169#435—41no—
170#435—41no—
171C8×D4—41no—
172C8×D4C2×C411yescharacteristic
173C8×D4C2×C411yescharacteristic
174C8×D4C2×C411yescharacteristic
175C8×D4C2×C411yescharacteristic
176C8×D4D411yescharacteristic
177C8×D4D411yescharacteristic
178C8×D4D411yescharacteristic
179C8×D4D411yescharacteristic
180C2×#108—21no—
181C2×#108—21no—
182C2×#108—21no—
183#427C2×C411yescharacteristic
184#427C2×C411yescharacteristic
185C2×#107C2×C411yescharacteristic
186C2×#107C2×C411yescharacteristic
187#423—21no—
188C2×C4⋊C8D411yescharacteristic
189#416—21no—
190#416—21no—
191C2×#102—21no—
192C2×#102—21no—
193#407—21no—
194#407—21no—
195C2×C22⋊C8D411yescharacteristic
196C2×C22⋊C8D411yescharacteristic
197C4×M16—21no—
198C2×C4×C8C2311yescharacteristic
199C4⋊C16—21no—
200C4⋊C16—21no—
201C22⋊C16—21no—
202C22⋊C16—21no—
203C22⋊C16—21no—
204C22⋊C16—21no—
205C22⋊C16C2311yescharacteristic
206C22⋊C16C2311yescharacteristic
207C22⋊C16C2311yescharacteristic
208C22⋊C16C2311yescharacteristic
209#346—21no—
210#346—21no—
211#341—21no—
212#341—21no—
213#341—21no—
214#341C2311yescharacteristic
215#341C2311yescharacteristic
216#341C2311yescharacteristic
217#341C2311yescharacteristic
218C2×#41—21no—
219C2×#41—21no—
220C2×#41—41no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—41no—
224C22×D4—41no—
225C22×D4—41no—
226C22×D4SD1611yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229#135—81no—
230#135—81no—
231C2×Q16C22×C411yescharacteristic
232C2×SD16—21no—
233C2×SD16—21no—
234C2×SD16—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—81no—
239C2×D8—81no—
240C2×D8C22×C411yescharacteristic
241C2×D8C22×C411yescharacteristic
242C2×D8C22×C411yescharacteristic
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—41no—
248C2×M16—41no—
249C2×M16—42no—
250C2×M16—42no—
251C2×M16—81no—
252C2×M16—81no—
253C22×C8—41no—
254C22×C8—41no—
255C22×C8—81no—
256C22×C8—81no—
257C22×C8C22×C411yescharacteristic
258C22×C8C22×C411yescharacteristic
259C22×C8C22×C411yescharacteristic
260C22×C8C22×C411yescharacteristic
261C22×C8C2×D411yescharacteristic
262C22×C8C2×D411yescharacteristic
263C22×C8C2×D411yescharacteristic
264C22×C8C2×D411yescharacteristic
265C22×C8C2×D411yescharacteristic
266C22×C8C2×D411yescharacteristic
267C22×C8C2×D411yescharacteristic
268C22×C8C2411yescharacteristic
269C4⋊Q8—21no—
270#127—21no—
271#127—41no—
272#126—41no—
273#126—41no—
274#126—41no—
275#125—21no—
276#125—41no—
277#124—21no—
278#124—41no—
279#124—41no—
280#124—41no—
281#123—41no—
282#123—41no—
283#123—41no—
284#123—41no—
285#123—41no—
286#123—41no—
287#123—41no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—41no—
292C22⋊Q8—41no—
293#121—21no—
294#121—21no—
295#121—21no—
296#121—21no—
297#121—21no—
298#121—21no—
299#121—21no—
300#121—21no—
301#121—21no—
302#121—41no—
303#121—41no—
304#121—41no—
305#121—41no—
306#121—41no—
307#121—41no—
308#121—41no—
309#121—41no—
310#121—41no—
311#121—41no—
312#121—41no—
313#121—41no—
314#121—41no—
315#120—41no—
316#120—41no—
317#120—41no—
318#120—41no—
319#120—41no—
320#120—41no—
321C4×Q8—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—41no—
326C4×D4—41no—
327C4×D4—41no—
328C4×D4—41no—
329C4×D4—41no—
330C4×D4—41no—
331C4×D4—41no—
332C4×D4—41no—
333C4×D4—41no—
334C4×D4—41no—
335C4×D4C22⋊C411yescharacteristic
336C4×D4C22⋊C411yescharacteristic
337C4×D4C22⋊C411yescharacteristic
338C4×D4C22⋊C411yescharacteristic
339C4×D4D811yescharacteristic
340C4×D4D811yescharacteristic
341C4×D4D811yescharacteristic
342C4×D4D811yescharacteristic
343#117—21no—
344#117—21no—
345#117—41no—
346#117—41no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4SD1611yescharacteristic
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4SD1611yescharacteristic
355C2×C22⋊C4SD1611yescharacteristic
356C2×C42C2×D411yescharacteristic
357M32—81no—
358M32—81no—
359C2×C16—21no—
360C2×C16—21no—
361C2×C16—21no—
362C2×C16—21no—
363C2×C16—81no—
364C2×C16—81no—
365#108—42no—
366#108—81no—
367#108—81no—
368#107—21no—
369#107—21no—
370#107—21no—
371#107C22×C411yescharacteristic
372#107C22×C411yescharacteristic
373#107C22×C411yescharacteristic
374#107C22×C411yescharacteristic
375#106—21no—
376#106—21no—
377#106—21no—
378C4⋊C8—41no—
379C4⋊C8—41no—
380C4⋊C8C22⋊C411yescharacteristic
381C4⋊C8C22⋊C411yescharacteristic
382C4⋊C8C22⋊C411yescharacteristic
383C4⋊C8C22⋊C411yescharacteristic
384#103—21no—
385#103—21no—
386#103—21no—
387#103—21no—
388#102—21no—
389#102—21no—
390#102—21no—
391#102—21no—
392#102—21no—
393#102—21no—
394#102—21no—
395#102—21no—
396#102—21no—
397#102—21no—
398#102—21no—
399#102—21no—
400C22⋊C8—41no—
401C22⋊C8—41no—
402C22⋊C8—41no—
403C22⋊C8—41no—
404C22⋊C8C22⋊C411yescharacteristic
405C22⋊C8C22⋊C411yescharacteristic
406C22⋊C8C22⋊C411yescharacteristic
407C22⋊C8C22⋊C411yescharacteristic
408C22⋊C8C22⋊C411yescharacteristic
409C22⋊C8C22⋊C411yescharacteristic
410C22⋊C8C22⋊C411yescharacteristic
411C22⋊C8C22⋊C411yescharacteristic
412#97—41no—
413C4×C8—41no—
414C4×C8C22×C411yescharacteristic
415C4×C8C22×C411yescharacteristic
416C4×C8C2×D411yescharacteristic
417C4×C8C2×D411yescharacteristic
418C24—41no—
419C24—41no—
420C24C2×SD1611yescharacteristic
421C24C2×SD1611yescharacteristic
422#41—81no—
423#41—81no—
424#41—81no—
425#41—81no—
426#41—162no—
427C2×Q8—21no—
428C2×Q8—41no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—42no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—81no—
449C2×D4—81no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4—84no—
453C2×D4—162no—
454C2×D4—162no—
455C2×D4#10211yescharacteristic
456C2×D4#10211yescharacteristic
457C2×D4#10211yescharacteristic
458C2×D4#10211yescharacteristic
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4C2×C22⋊C411yescharacteristic
471C22×C4C2×C22⋊C411yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C2×C22⋊C411yescharacteristic
474C22×C4C2×D811yescharacteristic
475C22×C4C2×D811yescharacteristic
476C22×C4C2×D811yescharacteristic
477C22×C4C2×D811yescharacteristic
478C22×C4C2×SD1611yescharacteristic
479C22×C4C2×SD1611yescharacteristic
480C22×C4C2×SD1611yescharacteristic
481C22×C4C2×SD1611yescharacteristic
482C22×C4C22×D411yescharacteristic
483Q16—41no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487D8—41no—
488D8—41no—
489D8—41no—
490D8—81no—
491D8—81no—
492D8—81no—
493M16—22no—
494M16—41no—
495M16—41no—
496M16—41no—
497M16—41no—
498M16—41no—
499M16—41no—
500M16—41no—
501M16—82no—
502M16—82no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—82no—
520C2×C8—82no—
521C2×C8C2×C22⋊C411yescharacteristic
522C2×C8C2×C22⋊C411yescharacteristic
523C2×C8C2×C22⋊C411yescharacteristic
524C2×C8C2×C22⋊C411yescharacteristic
525C2×C8C2×C22⋊C411yescharacteristic
526C2×C8C2×C22⋊C411yescharacteristic
527C2×C8C23×C411yescharacteristic
528C2×C8C22×D411yescharacteristic
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4#10211yescharacteristic
543C4⋊C4#10211yescharacteristic
544C4⋊C4#10211yescharacteristic
545C4⋊C4#10211yescharacteristic
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4#10211yescharacteristic
566C22⋊C4#10211yescharacteristic
567C22⋊C4#10211yescharacteristic
568C22⋊C4#10211yescharacteristic
569C22⋊C4#10211yescharacteristic
570C22⋊C4#10211yescharacteristic
571C22⋊C4#10211yescharacteristic
572C22⋊C4#10211yescharacteristic
573C42—41no—
574C42—41no—
575C42—41no—
576C42C2×C22⋊C411yescharacteristic
577C42C2×C22⋊C411yescharacteristic
578C42C2×D811yescharacteristic
579C42C2×D811yescharacteristic
580C16—41no—
581C16—41no—
582C16—41no—
583C16—41no—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—82no—
594C23—82no—
595C23—161no—
596C23—161no—
597C23—161no—
598C23—161no—
599C23C2×#10211yescharacteristic
600C23C2×#10211yescharacteristic
601C23C2×#10211yescharacteristic
602C23C2×#10211yescharacteristic
603C23C22×SD1611yescharacteristic
604Q8—41no—
605Q8—41no—
606Q8—161no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—82no—
618D4—82no—
619D4—82no—
620D4—82no—
621D4—82no—
622D4—82no—
623D4—161no—
624D4—161no—
625D4—161no—
626D4—161no—
627D4—161no—
628D4—161no—
629D4—161no—
630D4—161no—
631D4—161no—
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—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—82no—
656C2×C4—161no—
657C2×C4—161no—
658C2×C4—161no—
659C2×C4—161no—
660C2×C4—161no—
661C2×C4—161no—
662C2×C4C2×#10211yescharacteristic
663C2×C4C2×#10211yescharacteristic
664C2×C4C2×#10211yescharacteristic
665C2×C4C2×#10211yescharacteristic
666C2×C4C2×#10211yescharacteristic
667C2×C4C2×#10211yescharacteristic
668C2×C4C2×#10211yescharacteristic
669C2×C4C2×#10211yescharacteristic
670C2×C4C22×C22⋊C411yescharacteristic
671C2×C4C22×D811yescharacteristic
672C8—21no—
673C8—21no—
674C8—21no—
675C8—21no—
676C8—21no—
677C8—21no—
678C8—21no—
679C8—21no—
680C8—42no—
681C8—81no—
682C8—81no—
683C8—81no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—82no—
699C22—82no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—322no—
710C22—322no—
711C22#214312yes—
712C22C22×#10211yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—81no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4#288311yescharacteristic
728C4#290111yescharacteristic
729C2—22no—
730C2—41no—
731C2—41no—
732C2—41no—
733C2—41no—
734C2—161no—
735C2—161no—
736C2—161no—
737C2#1761311yescharacteristic
738C2C2×#214311yescharacteristic
739C2#3339211yescharacteristic
subgroupG/H
center, socleC22C22×#102
commutatorC2×C8C23×C4
Frattini, cosocleC22×C8C24
prime radical#62251C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×C8×D4 ◁ G
LECSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #33487C2semidirect
3. #22717C2semidirect
4. #11895C2semidirect
5. #11894C2semidirect
6. #11893C2semidirect
7. #11891C2semidirect
8. #11866C2semidirect
9. #11864C2semidirect
10. #11751C2semidirect
11. #11750C2semidirect
12. #11711C2semidirect
13. #11710C2semidirect
14. #11709C2semidirect
15. C2×#1349C2semidirect
44. #2163C22semidirect
45. #2163C22semidirect
46. #2112C22semidirect
47. #2112C22semidirect
48. C2×C22⋊C16C22semidirect
49. C2×C22⋊C16C22semidirect
53. #1837C22semidirect
54. #1810C22semidirect
55. #1810C22semidirect
56. C4×#108C22semidirect
57. C2×#341C22semidirect
58. C2×#341C22semidirect
59. #1350C22semidirect
60. #1350C22semidirect
61. #1350C22semidirect
62. #1350C22semidirect
67. #1349C22semidirect
68. #1349C22semidirect
69. #1349C22semidirect
70. #1349C22semidirect
71. #1349C22semidirect
72. #1349C22semidirect
73. #1349C22semidirect
74. #1349C22semidirect

Maximal subgroups

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

subgroupindex
#622512
#334872
#227172
#118952
#118942
#118932
#118912
#118662
#118642
#117512
#117502
#117112
#117102
#117092
C2×#13492