Finite Group Databasebeta

← #7685417

Subgroups — #7685417

Order 512.

7459 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C22×Q82C211yesmaximal, characteristic, complemented
3#59655C213yesmaximal, complemented
4#59136C213yesmaximal, complemented
5#59125C216yesmaximal, complemented
6#59084C213yesmaximal, complemented
7#44937C216yesmaximal, complemented
8#44896C216yesmaximal, complemented
9#39168C213yesmaximal, complemented
10#39125C213yesmaximal, complemented
11#37704C216yesmaximal, complemented
12#36580C213yesmaximal, complemented
13#36576C211yesmaximal, characteristic, complemented
14Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
15#36457C211yesmaximal, characteristic, complemented
16#36434C212yesmaximal, complemented
17#36122C213yesmaximal, complemented
18#35948C212yesmaximal, complemented
19#35748C212yesmaximal, complemented
20#34708C213yesmaximal, complemented
21#34335C211yesmaximal, characteristic, complemented
22#34294C212yesmaximal, complemented
23C4×D4×Q8C211yesmaximal, characteristic, complemented
24#3522—216no—
25C2×#559C2213yes—
26C2×Q82—216no—
27C2×Q82C2213yes—
28C2×Q82C2213yes—
29C2×Q82C2216yes—
30C2×Q82C2211yescharacteristic
31C2×Q82C2212yes—
32C2×Q82C2211yescharacteristic
33C2×#554C2213yes—
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2212yes—
37C2×#548C2212yes—
38C2×#548C2216yes—
39C2×#547C2216yes—
40C2×#542C2216yes—
41C2×#532C2213yes—
42C22×C4⋊Q8C2213yes—
43C22×C4⋊Q8C2216yes—
44C2×#529C2213yes—
45C2×#520C2212yes—
46C22×C4×Q8C2211yescharacteristic
47C22×C4×Q8C2212yes—
48C22×C4×Q8C2211yescharacteristic
49C22×C4×Q8C2213yes—
50#2858C2213yes—
51#2857C2213yes—
52#2856C2213yes—
53#2850C2216yes—
54#2731C22112yes—
55#2729C22112yes—
56#2729C22112yes—
57#2716C22112yes—
58#2674C22112yes—
59#2674C22112yes—
60#2674C22112yes—
61#2640C2216yes—
62#2628C2216yes—
63#2592C2216yes—
64#2582C2213yes—
65#2580C2216yes—
66#2567C2213yes—
67#2563C2213yes—
68#2550C2216yes—
69#2548C2213yes—
70#2548C2213yes—
71#2547C2216yes—
72#2545C2216yes—
73#2545C2216yes—
74#2542C2216yes—
75#2538C2213yes—
76#2536C2216yes—
77#2492C2216yes—
78#2492C2216yes—
79#2491C2216yes—
80#2491C2216yes—
81#2491C2216yes—
82#2491C2216yes—
83#2491C2216yes—
84#2481C2216yes—
85#2469C2216yes—
86#2458C22112yes—
87#2458C2216yes—
88#2453C2213yes—
89#2452C2216yes—
90#2452C2216yes—
91#2452C2216yes—
92#2452C2216yes—
93#2451C2216yes—
94#2448C2213yes—
95#2448C2216yes—
96#2443C22112yes—
97#2443C2216yes—
98#2442C2213yes—
99#2440C2216yes—
100#2440C2216yes—
101#2440C2216yes—
102#2436C2216yes—
103#2436C2213yes—
104#2432C2216yes—
105#2432C22112yes—
106#2429C2216yes—
107#2429C22112yes—
108#2426C2216yes—
109#2426C2216yes—
110#2426C2213yes—
111#2421C2213yes—
112#2417C2216yes—
113#2416C2213yes—
114#2416C2216yes—
115#2416C2216yes—
116#2409C22112yes—
117#2409C2211yescharacteristic
118#2398C2216yes—
119#2396C2216yes—
120#2369C2213yes—
121#2367C2216yes—
122#2367C2216yes—
123#2365C2216yes—
124#2365C2213yes—
125#2361C2216yes—
126#2361C2216yes—
127#2360C2216yes—
128#2360C2213yes—
129#2360C2213yes—
130#2355C2213yes—
131#2351C2212yes—
132Q8×C4⋊C4C2211yescharacteristic
133Q8×C4⋊C4C2211yescharacteristic
134Q8×C4⋊C4C2212yes—
135D4×C4⋊C4C2216yes—
136D4×C4⋊C4C2213yes—
137#2341C2212yes—
138#2341C2212yes—
139#2341C2212yes—
140Q8×C22⋊C4C2212yes—
141Q8×C22⋊C4C2211yescharacteristic
142Q8×C22⋊C4C2211yescharacteristic
143#2331C2216yes—
144#2326C2216yes—
145#2323C2216yes—
146C4×C4⋊Q8C2213yes—
147C4×C4⋊Q8C2213yes—
148C4×#124C2213yes—
149C4×C22⋊Q8C2213yes—
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2213yes—
152C4×#121C2213yes—
153C4×#121C2216yes—
154C4×#121C2216yes—
155#2295C2213yes—
156#2290C2216yes—
157#2276C2212yes—
158C42×Q8C2211yescharacteristic
159C42×D4C2213yes—
160C22×#41C2312yes—
161C22×#41C2316yes—
162C23×Q8C2311yescharacteristic
163C23×Q8C2311yescharacteristic
164C23×Q8C2311yescharacteristic
165C23×Q8C2316yes—
166#559—224no—
167Q82—224no—
168Q82—248no—
169Q82—28no—
170Q82—216no—
171Q82—224no—
172Q82D4116yescomplemented
173#554—224no—
174#550—28no—
175D4×Q8—28no—
176#548—216no—
177#548—216no—
178#548—424no—
179#547—248no—
180#542—248no—
181#532—224no—
182C2×C4⋊Q8—224no—
183C2×C4⋊Q8—248no—
184C2×C4⋊Q8C2313yes—
185C2×C4⋊Q8C2313yes—
186C2×C4⋊Q8C2316yes—
187C2×C4⋊Q8C23112yes—
188C2×C4⋊Q8C23112yes—
189C2×C4⋊Q8C2316yes—
190C2×C4⋊Q8C2316yes—
191C2×C4⋊Q8C2316yes—
192C2×C4⋊Q8C2316yes—
193C2×C4⋊Q8C2316yes—
194C2×C4⋊Q8C2313yes—
195C2×C4⋊Q8C2316yes—
196C2×#127C2313yes—
197#529—224no—
198C2×#126C2316yes—
199C2×#125C2313yes—
200C2×#124C2316yes—
201C2×#124C2316yes—
202C2×#124C2313yes—
203C2×#124C2313yes—
204C2×#124C2316yes—
205C2×#124C2316yes—
206C2×#124C23112yes—
207C2×#124C2316yes—
208C2×#123C2316yes—
209C2×#123C23112yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2313yes—
212C2×C22⋊Q8C2313yes—
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C23112yes—
216C2×C22⋊Q8C2316yes—
217C2×C22⋊Q8C2316yes—
218C2×C22⋊Q8C23112yes—
219C2×C22⋊Q8C23112yes—
220C2×#121C2316yes—
221C2×#121C2313yes—
222C2×#121C2313yes—
223C2×#121C2316yes—
224C2×#121C2316yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227#520—216no—
228C2×C4×Q8—28no—
229C2×C4×Q8—216no—
230C2×C4×Q8—224no—
231C2×C4×Q8—28no—
232C2×C4×Q8C2313yes—
233C2×C4×Q8C2313yes—
234C2×C4×Q8C2316yes—
235C2×C4×Q8C2316yes—
236C2×C4×Q8C2313yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2313yes—
244C2×C4×Q8C2313yes—
245C2×C4×Q8C2316yes—
246C2×C4×Q8C2313yes—
247C2×C4×Q8C2313yes—
248C2×C4×Q8C2316yes—
249C2×C4×Q8C2316yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2313yes—
253C2×C4×D4C2313yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C23112yes—
263C2×#117C2316yes—
264C22×C4⋊C4C2313yes—
265C22×C4⋊C4C2313yes—
266C22×C4⋊C4C2316yes—
267C22×C4⋊C4C2316yes—
268C22×C4⋊C4C2313yes—
269C22×C4⋊C4C2316yes—
270C22×C42C2316yes—
271C22×C42C2313yes—
272C22×C42C2313yes—
273#400C2316yes—
274#400C2316yes—
275#400C2316yes—
276#399C23112yes—
277#399C2316yes—
278#398C23112yes—
279#398C2316yes—
280#398C2316yes—
281#398C23112yes—
282#397C23112yes—
283#397C2316yes—
284#397C2316yes—
285#396C2316yes—
286#396C2316yes—
287#396C23112yes—
288#396C23112yes—
289#396C23112yes—
290#395C23112yes—
291#395C23112yes—
292#395C2312yes—
293#394C2316yes—
294#394C2316yes—
295#394C23112yes—
296#394C23112yes—
297#394C23112yes—
298#393C23112yes—
299#393C2316yes—
300#393C2316yes—
301#393C23112yes—
302#393C23112yes—
303#393C23112yes—
304#393C2312yes—
305#391C2313yes—
306#391C2316yes—
307#391C2313yes—
308#391C2316yes—
309#391C2313yes—
310#391C2313yes—
311#391C2316yes—
312#391C23112yes—
313#391C2313yes—
314#391C2316yes—
315#391C2313yes—
316#391C23112yes—
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#390C2316yes—
320#390C2316yes—
321#390C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2316yes—
328#390C2313yes—
329#390C2316yes—
330#390C2313yes—
331#389C2313yes—
332#389C2316yes—
333#389C2316yes—
334#389C2316yes—
335#389C2313yes—
336#389C2316yes—
337#389C2316yes—
338#389C23112yes—
339#389C2313yes—
340#389C2316yes—
341#389C2316yes—
342#389C2316yes—
343#389C2313yes—
344#389C2313yes—
345#389C2313yes—
346#389C2316yes—
347#388C23112yes—
348#388C23112yes—
349#388C2316yes—
350#388C23112yes—
351#388C23112yes—
352#388C23112yes—
353#388C23112yes—
354#388C2316yes—
355#388C2316yes—
356#388C2316yes—
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#387C2316yes—
361#387C2316yes—
362#387C23112yes—
363#387C2316yes—
364#387C2316yes—
365#387C2316yes—
366#387C2316yes—
367#387C2316yes—
368#386C2316yes—
369#386C23112yes—
370#386C2316yes—
371#386C2316yes—
372#386C2312yes—
373#386C2316yes—
374#385C23112yes—
375#385C23112yes—
376#385C23112yes—
377#385C23112yes—
378#385C2316yes—
379#385C2316yes—
380#385C2316yes—
381#385C2312yes—
382#385C2316yes—
383#384C2313yes—
384#384C2313yes—
385#384C2316yes—
386#382C2313yes—
387#382C2316yes—
388#380C2316yes—
389#380C2316yes—
390#380C2316yes—
391#380C2313yes—
392#380C2313yes—
393#380C2316yes—
394#380C2313yes—
395#380C2316yes—
396#380C2311yescharacteristic
397C4×C4⋊C4C2313yes—
398C4×C4⋊C4C2316yes—
399C4×C4⋊C4C2316yes—
400C4×C4⋊C4C2316yes—
401C4×C4⋊C4C2313yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2313yes—
408C4×C4⋊C4C2316yes—
409C4×C4⋊C4C2316yes—
410C4×C4⋊C4C2313yes—
411C4×C22⋊C4C2313yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2313yes—
419C4×C22⋊C4C23112yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2313yes—
422#376C2316yes—
423C43C2313yes—
424C2×#41—28no—
425C2×#41—224no—
426C2×#41—28no—
427C2×#41—28no—
428C2×#41—412no—
429C2×#41—86no—
430C22×Q8—24no—
431C22×Q8—24no—
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8—24no—
436C22×Q8—24no—
437C22×Q8—224no—
438C22×Q8—24no—
439C22×Q8—412no—
440C22×Q8—86no—
441C22×Q8#4118yescomplemented
442C22×Q8C2412yes—
443C22×Q8C2413yes—
444C22×Q8C2411yescharacteristic
445C22×Q8C2413yes—
446C22×Q8C2411yescharacteristic
447C22×Q8C24112yes—
448C22×Q8C2416yes—
449C22×Q8C2416yes—
450C22×Q8C2411yescharacteristic
451C22×D4C2416yes—
452C22×D4C2413yes—
453C22×D4C2416yes—
454C22×D4C2416yes—
455C22×D4C2411yescharacteristic
456C22×D4C2416yes—
457C23×C4C2412yes—
458C23×C4C2416yes—
459C23×C4C2413yes—
460C23×C4C2411yescharacteristic
461C23×C4C2416yes—
462C23×C4C2413yes—
463C23×C4C2413yes—
464C23×C4C2413yes—
465C23×C4C2411yescharacteristic
466C23×C4C24112yes—
467C4⋊Q8—248no—
468C4⋊Q8—224no—
469C4⋊Q8—212no—
470C4⋊Q8—224no—
471C4⋊Q8—224no—
472C4⋊Q8—224no—
473C4⋊Q8—224no—
474C4⋊Q8—248no—
475C4⋊Q8—212no—
476C4⋊Q8—224no—
477C4⋊Q8C2×D4124yes—
478C4⋊Q8C2×D4148yes—
479#127—212no—
480#126—224no—
481#125—212no—
482#124—212no—
483#124—224no—
484#124—224no—
485#124—212no—
486#124—224no—
487#124—412no—
488#124—424no—
489#124—86no—
490#123—224no—
491#123—248no—
492C22⋊Q8—24no—
493C22⋊Q8—248no—
494C22⋊Q8—224no—
495C22⋊Q8—212no—
496C22⋊Q8—24no—
497C22⋊Q8—212no—
498C22⋊Q8—224no—
499C22⋊Q8—412no—
500C22⋊Q8—424no—
501C22⋊Q8—812no—
502#121—224no—
503#121—224no—
504#121—212no—
505#121—212no—
506#121—224no—
507#121—224no—
508#121—412no—
509C4×Q8—24no—
510C4×Q8—212no—
511C4×Q8—24no—
512C4×Q8—28no—
513C4×Q8—28no—
514C4×Q8—24no—
515C4×Q8—24no—
516C4×Q8—212no—
517C4×Q8—224no—
518C4×Q8—212no—
519C4×Q8—212no—
520C4×Q8—224no—
521C4×Q8—212no—
522C4×Q8—212no—
523C4×Q8—212no—
524C4×Q8—224no—
525C4×Q8—224no—
526C4×Q8—412no—
527C4×Q8C2×D418yes—
528C4×Q8C2×D4116yes—
529C4×Q8C2×D4124yes—
530C4×D4—212no—
531C4×D4—224no—
532C4×D4—212no—
533C4×D4—24no—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—224no—
537C4×D4—224no—
538C4×D4—212no—
539C4×D4—424no—
540#117—224no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—212no—
543C2×C4⋊C4—212no—
544C2×C4⋊C4—224no—
545C2×C4⋊C4—212no—
546C2×C4⋊C4—224no—
547C2×C4⋊C4C2413yes—
548C2×C4⋊C4C2416yes—
549C2×C4⋊C4C2416yes—
550C2×C4⋊C4C2413yes—
551C2×C4⋊C4C2416yes—
552C2×C4⋊C4C2413yes—
553C2×C4⋊C4C2416yes—
554C2×C4⋊C4C2416yes—
555C2×C4⋊C4C24112yes—
556C2×C4⋊C4C2416yes—
557C2×C4⋊C4C2416yes—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C24112yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2413yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2416yes—
583C2×C22⋊C4C2416yes—
584C2×C22⋊C4C2416yes—
585C2×C22⋊C4C2413yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C24112yes—
590C2×C22⋊C4C2413yes—
591C2×C22⋊C4C2413yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2413yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2411yescharacteristic
596C2×C22⋊C4C2411yescharacteristic
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C24112yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C24112yes—
605C2×C22⋊C4C24112yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C24112yes—
608C2×C22⋊C4C2416yes—
609C2×C42—212no—
610C2×C42—224no—
611C2×C42—212no—
612C2×C42C2413yes—
613C2×C42C2413yes—
614C2×C42C2413yes—
615C2×C42C2416yes—
616C2×C42C2413yes—
617C2×C42C2411yescharacteristic
618C2×C42C2413yes—
619C2×C42C2416yes—
620C2×C42C2416yes—
621C2×C42C2413yes—
622C2×C42C2413yes—
623C2×C42C2416yes—
624C2×C42C2413yes—
625C2×C42C2413yes—
626C2×C42C2413yes—
627C2×C42C24112yes—
628C2×C42C2413yes—
629C2×C42C2416yes—
630C2×C42C2413yes—
631#95C2412yes—
632#95C2416yes—
633#95C2416yes—
634#95C2416yes—
635#95C2412yes—
636#95C2412yes—
637#95C2412yes—
638#95C2416yes—
639#95C2413yes—
640#95C2413yes—
641#95C2416yes—
642#95C2413yes—
643#95C2413yes—
644#95C2413yes—
645#95C2413yes—
646#95C2416yes—
647#95C2416yes—
648#95C2416yes—
649#95C2416yes—
650#95C2416yes—
651#95C2416yes—
652#95C2412yes—
653#95C2416yes—
654#95C2416yes—
655#95C2416yes—
656#95C24112yes—
657#95C2416yes—
658#95C24112yes—
659C24C2516yes—
660C24C2511yescharacteristic
661C24C2511yescharacteristic
662#41—432no—
663#41—848no—
664C2×Q8—232no—
665C2×Q8—232no—
666C2×Q8—24no—
667C2×Q8—26no—
668C2×Q8—22no—
669C2×Q8—26no—
670C2×Q8—212no—
671C2×Q8—224no—
672C2×Q8—26no—
673C2×Q8—24no—
674C2×Q8—24no—
675C2×Q8—26no—
676C2×Q8—22no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—26no—
680C2×Q8—46no—
681C2×Q8—46no—
682C2×Q8—46no—
683C2×Q8—412no—
684C2×Q8—412no—
685C2×Q8—46no—
686C2×Q8—416no—
687C2×Q8—848no—
688C2×Q8C22×D414yes—
689C2×Q8C22×D4124yes—
690C2×Q8C22×D414yes—
691C2×Q8C2×#41112yes—
692C2×Q8C2×#4114yes—
693C2×Q82−1+414yes—
694C2×Q82−1+414yes—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—212no—
698C2×D4—212no—
699C2×D4—212no—
700C2×D4—212no—
701C2×D4—26no—
702C2×D4—212no—
703C2×D4—212no—
704C2×D4—212no—
705C2×D4—212no—
706C2×D4—26no—
707C2×D4—26no—
708C2×D4—212no—
709C2×D4—46no—
710C2×D4—46no—
711C2×D4—46no—
712C2×D4H(5,𝔽2)14yes—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—26no—
716C22×C4—22no—
717C22×C4—24no—
718C22×C4—26no—
719C22×C4—22no—
720C22×C4—26no—
721C22×C4—26no—
722C22×C4—212no—
723C22×C4—22no—
724C22×C4—26no—
725C22×C4—212no—
726C22×C4—26no—
727C22×C4—26no—
728C22×C4—212no—
729C22×C4—26no—
730C22×C4—212no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—26no—
734C22×C4—212no—
735C22×C4—224no—
736C22×C4—43no—
737C22×C4—46no—
738C22×C4—43no—
739C22×C4—412no—
740C22×C4—412no—
741C22×C4C2×#41112yes—
742C22×C42−1+414yes—
743C22×C4C2511yescharacteristic
744C22×C4C2513yes—
745C22×C4C2511yescharacteristic
746C22×C4C2512yes—
747C22×C4C2513yes—
748C22×C4C2516yes—
749C22×C4C2513yes—
750C22×C4C2512yes—
751C22×C4C2516yes—
752C22×C4C2513yes—
753C22×C4C2513yes—
754C22×C4C2512yes—
755C22×C4C2513yes—
756C22×C4C2516yes—
757C22×C4C2513yes—
758C22×C4C2511yescharacteristic
759C22×C4C2512yes—
760C22×C4C2511yescharacteristic
761C22×C4C2513yes—
762C22×C4C2511yescharacteristic
763C4⋊C4—26no—
764C4⋊C4—212no—
765C4⋊C4—212no—
766C4⋊C4—212no—
767C4⋊C4—212no—
768C4⋊C4—212no—
769C4⋊C4—212no—
770C4⋊C4—224no—
771C4⋊C4—212no—
772C4⋊C4—212no—
773C4⋊C4—26no—
774C4⋊C4—26no—
775C4⋊C4—24no—
776C4⋊C4—22no—
777C4⋊C4—212no—
778C4⋊C4—212no—
779C4⋊C4—26no—
780C4⋊C4—212no—
781C4⋊C4—26no—
782C4⋊C4—212no—
783C4⋊C4—26no—
784C4⋊C4—212no—
785C4⋊C4—22no—
786C4⋊C4—26no—
787C4⋊C4—26no—
788C4⋊C4—22no—
789C4⋊C4—24no—
790C4⋊C4—412no—
791C4⋊C4—46no—
792C4⋊C4—46no—
793C4⋊C4—46no—
794C4⋊C4—46no—
795C4⋊C4C22×D4124yes—
796C4⋊C4C22×D4112yes—
797C4⋊C4C22×D4112yes—
798C4⋊C4C22×D4124yes—
799C22⋊C4—24no—
800C22⋊C4—26no—
801C22⋊C4—26no—
802C22⋊C4—26no—
803C22⋊C4—212no—
804C22⋊C4—22no—
805C22⋊C4—212no—
806C22⋊C4—212no—
807C22⋊C4—24no—
808C22⋊C4—212no—
809C22⋊C4—224no—
810C22⋊C4—212no—
811C22⋊C4—26no—
812C22⋊C4—212no—
813C22⋊C4—224no—
814C22⋊C4—212no—
815C22⋊C4—22no—
816C22⋊C4—212no—
817C22⋊C4—24no—
818C22⋊C4—212no—
819C22⋊C4—212no—
820C22⋊C4—412no—
821C22⋊C4—412no—
822C22⋊C4—46no—
823C22⋊C4—412no—
824C22⋊C4—46no—
825C42—26no—
826C42—26no—
827C42—26no—
828C42—212no—
829C42—212no—
830C42—26no—
831C42—212no—
832C42—26no—
833C42—26no—
834C42—212no—
835C42—26no—
836C42—26no—
837C42—22no—
838C42—26no—
839C42—26no—
840C42—412no—
841C42—43no—
842C42C22×D4112yes—
843C42C22×D4124yes—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—26no—
855C23—26no—
856C23—26no—
857C23—26no—
858C23—26no—
859C23—26no—
860C23—26no—
861C23C22×#4112yes—
862C23C2×H(5,𝔽2)12yes—
863C23C2×H(5,𝔽2)12yes—
864C23C2×2−1+412yes—
865C23C2611yescharacteristic
866Q8—216no—
867Q8—224no—
868Q8—28no—
869Q8—28no—
870Q8—424no—
871Q8—412no—
872Q8—812no—
873Q8—824no—
874Q8#548116yescomplemented
875D4—28no—
876D4—424no—
877D4—424no—
878D4—424no—
879D4—412no—
880D4—812no—
881C2×C4—216no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—23no—
885C2×C4—21no—
886C2×C4—23no—
887C2×C4—26no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—23no—
894C2×C4—23no—
895C2×C4—26no—
896C2×C4—224no—
897C2×C4—28no—
898C2×C4—21no—
899C2×C4—23no—
900C2×C4—23no—
901C2×C4—26no—
902C2×C4—23no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—23no—
906C2×C4—26no—
907C2×C4—22no—
908C2×C4—23no—
909C2×C4—23no—
910C2×C4—26no—
911C2×C4—26no—
912C2×C4—23no—
913C2×C4—23no—
914C2×C4—21no—
915C2×C4—23no—
916C2×C4—23no—
917C2×C4—21no—
918C2×C4—23no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—26no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—23no—
925C2×C4—21no—
926C2×C4—23no—
927C2×C4—22no—
928C2×C4—26no—
929C2×C4—23no—
930C2×C4—23no—
931C2×C4—412no—
932C2×C4—424no—
933C2×C4—412no—
934C2×C4—412no—
935C2×C4—424no—
936C2×C4—44no—
937C2×C4—824no—
938C2×C4C23×D414yes—
939C2×C4C23×D416yes—
940C2×C4C23×D4112yes—
941C2×C4C23×D416yes—
942C2×C4C23×D412yes—
943C2×C4C22×#4116yes—
944C2×C4C22×#4116yes—
945C2×C4C2×H(5,𝔽2)12yes—
946C2×C4C2×2−1+414yes—
947C2×C4C2×2−1+412yes—
948C2×C4C2×2−1+416yes—
949C2×C4C2×2−1+412yes—
950C2×C4C2×2−1+412yes—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—46no—
965C22—46no—
966C22—46no—
967C22—46no—
968C22—46no—
969C22—46no—
970C22—46no—
971C22#352214yescomplemented
972C22C24×D411yescharacteristic
973C22C23×#4111yescharacteristic
974C22C22×H(5,𝔽2)11yescharacteristic
975C22C22×2−1+411yescharacteristic
976C22C22×2−1+411yescharacteristic
977C22C22×2−1+411yescharacteristic
978C22H(7,𝔽2)11yescharacteristic
979C4—26no—
980C4—212no—
981C4—24no—
982C4—24no—
983C4—22no—
984C4—22no—
985C4—26no—
986C4—43no—
987C4—46no—
988C4—43no—
989C4—42no—
990C4—43no—
991C4—43no—
992C4—41no—
993C4—46no—
994C4—41no—
995C4—42no—
996C4—43no—
997C4C2×#548112yes—
998C4#348614yes—
999C2—24no—
1000C2—42no—
1001C2—86no—
1002C2C22×#54811yescharacteristic
1003C2C2×#348611yescharacteristic
1004C2C2×#352211yescharacteristic
1005C2#6294311yescharacteristic
1006C2D4×H(5,𝔽2)11yescharacteristic
1007C2#6299911yescharacteristic
1008C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3522C2semidirect
2. C22×Q82C2semidirect
3. #59655C2semidirect
4. #59136C2semidirect
5. #59125C2semidirect
6. #59084C2semidirect
7. #44937C2semidirect
8. #44896C2semidirect
9. #39168C2semidirect
10. #39125C2semidirect
11. #37704C2semidirect
12. #36580C2semidirect
13. #36576C2semidirect
14. Q8×C22⋊Q8C2semidirect
15. #36457C2semidirect
16. #36434C2semidirect
17. #36122C2semidirect
18. #35948C2semidirect
19. #35748C2semidirect
20. #34708C2semidirect
21. #34335C2semidirect
22. #34294C2semidirect
23. C4×D4×Q8C2semidirect
172. Q82D4semidirect
441. C22×Q8#41semidirect
874. Q8#548semidirect
971. C22#3522semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C22×Q822
#596552
#591362
#591252
#590842
#449372
#448962
#391682
#391252
#377042
#365802
#365762
Q8×C22⋊Q82
#364572
#364342
#361222
#359482
#357482
#347082
#343352
#342942
C4×D4×Q82