Finite Group Databasebeta

← #7684113

Subgroups — #7684113

Order 512.

10950 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3486C212yesmaximal, complemented
2C22×D4×Q8C212yesmaximal, complemented
3#59127C216yesmaximal, complemented
4#59005C216yesmaximal, complemented
5#58998C213yesmaximal, complemented
6#45418C213yesmaximal, complemented
7#45321C213yesmaximal, complemented
8#45248C216yesmaximal, complemented
9#37675C216yesmaximal, complemented
10#37651C216yesmaximal, complemented
11#36575C211yesmaximal, characteristic, complemented
12Q8×#120C212yesmaximal, complemented
13#36434C212yesmaximal, complemented
14#36097C216yesmaximal, complemented
15#35927C211yesmaximal, characteristic, complemented
16#35700C212yesmaximal, complemented
17#35687C211yesmaximal, characteristic, complemented
18#34655C213yesmaximal, complemented
19#34291C212yesmaximal, complemented
20C22×2−1+4C2211yescharacteristic, complemented
21C24×Q8C2211yescharacteristic
22C24×Q8C2212yescomplemented
23#3486—232no—
24C2×D4×Q8—232no—
25C2×D4×Q8C2216yes—
26C2×D4×Q8C2212yes—
27C2×D4×Q8C2216yes—
28C2×D4×Q8C2212yes—
29C2×D4×Q8C2216yescomplemented
30C2×D4×Q8C2216yescomplemented
31C2×D4×Q8C2212yescomplemented
32C2×D4×Q8C2216yescomplemented
33C2×D4×Q8C2212yescomplemented
34C2×D4×Q8C2212yescomplemented
35C2×D4×Q8C2216yescomplemented
36C2×D4×Q8C2211yescharacteristic, complemented
37C2×#548C2216yes—
38C2×#548C2212yescomplemented
39C2×#548C2212yescomplemented
40C2×#548C2216yescomplemented
41C2×#548C2211yescharacteristic, complemented
42C2×#536C2216yescomplemented
43C2×#536C2216yescomplemented
44C22×C4⋊Q8C2216yescomplemented
45C2×#525C2216yes—
46C2×#525C2216yescomplemented
47C22×C22⋊Q8C2216yes—
48C22×C22⋊Q8C2216yescomplemented
49C2×#519C2212yescomplemented
50C22×C4×Q8C2212yescomplemented
51C22×C4×D4C2216yes—
52#2850C2216yescomplemented
53#2848C2216yescomplemented
54#2847C2213yes—
55#2683C2216yescomplemented
56#2681C22112yescomplemented
57#2680C2216yescomplemented
58#2677C2216yescomplemented
59#2677C22112yescomplemented
60#2677C2216yescomplemented
61#2677C22112yescomplemented
62#2674C22112yescomplemented
63#2674C22112yescomplemented
64#2658C2213yescomplemented
65#2621C2216yescomplemented
66#2616C2213yescomplemented
67#2551C2216yescomplemented
68#2546C2216yescomplemented
69#2545C2216yescomplemented
70#2542C2213yescomplemented
71#2542C2216yescomplemented
72#2540C2216yescomplemented
73#2540C2213yescomplemented
74#2536C2216yescomplemented
75#2536C2216yescomplemented
76#2472C22112yescomplemented
77#2463C2213yes—
78#2463C22112yescomplemented
79#2463C2216yescomplemented
80#2461C22112yescomplemented
81#2456C2216yes—
82#2455C2213yes—
83#2452C22112yescomplemented
84#2449C2216yes—
85#2449C22112yescomplemented
86#2449C22112yescomplemented
87#2443C22112yes—
88#2443C2216yes—
89#2440C22112yescomplemented
90#2437C2213yes—
91#2436C2216yescomplemented
92#2436C2213yescomplemented
93#2434C2216yescomplemented
94#2434C2216yescomplemented
95#2434C2213yescomplemented
96#2434C2216yescomplemented
97#2432C2216yescomplemented
98#2429C2216yescomplemented
99#2429C2216yescomplemented
100#2429C2216yescomplemented
101#2426C2216yescomplemented
102#2424C2216yes—
103#2418C2216yes—
104#2417C2216yescomplemented
105#2416C2216yes—
106#2415C2216yescomplemented
107#2415C2216yescomplemented
108#2410C2216yes—
109#2409C2216yes—
110#2409C2213yescomplemented
111#2409C2216yescomplemented
112#2409C2216yescomplemented
113#2409C2213yescomplemented
114#2409C2216yescomplemented
115#2407C2216yescomplemented
116#2403C2211yescharacteristic
117#2397C2213yes—
118#2392C2216yes—
119#2388C2213yes—
120#2365C2216yescomplemented
121#2362C2216yescomplemented
122#2361C22112yes—
123#2360C2216yescomplemented
124#2358C2216yes—
125#2352C2216yes—
126#2351C2212yescomplemented
127#2341C2211yescharacteristic, complemented
128Q8×C22⋊C4C2212yescomplemented
129Q8×C22⋊C4C2212yescomplemented
130Q8×C22⋊C4C2211yescharacteristic, complemented
131Q8×C22⋊C4C2212yescomplemented
132#2327C2216yescomplemented
133#2323C2216yescomplemented
134C4×C22⋊Q8C2216yescomplemented
135C4×#121C2216yes—
136C4×#120C2213yes—
137C4×#120C2216yes—
138#2290C2216yes—
139#2276C2211yescharacteristic, complemented
140C2×2−1+4—216no—
141C2×2−1+4—44no—
142C22×#41C2311yescharacteristic
143C22×#41C2313yes—
144C22×#41C2316yes—
145C23×Q8—216no—
146C23×Q8—216no—
147C23×Q8—216no—
148C23×Q8—44no—
149C23×Q8—48no—
150C23×Q8C2311yescharacteristic
151C23×Q8C2312yes—
152C23×Q8C2316yes—
153C23×Q8C2313yes—
154C23×Q8C2316yes—
155C23×Q8C2316yes—
156C23×Q8C2316yes—
157C23×Q8C2313yes—
158C23×Q8C2312yes—
159C23×Q8C2312yes—
160C23×D4C2312yes—
161C24×C4C2313yes—
162C24×C4C2316yes—
163D4×Q8—216no—
164D4×Q8—216no—
165D4×Q8—216no—
166D4×Q8—248no—
167D4×Q8—248no—
168D4×Q8—248no—
169D4×Q8—248no—
170D4×Q8—248no—
171D4×Q8—216no—
172D4×Q8—248no—
173D4×Q8—44no—
174D4×Q8D4132yescomplemented
175#548—216no—
176#548—248no—
177#548—216no—
178#548—248no—
179#548—44no—
180#536—248no—
181#536—248no—
182C2×C4⋊Q8—248no—
183C2×C4⋊Q8C2316yes—
184C2×C4⋊Q8C23112yes—
185C2×C4⋊Q8C23112yes—
186C2×C4⋊Q8C2316yes—
187C2×C4⋊Q8C2316yes—
188C2×C4⋊Q8C23112yes—
189C2×C4⋊Q8C2316yes—
190C2×C4⋊Q8C2313yes—
191C2×C4⋊Q8C2316yes—
192C2×#124C2316yes—
193C2×#124C23112yes—
194C2×#124C2316yes—
195C2×#124C2313yes—
196#525—248no—
197#525—248no—
198C2×#123C2316yes—
199C2×#123C2316yes—
200C2×#123C23112yes—
201C2×C22⋊Q8—248no—
202C2×C22⋊Q8—248no—
203C2×C22⋊Q8C2316yes—
204C2×C22⋊Q8C2316yes—
205C2×C22⋊Q8C2316yes—
206C2×C22⋊Q8C2316yes—
207C2×C22⋊Q8C2316yes—
208C2×C22⋊Q8C2316yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C23112yes—
212C2×C22⋊Q8C23112yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C23112yes—
215C2×C22⋊Q8C23112yes—
216C2×C22⋊Q8C2316yes—
217C2×C22⋊Q8C2316yes—
218C2×C22⋊Q8C2316yes—
219C2×C22⋊Q8C23112yes—
220C2×C22⋊Q8C23112yes—
221C2×C22⋊Q8C2316yes—
222C2×C22⋊Q8C2313yes—
223C2×C22⋊Q8C2316yes—
224C2×C22⋊Q8C2316yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227C2×#121C2316yes—
228C2×#121C2316yes—
229C2×#121C2316yes—
230C2×#121C2313yes—
231C2×#120C2313yes—
232C2×#120C2312yes—
233C2×#120C2312yes—
234C2×#120C2316yes—
235#519—216no—
236C2×C4×Q8—216no—
237C2×C4×Q8C2316yes—
238C2×C4×Q8C2316yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2316yes—
243C2×C4×Q8C2316yes—
244C2×C4×Q8C2312yes—
245C2×C4×D4—248no—
246C2×C4×D4C23112yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C23112yes—
249C2×C4×D4C2316yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2316yes—
261C2×#117C2316yes—
262C2×#117C2316yes—
263C22×C4⋊C4C2316yes—
264C22×C4⋊C4C23112yes—
265C22×C4⋊C4C2316yes—
266C22×C22⋊C4C2316yes—
267C22×C22⋊C4C2316yes—
268C22×C42C2316yes—
269#399C2313yes—
270#399C2316yes—
271#399C2313yes—
272#399C2316yes—
273#399C23112yes—
274#398C23112yes—
275#398C23112yes—
276#398C2316yes—
277#398C23112yes—
278#397C2316yes—
279#397C23112yes—
280#396C2316yes—
281#396C2316yes—
282#396C23112yes—
283#396C23112yes—
284#395C2316yes—
285#395C2313yes—
286#395C23112yes—
287#395C2316yes—
288#395C23112yes—
289#395C23112yes—
290#394C2313yes—
291#394C23112yes—
292#394C2316yes—
293#394C2316yes—
294#394C2316yes—
295#394C2316yes—
296#394C23112yes—
297#393C2313yes—
298#393C23112yes—
299#393C2316yes—
300#393C23112yes—
301#392C2311yescharacteristic
302#392C2316yes—
303#392C2312yes—
304#392C2311yescharacteristic
305#392C2316yes—
306#392C2313yes—
307#391C2316yes—
308#391C2316yes—
309#391C2316yes—
310#391C2316yes—
311#391C2316yes—
312#391C2316yes—
313#391C2316yes—
314#390C2316yes—
315#390C2316yes—
316#390C23112yes—
317#390C2316yes—
318#389C2316yes—
319#389C23112yes—
320#389C2316yes—
321#389C23112yes—
322#389C23112yes—
323#389C2316yes—
324#388C2316yes—
325#388C23112yes—
326#388C23112yes—
327#388C23112yes—
328#388C23112yes—
329#388C23112yes—
330#388C2316yes—
331#388C2316yes—
332#388C2316yes—
333#387C23112yes—
334#387C2316yes—
335#387C23112yes—
336#387C23112yes—
337#387C2316yes—
338#386C23112yes—
339#386C2316yes—
340#386C2316yes—
341#386C23112yes—
342#386C2316yes—
343#386C2316yes—
344#386C2316yes—
345#386C2312yes—
346#386C2312yes—
347#386C2316yes—
348#386C2316yes—
349#386C2316yes—
350#386C2313yes—
351#385C23112yes—
352#385C23112yes—
353#385C23112yes—
354#385C2316yes—
355#385C23112yes—
356#385C2316yes—
357#385C2313yes—
358#385C2316yes—
359#385C2316yes—
360#385C2316yes—
361#385C2316yes—
362#385C2316yes—
363#384C2316yes—
364#382C2316yes—
365#380C2316yes—
366#380C2316yes—
367#380C2313yes—
368#380C2316yes—
369#380C2313yes—
370#380C2316yes—
371#379C2316yes—
372#379C2311yescharacteristic
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C23112yes—
377C4×C22⋊C4C2316yes—
378C4×C22⋊C4C2316yes—
379C4×C22⋊C4C2313yes—
380C4×C22⋊C4C2316yes—
381C4×C22⋊C4C2313yes—
382C4×C22⋊C4C23112yes—
383#376C2313yes—
384C25C2412yes—
385C25C2411yescharacteristic
3862−1+4—464no—
387C2×#41—224no—
388C2×#41—28no—
389C2×#41—24no—
390C2×#41—224no—
391C2×#41—224no—
392C2×#41—46no—
393C2×#41—412no—
394C22×Q8—28no—
395C22×Q8—28no—
396C22×Q8—28no—
397C22×Q8—28no—
398C22×Q8—224no—
399C22×Q8—224no—
400C22×Q8—224no—
401C22×Q8—224no—
402C22×Q8—28no—
403C22×Q8—224no—
404C22×Q8—224no—
405C22×Q8—28no—
406C22×Q8—28no—
407C22×Q8—224no—
408C22×Q8—24no—
409C22×Q8—28no—
410C22×Q8—224no—
411C22×Q8—224no—
412C22×Q8—224no—
413C22×Q8—412no—
414C22×Q8—412no—
415C22×Q8—412no—
416C22×Q8—46no—
417C22×Q8—412no—
418C22×Q8—46no—
419C22×Q8—464no—
420C22×Q8—4128no—
421C22×Q8C2×D4116yes—
422C22×Q8C2×D4116yescomplemented
423C22×Q8C2416yes—
424C22×Q8C2413yes—
425C22×Q8C24112yes—
426C22×Q8C2416yes—
427C22×Q8C2413yes—
428C22×Q8C2416yes—
429C22×Q8C2416yes—
430C22×Q8C2411yescharacteristic
431C22×D4—28no—
432C22×D4—28no—
433C22×D4—28no—
434C22×D4C2412yes—
435C22×D4C2412yes—
436C22×D4C2416yes—
437C22×D4C2413yes—
438C22×D4C2412yes—
439C22×D4C2411yescharacteristic
440C22×D4C2416yes—
441C22×D4C2411yescharacteristic
442C22×D4C2416yes—
443C22×D4C2412yes—
444C22×D4C2412yes—
445C22×D4C2413yes—
446C23×C4—224no—
447C23×C4—224no—
448C23×C4—224no—
449C23×C4—46no—
450C23×C4—412no—
451C23×C4C2412yes—
452C23×C4C2416yes—
453C23×C4C2413yes—
454C23×C4C2413yes—
455C23×C4C2416yes—
456C23×C4C2416yes—
457C23×C4C2416yes—
458C23×C4C2416yes—
459C23×C4C2413yes—
460C23×C4C2416yes—
461C23×C4C2416yes—
462C23×C4C2416yes—
463C23×C4C2416yes—
464C4⋊Q8—224no—
465C4⋊Q8—224no—
466C4⋊Q8—224no—
467C4⋊Q8—248no—
468C4⋊Q8—248no—
469C4⋊Q8—248no—
470C4⋊Q8—224no—
471C4⋊Q8—46no—
472C4⋊Q8C2×D4148yescomplemented
473#124—224no—
474#124—248no—
475#124—224no—
476#124—46no—
477#123—224no—
478#123—248no—
479#123—224no—
480C22⋊Q8—224no—
481C22⋊Q8—224no—
482C22⋊Q8—224no—
483C22⋊Q8—224no—
484C22⋊Q8—224no—
485C22⋊Q8—224no—
486C22⋊Q8—224no—
487C22⋊Q8—248no—
488C22⋊Q8—248no—
489C22⋊Q8—224no—
490C22⋊Q8—224no—
491C22⋊Q8—224no—
492C22⋊Q8—248no—
493C22⋊Q8—248no—
494C22⋊Q8—224no—
495C22⋊Q8—248no—
496C22⋊Q8—248no—
497C22⋊Q8—224no—
498C22⋊Q8—46no—
499C22⋊Q8—412no—
500C22⋊Q8C2×D4148yes—
501C22⋊Q8C2×D4148yescomplemented
502#121—224no—
503#121—224no—
504#121—224no—
505#121—224no—
506#121—224no—
507#121—46no—
508#120—212no—
509#120—28no—
510#120—28no—
511#120—224no—
512C4×Q8—28no—
513C4×Q8—28no—
514C4×Q8—24no—
515C4×Q8—224no—
516C4×Q8—224no—
517C4×Q8—224no—
518C4×Q8—224no—
519C4×Q8C2×D4116yescomplemented
520C4×D4—224no—
521C4×D4—224no—
522C4×D4—224no—
523C4×D4—224no—
524C4×D4—224no—
525C4×D4—224no—
526C4×D4—248no—
527C4×D4—224no—
528C4×D4—224no—
529C4×D4—248no—
530C4×D4—224no—
531C4×D4—224no—
532C4×D4—46no—
533C4×D4—46no—
534C4×D4C2×D4148yes—
535#117—224no—
536#117—224no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4—224no—
539C2×C4⋊C4—248no—
540C2×C4⋊C4C2416yes—
541C2×C4⋊C4C2416yes—
542C2×C4⋊C4C2416yes—
543C2×C4⋊C4C2416yes—
544C2×C4⋊C4C24112yes—
545C2×C4⋊C4C24112yes—
546C2×C4⋊C4C24112yes—
547C2×C4⋊C4C24112yes—
548C2×C4⋊C4C2416yes—
549C2×C4⋊C4C2416yes—
550C2×C4⋊C4C2416yes—
551C2×C4⋊C4C2416yes—
552C2×C4⋊C4C24112yes—
553C2×C4⋊C4C2416yes—
554C2×C4⋊C4C2416yes—
555C2×C4⋊C4C2413yes—
556C2×C4⋊C4C2416yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2413yes—
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C24112yes—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4C2416yes—
567C2×C22⋊C4C2416yes—
568C2×C22⋊C4C2416yes—
569C2×C22⋊C4C2416yes—
570C2×C22⋊C4C2416yes—
571C2×C22⋊C4C2416yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2416yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2416yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2416yes—
578C2×C22⋊C4C24112yes—
579C2×C22⋊C4C2416yes—
580C2×C22⋊C4C2416yes—
581C2×C22⋊C4C24112yes—
582C2×C22⋊C4C2416yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2413yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2411yescharacteristic
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C2413yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2411yescharacteristic
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2416yes—
598C2×C42—224no—
599C2×C42C2416yes—
600C2×C42C24112yes—
601C2×C42C2416yes—
602C2×C42C2416yes—
603C2×C42C2416yes—
604C2×C42C2413yes—
605C2×C42C2416yes—
606C2×C42C2416yes—
607#95C2411yescharacteristic
608#95C2413yes—
609#95C2416yes—
610#95C2411yescharacteristic
611#95C2416yes—
612#95C2413yes—
613#95C24112yes—
614#95C2416yes—
615#95C24112yes—
616#95C2416yes—
617#95C2416yes—
618#95C2416yes—
619#95C2416yes—
620#95C2416yes—
621#95C2412yes—
622#95C24112yes—
623#95C2416yes—
624#95C24112yes—
625#95C2416yes—
626C24—24no—
627C24—24no—
628C24—24no—
629C24—24no—
630C24—24no—
631C24—24no—
632C24—24no—
633C24—41no—
634C24—42no—
635C24—41no—
636C24—42no—
637C242−1+414yescomplemented
638C24C2513yes—
639C24C2512yes—
640C24C2511yescharacteristic
641C24C2512yes—
642C24C2512yes—
643#41—448no—
644#41—496no—
645#41—416no—
646C2×Q8—264no—
647C2×Q8—264no—
648C2×Q8—212no—
649C2×Q8—212no—
650C2×Q8—224no—
651C2×Q8—212no—
652C2×Q8—224no—
653C2×Q8—224no—
654C2×Q8—212no—
655C2×Q8—212no—
656C2×Q8—212no—
657C2×Q8—212no—
658C2×Q8—212no—
659C2×Q8—26no—
660C2×Q8—212no—
661C2×Q8—412no—
662C2×Q8—46no—
663C2×Q8—43no—
664C2×Q8—496no—
665C2×Q8—496no—
666C2×Q8—496no—
667C2×Q8—448no—
668C2×Q8—496no—
669C2×Q8—448no—
670C2×Q8—432no—
671C2×Q8—416no—
672C2×Q8C22×D4124yes—
673C2×Q8C22×D4124yes—
674C2×Q8C22×D418yes—
675C2×Q8H(5,𝔽2)14yes—
676C2×D4—264no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—212no—
687C2×D4—24no—
688C2×D4—212no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—212no—
692C2×D4—212no—
693C2×D4—212no—
694C2×D4—26no—
695C2×D4—24no—
696C2×D4—212no—
697C2×D4—212no—
698C2×D4—212no—
699C2×D4—26no—
700C2×D4—24no—
701C2×D4—41no—
702C2×D4—46no—
703C2×D4—42no—
704C2×D4—46no—
705C2×D4—41no—
706C2×D4—43no—
707C2×D4—43no—
708C2×D4C22×D418yes—
709C2×D42−1+418yescomplemented
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—212no—
713C22×C4—212no—
714C22×C4—212no—
715C22×C4—212no—
716C22×C4—24no—
717C22×C4—212no—
718C22×C4—212no—
719C22×C4—212no—
720C22×C4—212no—
721C22×C4—212no—
722C22×C4—212no—
723C22×C4—212no—
724C22×C4—212no—
725C22×C4—212no—
726C22×C4—212no—
727C22×C4—212no—
728C22×C4—212no—
729C22×C4—212no—
730C22×C4—224no—
731C22×C4—212no—
732C22×C4—212no—
733C22×C4—26no—
734C22×C4—212no—
735C22×C4—26no—
736C22×C4—46no—
737C22×C4—46no—
738C22×C4—43no—
739C22×C4—46no—
740C22×C4—46no—
741C22×C4—46no—
742C22×C4—46no—
743C22×C4—448no—
744C22×C4—496no—
745C22×C4C22×D4124yes—
746C22×C4C22×D4124yes—
747C22×C4C2511yescharacteristic
748C22×C4C2513yes—
749C22×C4C2516yes—
750C22×C4C2512yes—
751C22×C4C2516yes—
752C22×C4C2516yes—
753C22×C4C2513yes—
754C22×C4C2511yescharacteristic
755C22×C4C2512yes—
756C22×C4C2516yes—
757C22×C4C2516yes—
758C22×C4C2516yes—
759C22×C4C2512yes—
760C22×C4C2513yes—
761C4⋊C4—212no—
762C4⋊C4—212no—
763C4⋊C4—212no—
764C4⋊C4—224no—
765C4⋊C4—212no—
766C4⋊C4—224no—
767C4⋊C4—224no—
768C4⋊C4—224no—
769C4⋊C4—212no—
770C4⋊C4—212no—
771C4⋊C4—212no—
772C4⋊C4—224no—
773C4⋊C4—212no—
774C4⋊C4—212no—
775C4⋊C4—212no—
776C4⋊C4—26no—
777C4⋊C4—212no—
778C4⋊C4—46no—
779C4⋊C4—43no—
780C4⋊C4—43no—
781C4⋊C4—46no—
782C4⋊C4C22×D4124yes—
783C4⋊C4C22×D4124yes—
784C4⋊C4C22×D4148yes—
785C22⋊C4—212no—
786C22⋊C4—212no—
787C22⋊C4—24no—
788C22⋊C4—212no—
789C22⋊C4—26no—
790C22⋊C4—212no—
791C22⋊C4—24no—
792C22⋊C4—212no—
793C22⋊C4—212no—
794C22⋊C4—212no—
795C22⋊C4—212no—
796C22⋊C4—212no—
797C22⋊C4—24no—
798C22⋊C4—212no—
799C22⋊C4—212no—
800C22⋊C4—24no—
801C22⋊C4—224no—
802C22⋊C4—212no—
803C22⋊C4—212no—
804C22⋊C4—224no—
805C22⋊C4—24no—
806C22⋊C4—24no—
807C22⋊C4—212no—
808C22⋊C4—46no—
809C22⋊C4—46no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—46no—
813C22⋊C4—43no—
814C22⋊C4—46no—
815C22⋊C4C22×D4124yes—
816C22⋊C4C22×D4124yes—
817C42—212no—
818C42—212no—
819C42—212no—
820C42—224no—
821C42—212no—
822C42—26no—
823C42—46no—
824C42C22×D4124yes—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—216no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—216no—
847C23—26no—
848C23—23no—
849C23—26no—
850C23—23no—
851C23—23no—
852C23—44no—
853C23—44no—
854C23—48no—
855C23—48no—
856C23—48no—
857C23—48no—
858C23—44no—
859C23—48no—
860C23—48no—
861C23—48no—
862C23C23×D414yes—
863C23C23×D414yes—
864C23C2×2−1+412yes—
865C23C2×2−1+414yes—
866C23C2×2−1+414yes—
867C23C2×2−1+414yes—
868C23C2611yescharacteristic
869Q8—248no—
870Q8—248no—
871Q8—448no—
872Q8—424no—
873Q8—412no—
874Q8—424no—
875Q8—412no—
876Q8D42116yes—
877D4—216no—
878D4—216no—
879D4—216no—
880D4—216no—
881D4—424no—
882D4—424no—
883D4—48no—
884D4—44no—
885D4—44no—
886D4—424no—
887D4—412no—
888D4—86no—
889C2×C4—216no—
890C2×C4—22no—
891C2×C4—26no—
892C2×C4—26no—
893C2×C4—26no—
894C2×C4—26no—
895C2×C4—26no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—26no—
900C2×C4—248no—
901C2×C4—248no—
902C2×C4—22no—
903C2×C4—26no—
904C2×C4—26no—
905C2×C4—26no—
906C2×C4—22no—
907C2×C4—26no—
908C2×C4—26no—
909C2×C4—21no—
910C2×C4—23no—
911C2×C4—23no—
912C2×C4—21no—
913C2×C4—26no—
914C2×C4—26no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—26no—
918C2×C4—23no—
919C2×C4—26no—
920C2×C4—23no—
921C2×C4—26no—
922C2×C4—22no—
923C2×C4—424no—
924C2×C4—412no—
925C2×C4—424no—
926C2×C4—424no—
927C2×C4—424no—
928C2×C4—424no—
929C2×C4—424no—
930C2×C4—424no—
931C2×C4—412no—
932C2×C4—412no—
933C2×C4C23×D414yes—
934C2×C4C23×D4112yes—
935C2×C4C23×D4112yes—
936C2×C4C23×D4112yes—
937C2×C4C23×D4112yes—
938C2×C4C2×H(5,𝔽2)16yes—
939C2×C4C2×2−1+414yes—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—22no—
953C22—24no—
954C22—416no—
955C22—432no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—46no—
968C22—43no—
969C22—46no—
970C22—43no—
971C22—43no—
972C22#348618yescomplemented
973C22C24×D412yes—
974C22C22×H(5,𝔽2)11yescharacteristic
975C22C22×2−1+412yes—
976C22C22×2−1+411yescharacteristic
977C222−1+611yescharacteristic
978C4—212no—
979C4—24no—
980C4—24no—
981C4—212no—
982C4—212no—
983C4—46no—
984C4—42no—
985C4—41no—
986C4—46no—
987C4—43no—
988C4—41no—
989C4—46no—
990C4—43no—
991C4C2×D42112yes—
992C2—28no—
993C2—44no—
994C2—44no—
995C2—42no—
996C2—83no—
997C2C22×D4211yescharacteristic
998C2C2×#348612yes—
999C2#6289311yescharacteristic
1000C2D4×2−1+412yes—
1001C2#6301611yescharacteristic
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×#3486C2semidirect
2. C22×D4×Q8C2semidirect
3. #59127C2semidirect
4. #59005C2semidirect
5. #58998C2semidirect
6. #45418C2semidirect
7. #45321C2semidirect
8. #45248C2semidirect
9. #37675C2semidirect
10. #37651C2semidirect
11. #36575C2semidirect
12. Q8×#120C2semidirect
13. #36434C2semidirect
14. #36097C2semidirect
15. #35927C2semidirect
16. #35700C2semidirect
17. #35687C2semidirect
18. #34655C2semidirect
19. #34291C2semidirect
20. C22×2−1+4C22semidirect
22. C24×Q8C22semidirect
29. C2×D4×Q8C22semidirect
30. C2×D4×Q8C22semidirect
31. C2×D4×Q8C22semidirect
32. C2×D4×Q8C22semidirect
33. C2×D4×Q8C22semidirect
34. C2×D4×Q8C22semidirect
35. C2×D4×Q8C22semidirect
36. C2×D4×Q8C22semidirect
38. C2×#548C22semidirect
39. C2×#548C22semidirect
40. C2×#548C22semidirect
41. C2×#548C22semidirect
42. C2×#536C22semidirect
43. C2×#536C22semidirect
44. C22×C4⋊Q8C22semidirect
46. C2×#525C22semidirect
48. C22×C22⋊Q8C22semidirect
49. C2×#519C22semidirect
50. C22×C4×Q8C22semidirect
52. #2850C22semidirect
53. #2848C22semidirect
55. #2683C22semidirect
56. #2681C22semidirect
57. #2680C22semidirect
58. #2677C22semidirect
59. #2677C22semidirect
60. #2677C22semidirect
61. #2677C22semidirect
62. #2674C22semidirect
63. #2674C22semidirect
64. #2658C22semidirect
65. #2621C22semidirect
66. #2616C22semidirect
67. #2551C22semidirect
68. #2546C22semidirect
69. #2545C22semidirect
70. #2542C22semidirect
71. #2542C22semidirect
72. #2540C22semidirect
73. #2540C22semidirect
74. #2536C22semidirect
75. #2536C22semidirect
76. #2472C22semidirect
78. #2463C22semidirect
79. #2463C22semidirect
80. #2461C22semidirect
83. #2452C22semidirect
85. #2449C22semidirect
86. #2449C22semidirect
89. #2440C22semidirect
91. #2436C22semidirect
92. #2436C22semidirect
93. #2434C22semidirect
94. #2434C22semidirect
95. #2434C22semidirect
96. #2434C22semidirect
97. #2432C22semidirect
98. #2429C22semidirect
99. #2429C22semidirect
100. #2429C22semidirect
101. #2426C22semidirect
104. #2417C22semidirect
106. #2415C22semidirect
107. #2415C22semidirect
110. #2409C22semidirect
111. #2409C22semidirect
112. #2409C22semidirect
113. #2409C22semidirect
114. #2409C22semidirect
115. #2407C22semidirect
120. #2365C22semidirect
121. #2362C22semidirect
123. #2360C22semidirect
126. #2351C22semidirect
127. #2341C22semidirect
128. Q8×C22⋊C4C22semidirect
129. Q8×C22⋊C4C22semidirect
130. Q8×C22⋊C4C22semidirect
131. Q8×C22⋊C4C22semidirect
132. #2327C22semidirect
133. #2323C22semidirect
134. C4×C22⋊Q8C22semidirect
139. #2276C22semidirect
174. D4×Q8D4semidirect
422. C22×Q8C2×D4semidirect
472. C4⋊Q8C2×D4semidirect
501. C22⋊Q8C2×D4semidirect
519. C4×Q8C2×D4semidirect
637. C242−1+4semidirect
709. C2×D42−1+4semidirect
972. C22#3486semidirect

Maximal subgroups

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

subgroupindex
C2×#34862
C22×D4×Q82
#591272
#590052
#589982
#454182
#453212
#452482
#376752
#376512
#365752
Q8×#1202
#364342
#360972
#359272
#357002
#356872
#346552
#342912