Finite Group Databasebeta

← #7985578

Subgroups — #7985578

Order 512.

5165 conjugacy classes of subgroups.

The subgroup lattice has 1175 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59668C212yesmaximal, complemented
3#59243C212yesmaximal, complemented
4#59219C212yesmaximal, complemented
5#49981C218yesmaximal, complemented
6#45595C214yesmaximal, complemented
7#45325C214yesmaximal, complemented
8#45037C214yesmaximal, complemented
9#42556C214yesmaximal, complemented
10#42446C214yesmaximal, complemented
11#40174C214yesmaximal, complemented
12#39481C212yesmaximal, complemented
13#39470C212yesmaximal, complemented
14#39343C212yesmaximal, complemented
15#39201C212yesmaximal, complemented
16#36594C211yesmaximal, characteristic, complemented
17#36544C212yesmaximal, complemented
18#36463C212yesmaximal, complemented
19#36194C211yesmaximal, characteristic, complemented
20#36194C211yesmaximal, characteristic, complemented
21#35207C212yesmaximal, complemented
22#35178C212yesmaximal, complemented
23#34941C211yesmaximal, characteristic, complemented
24#34925C211yesmaximal, characteristic
25#34368C212yesmaximal, complemented
26C4×D4×Q8C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×#554C2212yes—
29C2×D4×Q8C2211yescharacteristic
30C2×#536C2214yes—
31C2×#532C2212yes—
32C2×#532C2212yes—
33C22×C4×Q8C2212yes—
34#2868C2211yescharacteristic
35#2858C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2854C2214yes—
39#2854C2214yes—
40#2851C2214yes—
41#2827C2218yes—
42#2806C2218yes—
43#2800C2218yes—
44#2786C2218yes—
45#2773C2218yes—
46#2765C2218yes—
47#2745C2218yes—
48#2741C2218yes—
49#2732C2214yes—
50#2716C2218yes—
51#2712C2218yes—
52#2710C2218yes—
53#2705C2218yes—
54#2700C2218yes—
55#2695C2218yes—
56#2681C2218yes—
57#2674C2218yes—
58#2672C2218yes—
59#2653C2218yes—
60#2630C2218yes—
61#2624C2214yes—
62#2618C2218yes—
63#2616C2214yes—
64#2594C2218yes—
65#2584C2214yes—
66#2580C2214yes—
67#2574C2214yes—
68#2571C2212yes—
69#2571C2212yes—
70#2567C2211yescharacteristic
71#2563C2212yes—
72#2563C2211yescharacteristic
73#2563C2212yes—
74#2557C2218yes—
75#2555C2214yes—
76#2552C2212yes—
77#2552C2211yescharacteristic
78#2551C2211yescharacteristic
79#2551C2214yes—
80#2550C2214yes—
81#2548C2214yes—
82#2547C2212yes—
83#2546C2214yes—
84#2545C2214yes—
85#2545C2218yes—
86#2542C2212yes—
87#2541C2211yescharacteristic
88#2541C2211yescharacteristic
89#2538C2212yes—
90#2538C2212yes—
91#2538C2214yes—
92#2538C2212yes—
93#2538C2211yescharacteristic
94#2538C2212yes—
95#2538C2212yes—
96#2537C2211yescharacteristic
97#2536C2214yes—
98#2536C2214yes—
99#2521C2218yes—
100#2513C2214yes—
101#2513C2214yes—
102#2512C2214yes—
103#2512C2214yes—
104#2508C2212yes—
105#2507C2214yes—
106#2507C2214yes—
107#2499C2214yes—
108#2497C2214yes—
109#2497C2214yes—
110#2497C2212yes—
111#2494C2214yes—
112#2494C2214yes—
113#2494C2214yes—
114#2492C2214yes—
115#2492C2214yes—
116#2491C2212yes—
117#2491C2214yes—
118#2491C2212yes—
119#2490C2214yes—
120#2490C2214yes—
121#2486C2214yes—
122#2470C2218yes—
123#2465C2218yes—
124#2459C2218yes—
125#2458C2218yes—
126#2454C2214yes—
127#2454C2212yes—
128#2451C2218yes—
129#2449C2218yes—
130#2445C2214yes—
131#2445C2214yes—
132#2439C2214yes—
133#2439C2214yes—
134#2428C2212yes—
135#2428C2212yes—
136#2423C2212yes—
137#2423C2214yes—
138#2422C2214yes—
139#2422C2214yes—
140#2420C2214yes—
141#2417C2214yes—
142#2415C2214yes—
143#2415C2214yes—
144#2409C2214yes—
145#2396C2214yes—
146#2388C2214yes—
147#2379C2218yes—
148#2370C2214yes—
149#2369C2212yes—
150#2369C2214yes—
151#2369C2212yes—
152#2366C2212yes—
153#2366C2214yes—
154#2365C2211yescharacteristic
155#2365C2212yes—
156#2360C2214yes—
157#2360C2214yes—
158#2360C2212yes—
159#2357C2214yes—
160#2355C2212yes—
161#2355C2212yes—
162#2354C2214yes—
163#2354C2212yes—
164#2354C2212yes—
165#2354C2212yes—
166#2354C2212yes—
167Q8×C4⋊C4C2211yescharacteristic
168D4×C4⋊C4C2212yes—
169D4×C4⋊C4C2211yescharacteristic
170D4×C4⋊C4C2212yes—
171D4×C4⋊C4C2214yes—
172Q8×C22⋊C4C2212yes—
173#2324C2214yes—
174#2324C2214yes—
175#2324C2218yes—
176#2314C2214yes—
177#2311C2214yes—
178#2311C2214yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#127C2211yescharacteristic
184C4×#125C2212yes—
185C4×C22⋊Q8C2214yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190C4×#121C2214yes—
191#2293C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2212yes—
199C22×#41C2314yes—
200C23×Q8C2312yes—
201#556—48no—
202#554—48no—
203D4×Q8—28no—
204#536—416no—
205#532—216no—
206#532—48no—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2318yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×#127C2311yescharacteristic
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#126C2318yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#124C2314yes—
223C2×#124C2314yes—
224C2×#124C2318yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2314yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×#121C2314yes—
246C2×#121C2312yes—
247C2×C4×Q8—48no—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2314yes—
272C2×C4×D4C2318yes—
273C2×C4×D4C2311yescharacteristic
274C2×#117C2314yes—
275C2×#117C2314yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2314yes—
280C22×C4⋊C4C2314yes—
281C22×C42C2312yes—
282C22×C42C2312yes—
283C22×C42C2314yes—
284#401C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2314yes—
288#399C2318yes—
289#399C2314yes—
290#399C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2314yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2314yes—
312#396C2318yes—
313#395C2314yes—
314#395C2318yes—
315#395C2318yes—
316#395C2314yes—
317#394C2314yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2314yes—
326#394C2314yes—
327#393C2314yes—
328#393C2318yes—
329#393C2318yes—
330#393C2318yes—
331#393C2314yes—
332#392C2314yes—
333#392C2314yes—
334#392C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2314yes—
338#391C2314yes—
339#391C2318yes—
340#391C2318yes—
341#391C2312yes—
342#391C2312yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2318yes—
347#391C2318yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2314yes—
352#390C2314yes—
353#390C2312yes—
354#390C2318yes—
355#390C2318yes—
356#390C2314yes—
357#390C2318yes—
358#390C2312yes—
359#390C2314yes—
360#390C2312yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2312yes—
365#390C2314yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2314yes—
374#389C2312yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2318yes—
383#389C2314yes—
384#389C2314yes—
385#389C2312yes—
386#389C2318yes—
387#389C2318yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2312yes—
392#389C2312yes—
393#389C2318yes—
394#389C2312yes—
395#389C2312yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2314yes—
424#387C2314yes—
425#387C2318yes—
426#387C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2314yes—
434#386C2314yes—
435#385C2314yes—
436#385C2318yes—
437#385C2314yes—
438#385C2314yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2314yes—
444#384C2311yescharacteristic
445#384C2311yescharacteristic
446#384C2312yes—
447#384C2311yescharacteristic
448#384C2312yes—
449#384C2314yes—
450#384C2312yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#384C2312yes—
455#382C2312yes—
456#382C2314yes—
457#382C2314yes—
458#382C2314yes—
459#382C2314yes—
460#382C2314yes—
461#381C2318yes—
462#380C2312yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2314yes—
470#380C2312yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2312yes—
475#380C2314yes—
476#380C2312yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2318yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2318yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2312yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C2×#41—216no—
527C2×#41—48no—
528C2×#41—48no—
529C22×Q8—28no—
530C22×Q8—28no—
531C22×Q8—44no—
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2412yes—
536C22×Q8C2414yes—
537C22×Q8C2414yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C22×D4C2411yescharacteristic
543C22×D4C2412yes—
544C22×D4C2414yes—
545C22×D4C2414yes—
546C22×D4C2414yes—
547C22×D4C2414yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2414yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2414yes—
557C23×C4C2418yes—
558C4⋊Q8—28no—
559C4⋊Q8—28no—
560C4⋊Q8—24no—
561C4⋊Q8—24no—
562C4⋊Q8—28no—
563C4⋊Q8—44no—
564C4⋊Q8—44no—
565C4⋊Q8—416no—
566C4⋊Q8—82no—
567#127—28no—
568#127—24no—
569#127—44no—
570#126—416no—
571#125—28no—
572#125—48no—
573#124—216no—
574#124—48no—
575#124—48no—
576#124—416no—
577#124—84no—
578#123—416no—
579#123—416no—
580#123—88no—
581C22⋊Q8—28no—
582C22⋊Q8—216no—
583C22⋊Q8—28no—
584C22⋊Q8—216no—
585C22⋊Q8—416no—
586C22⋊Q8—48no—
587C22⋊Q8—48no—
588C22⋊Q8—48no—
589C22⋊Q8—84no—
590#121—28no—
591#121—28no—
592#121—28no—
593#121—216no—
594#121—48no—
595#121—44no—
596#121—44no—
597#121—44no—
598C4×Q8—24no—
599C4×Q8—24no—
600C4×Q8—24no—
601C4×Q8—28no—
602C4×Q8—48no—
603C4×Q8—44no—
604C4×Q8—48no—
605C4×Q8—48no—
606C4×Q8—44no—
607C4×Q8—44no—
608C4×D4—28no—
609C4×D4—216no—
610C4×D4—24no—
611C4×D4—28no—
612C4×D4—24no—
613C4×D4—28no—
614C4×D4—24no—
615C4×D4—24no—
616C4×D4—44no—
617C4×D4—48no—
618C4×D4—42no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—44no—
622C4×D4—88no—
623C4×D4#4118yes—
624#117—48no—
625#117—48no—
626#117—48no—
627#117—84no—
628C2×C4⋊C4—44no—
629C2×C4⋊C4—48no—
630C2×C4⋊C4—48no—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2412yes—
715C2×C42—28no—
716C2×C42—28no—
717C2×C42—48no—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2418yes—
735C2×C42C2418yes—
736C2×C42C2418yes—
737C2×C42C2414yes—
738C2×C42C2414yes—
739C2×C42C2412yes—
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#95C2414yes—
745#95C2414yes—
746#95C2412yes—
747#95C2412yes—
748#95C2414yes—
749#95C2412yes—
750#95C2414yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2412yes—
760#95C2414yes—
761#95C2412yes—
762#95C2412yes—
763#95C2414yes—
764#95C2418yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768#95C2414yes—
769#95C2418yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778#95C2414yes—
779#95C2418yes—
780C24C2514yes—
781C24C2512yes—
782C24C2512yes—
783#41—832no—
784C2×Q8—22no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—28no—
788C2×Q8—22no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—28no—
792C2×Q8—24no—
793C2×Q8—28no—
794C2×Q8—44no—
795C2×Q8—44no—
796C2×Q8—42no—
797C2×Q8—42no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—432no—
802C2×Q8H(5,𝔽2)14yes—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—24no—
807C2×D4—28no—
808C2×D4—24no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—28no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—42no—
832C2×D4C2×#4114yes—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—28no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—28no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—44no—
853C22×C4—42no—
854C22×C4—44no—
855C22×C4—42no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—42no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4C2×#4118yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2511yescharacteristic
870C22×C4C2514yes—
871C22×C4C2518yes—
872C22×C4C2512yes—
873C22×C4C2514yes—
874C22×C4C2512yes—
875C22×C4C2514yes—
876C22×C4C2514yes—
877C22×C4C2512yes—
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2512yes—
881C22×C4C2511yescharacteristic
882C22×C4C2512yes—
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—28no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—24no—
897C4⋊C4—28no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—28no—
901C4⋊C4—22no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—216no—
906C4⋊C4—28no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—24no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—24no—
915C4⋊C4—22no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—48no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—42no—
923C4⋊C4—44no—
924C4⋊C4—42no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—42no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4C2×#4114yes—
937C4⋊C42−1+414yes—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—24no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—216no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—42no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—44no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—48no—
969C22⋊C4C2×#4118yes—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—28no—
979C42—22no—
980C42—24no—
981C42—22no—
982C42—24no—
983C42—24no—
984C42—28no—
985C42—22no—
986C42—44no—
987C42—44no—
988C42—48no—
989C42—48no—
990C42—48no—
991C42—42no—
992C42—41no—
993C42C2×#4114yes—
994C42H(5,𝔽2)14yes—
995C422−1+414yes—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—22no—
1004C23—24no—
1005C23—22no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—24no—
1012C23—22no—
1013C23—24no—
1014C23—22no—
1015C23—24no—
1016C23C22×#4114yes—
1017C23C2611yescharacteristic
1018Q8—28no—
1019Q8—416no—
1020Q8—48no—
1021Q8—88no—
1022Q8—84no—
1023Q8—88no—
1024D4—28no—
1025D4—416no—
1026D4—48no—
1027D4—48no—
1028D4—44no—
1029D4—84no—
1030D4—88no—
1031D4—88no—
1032D4—88no—
1033D4—88no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—216no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—21no—
1059C2×C4—24no—
1060C2×C4—28no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—28no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—28no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—48no—
1090C2×C4—416no—
1091C2×C4—48no—
1092C2×C4—416no—
1093C2×C4—48no—
1094C2×C4—48no—
1095C2×C4—84no—
1096C2×C4—88no—
1097C2×C4—168no—
1098C2×C4C22×#4112yes—
1099C2×C4C22×#4114yes—
1100C2×C4C22×#4112yes—
1101C2×C4C22×#4112yes—
1102C2×C4C2×H(5,𝔽2)12yes—
1103C2×C4C2×H(5,𝔽2)14yes—
1104C2×C4C2×H(5,𝔽2)12yes—
1105C2×C4C2×H(5,𝔽2)12yes—
1106C2×C4C2×H(5,𝔽2)12yes—
1107C2×C4C2×2−1+412yes—
1108C2×C4C2×2−1+414yes—
1109C2×C4C2×2−1+412yes—
1110C2×C4C2×2−1+412yes—
1111C2×C4C2×2−1+412yes—
1112C2×C4#58512yes—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—44no—
1122C22—44no—
1123C22—42no—
1124C22—42no—
1125C22—44no—
1126C22—42no—
1127C22—44no—
1128C22—44no—
1129C22—42no—
1130C22—44no—
1131C22—42no—
1132C22—44no—
1133C22—42no—
1134C22C23×#4111yescharacteristic
1135C22C22×H(5,𝔽2)11yescharacteristic
1136C22C22×H(5,𝔽2)11yescharacteristic
1137C22C22×2−1+411yescharacteristic
1138C22C22×2−1+411yescharacteristic
1139C22C2×#58511yescharacteristic
1140C22H(7,𝔽2)11yescharacteristic
1141C4—22no—
1142C4—24no—
1143C4—24no—
1144C4—24no—
1145C4—22no—
1146C4—22no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—44no—
1151C4—44no—
1152C4—42no—
1153C4—42no—
1154C4—41no—
1155C4—44no—
1156C4—48no—
1157C4—42no—
1158C4—44no—
1159C4—42no—
1160C4—44no—
1161C4#350714yes—
1162C4#351914yes—
1163C4#355014yes—
1164C2—44no—
1165C2—82no—
1166C2—84no—
1167C2C2×#355011yescharacteristic
1168C2C2×#351911yescharacteristic
1169C2C2×#350711yescharacteristic
1170C2#6291711yescharacteristic
1171C2#6293011yescharacteristic
1172C2#6300011yescharacteristic
1173C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34925C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59823C2semidirect
2. #59668C2semidirect
3. #59243C2semidirect
4. #59219C2semidirect
5. #49981C2semidirect
6. #45595C2semidirect
7. #45325C2semidirect
8. #45037C2semidirect
9. #42556C2semidirect
10. #42446C2semidirect
11. #40174C2semidirect
12. #39481C2semidirect
13. #39470C2semidirect
14. #39343C2semidirect
15. #39201C2semidirect
16. #36594C2semidirect
17. #36544C2semidirect
18. #36463C2semidirect
19. #36194C2semidirect
20. #36194C2semidirect
21. #35207C2semidirect
22. #35178C2semidirect
23. #34941C2semidirect
25. #34368C2semidirect
26. C4×D4×Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#596682
#592432
#592192
#499812
#455952
#453252
#450372
#425562
#424462
#401742
#394812
#394702
#393432
#392012
#365942
#365442
#364632
#361942
#352072
#351782
#349412
#349252
#343682
C4×D4×Q82